Mrcc is a suite of ab initio and density functional quantum chemistry programs for high-accuracy electronic structure calculations developed and maintained by the quantum chemistry research group at the Department of Physical Chemistry and Materials Science, TU Budapest [66]. Its special feature, the use of automated programming tools enabled the development of tensor manipulation routines which are independent of the number of indices of the corresponding tensors, thus significantly simplifying the general implementation of quantum chemical methods. Applying the automated tools of the program several quantum chemistry models and techniques of high complexity have been implemented so far including arbitrary single-reference coupled-cluster (CC) and configuration interaction (CI) methods, multi-reference CC approaches, CC and CI energy derivatives and response functions, arbitrary perturbative CC approaches. Many features of the package are also available with relativistic Hamiltonians allowing for accurate calculations on heavy element systems. The developed cost-reduction techniques and local correlation approaches also enable high-precision calculations for medium-sized and large molecules.

In the following, words set in typewriter font denote file names, shell commands, environment variables, and input records of the input file. These must be typed as shown. Variables, that is, numbers, options, etc. which must be specified by the user will be given as variable$\mathrm{>}$. These must be replaced by the corresponding values of the variables. Optional items are denoted by brackets, e.g., as [variable$\mathrm{>}$].

The main authors of the Mrcc code and their major contributions are as follows.

Mihály  Kállay:

general design; driver program (dmrcc); input analyzer (minp); automated, string-based many-body code (goldstone, xmrcc, mrcc); domain construction for local correlation calculations (mulli); particular integral evaluation algorithms (integ); direct and density-fitting (DF) Hartree–Fock (HF) algorithms, DFT algorithms (scf); density-fitting MP2 and RPA algorithms (drpa); explicitly correlated models (mp2f12)

Péter R.  Nagy:

local correlation methods and multi-level approaches (drpa); closed-shell coupled-cluster singles and doubles with perturbative triples [CCSD(T)] code (ccsd); parallelization of CCSD(T)

Dávid  Mester:

excited-state approaches (cis), range-separated double hybrid functionals (dft), bond functions (integ)

László  Gyevi-Nagy:

closed-shell CCSD(T) code (ccsd); parallelization of CCSD(T)

József  Csóka:

quadratic and multi-configurational self-consistent field algorithms, reduced-cost SCF algorithms (scf); analytic gradients for local density fitting SCF (prop)

P.  Bernát  Szabó:

open-shell CCSD(T) code (uccsd), open-shell local correlation approaches (drpa)

Zoltán  Rolik:

integral transformation and orbital optimization code (ovirt); domain construction for local correlation calculations (mulli)

Gyula  Samu:

density-fitting integrals (integ)

József  Csontos:

installation script (build.mrcc), geometry optimization, basis set optimization, the Mrcc homepage

Bence  Hégely:

QM/MM and embedding approaches (qmmod)

Ádám  Ganyecz:

solvation models

István  Ladjánszki:

Hartree–Fock self-consistent field code (scf)

Lóránt  Szegedy:

closed-shell CCSD(T) code (ccsd)

Bence  Ladóczki:

four-center atomic orbital integral code (integ)

Klára  Petrov:

orbital relaxation contribution to gradients for density-fitting methods, density-fitting MP2 gradient (prop)

Máté  Farkas:

orbital relaxation contribution to gradients for coupled-cluster methods (prop)

Pál  D.  Mezei:

double hybrid and van der Waals density functionals (dft)

Réka  A.  Horváth:

explicitly correlated models (mp2f12)

In addition, Bence Kornis, Levente Dojcsák, Huliyar S. Nataraj, and Sanghamitra Das have also contributed to the development of the Mrcc code.

If results obtained with the Mrcc code are published, the publication must acknowledge the following two references.

If Mrcc is used combined with other program systems or libraries, the users are also requested to include appropriate citations to those packages as required by their authors.

Mrcc can be used as a standalone code, but interfaces have been developed to the Cfour, Columbus, Dirac, Molpro, Orca, and Psi quantum chemistry packages, the xTB and Mopac semi-empirical programs as well as the Amber molecular dynamics (MD) code. Mrcc, in standalone mode, can currently be used for single-point energy calculations, evaluation of first-order properties, geometry optimizations, and harmonic vibrational frequency calculations with the standard nonrelativistic Hamiltonian and effective core potentials. The interfaces enable the calculation of further molecular properties as well as several other features, such as the use of relativistic Hamiltonians and MCSCF orbitals or quantum mechanics/molecular mechanics (QM/MM) simulations. If Mrcc is used together with the aforementioned quantum chemistry packages, the integral, property integral, HF, MCSCF, and CPHF calculations, the integral and density-matrix transformations, etc. are performed by these program systems. Transformed MO (property) integrals are passed over to Mrcc, which carries out the correlation calculation and returns unrelaxed MO density matrices if necessary.

In the following we describe the use of the Cfour, Columbus, Dirac, Molpro, xTB, Mopac, and Amber interfaces and the features that they enable. For a complete list of available features, see Sect. 6. See also the description of keyword iface. For the Orca and Psi interfaces see the manual of these packages.

In this section the available features of the Mrcc code are summarized. We also specify what type of reference states (orbitals) can be used, and if a particular feature requires one of the interfaces or is available with Mrcc in standalone mode. We also give the corresponding references which describe the underlying methodological developments.

Once you have successfully installed Mrcc, you may wish to test the correctness of the installation. For that purpose, numerous test jobs are at your disposal. The corresponding input files can be found in the MTEST directory created at the installation, where a test script, mtest, is also available. Your only task is to change to the MTEST directory and execute the mtest script. (Please do not forget to add the directory where the Mrcc executables are located to your PATH environment variable.) The test jobs will be automatically executed and you will receive feedback about the results of the tests. The corresponding output files will be left in the MTEST directory, and you can also check them. If all the tests complete successfully, your installation is correct with high probability.

The execution of the test jobs will take for a couple of hours. If you want to run the test on another machine, e.g., on a node of a cluster, you should copy the entire MTEST directory to that machine and start the mtest script there.

Please note that there are some test jobs that allocate a small amount of memory to test the out-of-core algorithms of the program (MINP_*smallmem). These test jobs run with four threads by default when testing OpenMP-parallel executables (i.e., the build.mrcc script was run with the -pOMP switch) with the mtest script. If you run these test jobs with more than four threads, some of them will fail since the memory requirement for OpenMP-parallel runs grows with the number of threads. In this case, the failure of these tests does not indicate a problem with your installation.

Testing of the MPI-parallel executables is also supported. The mtest script automatically detects MPI-parallel executables in PATH if the build.mrcc script was run with the -pMPI switch and runs the appropriate MPI-parallel test jobs (MINP_*_MPI).

To test other external libraries, two switches can be used. With the -l switch, Libxc test jobs (containing _Libxc in the name) are also run, while with the -p switch, the PCMSolver library is also tested (_PCM in the file name). The two options can also be used at the same time, i.e., if mtest is invoked as mtest -l -p, all the test jobs will be executed.

Testing of the features available with external semi-empirical and MM programs, such as ONIOM models including semi-empirical layers or RISM solvation calculations, is also automated. The mtest script automatically searches for those programs, and the corresponding test jobs are executed if they are available.

Please note that you can also create your own test jobs, e.g., if you modify the code, compile the program with new compiler versions, or use unusual combination of keywords. To that end you should calculate a reliable energy for your test job (e.g., using a stable compiler version), include the test keyword and the calculated energy to the MINP file (see the description of the keyword for more details), and copy the MINP file to the MTEST directory renaming it as MINP_job_name$\mathrm{>}$. Then the new job will be automatically executed when the mtest script is invoked next time.

Please be sure that the directory where the Mrcc executables are located are included in your PATH environment variable. Note that the package includes several executables, and all of them must be copied to the aforementioned directory, not only the driver program dmrcc. Please also check your LD_LIBRARY_PATH environment variable, which must include the directories containing the libraries linked with the program. This variable is usually set before the installation, but you should not change by removing the names of the corresponding directories. Please do not forget to copy the input file MINP (see Sect. 11) to the directory where the program is invoked.

In this section, we discuss the major characteristics of the programs of the Mrcc package, and also provide some information about their use and the corresponding outputs.

dmrcc

Driver for the program system. It calls the programs of the suite (except build.mrcc). It is recommended to run always dmrcc, but advanced users may run the programs one-by-one (e.g., for the purpose of debugging). See also Sect. 9 for further details.

minp

Input reader and analyzer. This program reads the input file MINP, checks keywords, options, and dependencies; sets default values for keywords.

integ

An open-ended atomic orbitals integral code. This code reads and analyzes the molecular geometry, reads the basis sets, and calculates one- and two-electron integrals as well as property integrals over Gaussian-type atomic orbitals. Both the Obara–Saika and the Rys quadrature schemes are implemented for the evaluation of two-electron integrals. In principle integrals over basis functions of arbitrary high angular momentum can be evaluated using the Obara–Saika algorithm.

scf

Hartree–Fock and Kohn–Sham SCF code. It solves the RHF, UHF, ROHF, RKS, UKS, or ROKS equations using either conventional or direct SCF techniques. It also performs the semi-canonicalization of orbitals (if requested) for ROHF wave functions.

orbloc

Orbital localization program. It performs the localization of MOs using the Cholesky, Boys, or generalized Boys procedures. It also constructs the domains for local correlation calculations.

drpa

An efficient three-index integral transformation, density-fitting MP2, RPA, dRPA, SOSEX, and RPAX2 code. The dRPA method is implemented using the modified algorithm of Ref. 54, which scales as the fourth power of the system size, see Ref. 71. drpa is also the driver for local correlation calculations.

mulli

Domain construction for local correlation calculations. It assigns the localized MOs (LMOs) to atoms using the Boughton–Pulay method, and for each occupied LMO it constructs a domain of occupied and virtual LMOs on the basis of their spatial distance. Projected atomic orbitals (PAOs) are also constructed if requested.

ovirt

Integral transformation and orbital optimization code. This program performs the four-index integral transformations of AO integral for correlation calculations. It also carries out the construction of optimized virtual orbitals (OVOs) or MP2 natural orbitals in the case of reduced-cost CC calculations.

ccsd

A very fast, hand-coded, MO-integral-based (DF) CCSD and CCSD(T) code. The code has been designed for local CC calculations but is also very efficient for conventional CC calculations. Currently it only functions for closed-shell systems, and the spatial symmetry is not utilized.

uccsd

A fast, hand-coded, MO-integral-based open-shell (DF) CCSD and CCSD(T) code. The code has been designed for local CC calculations but is also efficient for conventional CC calculations. Currently, the spatial symmetry is not utilized.

mp2f12

An efficient explicitly correlated MP2 (MP2-F12) program. It also computes the intermediates for explicitly correlated CCSD and CCSD(T) calculations.

cis

A very fast, hand-coded, integral direct DF CIS, TDA, TD-DFT, ADC(2), CIS(D), CIS(D${}_{\mathrm{\infty }}$), and CC2 code. Currently it only works for closed-shell systems, and the spatial symmetry is not utilized.

prop

This program solves the CPHF/KS equations, constructs relaxed density matrices, calculates first-order molecular properties and Cartesian gradients.

qmmod

Interface program for QM/MM and embedding calculations.

goldstone

This program generates the formulas for mrcc. The program also estimates the memory requirement of the calculation. This is a very crude (the symmetry and spin is not treated exactly) but quick estimate. The real memory requirement, which is usually much smaller, is calculated by xmrcc after the termination of goldstone.

xmrcc

It calculates the exact memory requirement for mrcc. Note that it may take a couple of minutes for complicated wave functions (e.g., MRCC derivatives). It prints out five numbers at the end (in MBytes):

Real*8

Minimal and optimal memory for double-precision (real*8) arrays.

Integer

Memory allocated by mrcc for integer arrays.

Total

(= Real*8 + Integer) The minimal and the optimal amount of total required memory. It is not worth starting the calculation if the real physical memory of the machine is smaller than the Minimal value. The performance of the program is optimal if it can use at least as much memory as the Optimal value. If the memory is between the Minimal and Optimal values, out-of-core algorithms will be executed for particular tasks, and it may result in slow down of the code. Please note that the memory available to the program can be specified by keyword mem (see page 12).

mrcc

Automated, string-based many-body code. It performs the single-point energy as well as derivative calculations for general CC, LR-CC, and CI methods. Abelian spatial symmetry is utilized and a partial spin adaptation is also available for closed-shell systems.

build.mrcc

Installation script of the suite. See Sect. 7 for a detailed description.

The input file of the Mrcc package is the MINP file. This file must be placed in the directory where the program is invoked. In addition, if you use your own basis sets (see keyword basis), angular integration grids for DFT calculations (see keyword agrid), or Laplace-quadrature for Laplace transform calculations (see keyword dendec), you may also need the GENBAS file, and then it must be also copied to the above directory.

In general, the execution of Mrcc is controlled by keywords. The list of the keywords is presented in Sect. 12. The keywords and the corresponding options must be given in the MINP file as
…
keyword$\mathrm{>}$[=option$\mathrm{>}$]
…
You can add only one keyword per line, but there are keywords which require multiple-line input, and the corresponding variables must be specified in the subsequent lines as
…
keyword$\mathrm{>}$[=option$\mathrm{>}$]
input record 1$\mathrm{>}$
input record 2$\mathrm{>}$
…
input record n$\mathrm{>}$
…
The input is not case-sensitive. Any number of lines can be left blank between two items, however, if a keyword requires multiple-line input, the lines including the keyword and its input records cannot be separated. Under similar conditions any line can be used for comments, but the beginning of a comment line must not be identical to a keyword because that line may be identified as a keyword by the input reader and misinterpreted. Thus it is recommended to start comment lines with some special character, e.g., hash mark.

Please note that you can find input files for numerous test jobs in the MTEST directory created at the installation of Mrcc (see Sect. 8). The input files have self-explanatory names and also include a short description at the beginning. You should look at these files for examples for the structure of the input file and the use of various keywords. You can use these files as templates, but please note that these files have been created to thoroughly check the correctness of the code and the installation, and thus some of them contain very tight convergence thresholds as well as unusual combination of (auxiliary) basis sets. In production calculations, you should use the default convergence thresholds (i.e., delete the lines including keywords itol, scftol, cctol, etc.), select the basis set carefully (i.e., set the appropriate option for keyword basis), and use the default auxiliary basis sets (i.e., delete the lines including keywords dfbasis_scf or dfbasis_cor). Please also do not forget to remove keyword test and to specify the amount of memory available to the program by setting the mem keyword.

In this section, the keywords of the Mrcc input file are listed in alphabetical order. To help the reader, the list of the keywords can also be found at the end of the manual.

active

The active orbitals for multi-reference (active-space) CI/CC calculations can be specified using this keyword. Note that this keyword overwrites the effect of keywords nacto and nactv. Note also that this keyword only sets the active orbitals for the post-SCF calculation, the MCSCF active orbitals can be specified by keyword mact.

Options:

none

All orbitals are inactive (i.e., single-reference calculation).

serialno

Using this option one can select the active orbitals specifying their serial numbers. The latter should be given in the subsequent line as ,,…,-,…, where $n_i$’s are the serial numbers of the correlated orbitals. Serial numbers separated by dash mean that through are active. Note that the numbering of the orbitals is relative to the first correlated orbital, that is, frozen orbitals are excluded.

vector

Using this option one can set the active/inactive feature for each correlated orbital. In the subsequent line an integer vector should be supplied with as many elements as the number of correlated orbitals. The integers must be separated by spaces. Type 1 for active orbitals and 0 for inactive ones.

Default:

active=none

Examples:

1.

We have 20 correlated orbitals. Orbitals 1, 4, 5, 6, 9, 10, 11, 12, and 14 are active. Using the serialno option the input should include the following two lines:
active=serialno
1,4-6,9-12,14

2.

The same using the vector option:
active=vector
1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0

agrid

Specifies the angular integration grid for DFT calculations. Angular grids are taken from the Grid file which is located in the BASIS directory created at the installation. By default, the 6-, 14-, 26-, 38-, 50-, 74-, 86-, 110-, 146-, 170-, 194-, 230-, 266-, 302-, 350-, 434-, 590-, 770-, 974-, 1202-, 1454-, and 1730-point Lebedev quadratures [6] are included in the file, which are labeled, respectively, by LD0006, LD0014, etc. In addition to the above grids, any angular integration grid can be used by adding it to the BASIS/Grid file or alternatively to the GENBAS file to be placed in the directory where Mrcc is executed. The format is as follows. On the first line give the label of the grid as XXNNNN, where XX is any character and NNNN is the number of the grid points (see the above examples). The subsequent NNNN lines must contain the Cartesian coordinates and the weights for the grid points. See also the description of keywords grid, rgrid, and grtol.

Options:

name of the grid$\mathrm{>}$

the name of the quadrature as it is specified in the BASIS/Grid (or GENBAS) file. This angular quadrature will be used in each radial point.

LDMMMM-LDNNNN

An adaptive integration grid will be used. For each radial point, depending on its distance from the nucleus, a different Lebedev grid will be selected. The minimal and maximal number of points are MMMM and NNNN, respectively. The angular grids are selected for each radial point so that the error in the angular integrals will not be larger than ${10}^{1-\mathrm{𝚐𝚛𝚝𝚘𝚕}}$. If grid=TA*, the above procedure is not carried out, but the angular grids are taken from Ref. AhlrichsGrid.

Default:

agrid=LD0006-LD0590

Examples:

1.

for a 974-point Lebedev grid set agrid=LD0974

2.

to use an adaptive grid with at least 110 and at most 974 angular points set agrid=LD0110-LD0974

3.

for a very fine grid use
agrid=LD0110-LD0974
grtol=12

agrid_pssp

Specifies the angular integration grid for COSX calculations. For more information about the usage and available options, see keyword agrid. To learn more about COSX calculations, see keywords pssp and dual_df.

Options:

Same as for agrid

Default:

agrid_pssp=LD0006-LD0194

Example:

for a fine grid use agrid=LD0006-LD0590

agrid_pssp_sm

Specifies the small grid for dual grid COSX calculations. For more information about COSX calculations, see keywords pssp and dual_df.

Options:

Same as for agrid and agrid_pssp

Default:

agrid_pssp_sm=LD0006-LD0074

Example:

for a fine grid use agrid=LD0006-LD0194

basis

Specifies the basis set used in all calculations. By default the basis sets are taken from the files named by the chemical symbol of the elements, which can be found in the BASIS directory created at the installation. The basis sets are stored in the format used by the Cfour package (see Sect. 6.9). In addition to the basis sets provided by default, any basis set can be used by adding it to the corresponding files in the BASIS directory. Alternatively, you can also specify your own basis sets in the file GENBAS which must be copied to the directory where Mrcc is executed.

Options:

basis set label$\mathrm{>}$

If the same basis set is used for all atoms, the label of the basis set must be given.

atomtype

If different basis set are used, but the basis sets are identical for atoms of the same type, basis=atomtype should be given, and the user must specify the basis sets for each atomtype in the subsequent lines as atomic symbol$\mathrm{>}$:basis set$\mathrm{>}$ .

mixed

Mixed basis sets will be used, that is, different basis sets will be used for different groups of atoms specified by their serial number. The number of groups, the basis sets, and corresponding atoms must be specified in the subsequent lines as
number of groups$\mathrm{>}$
basis set label 1$\mathrm{>}$ ,,…,-,…
basis set label 2$\mathrm{>}$ ,,…,-,…
…
where $n_i$’s, $m_i$’s, …are the serial numbers of the atoms. Serial numbers separated by dash mean that atoms through are included.

embed

A mixed basis set composed of two AO bases will be used in the case of an embedding calculation. It only works if keyword embed is also specified. The two basis sets must be given in the following two lines. The first basis will be used for the environment, while the second one is the AO basis for the embedded subsystem (see also the description of keyword embed).

corembed

It is the same as embed, but the partitioning defined by keyword corembed will be used.

special

In the general case, if different basis set are used for each atom, then one should give basis=special and specify the basis sets for each atom in the subsequent lines by giving the label of the corresponding basis sets in the order the atoms appear at the specification of the geometry.

Notes:

• 1.

  By default the following basis sets are available for elements H to Kr in Mrcc:

  • –

    Dunning’s correlation consistent basis sets [21, 74, 157, 158, 121, 20]: cc-pV$X$Z, cc-pCV$X$Z, aug-cc-pV$X$Z, aug-cc-pCV$X$Z, aug-cc-pwCV$X$Z, cc-pV($X$+d)Z,
    aug-cc-pV($X$+d)Z ($X$ = D, T, Q, 5, 6)

  • –

    Gaussian basis sets of Pople and co-workers [42, 78, 50, 18, 28, 7, 34, 88, 11]: STO-3G, 3-21G, 6-31G, 6-311G, 6-31G*, 6-311G*, 6-31G**, 6-311G**, 6-31+G*, 6-31+G**, 6-31++G**, 6-311+G*, 6-311+G**, 6-311++G**

  • –

    the def2 Gaussian basis sets of Weigend and Ahlrichs [152]: def2-SV(P), def2-SVP, def2-TZVP, def2-TZVPP, def2-QZVP, def2-QZVPP

  • –

    the augmented def2 Gaussian basis sets of Rappoport and Furche [130]: def2-SVPD, def2-TZVPD, def2-TZVPPD, def2-QZVPD, def2-QZVPPD

  • –

    F12 basis sets for explicitly correlated wave functions developed by Peterson et al. [120]: cc-pV$X$Z-F12 ($X$ = D, T, Q)

  • –

    the Gaussian basis sets of Dunning and Hay (LANL2DZ) [19]

  • –

    the auxiliary basis sets of Weigend et al. for correlation calculations using the density-fitting/resolution-of-identity approximation [153, 154]: cc-pV$X$Z-RI, aug-cc-pV$X$Z-RI ($X$ = D, T, Q, 5, 6); def2-SV(P)-RI, def2-SVP-RI, def2-TZVP-RI, def2-TZVPP-RI, def2-QZVP-RI, def2-QZVPP-RI

  • –

    the auxiliary basis sets of Hellweg and Rappoport for the augmented def2 Gaussian basis sets [53]: def2-SVPD-RI, def2-TZVPD-RI, def2-TZVPPD-RI, def2-QZVPD-RI, def2-QZVPPD-RI

  • –

    Weigend’s Coulomb/exchange auxiliary basis sets for density fitting/resolution of the identity SCF calculations [155]: cc-pV$X$Z-RI-JK, aug-cc-pV$X$Z-RI-JK ($X$ = D, T, Q, 5), def2-QZVPP-RI-JK

  • –

    Weigend’s universal Coulomb fitting auxiliary basis sets for density fitting/resolution of the identity DFT calculations [Weigend_JFIT]: def2-QZVPP-RI-J

  • –

    the complementary auxiliary basis sets (CABSs) for explicitly correlated calculations developed by Yousaf and Peterson [OPTRI1, OPTRI2]: cc-pV$X$Z-F12-OPTRI ($X$ = D, T, Q), aug-cc-pV$X$Z-OPTRI ($X$ = D, T, Q, 5)

  From Na to Og the following basis sets are available, which must be used together with the corresponding ECP (see also the description of keyword ECP):

  • –

    the LANL2DZ basis sets of Hay and Wadt [45, 151, 44]

  • –

    the def2 Gaussian basis sets of Weigend and Ahlrichs [152]: def2-SV(P), def2-SVP, def2-TZVP, def2-TZVPP, def2-QZVP, def2-QZVPP

  • –

    the augmented def2 Gaussian basis sets of Rappoport and Furche [130]: def2-SVPD, def2-TZVPD, def2-TZVPPD, def2-QZVPD, def2-QZVPPD

  • –

    the correlation consistent PP basis sets of Peterson and co-workers [124, 123, 119, 122, 23, aug-cc-pwCVXZ-PP]: cc-pV$X$Z-PP, aug-cc-pV$X$Z-PP, aug-cc-pwCV$X$Z-PP ($X$ = D, T, Q, 5)

  • –

    the auxiliary basis sets of Hellweg and Rappoport for the augmented def2 Gaussian basis sets [53]: def2-SVPD-RI, def2-TZVPD-RI, def2-TZVPPD-RI, def2-QZVPD-RI, def2-QZVPPD-RI

  • –

    the auxiliary basis sets of Hättig and Hill for correlation calculations with the core-valence and PP basis sets [cc-pwCVXZ-RI, aug-cc-pwCVXZ-PP-RI]: aug-cc-pwCV$X$Z-RI, cc-pV$X$Z-PP-RI and aug-cc-pV$X$Z-PP-RI, aug-cc-pwCV$X$Z-PP-RI ($X$ = D, T, Q, 5)

  Please note that some of the above basis sets are not available for all elements.

• 2.

  If you need basis sets other than the default ones, you can, e.g., download them from the Basis Set Exchange [5, 22, 142, 128]. Please choose format “CFOUR” when downloading the basis sets.

• 3.

  If you use your own basis sets, these must be copied to the end of the corresponding file in the BASIS directory. Alternatively, you can also create a file called GENBAS in the directory where Mrcc is executed, and then you should copy your basis sets to that file.

• 4.

  The labels of the basis sets must be identical to those used in the BASIS/* files (or the GENBAS file). For the default basis sets just type the usual name of the basis set as given above, e.g., cc-pVDZ, 6-311++G**, etc. If you employ non-default basis sets, you can use any label.

• 5.

  For Dunnings’s aug-cc-p(C)V$X$Z basis sets one, two, or three additional diffuse function sets can be automatically added by attaching the prefix d-, t-, or q-, respectively, to the name of the basis set. To generate a d-aug basis set one even tempered diffuse function is added to each primitive set. Its exponent is calculated by multiplying the exponent of the most diffuse function by the ratio of the exponents of the most diffuse and the second most diffuse functions in the primitive set. If there is only one function in the set, the exponent of the most diffuse function is divided by 2.5. To generate t-aug and q-aug sets this procedure is repeated.

• 6.

  For Dunnings’s basis sets, to use the aug-cc-p(C)V$X$Z set for the non-hydrogen atoms and the corresponding cc-p(C)V$X$Z set for the hydrogens give
  aug’-cc-p(C)V$\mathrm{X}$Z. Then the diffuse functions will be automatically removed from the hydrogen atoms.

• 7.

  Only the conventional AO basis set can be specified with this keyword. For the auxiliary basis sets used in density-fitting or F12 approximations see the description of keywords dfbasis_*.

• 8.

  The cc-pVDZ-RI-JK basis set has been generated from cc-pVTZ-RI-JK by dropping the functions of highest angular momentum. The aug-cc-pV$X$Z-RI-JK (def2-QZVPPD-RI-JK) basis sets are constructed automatically from the corresponding cc-pV$X$Z-RI-JK (def2-QZVPP-RI-JK) sets by adding diffuse functions as described above for the d-aug-cc-p(C)V$X$Z basis sets.

• 9.

  For Dunnings’s and Pople’s basis sets add the -min postfix to the basis set name to generate a minimal basis set dropping all the polarization (correlation) functions.

• 10.

  If the (aug-)cc-pV$X$Z-PP basis set does not exist for an element with $Z\le 28$, the program will automatically attempt to use the corresponding (aug-)cc-pV$X$Z basis instead.

• 11.

  If the (aug-)cc-pV($X$+d)Z basis set does not exist for an element (i.e., $Z\le 12$ or $Z\ge 19$), the program will automatically attempt to use the corresponding (aug-)cc-pV$X$Z basis instead.

Default:

none, that is, the basis set must be specified (excepting the case when Mrcc is used together with another code, that is, iface $\ne$ none).

Examples:

1.

Consider any molecule and suppose that the cc-pVDZ basis set is used for all atoms. The input must include the following line:
basis=cc-pVDZ

2.

To use Dunning’s doubly augmented cc-pVDZ basis set (d-aug-cc-pVDZ) for all atoms the input must include the following line:
basis=d-aug-cc-pVDZ

3.

Consider the water molecule and use the cc-pVDZ basis set for the hydrogens and cc-pVTZ for the oxygen. The input must include the following lines:
basis=atomtype
O:cc-pVTZ
H:cc-pVDZ

4.

Consider water again and use the cc-pVQZ, cc-pVTZ, and cc-pVDZ basis sets for the oxygen atom, for the first hydrogen, and for the second hydrogen, respectively. Note that the order of the basis set labels after the basis=special statement must be identical to the order of the corresponding atoms in the Z-matrix/Cartesian coordinates:
geom
O
H 1 R
H 1 R 2 A

R=0.9575
A=104.51

basis=special
cc-pVQZ
cc-pVTZ
cc-pVDZ

5.

Consider the water molecule and use the cc-pVTZ basis set for the hydrogens and aug-cc-pVTZ for the oxygen. The following two inputs are identical:
basis=atomtype
O:aug-cc-pVTZ
H:cc-pVTZ
or
basis=aug’-cc-pVTZ

6.

Consider the water molecule. If you specify
basis=cc-pVTZ-min
minimal basis sets generated from cc-pVTZ will be used for the atoms, that is, only one $s$ function (two $s$ and one $p$ shells) will be retained from the $s$–$p$ kernel of the H (O) cc-pVTZ basis set.

7.

Consider the PbO molecule. If you want to use the cc-pVDZ basis set for O and the cc-pVDZ-PP basis with the corresponding ECP for Pb, you only need to set
basis=cc-pVDZ-PP
in the MINP file.

8.

Mixed basis approach with two basis sets, the cc-pVTZ basis is used for atoms 1, 2, 3, and 5, while cc-pVDZ is employed for atoms 4, 6, 7, 8:
basis=mixed
2
cc-pVTZ 1-3,5
cc-pVDZ 4,6-8

basis_sm

Specifies the small basis set used in dual basis-set calculations as well as for generating SCF initial guess (scfiguess=small).

Options:

the options are the same as for keyword basis, but there is an additional one, none, which means that no small basis is defined.

Default:

basis_sm=none

Examples:

1.

To restart an SCF calculation with the cc-pVQZ basis set from the densities obtained with the cc-pVDZ basis give
basis=cc-pVQZ
basis_sm=cc-pVDZ
scfiguess=small

2.

To perform a dual basis set DF-HF calculation with the 6-311G** and 6-31G** basis sets you need:
basis=6-311G**
basis_sm=6-31G**
dual=on
calc=DF-HF

basopt

Use this keyword to turn on/off basis set optimization. Besides setting this keyword a user supplied GENBAS file is also required for basis set optimization jobs. It is also possible to set the value of basopt to be equal to an appropriate energy. In this case the basis set parameters are optimized so that the absolute value of the difference between this value and the actual energy is minimized. This option comes handy when optimizing a density fitting basis set. In this case the difference between the actual and non-density-fitting energy (obtained from a previous calculation) will be minimized. See also Sect. 6.9.

Options:

on, off, or any real number$\mathrm{>}$

Default:

basopt=off

Examples:

1.

To optimize a basis set variationally set basopt=on

2.

To optimize a basis set minimizing the difference of the calculated energy and -76.287041 E${}_h$ set basopt=-76.287041

bfbasis

Specifies the bond function (BF) basis (see Ref. 89 for details).

Options:

none

No BFs are used.

BF basis name$\mathrm{>}$

name of the BF basis to be used.

Notes:

• 1.

  The format of the name of the BF basis, BF basis name$\mathrm{>}$, is AO basis name$\mathrm{>}$-BF type$\mathrm{>}$. E.g., 6-31G-1s1p is a BF basis optimized for the 6-31G AO basis and one s and one p function set are placed on the corresponding bonds.

• 2.

  The BF basis sets are stored in the BASIS/Bond file but the BF basis can also be specified in the GENBAS file similar to the AO basis sets (see the description of keyword basis). The format of the label of the BF basis in the file is Bbond name$\mathrm{>}$:BF basis name$\mathrm{>}$. E.g., BCH:6-31G-1s1p is 6-31G-1s1p BF basis optimized for the C–H bond.

• 3.

  If BF bases are used, the geometry must be given in mol format (see the description of keyword geom)

Default:

bfbasis=none

Example:

hydrogen-fluoride molecule, the 6-31G basis and the 6-31G-1s1p bond function basis are used:
basis=6-31G
bfbasis=6-31G-1s1p
geom=mol
2 1
0.00000000 0.00000000 0.00000000 F
0.00000000 0.00000000 0.91690000 H
1 2 1

bfgsmem

Specifies the number of gradient vectors used for the BFGS update in quadratic SCF calculations using the BFGS algorithm (qscf=BFGS).

Options:

any positive integer$\mathrm{>}$

Default:

bfgsmem=10

Example:

to increase the number of vectors to 15 set bfgsmem=15

bfgstol

Threshold (in E${}_h$) for starting the BFGS algorithm in quadratic SCF calculations using the BFGS algorithm (qscf=BFGS). The calculation starts with the conventional DIIS-based convergence acceleration, and the BFGS algorithm will be switched on if the maximum norm of the gradient is smaller than bfgstol.

Options:

any positive real number$\mathrm{>}$

Default:

bfgstol=1e-3

Example:

for a convergence threshold of ${10}^{-4}$ E${}_h$ set bfgstol=1e-4

boysalg

Specifies the optimization algorithm used for the Boys–Foster localization.

Options:

Jacobi

Uses standard Jacobi rotations.

Newton

Uses trust-region optimization technique.

Default:

boysalg=Jacobi

Example:

for the trust-region optimization set boysalg=Newton

bpcompo

Boughton–Pulay completeness criterion [9] for occupied orbitals. In various local correlation approaches the Boughton–Pulay procedure is used to identify the atoms on which an LMO is localized. The least-squares residual of the parent LMO and the LMO truncated to the selected atoms is required to be less than one minus this criterion.

Options:

any real number in the [0,1] interval$\mathrm{>}$

This number will be used as the completeness criterion.

Default:

bpcompo=0.95 for local excited-state calculations, bpcompo=0.985 otherwise

Note:

Atom domains determined by bpcompo are also utilized to construct local fitting domains in the case of localcc$\mathrm{\ge }$2016 according to Ref. 107.

Example:

to set a threshold of 0.99 type bpcompo=0.99

bpcompv

Boughton–Pulay completeness criterion [9] for virtual orbitals (projected atomic orbitals). See also keyword bpcompo.

Options:

any real number in the [0,1] interval$\mathrm{>}$

This number will be used as the completeness criterion.

Default:

bpcompv=0.98

Example:

to set a threshold of 0.95 type bpcompv=0.95

bpedo

Boughton–Pulay completeness criterion [9] for the occupied orbitals of an extended domain. See also keyword bpcompo.

Options:

any real number in the [0,1] interval$\mathrm{>}$

This number will be used as the completeness criterion.

Default:

bpedo=0.9999 is set as default in the case of localcc$\mathrm{\ge }$2018 and lcorthr=normal for both LMP2 and LNO-CC computations, according to Refs. 107 and 108. See the description of lcorthr for further details on the predefined values of bpedo for other cases

Note:

bpedo=bpcompo is set if bpedo is not specified and not employed in the local correlation calculation

Example:

to set a threshold of 0.9998 type bpedo=0.9998

bpedv

Boughton–Pulay completeness criterion [9] for the virtual orbitals (projected atomic orbitals) of an extended domain. See also keyword bpcompo.

Options:

any real number in the [0,1] interval$\mathrm{>}$

This number will be used as the completeness criterion.

Default:

bpedv=0.995 is set as default in the case of localcc$\mathrm{\ge }$2016 according to Ref. 107.

Note:

bpedv=bpcompv is set if bpedv is not specified and not employed in the local correlation calculation

Example:

to set a threshold of 0.99 type bpedv=0.99

bppdo

Boughton–Pulay completeness criterion [9] for the occupied orbital of a primary domain. See also keyword bpcompo.

Options:

any real number in the [0,1] interval$\mathrm{>}$

This number will be used as the completeness criterion.

Default:

bppdo=0.999 is set as default in the case of localcc$\mathrm{\ge }$2016 according to Ref. 107.

Note:

bppdo=bpcompo is set if bppdo is not specified and not employed in the local correlation calculation

Example:

to set a threshold of 0.99 type bppdo=0.99

bppdv

Boughton–Pulay completeness criterion [9] for virtual orbitals (projected atomic orbitals) of a primary domain. See also keywords bppdo and bpcompo.

Options:

any real number in the [0,1] interval$\mathrm{>}$

This number will be used as the completeness criterion.

Default:

bppdv=bpcompv

Example:

to set a threshold of 0.99 type bppdv=0.99

calc

Specifies the type of the calculation.

Options:

SCF, HF, or KS

     

Hartree–Fock or Kohn–Sham SCF calculation, the type of the calculation can be controlled by keyword scftype (see also keyword scftype).

RHF, UHF, ROHF, RKS, UKS, ROKS, MCSCF

     

Restricted, unrestricted, restricted open-shell Hartree–Fock SCF; restricted, unrestricted, restricted open-shell Kohn–Sham SCF; or multi-configurational SCF calculation, respectively. The type of the HF/KS/MCSCF procedure is also defined at the same time if these options are chosen, and it is not necessary to set scftype. That is, calc=RHF is equivalent to calc=SCF plus scftype=RHF, etc.

B3LYP, PBE0, B3PW91, B3LYP-D3, B2PLYP-D3, …

     

Kohn–Sham SCF calculation with the specified density functional. The type of the Kohn–Sham procedure (i.e., RKS, UKS, or ROKS) can be controlled by keyword scftype (see also keyword scftype). The options are identical to those of keyword dft (except for off, user, userd, and rsdh), see the description of keyword dft. Note that for a correlated calculation with KS orbitals you can only select the functional with keyword dft, the value of keyword calc must be set to the desired correlation method. Note also that for DFT calculations the density fitting approximation is used by default, i.e., dfbasis_scf is set to auto. To run a conventional KS calculation set dfbasis_scf=none.

TDHF

     

Time-dependent HF (TD-HF, also known as random-phase approximation). If calc=SCF and number of the states is greater than one (set by keywords nsing, ntrip, or nstate), also TD-HF calculations are performed for the excited states. It is only available with density fitting.

TDDFT

     

Full time-dependent DFT (TD-DFT). The density functional must be set using keyword dft. Alternatively, if calc is set to the name of the functional, and the number of the states is greater than one (set by keywords nsing, ntrip, or nstate), also TD-DFT calculations are performed for the excited states using the given functional. For HF reference it is equivalent to TD-HF. It is only available with density fitting. For excited-state calculations with double hybrid functionals see also keyword dhexc.

TDA

     

TD-DFT in the Tamm–Dancoff approximation (TDA). For HF reference it is equivalent to CIS. It is only available with density fitting. For excited-state calculations with double hybrid functionals see also keyword dhexc.

MP2

     

Second-order Møller–Plesset (MP2) calculation. Note that efficient MP2 calculations are only possible with the density-fitting (resolution-of-identity) approximation, which can be performed with the DF-MP2 or the RI-MP2 keywords or by setting dfbasis_cor$\mathrm{\ne }$none. In the case of a DF-MP2 calculation, the spin-component scaled MP2 (SCS-MP2) [39] and the scaled opposite-spin MP2 (SOS-MP2) [59] energy will also be computed (see also keywords scsps and scspt).

MP3

     

Third-order Møller–Plesset (MP3) calculation [41]. Note that MP3 calculations without the density-fitting (resolution-of-identity) approximation are not possible with RHF reference wave functions.

SOS-MP2

     

Scaled opposite-spin second-order Møller–Plesset (SOS-MP2) calculation [59] using an $N^4$-scaling algorithm based on the Cholesky decomposition/Laplace transform of energy denominators (in practice one dRPA iteration is performed, see below). Note that it is only possible with the density-fitting (resolution-of-identity) approximation, and, by default, a DF-SOS-MP2 ($\equiv$ RI-SOS-MP2) calculation is performed (that is, options SOS-MP2, DF-SOS-MP2, and RI-SOS-MP2 are synonyms).

SCS-MP2

     

For canonical calculations it is equivalent to option MP2. If a local correlation calculation is executed, only the spin-component scaled MP2 (SCS-MP2) energy will be computed.

dRPA

     

Direct random-phase approximation (dRPA) calculation (see Eqs. 7 and 8 in Ref. 148). Note that dRPA calculations are only possible with the density-fitting (resolution-of-identity) approximation, and, by default, a DF-dRPA ($\equiv$ RI-dRPA) calculation is performed (that is, options dRPA, DF-dRPA, and RI-dRPA are synonyms).

RPA

     

Random-phase approximation (RPA) calculation (see Eqs. 10 and 13 in Ref. 148, where it is referred to as RPAx-SO2). Note that RPA calculations are only possible with the density-fitting (resolution-of-identity) approximation, and, by default, a DF-RPA ($\equiv$ RI-RPA) calculation is performed (that is, options RPA, DF-RPA, and RI-RPA are synonyms).

SOSEX

     

Second-order screened exchange (SOSEX) [40] calculation (see Eqs. 7 and 9 in Ref. 148), the dRPA and the rPT2 [132] energies are also computed. Note that SOSEX calculations are only possible with the density-fitting (resolution-of-identity) approximation, and, by default, a DF-SOSEX ($\equiv$ RI-SOSEX) calculation is performed (that is, options SOSEX, DF-SOSEX, and RI-SOSEX are synonyms).

sedRPA, seSOSEX, dsdRPA, dsSOSEX

     

The scaled-equation and down-scaled dRPA and SOSEX methods of Ref. 100. See also the notes for options dRPA and SOSEX as well as the descriptions of keywords scspe and scsph.

RPAX2

     

RPAX2 calculation (see Eqs. 17 to 19 in Ref. 54). Note that RPAX2 calculations are only possible with the density-fitting (resolution-of-identity) approximation, and, by default, a DF-RPAX2 ($\equiv$ RI-RPAX2) calculation is performed (that is, options RPAX2, DF-RPAX2, and RI-RPAX2 are synonyms).

CIS

     

Configuration interaction singles (CIS) calculation [91]. Efficient CIS calculations are only possible with the density-fitting (resolution-of-identity) approximation, and, by default, a DF-CIS ($\equiv$ RI-CIS) calculation is performed (that is, options CIS, DF-CIS, and RI-CIS are synonyms). If you are still interested in the CIS energy without DF, set ccprog=mrcc, dfbasis_scf=none, and dfbasis_cor=none.

CIS(D)

     

Configuration interaction singles with perturbative correction for double excitations [CIS(D)] calculation [46, 90]. Note that CIS(D) calculations are only possible with the density-fitting (resolution-of-identity) approximation, and, by default, a DF-CIS(D) [$\equiv$ RI-CIS(D)] calculation is performed [that is, options CIS(D), DF-CIS(D), and RI-CIS(D) are synonyms].

CIS(Di)

     

Iterative doubles correction to configuration interaction singles [CIS(D${}_{\mathrm{\infty }}$)] calculation [46, 93, 94]. Note that CIS(D${}_{\mathrm{\infty }}$) calculations are only possible with the density-fitting (resolution-of-identity) approximation, and, by default, a DF-CIS(D${}_{\mathrm{\infty }}$) [$\equiv$ RI-CIS(D${}_{\mathrm{\infty }}$)] calculation is performed [that is, options CIS(Di), DF-CIS(Di), and RI-CIS(Di) are synonyms].

ADC(2)

     

Second-order algebraic diagrammatic construction [ADC(2)] calculation [141, 43, 93, 94]. Note that ADC(2) calculations are only possible with the density-fitting (resolution-of-identity) approximation, and, by default, a DF-ADC(2) [$\equiv$ RI-ADC(2)] calculation is performed [that is, options ADC(2), DF-ADC(2), and RI-ADC(2) are synonyms].

CC2

     

Second-order coupled-cluster singles and doubles (CC2) calculation [10, 43, 93, 94]. Efficient CC2 calculations are only possible with the density-fitting (resolution-of-identity) approximation, and, by default, a DF-CC2 ($\equiv$ RI-CC2) calculation is performed (that is, options CC2, DF-CC2, and RI-CC2 are synonyms). If you are still interested in the CC2 energy without DF, set ccprog=mrcc, dfbasis_scf=none, and dfbasis_cor=none.

SOS-CC2, SOS-CIS(D), SOS-CIS(Di), SOS-ADC(2)

     

Scaled opposite-spin CC2, CIS(D), CIS(D${}_{\mathrm{\infty }}$), and ADC(2) [SOS-CC2, SOS-CIS(D), SOS-CIS(D${}_{\mathrm{\infty }}$), SOS-ADC(2)] calculation [10, 156, 93, 94, 90]. An $N^4$-scaling algorithm based on the Cholesky decomposition/Laplace transform of energy denominators is executed. It is only available with density fitting. Note that two different parameterizations are implemented for SOS-CIS(D) (see Refs. 52 and 133). See also keywords scsps, scspt, scsps_t, and scspt_t.

SCS-CC2, SCS-CIS(D), SCS-CIS(Di), SCS-ADC(2)

     

Spin-component scaled CC2, CIS(D), CIS(D${}_{\mathrm{\infty }}$), and ADC(2) [SCS-CC2, SCS-CIS(D), SCS-CIS(D${}_{\mathrm{\infty }}$), SCS-ADC(2)] calculation [10, 156, 93, 94, 90]. It is only available with density fitting. Note that two different parameterizations are implemented for SCS-CIS(D) (see Refs. 52 and 133). See also keywords scsps, scspt, scsps_t, and scspt_t.

CCS, CCSD, CCSDT, CCSDTQ, CCSDTQP, CC(n$\mathrm{>}$)

     

The corresponding single-reference CC calculation if the number of active orbitals is zero (see Ref. 69); the corresponding SRMRCCSD, SRMRCCSDT, etc. calculation otherwise (see Ref. 70).

CCSD[T], CCSDT[Q], CCSDTQ[P], CC(n-1$\mathrm{>}$)[n$\mathrm{>}$]

     

The corresponding single-reference CC calculation with perturbative corrections (see Ref. 63).

CCSD(T), CCSDT(Q), CCSDTQ(P), CC(n-1$\mathrm{>}$)(n$\mathrm{>}$)

     

The corresponding single-reference CC calculation with perturbative corrections (see Ref. 63).

CCSD(T)_L, CCSDT(Q)_L, CCSDTQ(P)_L, CC(n-1$\mathrm{>}$)(n$\mathrm{>}$)_L

     

The corresponding CCSD(T)${}_{\mathrm{\Lambda }}$, CCSDT(Q)${}_{\mathrm{\Lambda }}$, etc. calculation (see Ref. 63).

CCSDT-1a, CCSDTQ-1a, CCSDTQP-1a, CC(n$\mathrm{>}$)-1a

     

The corresponding iterative approximate single-reference CC calculation (see Ref. 63).

CCSDT-1b, CCSDTQ-1b, CCSDTQP-1b, CC(n$\mathrm{>}$)-1b

     

The corresponding iterative approximate single-reference CC calculation (see Ref. 63).

CC2, CC3, CC4, CC5, CCn$\mathrm{>}$

     

The corresponding iterative approximate single-reference CC calculation (see Ref. 63).

CCSDT-3, CCSDTQ-3, CCSDTQP-3, CC(n$\mathrm{>}$)-3

     

The corresponding iterative approximate single-reference CC calculation (see Ref. 63).

CCSDT[Q]/A, CCSDTQ[P]/A, CC(n-1$\mathrm{>}$)[n$\mathrm{>}$]/A

     

The corresponding single-reference CC calculation with perturbative corrections using ansatz A (see Ref. 65).

CCSDT[Q]/B, CCSDTQ[P]/B, CC(n-1$\mathrm{>}$)[n$\mathrm{>}$]/B

     

The corresponding single-reference CC calculation with perturbative corrections using ansatz B (see Ref. 65).

CCSDT(Q)/A, CCSDTQ(P)/A, CC(n-1$\mathrm{>}$)(n$\mathrm{>}$)/A

     

The corresponding single-reference CC calculation with perturbative corrections using ansatz A (see Ref. 65).

CCSDT(Q)/B, CCSDTQ(P)/B, CC(n-1$\mathrm{>}$)(n$\mathrm{>}$)/B

     

The corresponding single-reference CC calculation with perturbative corrections using ansatz B (see Ref. 65).

CIS, CISD, CISDT, CISDTQ, CISDTQP, CI(n$\mathrm{>}$), FCI

     

The corresponding single-reference CI calculation if the number of active orbitals is zero (see Ref. 69), the corresponding MRCISD, MRCISDT, etc. calculation otherwise (see Ref. 70).

MP2-F12

     

The explicitly correlated MP2 (MP2-F12) method using the 2B ansatz, the F + K commutator approximation, fixed amplitudes, spin-flipped geminals in open-shell calculations [MP2-R12_Noga, MP2-F12_TM, F12pT]. It is only available with DF.

CCSD-F12 or CCSD(F12*), CCSD(T)-F12 or CCSD(F12*)(T)

     

The explicitly correlated CCSD and CCSD(T) utilizing the CCSD(F12*) [CCSD(F12)] and (T+) [F12pT] models and the above MP2-F12 approximation. It is only available with DF.

Notes:

• 1.

  In the above options, $n$ is a positive integer, which is the excitation level of the highest excitation. $n$ is supposed to be equal to or greater than 6 since for smaller $n$’s the CC(n$\mathrm{>}$) and similar options are equivalent to one of the other options, e.g., CC(5) is equivalent to CCSDTQP or CC(3)(4) is identical with CCSDT(Q).

• 2.

  For excited-state calculations with the TD-HF, TDA, TD-DFT (including double hybrid approaches), CIS, CIS(D), CIS(D${}_{\mathrm{\infty }}$), ADC(2), CC2 and various CC and CI methods the number of states should be greater than one (keywords nsing, ntrip, or nstate). If more than one state is requested for CC calculations, the corresponding linear-response (LR) CC (for excitation energies it is equivalent to equation-of-motion CC, EOM-CC) calculation is performed automatically for the excited states. If more than one state is requested and calc=SCF, TD-HF (dft=off) or TD-DFT (dft$\mathrm{\ne }$off) calculations will be carried out for the excited states.

• 3.

  The active orbitals can be selected and the MRCI/CC calculations can be controlled by keywords nacto, nactv, active, maxex, and maxact. Note that, by default, MRCI/CC calculations are executed using HF reference. To use MCSCF orbitals scftype must be set to MCSCF, and the MCSCF wave function must be defined by keywords docc and mact. In this case nacto and nactv are taken over from the MCSCF calculation, and a MRCI/CC calculation will be run automatically. You should only set the above keywords if you want to run the post-MCSCF calculation with an active space different from the MCSCF one.

• 4.

  In principle, all methods can be used with the density fitting (resolution-of-identity) approximation. It is possible in two ways. You can attach the prefix DF- or RI- to the corresponding option from the above list. Then, for a HF calculation keyword dfbasis_scf will be set to auto, while for a correlated calculation both dfbasis_scf and dfbasis_cor will be given the value auto. Alternatively, you can also set the values for keywords dfbasis_scf and dfbasis_cor, see their description.

• 5.

  Local correlation methods, for both ground and excited states, can be run if the prefix “L” is added to the corresponding option of the keyword, e.g., as LMP2, LdRPA, LCCSD(T), LADC(2), LCC2, etc. Additionally, the prefix “LNO-” can also be used as a synonym in the case of local coupled-cluster approaches, e.g., as LNO-CCSD, LNO-CCSD(T), LNO-CCSDT, etc., and for ADC(2) [LNO-ADC(2)]. Both options are equivalent to setting localcc=on.

• 6.

  For the dRPA, RPA, and SOSEX methods the use of PBE orbitals is recommended (this is set by default).

• 7.

  For the RPAX2 method the use of PBEx orbitals is recommended (this is set by default).

• 8.

  If FNO-CCSD or FNO-CCSD(T) is set, a CCSD or CCSD(T) calculation is performed utilizing the FNO and NAF approximations [FNONAF] and the PPL+ and (T+) corrections [FNOExt]. In these cases, ovirt=ppl, naf_cor=on, and dfbasis_cor=auto are set by default. CCSD-PPL+ and CCSD-PPL+(T+) are equivalent to FNO-CCSD and FNO-CCSD(T).

• 9.

  If the FNO- prefix is added to the acronym of an explicitly correlated CC method, that is, if FNO-CCSD-F12, FNO-CCSD(T)-F12, FNO-CCSD(F12*)(T+), etc. is set, the corresponding calculation is performed utilizing the FNO, NAF, and NAB approximations [RedCostF12]. In these cases, ovirt=mp2, naf_cor=on, naf_f12=on, nab=on, and dfbasis_cor=auto are set by default.

Default:

calc=SCF

Examples:

1.

To run a CCSD(T) calculation, the user should set calc=CCSD(T)

2.

For DF-HF (RI-HF) calculations type:
calc=DF-HF
which is equivalent to the following input:
calc=SCF
dfbasis_scf=auto

3.

For a local CCSD(T) calculation using the local natural orbital approximation set calc=LCCSD(T) or calc=LNO-CCSD(T)

4.

For a RI-MP2 calculation set calc=MP2

5.

For a DFT calculation with the B3LYP functional set calc=B3LYP

6.

Direct RPA calculation with Kohn–Sham orbitals calculated with the PBE functional:
calc=dRPA
dft=PBE

7.

TD-DFT calculation for the 3 lowest singlet excited states of a molecule using the PBE functional:
calc=TDDFT
dft=PBE
nsing=4
A somewhat less complicated input for the same purpose:
calc=PBE
nsing=4

ccmaxit

Maximum number of iteration steps in correlated calculations (CC, CI, RPA, …).

Options:

any positive integer$\mathrm{>}$

Default:

ccmaxit=50

Example:

to increase the maximum number of CC iterations to 100 give ccmaxit=100

ccprog

Specifies the CC program to be used.

Options:

mrcc

The automated, string-based CC program mrcc will be called.

ccsd

The very fast, hand-coded CCSD(T) codes, ccsd or uccsd, will be executed (currently the spatial symmetry cannot be utilized).

cis

The very fast, hand-coded, integral direct DF-CIS code cis will be executed (currently the spatial symmetry cannot be utilized).

Note:

Please note that the mrcc code was optimized for high-order CC calculations, such as CCSDT(Q) and CCSDTQ, which require different algorithms than CCSD(T). Thus it is slow for CCSD(T), but optimal for high-order CC models.

Default:

ccprog=ccsd for conventional and explicitly correlated CCSD and CCSD(T) calculations, ccprog=cis for CIS, CIS(D), CIS(D${}_{\mathrm{\infty }}$), ADC(2), and CC2 calculations, ccprog=mrcc otherwise.

Example:

to use the mrcc code for CCSD or CCSD(T) calculations give ccprog=mrcc

ccsdalg

Specifies the CCSD algorithm employed in the ccsd or uccsd program if ccprog=ccsd.

Options:

disk

An MO-based, hand-coded, OpenMP-parallel CCSD algorithm is invoked [138]. All the necessary four-center integrals (including the ones with four virtual orbitals) are stored on disk after the integral transformation (and integral assembly) steps. The four-center integrals are read in each CCSD iteration from these files. Careful optimization was performed significantly improving both the CPU usage and the OpenMP parallelization efficiency of the implementation (see Ref. 41 for ccsd).

dfdirect

For ccsd: A highly-optimized, hand-coded, OpenMP-parallel, extremely low-memory, in-core, integral-direct $t_1$-transformed DF-CCSD algorithm is invoked [41]. The necessary four-center integrals and intermediates are constructed completely in memory in an integral direct manner in each iteration, and disk I/O is avoided. This implementation, including the cost of the repeated integral assembly, is still more efficient than the optimized ccsdalg=disk one, especially if the OpenMP parallelization is employed. For uccsd: currently the most storage-intensive four-external four-center integrals are assembled on-the-fly from the corresponding two- and three-center DF integrals in each CCSD iteration. The remaining four-center integrals are stored on disk.

Note:

The dfdirect algorithm is currently only available with the ccsd or uccsd programs, i.e., via ccprog=ccsd.

Default:

ccsdalg=dfdirect if density fitting is applied for the correlation energy calculation, e.g., for calc=DF-CCSD, calc=DF-CCSD(T), calc=LNO-CCSD(T), etc. If density fitting is not employed, i.e., dfbasis_cor=none, then ccprog=disk is selected automatically.

Example:

ccsdalg=disk switches to the CCSD algorithm that stores the four-center integrals on disk.

ccsdmkl

Controls the parallel execution of Intel MKL subroutines in program ccsd.

Options:

thr

Threaded/parallel version of MKL is used

seq

Sequential MKL procedures are called in parallel

Default:

ccsdmkl=seq

Example:

to run BLAS subroutines on more than $1$ thread in program ccsd set ccsdmkl=thr

ccsdrest

Use this keyword to restart canonical or reduced-cost (i.e., not local) CC calculations from previously calculated amplitudes if ccprog=ccsd and talg=occ. For restarting local correlation calculations, see keyword lccrest. For restarting canonical CI or CC calculations with ccprog=mrcc, see keyword rest.

Options:

off

Turns off checkpointing and performs the CC calculation normally

trf

Turns on checkpointing creating the ccsd.rst and pt.rst files and performs the CC calculation normally

ccsd

Turns on checkpointing and restarts the CC calculation from the last completed iteration for CCSD or the next unfinished $ijk$ index triplet for the (T) correction

Note:

In the case of restarting a CC calculation, program ccsd is run directly skipping the SCF procedure and the integral transformation. Therefore, the VARS, 55, and DFINT_* files, as well as the checkpoint files ccsd.rst and pt.rst from the previous run need to be present in the working directory.

Default:

ccsdrest=trf

Example:

to restart a CCSD/CCSD(T) calculation set ccsdrest=ccsd

ccsdthreads

Sets the number of outer OpenMP threads in program ccsd while performing the CCSD iteration.

Options:

any positive integer$\mathrm{>}$

Default:

ccsdthreads=2

Example:

to reduce the memory requirement of a CCSD calculation by turning off nested OpenMP set ccsdthreads=1

cctol

Convergence threshold for the energy in correlated calculations (CC, CI, dRPA, RPA, etc.). The energy will be accurate to ${10}^{-\mathrm{𝚌𝚌𝚝𝚘𝚕}}$ E${}_h$.

Options:

any integer$\mathrm{>}$

Default:

cctol=8 for property calculations, cctol=[-${\log }_{10}$(optetol)]+2 for geometry optimizations, cctol=5 for localcc$\mathrm{\ge }$2016, cctol=6 otherwise

Example:

for an accuracy of ${10}^{-8}$ E${}_h$ one must give cctol=8

charge

Charge of the system.

Options:

any integer$\mathrm{>}$

Default:

charge=0

Example:

for the Cl${}^{-}$ ion one should give charge=-1

cialg

Specifies what type of algorithm is to be used in CIS, TDA, TD-HF, and TD-DFT calculations.

Options:

disk

Conventional algorithm, two-electron integrals are stored on disk

direct

Completely I/O-free, integral-direct algorithm, two-electron integrals are recalculated in each iteration step.

direct2

Partially I/O-free, integral-direct algorithm; recommended if the I/O is fast and/or few states are required.

direct3

Variant of direct2, but usually slower.

auto

Based on the size of the molecule the program will automatically select the most efficient one from the above options.

Default:

cialg=auto

Example:

to use disk-based algorithm set cialg=disk

ciguess

The initial guess vectors for CI and LR-CC calculations can be specified using this keyword.

Options:

on

The initial trial vectors are supplied by the user and should be given in the subsequent lines as follows. For each state the corresponding initial guess vector must given by the number of non-zero elements of the vector on the first line, followed by as many lines as the number of non-zero elements. In each line the corresponding excitation operator and the value for this element of the vector must be provided in the following format:

where is the level of excitation, and the electrons are promoted from occupied orbitals to virtual orbitals with spins ( is 1 for alpha and 0 for beta), respectively. is the corresponding coefficient.

off

Initial trial vectors are not specified, the program applies simple unit vectors as initial guess. The unit vectors are determined on the basis of the diagonal elements of the Hamiltonian: if $n$ roots are requested, $n$ unit vectors corresponding to the $n$ lowest diagonals will be used.

Default:

ciguess=off

Example:

Suppose that we have two excited states in a LR-CC calculation. Then the initial guess can be given as follows.
ciguess=on
1
1 1 6 4 1.0
3
1 1 7 3 0.1
2 1 0 7 7 5 5 1.0
2 1 1 7 6 3 4 0.1
For the first state there is only one entry, a single excitation of the alpha electron from orbital 4 to orbital 6 with a coefficient of 1.0. For the second root the initial guess vector contains three entries. A single excitation from orbital 3 to orbital 7 with alpha spin and a relative weight of 0.1, a double excitation from orbital 5 to orbital 7 with a weight of 1.0, and another double excitation of the alpha electrons from orbitals 3 and 4 to orbitals 6 and 7 with a weight of 0.1.

Notes:

1.

For $M_S=0$ states the vector is automatically spin-adapted, and you do not need to specify the coefficients for the corresponding spin-reversed excitations. E.g., in the above example, for root 1 the 1 0 6 4 1.0 entry is unnecessary.

2.

The guess vector is not required to be normalized, it is done automatically.

3.

In the case of four-component relativistic calculations (Dirac interface) the serial numbers of the spinors should be specified. In addition, the second number in the above strings must be 1 (that is, all excitations are formally considered as excitations of alpha electrons).

cmpgrp

Specifies the computational point group. All calculations will use the specified Abelian group. See Sect. 13 for more details.

Options:

auto

The molecular symmetry is automatically recognized.

point group symbol$\mathrm{>}$

Schönflies symbol of the Abelian point group such as C1, Ci, Cs, C2, C2v, C2h, D2, D2h

Note:

cmpgrp=C1 is equivalent to symm=off

Default:

cmpgrp=auto

Example:

to use $C_{2v}$ point group for benzene set cmpgrp=C2v

comprest

Controls the restart procedure for composite calculations. Currently, only ONIOM calculations can be restarted with the keyword.

Options:

0

The ONIOM calculation is restarted and halted after the layer boundaries are defined. This option is designed for the setup of layer boundaries after a successful calculation on the full system.

any positive integer n$\mathrm{>}$

The composite calculation is restarted after the $n$th subcalculation is completed. This option is designed for the modification of composite calculations after successful subcalculations of a composite method. See the keyword subminp to modify the initial settings.

auto

The composite calculation is restarted from the last successful subcalculation of a composite method. This option is designed, e.g., for power failures.

off

No restart is requested

Notes:

1.

The comprest=0 option requires the MOCOEF file for Mrcc, the corresponding auxiliary file (aux) for Mopac, and the wbo file for xTB calculations.

2.

In the case of single point ONIOM calculations with option comprest $\mathrm{>}$ 0, the ONIOMSPEC and iface* files of the corresponding subcalculations are checked if they are available. Additionally, the GRAD* and VARS* files are also searched for if gradient or electronic embedding calculations are requested. Calculations using the Mopac or the xTB programs are automatically checked by the external codes.

3.

Except of comprest=0, the boundary settings are read from the ONIOMSPEC file, while the boundary specification in the MINP file is ignored.

4.

In the case of comprest=auto, the keyword scfiguess is set to restart, and the SCFDENSITIES file is reused if the upcoming calculation uses Mrcc.

Default:

comprest=off

Example:

1.

If a series of ONIOM calculations are stopped due to power failure at unknown points of the composite procedure, type comprest=auto to continue from the last successful subcalculation.

2.

To reconfigure the boundary settings after the first ONIOM subcalculation, type comprest=0. After the setup is made, type comprest=1 to continue with the second subcalculation.

core

Specifies whether the core electrons are correlated.

Options:

frozen

Frozen core approximation

corr

All core electrons are correlated

any non-negative integer n$\mathrm{>}$

The lowest (according to orbital energy order) $n$ pieces of spatial orbitals (the lowest $n$ pieces of alpha and $n$ pieces of beta spin orbitals for UHF/semicanonical ROHF reference) will be dropped.

Default:

core=frozen

Example:

to correlate all core electrons set core=corr or core=0

corembed

This keyword controls the models and subsystems selected for multi-level local correlation methods. Currently it is only available for closed-shell systems using density-fitting.

Options:

off

Conventional case, a single model defined by calc is used for the entire system.

on

Multi-level calculation is performed with different local correlation methods for the active (high-level) and the environmental (low-level) subsystems. The three input lines following corembed define the list of active atoms, the computational model for the environment level, and the number of embedded orbitals (if it is specified). The syntax for these three lines is analogous with that for keyword embed. (See the description of keyword embed.) The high-level method for the active region should be specified by the keyword calc.

Default:

corembed=off

Notes:

1.

Local correlation methods available with localcc$\mathrm{\ge }$2015 (e.g., MP2 or arbitrary single-reference CC) can be chosen for both the active and the environmental subsystem. Additionally, HF or HF+LRC are also available choices for the low-level model. If the latter is set, the environment is treated at the HF level but the long-range correlation (LRC) between the active subsystem and its environment is also taken into account (see Ref. 48). Note that models with KS-DFT reference, such as dRPA, SOSEX, etc., are not available for multi-level local correlation calculations.

2.

The threshold settings of the local correlation method chosen for the high-level model can be given (as in the case of corembed=off) by the keywords controlling the local correlation methods (see their list in Sect. 6.8). Default settings according to lcorthr=normal and localcc=2018 or 2021 (or for previous versions according to lcorthr=loose and localcc=2015 or localcc=2016) are employed for the low-level model of the environment.

Examples:

1.

LNO-CCSD(T)-in-LMP2 scheme, where LNO-CCSD(T) is performed for the active orbitals with tight thresholds, atoms 1 and 2 are included in the high-level region, and the number of the active orbitals is determined automatically:
calc=LNO-CCSD(T)
lcorthr=tight
corembed=on
1-2
LMP2
0

2.

LNO-CCSDT-in-LNO-CCSD scheme, where the local CCSDT calculation is performed with the mrcc program for the active orbitals and the local CCSD is calculation performed with the ccsd program for the environment:
calc=LCCSDT
corembed=on
1-2
LCCSD
0

3.

LNO-CCSD(T)-in-HF+LRC embedding where only HF is used for the environment but the additional LRC term accounts for the interaction of the active and environmental parts. Atoms 1, 2, 3, and 5 define the active subsystem, and 10 orbitals are included in the active region:
calc=LNO-CCSD(T)
corembed=on
1-3,5
HF+LRC
10

csapprox

Switches on the approximate long-range spin polarization approach of Ref. ROLocalMP2 for the restricted open-shell local correlation methods with localcc$\mathrm{\ge }$2021. This option treats the orbital domains without singly occupied orbitals via a closed-shell formalism with negligible approximations and considerable gain in efficiency.

Options:

on or off

Default:

csapprox=on

cvs

Switches on the core-valence separation (CVS) for excited-state calculations [CVS, CVS2]. Only excitations including at least one core orbital specified by this keyword will be included in the excited-state wave function.

Options:

off

The CVS approximation will not be used.

serial no. of the orbitals$\mathrm{>}$

The serial number of the core orbitals (i.e., absolute serial number according to orbital energy order) must be given separated by commas. Serial numbers separated by dash means that all the orbitals in the specified interval will be included. For unrestricted orbitals, only the serial numbers of the alpha orbitals must be given.

Notes:

1.

A projected eigenvalue equation [CVS] is used for ccprog=ccsd. It is recommended for higher-order linear-response CC and CI calculations.

2.

A decoupled Hamiltonian [CVS2] is used for ccprog=cis. It is recommended for CIS, TDHF, CIS(D), ADC(2), and various (DH-)TDDFT calculations [CVS_DH]. In these cases, the reduced-cost and reduced-scaling approximations are also available (see the description of keyword redcost_exc and Ref. RedCostCVS).

3.

If the CVS approximation is employed, it is recommended to give an appropriate initial guess using the ciguess keyword.

Default:

cvs=off

Example:

to consider orbitals 1, 3, 4, and 5 set:
cvs=1,3-5

dboc

Diagonal Born–Oppenheimer correction (DBOC) (available only with Cfour).

Options:

on or off

Default:

dboc=off

Example:

for a DBOC calculation set dboc=on

dendec

Selects the algorithm for the decomposition of energy denominators, Cholesky-decomposition or Laplace transform, for canonical SOS-MP2, dRPA (also required for SOSEX), SOS-CC2, SOS-CIS(D), SOS-CIS(D${}_{\mathrm{\infty }}$), and SOS-ADC(2) as well as for local MP2 and dRPA calculations. The dRPA calculation is performed using the modified algorithm of Heßelmann [54] based on the decomposition of energy denominators. For the calculation of the SOS-MP2 energy, in practice one dRPA iteration is performed with the aforementioned algorithm. In the case of local MP2 and dRPA calculations the correlation energy contributions are also evaluated with the aid of the decomposition of energy denominators (see Ref. 72). The algorithm for the decomposition can be set using this keyword in all of the above cases. The number of retained Cholesky vectors/quadrature points can be controlled by keyword nchol.

Options:

off

for SOS-CC2, SOS-CIS(D), SOS-CIS(D${}_{\mathrm{\infty }}$), and SOS-ADC(2) calculations the decomposition will not be used, but a fifth-power scaling algorithm will be executed

Cholesky

Cholesky decomposition will be used

Laplace

Laplace transform will be used

Default:

dendec=Laplace for SOS-MP2, SOS-CC2, SOS-CIS(D) SOS-CIS(D${}_{\mathrm{\infty }}$), and SOS-ADC(2); dendec=Cholesky otherwise

Notes:

1.

The algorithms based on the Laplace-transformed technique use minimax quadratures obtained from Ref. 146.

2.

The default quadratures are taken from the Quad file which is located in the BASIS directory created at the installation. In addition to the default quadratures, any further quadrature can be used by adding it to the BASIS/Quad file or alternatively to the GENBAS file to be placed in the directory where Mrcc is executed. The format is as follows. On the first line give the label of the quadrature as KNNRXXX, where NN is the number of the quadrature points and XXX is the upper limit of the interval in which the Laplace transform is approximated (variable $R$ in Ref. 146). The subsequent NN lines must contain, respectively, the weights and quadrature points.

Example:

to use Laplace transform give dendec=Laplace

dens

Construction of density, derivative density, and transition density matrices for property calculations. If mod(dens,2)=1, only one-particle, if mod(dens,2)=0, both one- and two-particle density matrices will be calculated and contracted with the available property integrals. See Refs. 60, 61, 62, 64, 113, 114 for more details.

Options:

1, 2

Density-matrix calculation (for geometry optimizations, first-order properties, etc.)

3, 4

Density-matrix first derivatives (for second-order property calculations, available only with Cfour)

5, 6

Transition density matrices (for transition moment calculations)

7, 8

Second and third derivatives of the density-matrix (for third-order property calculations, available only with Cfour)

Default:

dens=2 for geometry optimizations and QM/MM calculations, dens=0 otherwise

Notes:

1.

Transition moment as well as excited-state gradient calculations can be performed for only one excited state at a time, that is, nsing, ntrip, or nstate cannot exceed 2. To compute the transition moment or gradient for a higher excited state you need to converge the equations to that root. The best practice is to run a calculation with the desired number of excited states, and then restart the calculation selecting a higher solution (see the description of keyword rest). You can also try to start the calculation from a good initial guess (see the description of keyword ciguess).

2.

If dens $\ne$ 0, a population analysis is also performed, and Mulliken and Löwdin atomic charges as well as Mayer bond orders are computed.

Example:

for the calculation of both one- and two-particle density matrices set dens=2

denscorr

Specifies whether the density-based basis-set correction proposed by Giner, Toulouse, and co-workers [83] is calculated.

Options:

0

The density-based basis-set correction is not calculated.

1

Both the CCSD(T) energy and the correction are calculated.

2

Only the density-based basis-set correction is calculated.

Notes:

1.

To calculate the correction, even if the CCSD(T) energy is not required, the following format should be used (see keyword dft):
denscorr=2
calc=DF-CCSD(T)
dft=userd
1
1.00 HFx
1
1.0 ECMD_PBEc

2.

In the case of ROHF calculations, the semicanonical orbitals are used by default (see keywords rohfcore and rohftype). When comparing the results from other programs, it might be important to verify the ROHF orbitals.

Default:

denscorr=0

Example:

for only the density-based basis-set correction, the user should set denscorr=2

dfalg

Specifies how the inverse of the two-center Coulomb integral matrix is decomposed in density fitting direct SCF calculations.

Options:

LinEq

The fitting coefficients are computed by solving the corresponding system of linear equations. It is efficient and numerically stable. It is the best choice for very large auxiliary basis sets for which the diagonalization of the two-center integral matrix is prohibitive.

InvSqrt

Inverse square root of the two-center integral matrix is used. It is relatively stable numerically, but the diagonalization is slow and requires much memory.

Cholesky

Cholesky decomposition of the inverse of the two-center integral matrix is used. It is an efficient algorithm but numerically unstable if the two-center matrix tends to be singular.

Default:

dfalg=InvSqrt for property calculations, dfalg=LinEq otherwise

Example:

to use Cholesky decomposition set dfalg=Cholesky

dfbasis_cab

Specifies the complimentary auxiliary basis set (CABS) for explicitly correlated methods.

Options:

none

No CABS.

basis set label$\mathrm{>}$, atomtype, special

The specified basis set is used as CABS. For the specification of the basis the same rules apply as for keyword basis, see the description of keyword basis.

auto

This option can only be used if Dunning’s aug-cc-pV$X$Z or Peterson’s cc-pV$X$Z-F12 basis sets are used as the normal basis set. In this case, if dfbasis_cab= auto, the corresponding “OPTRI” basis set will be used as CABS.

Note:

For the available CABSs, see the notes for keyword basis.

Default:

dfbasis_cab=auto for all the explicitly correlation methods, dfbasis_cab=none otherwise.

Example:

To use the cc-pVTZ-F12-OPTRI CABS with the aug-cc-pVDZ AO basis set:
basis=aug-cc-pVDZ
dfbasis_cab=cc-pVTZ-F12-OPTRI

dfbasis_cor

Specifies whether the density fitting approximation will be used in the correlated calculations and also specifies the fitting basis set.

Options:

none

The density fitting approximation is not used for the correlated calculation.

basis set label$\mathrm{>}$, atomtype, special

The density fitting approximation is invoked, and the specified basis set is used as fitting basis set. For the specification of the basis the same rules apply as for keyword basis, see the description of keyword basis.

auto

This option can only be used if Dunning’s (aug-)cc-pV$X$Z or (aug-)cc-pV($X$+d)Z, Weigend and Ahlrichs’ def2, the augmented def2 basis sets of Rappoport and Furche, Peterson’s cc-pV$X$Z-F12 or (aug-)cc-pV$X$Z-PP, or Pople’s basis sets are used as the normal basis set. In this case, if dfbasis_cor=auto, the density fitting approximation is invoked. For the (aug-)cc-pV$X$Z(-PP) and (aug-)cc-pV($X$+d)Z basis sets the corresponding (aug-)cc-pV$X$Z(-PP)-RI basis sets will be used automatically as the fitting basis sets, while for a cc-pV$X$Z-F12 basis set the corresponding aug-cc-pV$X$Z-RI basis will be taken. For the (augmented) def2 basis sets also the corresponding RI basis sets will be used, e.g., def2-TZVPP-RI for def2-TZVPP, def2-QZVPP-RI for def2-QZVPP, def2-TZVPPD-RI for def2-TZVPPD, etc. For Pople-type minimal and double-$\zeta$ basis sets (i.e., STO-3G, 3-21G, 6-31G**, etc.) the cc-pVDZ-RI basis set, while for triple-$\zeta$ basis sets (i.e., 6-311G, 6-311G**, etc.) the cc-pVTZ-RI basis set will be used as the auxiliary basis; if the basis also includes diffuse functions (i.e., 6-31+G**, 6-311++G**, etc.) the aug-cc-pVDZ-RI and aug-cc-pVTZ-RI basis sets are employed by default.

Notes:

1.

For the available fitting basis sets see the notes for keyword basis on page 12.

2.

The density fitting approximation can also be invoked by attaching the prefix DF- or RI- to the corresponding option of keyword calc, see the description of calc.

Default:

dfbasis_cor=auto for all the correlation methods that use the density fitting approximation by default as well as for local correlation calculations (i.e., localcc $\ne$ off), dfbasis_cor=none otherwise.

Examples:

1.

To use the cc-pVTZ-RI fitting basis in the correlated calculation for all atoms the input must include dfbasis_cor= cc-pVTZ-RI

2.

Consider the water molecule and use the cc-pVTZ-RI fitting basis set for the hydrogens and aug-cc-pVTZ-RI for the oxygen. The following inputs are equivalent:
dfbasis_cor=atomtype
O:aug-cc-pVTZ-RI
H:cc-pVTZ-RI
or
dfbasis_cor=aug’-cc-pVTZ-RI

3.

Consider the water molecule and use the cc-pVTZ (cc-pVTZ-RI) basis set (fitting basis set) for the hydrogens and aug-cc-pVTZ (aug-cc-pVTZ-RI.) for the oxygen in a local correlation calculation. The following inputs are equivalent:
calc=CCSD(T)
localcc=on
basis=aug’-cc-pVTZ
dfbasis_scf=aug’-cc-pVTZ-RI
dfbasis_cor=aug’-cc-pVTZ-RI
or
calc=LCCSD(T)
basis=aug’-cc-pVTZ

4.

To run a DF-HF calculation with the cc-pVTZ-F12 basis set and the aug-cc-pVTZ-RI auxiliary basis the input should only include the following lines:
basis=cc-pVTZ-F12
calc=DF-HF

dfbasis_scf

Specifies whether the density fitting approximation will be used in the HF- or KS-SCF calculation and also specifies the fitting basis set. For the syntax see the description of keyword dfbasis_cor. The important difference is that, if dfbasis_scf=auto, the (aug-)cc-pV$X$Z-RI-JK basis sets will be used as auxiliary basis sets for Dunning’s, Peterson’s, and Pople’s basis sets, while for the def2 basis sets the def2-QZVPP-RI-JK auxiliary basis is taken. For the augmented def2 as well as for the aug-cc-pV$X$Z-PP basis sets the def2-QZVPPD-RI-JK auxiliary basis will be used. Exceptions are the KS-DFT calculations with non-hybrid functionals, where the def2-QZVPPD-RI-J basis set will be used in the following cases: for H with the cc-pVDZ, aug-cc-pVDZ, cc-pVDZ-F12, def2-SV(P), def2-SVP, def2-TZVP, def2-SVPD, def2-TZVPD, and LANL2DZ AO basis sets; for other atoms with the cc-pVDZ, cc-pVTZ, cc-pV(D+d)Z, cc-pV(T+d)Z, aug-cc-pVDZ, aug-cc-pVTZ, aug-cc-pV(D+d)Z, aug-cc-pV(T+d)Z, cc-pVDZ-F12, def2-SV(P), def2-SVP, def2-TZVP, def2-TZVPP, def2-SVPD, def2-TZVPD, def2-TZVPPD, and LANL2DZ AO basis sets.

Default:

dfbasis_scf=auto if dfbasis_cor$\mathrm{\ne }$none and for DFT calculations, dfbasis_scf= none otherwise.

dfbasis_scf_sm

Specifies the small fitting basis set for dual auxiliary basis set calculations. Any basis set can be used as a small auxiliary basis set which is available in Mrcc or you can use your own sets using the GENBAS file. For a small set of atoms (H, C, N, O, F, P, S, and Cl), preoptimized cc-pV(T,Q)Z-RI-JK-dual basis sets are also available [DualDF]. These are the recommended ones for calculations with the (aug-)cc-pV(T,Q)Z AO basis sets. See also the description of keyword dual_df for further details and examples.

Options:

Same as dfbasis_scf.

Default:

dfbasis_scf_sm=dfbasis_scf

Notes:

For more information on dual auxiliary basis calculations see the keyword dual_df.

dfintran

Specifies the integral transformation program to be used for the transformation of three-center Coulomb integrals.

Options:

drpa

the drpa program will be called

ovirt

the ovirt program will be called

Default:

dfintran=ovirt if ovirt$\mathrm{\ne }$off, dfintran=drpa otherwise.

Example:

to use the ovirt code set dfintran=ovirt

dft

Use this keyword to perform DFT calculations and to specify the functional.

Options:

off

No DFT calculation is carried out.

functional name$\mathrm{>}$

The name of the functional, see Table LABEL:FuncTable for the available functionals.

Libxc identifier$\mathrm{>}$

The identifier of a functional implemented in the Libxc library (if installed), such as LDA_X, LDA_C_VWN_1, GGA_X_B88, etc. (see the homepage of the Libxc project [56]).

user

User-defined functional. Any combination of the following contributions can be defined:

• •

  the available standalone functionals, see column “User” in Table LABEL:FuncTable.

• •

  the functionals available in the Libxc library (if installed), use simply the Libxc identifier of the functionals (see the homepage of the Libxc project [56]).

• •

  the HF exchange, denoted by HFx

• •

  the long-range HF exchange, denoted by lrHFx. The range-separation parameter ($\omega$) should be specified in a.u. after the lrHFx flag separated by space, see the example below. If the parameter is not set, $\omega$ $=$ 0.15 a.u. will be used.

• •

  the short-range HF exchange, denoted by srHFx. The syntax is same as for lrHFx, see the example below.

• •

  the MP2, MP3, dRPA, and SOSEX correlation, denoted, respectively, by MP2, MP3, dRPA, and SOSEX;

• •

  the antiparallel- and parallel-spin components of the latter correlation corrections, add the s and t postfix to the above labels, respectively, e.g., instead of the MP2 label, the MP2s and MP2t labels should be used.

• •

  the long- and short-range dRPA correlation denoted, respectively, by lrdRPA and srdRPA. The corresponding spin components, lrdRPAs, srdRPAs, lrdRPAt, and srdRPAt, are also available; the syntax is same as for lrHFx.

Note that for hybrid functionals, such as B97, the HF exchange will be neglected. The combination should be specified in the subsequent lines as follows (see also the examples below):
number of entries$\mathrm{>}$
coefficient 1$\mathrm{>}$ functional name 1$\mathrm{>}$
coefficient 2$\mathrm{>}$ functional name 2$\mathrm{>}$
coefficient 3$\mathrm{>}$ functional name 3$\mathrm{>}$
…

userd

User-defined functional, but different functionals are used for the calculation of the density and the energy. It is useful for defining special double-hybrid functionals. The combination should be specified in the subsequent lines as follows (see also the examples below):
number of entries for density$\mathrm{>}$
coefficient 1$\mathrm{>}$ functional name 1$\mathrm{>}$
coefficient 2$\mathrm{>}$ functional name 2$\mathrm{>}$
coefficient 3$\mathrm{>}$ functional name 3$\mathrm{>}$
…
number of entries for energy$\mathrm{>}$
coefficient 1’$\mathrm{>}$ functional name 1’$\mathrm{>}$
coefficient 2’$\mathrm{>}$ functional name 2’$\mathrm{>}$
coefficient 3’$\mathrm{>}$ functional name 3’$\mathrm{>}$
…
See option user for the possible values of functional name n$\mathrm{>}$ and functional name n’$\mathrm{>}$. The weight of the HF exchange (HFx), if any, can be different for the density and the energy, and, in contrast to previous versions of Mrcc, must be specified also in the second block.

rsdh

Range-separated double hybrid functionals of Mester and Kállay [RSDH] based on the ansatz of Kalai and Toulouse [Toulouse_RSDH]. The entries should be specified in the subsequent lines as follows (see also the examples below):
ssrfunctional name 1$\mathrm{>}$
ssrfunctional name 2$\mathrm{>}$
…
coefficient 1$\mathrm{>}$
coefficient 2$\mathrm{>}$
Here, coefficient 1$\mathrm{>}$ and coefficient 2$\mathrm{>}$ stand for the parameters $\lambda$ and $\omega$, respectively. ssrfunctional name i$\mathrm{>}$ is the range-separated variant of the corresponding functional evaluated utilizing the local-scaling approximation proposed by Scuseria and co-workers [30]. This framework works with arbitrary combination of LDA/GGA/meta-GGA exchange and correlation functionals using either the built-in ones or those from the Libxc library.

Default:

dft=PBE for dRPA, RPA, SOSEX, and for scaled-equation and down-scaled dRPA and SOSEX; dft=PBEx for RPAX2; otherwise dft=off

Notes:

1.

Most of the the built-in functionals implemented in Mrcc were obtained from the Density Functional Repository [29, 145]. Other functionals are available via the Libxc interface [85, 56] and require the Libxc library, see Sect. 7.2 for the installation of Libxc.

2.

Empirical dispersion corrections can be calculated for particular functionals and also for the HF energy using the DFT-D3 approach of Grimme and co-workers [36, 37] by attaching the -D3 postfix to the corresponding options: BLYP-D3, BHLYP-D3, B3LYP-D3, B3PW91-D3, BP86-D3, PBE-D3, PBE0-D3, HCTH120-D3,
B2PLYP-D3, mPW1B95-D3, TPSS-D3, TPSSh-D3, B2GPPLYP-D3, DSDPBEP86-D3, DSDPBEhB95-D3, CAM-B3LYP-D3, wB97X-D3, M06-L-D3, MN15-D3, M06-2X-D3, LC-wPBE-D3, PW91-D3, SCAN-D3, dRPA75-D3, HF-D3. See also the description of keyword edisp.

3.

For a simple DFT calculation (i.e., without subsequent correlation calculations) the value of keyword calc can be SCF, HF, RHF, or UHF. Note that you do not need to set its value since it is set to SCF by default. Alternatively, you can select the DFT functional using keyword calc, and in this case you do not have to set keyword dft (see the description of calc).

4.

For a correlated calculation with KS orbitals you should select the functional with this keyword, and the value of keyword calc must be set to the desired correlation method. Note that you can also accelerate the post-KS calculation using local correlation schemes (e.g., local dRPA). See the examples below.

5.

For a correlated calculation with KS orbitals (excluding calculations with double hybrid functionals) the HF energy computed with KS orbitals is used as reference energy.

6.

For the B2PLYP, B2GPPLYP, DSDPBEP86, DSDPBEhB95, dRPA75, etc. double hybrid functionals as well as for user-defined double hybrid functionals including MP2 (SCS-MP2), dRPA, etc. correlation calc is automatically set to MP2, dRPA, etc. Note that you can accelerate the MP2, dRPA, …part of a double hybrid DFT calculation for large molecules using local correlation approaches. For the built-in double hybrid functionals just add the “L” prefix, while for the user-defined functionals set localcc=on. See the examples below.

7.

The DSDPBEP86, DSDPBEhB95, and dRPA75 functionals use special parameters for the calculation of the D3 correction which are read by the DFT-D3 program from the .dftd3par.$HOST file located in your home directory. This file will be created by the program, but you must be sure that the program is able to access your home directory. Also note that, if you already have this file in your home, it will be overwritten, so please do not forget to save it before executing Mrcc.

8.

For the VV10 van der Waals functional you can modify parameters $b$ and $C$ (see Ref. 150) if it is used with the user or userd options. For that purpose the two parameters should be specified after the VV10 or VV10NL flag separated by spaces, see the example below. If the parameters are not set, those of Ref. 150 will be used.

9.

The range-separated variant of a functional is available with the ssr prefix utilizing the local-scaling approximation proposed by Scuseria and co-workers [30]. This framework works for arbitrary LDA/GGA/meta-GGA exchange and correlation functionals using the either built-in ones or those from the Libxc library.

10.

ECMD functionals proposed by Giner and co-workers [83] are available with the ECMD_ prefix. This framework works for the built-in PBEc functional or arbitrary LDA/GGA/meta-GGA correlation functionals from the Libxc library.

Examples:

1.

To perform a DFT calculation with the B3LYP functional give dft=B3LYP or calc=B3LYP

2.

The B3LYP functional can also be defined using the user option as
calc=scf
dft=user
5
0.08 LDA
0.72 B88
0.20 HFx
0.19 VWN5
0.81 LYP

3.

The B2PLYP double-hybrid functional can also be defined using the user option as
calc=scf
dft=user
4
0.47 B88
0.73 LYP
0.53 HFx
0.27 MP2

4.

The DSDPBEP86 double-hybrid functional can also be defined using the user option as
calc=SCF
dft=user
5
0.30 PBEx
0.43 P86
0.70 HFx
0.53 MP2s
0.25 MP2t

5.

SOSEX calculation with Kohn–Sham orbitals calculated with the LDA exchange functional:
calc=SOSEX
dft=LDA

6.

To perform a DFT calculation with the B2PLYP double-hybrid functional and add the D3 dispersion correction set dft=B2PLYP-D3 or calc=B2PLYP-D3

7.

B2PLYP calculation, the MP2 contribution is evaluated using local MP2 approximation:
calc=LB2PLYP

8.

User-defined functional, different functionals are used for the calculation of the density (0.25 PBEx + 0.75 HF exchange + PBEc) and the energy (0.50 PBEx + 0.50 HF exchange + MP2 correlation).
dft=userd
3
0.75 HFx
0.25 PBEx
1.00 PBEc
3
0.50 HFx
0.50 PBEx
1.00 MP2

9.

The dRPA75 dual-hybrid functional can also be defined using the userd option as
dft=userd
3
0.75 HFx
0.25 PBEx
1.00 PBEc
3
0.75 HFx
0.25 PBEx
1.00 dRPA

10.

Local dRPA calculation with Kohn–Sham orbitals calculated with the PBE functional:
calc=LdRPA
dft=PBE

11.

To perform a DFT calculation with the B3LYP functional using its Libxc implementation set calc=HYB_GGA_XC_B3LYP5

12.

The B3LYP functional can also be defined using the user option and the functionals implemented in the Libxc library as
dft=user
5
0.08 LDA_X
0.72 GGA_X_B88
0.20 HFx
0.19 LDA_C_VWN
0.81 GGA_C_LYP

13.

DFT calculation with a user-defined PBE0-VV10 functional. Parameter $b$ of VV10 is modified, while for $C$ its default value, 0.0093, is used. If you do not want to modify either $b$ or $C$, simply drop the two numbers for the VV10 entry.
dft=userd
3
0.75 PBEx
0.25 HFx
1.00 PBEc
4
0.75 PBEx
0.25 HFx
1.00 PBEc
1.00 VV10 8.0 0.0093

14.

DFT calculation with a user-defined CAM-B3LYP functional. A range-separation parameter ($\omega$) of 0.33 a.u. is set. If you want to use the default $\omega$ $=$ 0.15 a.u., simply drop the last number for the lrHFx entry.
dft=user
3
1.00 HYB_GGA_XC_CAM_B3LYP
0.19 HFx
0.46 lrHFx 0.33

15.

An alternative implementation of CAM-B3LYP:
dft=user
3
1.00 HYB_GGA_XC_CAM_B3LYP
0.65 HFx
-0.46 srHFx 0.33

16.

Alternative definition for the RS-PBE-P86 functional utilizing built-in functionals:
dft=rsdh
ssrPBEx
ssrP86
0.5
0.7

17.

Alternative definition for the RS-PBE-P86 functional utilizing functionals from the Libxc library:
dft=rsdh
ssrGGA_X_PBE
ssrGGA_C_P86
0.5
0.7

18.

To define third-order double hybrid functionals containing a perturbative third-order correction [XYG3MP3, DSDdRPA_DSD3], the MP3 option can be used. For example, the XYG9[f2]@B44LYP functional of Ref. XYG3MP3 can be specified as
dft=userd
4
0.56 B88
0.44 HFx
0.19 VWN5
0.81 LYP
7
0.0881 LDA
-0.0644 B88
0.9692 HFx
0.2730 VWN5
0.6447 MP2s
0.6467 MP2t
0.2761 MP3

19.

Density-based basis-set correction, see keyword denscorr, using the built-in PBEc-based functional:
denscorr=2
calc=DF-CCSD(T)
dft=userd
1
1.00 HFx
1
1.0 ECMD_PBEc

20.

Density-based basis-set correction, see keyword denscorr, utilizing correlation functionals from the Libxc library:
denscorr=2
calc=DF-CCSD(T)
dft=userd
1
1.00 HFx
1
1.0 ECMD_GGA_C_PW91

dhexc

This keyword can be used to select the wave function method for the evaluation of the second-order contributions in the case of excited-state double hybrid TD-DFT approaches. See Ref. 90 for further details.

Options:

ADC(2), CIS(D), SOS-ADC(2), SOS-CIS(D), SCS-ADC(2), SCS-CIS(D)

The corresponding methods will be used for the evaluation of second-order terms.

Default:

dhexc=ADC(2)

Note:

If a spin-scaled DH is employed, the corresponding spin-scaled ADC(2) or CIS(D) method will be used even if ADC(2) or CIS(D) is set. For a non-spin-scaled DH, if a spin-scaled approach is selected, the default spin-scaling parameters described in Ref. 90 will be set. To change the spin-scaling parameters use keywords scsps and scspt. For the CIS(D)-based ansatz, the keywords scsps_t and scspt_t can also be varied.

Examples:

1.

To use the CIS(D)-based TD-B2PLYP approach of Ref. 38 for the lowest excited state of a molecule set:
calc=B2PLYP
nstate=2
dhexc=CIS(D)

2.

To use the SOS-ADC(2)-based DSDPBEP86 approach of Ref. 90 for the lowest excited state of a molecule set:
calc=DSDPBEP86
nstate=2
dhexc=SOS-ADC(2)

diag

Type of diagonalization algorithm used for the CI and LR-CC calculations.

Options:

david

Standard Davidson diagonalization

olsen

Another algorithm proposed by Olsen using only two expansion vectors (see Refs. 116, 68, and 69), useful for very large CI/LR-CC vectors

follow

Davidson diagonalization with root-following, recommended for excited-state calculations if the initial guess is given manually or the calculation is restarted

Default:

diag=david

Example:

for root-following type diag=follow

docc

Specifies the number of doubly occupied orbitals in an MCSCF calculation. See also the description of keyword mact.

Options:

The number of doubly occupied orbitals per irrep should be given in the following format:
docc=
where is the number of doubly occupied orbitals in irrep $i$, and $N_{ir}$ is the number of irreps.

Default:

There is no default, the occupation must be set in the case of an MCSCF calculation.

Examples:

1.

Water, $2\times 2$ CAS calculation, the active space includes an A${}_1$ and a B${}_1$ orbital:
docc=3,1,0,0
mact=1,0,1,0

2.

Oxygen, $4\times 4$ CAS calculation, the active space includes four orbitals of B${}_{2g}$, B${}_{3g}$, B${}_{2u}$, and B${}_{3u}$ symmetry. Note that the multiplicity and the symmetry of the state must also be specified, and, if the MCSCF calculation is restarted from HF MOs, the HF occupation should also be given.
occ=3,0,1,1,0,2,1,1/3,0,0,0,0,2,1,1
docc=3,0,0,0,0,2,0,0
mact=0,0,1,1,0,0,1,1
mult=3
symm=2

domrad

Radius of atom domains for the local correlation method of Ref. 138 (localcc=2013). For each localized MO (LMO), using the Boughton–Pulay procedure [9], we assign those atoms to the LMO on which it is localized. Then, for each LMO an atom domain is constructed in two steps, the LMO is called the central LMO of the domain. In the first step, those atoms are included in the domain whose distance from the atoms assigned to the central LMO is smaller than domrad. In the second step, those LMOs are identified which are localized on the atoms selected in the first step, and the domain is extended to include all atoms assigned to these LMOs.

Options:

any positive real number$\mathrm{>}$

In the first step of the construction of atom domains all atoms whose distance from the atoms assigned to the central LMO is smaller than this number (in bohr) will be included in the domain.

inf

Infinite radius will be applied, i.e., there is only one atom domain including all atoms.

Default:

domrad=10.0

Note:

To use the local CC methods as defined in Ref. 135 set domrad=inf, that is, use only one atom domain including all atoms.

Example:

to set a threshold of 12.0 bohr type domrad=12.0

drpaalg

Specifies the type of the algorithm for the solution of the dRPA equations or the calculation of SOS-MP2 energies. See Ref. 72 for more details.

Options:

fit

The algorithm of Ref. 54 will be used, the fitting of integral lists will be performed before the dRPA iterations (SOS-MP2 calculation).

nofit

The algorithm of Ref. 72 will be executed, the fitting of the integrals is not performed. This algorithm is efficient for large molecules.

plasmon

The dRPA correlation energy is calculated using the plasmon formula.

auto

The algorithm is automatically selected on the basis of the size of the molecule (canonical dRPA) or the HOMO-LUMO gap (local dRPA).

Notes:

1.

For SOSEX calculations drpaalg=fit is the only option, which is forced by the program.

2.

For canonical dRPA the algorithm using the plasmon formula scales as $N^6$, it is only competitive for smaller molecules but inefficient for bigger ones. It avoids, however, the problems of the other algorithms, that is, convergence problems and unphysical solutions. Thus, it is useful for testing.

3.

For local dRPA drpaalg=plasmon is also linear scaling but typically 2- to 4-times slower than drpaalg=fit. It is advantageous for the aforementioned reasons. If drpaalg=auto, the plasmon formula-based algorithm is executed if the HOMO-LUMO gap is lower than 0.05 E${}_h$.

Default:

drpaalg=fit and drpaalg=auto for canonical and local dRPA, respectively.

Example:

to set the second option give drpaalg=nofit

dual

Activates dual basis set calculations. For these calculations two basis sets must be specified: a smaller one by keyword basis_sm (see the description of the keyword) and a bigger basis defined by keyword basis. The energy evaluated with the bigger basis set is estimated from a small-basis calculation. See Ref. 49 for more details. This feature can be combined with dual auxiliary basis, dual metric, dual grid, etc. approximations, see keywords grid_sm and dual_df.

Options:

off No dual basis calculation.

on Dual basis set calculation for conventional SCF and correlated methods. First, an SCF calculation will be performed using the small basis set. Second, one iteration of a SCF calculation is carried out with the large basis, and the energy is extrapolated using a first-order formula. If a correlation calculation is requested, the orbitals obtained in the second SCF step will be used for that purpose.

e1 Dual basis set embedding, Ansatz 1 of Ref. 49. A Huzinaga-embedding calculation is performed with the small basis set. The steps of the large-basis Huzinaga-embedding calculation are non-iterative. See also the description of keyword embed.

e2 Dual basis set embedding, Ansatz 2 of Ref. 49. Similar to e1, but there is also an iterative step with the large basis.

Default:

dual=off

Examples:

1.

To perform a dual basis set PBE calculation with the cc-pVTZ and cc-pVDZ basis sets you need:
basis=cc-pVTZ
basis_sm=cc-pVDZ
dual=on
calc=PBE

2.

Dual basis set PBE-in-LDA calculation with Ansatz 1 using the cc-pVTZ and cc-pVDZ basis sets as large and small basis set, respectively; atoms 1 to 5 are included in the embedded subsystem:
basis=cc-pVTZ
basis_sm=cc-pVDZ
calc=PBE
dual=e1
embed=Huzinaga
1-5
LDA
0

3.

Dual basis set PBE-in-LDA calculation with Ansatz 1 using a mixed large basis (cc-pVTZ for atoms 1 to 5, cc-pVDZ otherwise) and the cc-pVDZ basis sets as the small basis set; atoms 1 to 5 are included in the embedded subsystem:
basis=embed
cc-pVTZ
cc-pVDZ
basis_sm=cc-pVDZ
calc=PBE
dual=e1
embed=Huzinaga
1-5
LDA
0

dual_df

Set this keyword to perform dual auxiliary basis, dual metric DF-SCF, or dual grid COSX calculations [DualDF]. For dual grid DFT calculations, see keyword grid_sm.

Options:

dab

Performs dual auxiliary basis SCF calculations. To specify the small auxiliary basis, set the dfbasis_scf_sm keyword.

dm

Performs a dual metric DF-SCF calculation.

grid

Performs a dual grid COSX calculation. To specify the small angular integration grid, set the agrid_pssp_sm keyword.

off

Turns off this feature.

Default:

dual_df=off for all calculations except COSX, where dual_df=grid is the default. For more information about COSX calculations, see the keyword pssp.

Note:

The dm option can be used in conjunction with the non-local direct SCF method only. The dual auxiliary basis algorithm can be applied to both local and non-local SCF calculations.

Examples:

1.

Dual auxiliary basis calculation with local fitting with the cc-pVTZ AO basis set, the default large fitting basis set, and the cc-pVTZ-RI-JK-dual small fitting basis set:
basis=cc-pVTZ
dfbasis_scf_sm=cc-pVTZ-RI-JK-dual
calc=DF-HF
scfalg=locfit2
dual_df=dab

2.

Dual metric calculation with the cc-pVTZ AO basis set and the default fitting basis set:
basis=cc-pVTZ
calc=DF-HF
scfalg=direct
dual_df=dm

ecp

Specifies the effective core potential (ECP) used in all calculations. By default the ECPs are taken from the files named by the chemical symbol of the elements, which can be found in the BASIS directory created at the installation. The ECPs are stored in the format used by the Cfour package. In addition to the ECPs provided by default, any ECP can be used by adding it to the corresponding files in the BASIS directory. Alternatively, you can also specify your own ECP in the file GENBAS which must be copied to the directory where Mrcc is executed.

Options:

none

No ECPs will be used.

auto

The ECPs will be automatically selected: no ECP will be used for atoms with all-electron basis sets, while the ECP adequate for the basis set of the atom will be selected otherwise.

ECP label$\mathrm{>}$

If the same ECP is used for all atoms, the label of the ECP can be given here.

atomtype

If different ECPs are used or no ECP is used for particular atoms, but the atoms of the same type are treated in the same way, ecp=atomtype should be given, and the user must specify the ECP for each atomtype (for which an ECP is used) in the subsequent lines as atomic symbol$\mathrm{>}$:ECP label$\mathrm{>}$ .

special

In the general case, if different ECPs are used for each atom, then one should give ecp=special and specify the ECP for each atom in the subsequent lines by giving the label of the corresponding ECP (or none if no ECP is used for that atom) in the order the atoms appear at the specification of the geometry.

Notes:

• 1.

  By default, the following ECP are available for elements Na to Rn in Mrcc:

  • –

    the LANL2DZ ECPs of Hay and Wadt [45, 151, 44]: LANL2DZ-ECP-10,
    LANL2DZ-ECP-18, LANL2DZ-ECP-28, LANL2DZ-ECP-36, LANL2DZ-ECP-46, LANL2DZ-ECP-60, LANL2DZ-ECP-68, LANL2DZ-ECP-78

  • –

    the Stuttgart–Köln ECPs for the def2 basis sets [3, 73, 79]: def2-ECP-28, def2-ECP-46, def2-ECP-60

  • –

    the Stuttgart–Köln multiconfiguration Dirac–Hartree–Fock-adjusted ECPs [95, 96, 123, 122, 118, 23, 24]: MCDHF-ECP-10, MCDHF-ECP-28, MCDHF-ECP-60

  Please note that some of the above ECPs are not available for all elements.

• 2.

  If you need ECPs other than the default ones, you can, e.g., download them from the Basis Set Exchange [5, 22, 142, 128]. Please choose format “CFOUR” when downloading the ECPs.

• 3.

  If you use your own ECPs, these must be copied to the end of the corresponding file in the BASIS directory. Alternatively, you can also create a file called GENBAS in the directory where Mrcc is executed, and then you should copy your ECPs to that file.

• 4.

  The labels of the ECPs must be identical to those used in the BASIS/* files (or the GENBAS file). For the default ECPs just type the name of the ECPs as given above, e.g., LANL2DZ-ECP-10, def2-ECP-28, etc. If you employ non-default ECPs, you can use any label.

Default:

ecp=auto

Examples:

1.

To use the MCDHF-ECP-10 pseudopotential for all atoms the input must include ecp=MCDHF-ECP-10

2.

Consider the PbO molecule and use the def2-SVP basis set for both elements as well as the def2-ECP-60 pseudopotential for Pb. The following inputs are equivalent.
Input 1:
 basis=def2-SVP
 geom
 Pb
 O 1 R
 
 R=1.921813
 
Input 2:
 basis=def2-SVP
 ecp=atomtype
 Pb:def2-ECP-60
 geom
 Pb
 O 1 R
 
 R=1.921813
 
Input 3:
 basis=def2-SVP
 ecp=special
 def2-ECP-60
 none
 geom
 Pb
 O 1 R
 
 R=1.921813

edisp

This keyword controls the calculation of empirical dispersion corrections for DFT and HF calculations using the DFT-D3 approach of Grimme and co-workers [36, 37]. The corrections are evaluated by the dftd3 program of the latter authors, which is available at http://www.thch.uni-bonn.de/tc/ and interfaced to Mrcc. You need to separately install this code and add the directory where the dftd3 executable is located to your PATH environment variable.

Options:

off

No dispersion correction will be computed.

auto

The dispersion correction will be automatically evaluated to the KS or HF energy. Note that it is only possible for particular functionals listed in the description of keyword dft (and the HF method). For these methods, however, you can also turn on the calculations of the dispersion corrections by attaching the -D3 postfix to the corresponding options, e.g., as BLYP-D3, B3LYP-D3, B2PLYP-D3, etc. (see the description of keyword dft).

any options of the dftd3 program$\mathrm{>}$

You can directly give any options of the dftd3 code. The options will be passed over to dftd3 without any consistency check, the user should take care of the compatibility of these options with the calculation performed by Mrcc. Note that the coordinate file name must not be specified here, the coordinates will be taken from the COORD.xyz file generated by Mrcc.

Note:

If edisp=auto or the -D3 postfix is added to the corresponding options, the empirical dispersion correction is by default evaluated with the Becke and Johnson (BJ) damping function [37].

Default:

edisp=off

Example:

1.

to calculate the D3 dispersion correction including BJ damping to the B3LYP energy give calc=B3LYP-D3

2.

to calculate the D3 dispersion correction to the B3LYP energy without the BJ damping the input should include:
calc=B3LYP
edisp=-func b3-lyp -zero

edisp_embed

This keyword controls the calculation of empirical dispersion corrections for low-level methods (environment) in embedding calculations using the DFT-D3 approach of Grimme and co-workers [36, 37]. See the keywords edisp and embed for more details. Note that the empirical corrections are only calculated with the embedded atom list in the case of the subsystem calculations (see keyword embed). Note also that edisp_embed is not usable in the case of energy-based subsystem separation.

Options:

off

No dispersion correction will be computed.

auto

The dispersion energy correction will be automatically evaluated for the low-level theory of the embedding approach. Other considerations are same as for edisp=auto.

any options of the dftd3 program$\mathrm{>}$

You can directly give any options of the dftd3 code. Other considerations are same as for edisp=auto. Note that the coordinates will be taken from the COORD.xyz and the COORD_SUBSYSA.xyz files generated by Mrcc for the full system and the subsystem calculations, respectively.

Note:

If edisp_auto=auto or the -D3 postfix is added to the corresponding options, the empirical dispersion correction is by default evaluated with the Becke and Johnson (BJ) damping function [37].

Default:

edisp_embed=off

Example:

1.

To calculate the D3 dispersion correction (including BJ damping) for the interaction of the embedded subsystem and the environment in the case of a LNO-CCSD(T)-in-BLYP type embedding give
calc=LNO-CCSD(T)
embed=huzinaga
1-2
BLYP-D3
0

2.

To calculate the D3 dispersion correction to the BLYP energy without the BJ damping, the input should include:
calc=LCCSD(T)
edisp_embed=-func b-lyp -zero
embed=huzinaga
1-2
BLYP
0

etemp

The electronic temperature in K at which the Fermi-smearing of the occupied orbitals is made in the case of scfiguess=gfn1 and scfiguess=gfn2.

Options:

any positive real number$\mathrm{>}$

Default:

temp=300.0

Example:

for 10000 K set etemp=10000.0

embed

This keyword controls DFT embedding calculations. Currently, it is only available using density-fitting. Both restricted closed-shell determinants and unrestricted open-shell determinants are applicable for embedding calculations, however, only those open-shell cases are supported where the environmental subsystem has singlet multiplicity. See also keywords corembed and oniom for further embedding approaches.

Options:

off

No embedding.

Huzinaga

The Huzinaga-equation-based embedding approach [48, 49] will be used. The embedded atoms and the low-level DFT approach (or HF) used for the embedding must be specified and the number of embedded orbitals can be given in the subsequent lines as follows. The embedded atoms must be given by their serial numbers in the first line as ,,…,-,…, where $n_i$’s are the serial numbers of the atoms. Serial numbers separated by dash mean that through are embedded atoms. Note that the numbering of the atoms must be identical to that used in the Z-matrix or Cartesian coordinate specification, but dummy atoms must be excluded. The low-level DFT (LDA, GGA, or hybrid) or HF approach must be specified in the second line using the corresponding option of keyword dft (for HF simply HF). Note that the user option of keyword dft is also supported. The high-level method (any DFT, HF, or any correlation method) for the active region should be specified by the keyword calc (or keywords calc and dft if a KS reference is used in a correlation calculation). In the third line an integer, $i$, should be given which is the number of the embedded orbitals or zero. If zero is given, then the number of embedded orbitals are determined automatically. In addition, the algorithm for the selection of the orbitals can also be given in the third line after the integer. The options are amul, nmul, spad, nspad, ecore, bopu, and serialno. The amul and nmul mean the Mulliken population-based orbital selection scheme of Refs. 48 and 49. For amul, you can also specify the Mulliken population threshold (see the appendix of Ref. 49), the default threshold is 0.3. The nmul scheme selects $i$ pieces of active orbitals with the largest Mulliken populations. The spad and nspad techniques employ the orbital selection scheme of Ref. 12, where the active orbitals are selected based on the difference of the MO populations. Note that spad does not require a threshold for the selection, algorithm nspad selects $i$ orbitals which have the largest eigenvalues of the SPADE projector, and both schemes require orbloce=spade. The energy-based ecore algorithm is also supported, which does not require orbital localization and selects the high-energy orbitals as active orbitals: the ecore algorithm automatically selects the valence orbitals as active, while if $i$ is nonzero, then $i$ pieces of orbitals with the largest orbital energies are selected. Note that in the case of the ecore algorithm, the embedded atom list is not used in the calculation. bopu means the Boughton–Pulay algorithm-based scheme, see Ref. 48 for more details. For the default MO completeness criteria of the bopu algorithm, see keywords bpcompo and bpcompv. Lastly, if serialno is specified, the active orbitals are selected manually by giving the appropriate serial numbers of the orbitals after the keyword serialno. Note that the ordering of the orbitals are based on their orbital energies and this scheme does not require a list of active atoms. The default automatic selection scheme is spad if the orbloce=spade, and amul otherwise. If $i$ is not zero, nspad is the default scheme when orbloce=spade, and nmul is the default algorithm otherwise.

Finally, the embedding calculations can also be executed with selected active virtual orbitals if orblocv is defined by using orbloce=special. The orbital selection scheme of the virtual orbitals is specified in the fifth line, and all the previously described schemes are supported with a single modification: the ecore algorithm does not have an automatic selection mode and it will select the $i$ number of virtual orbitals with the lowest eigenvalues. In this case, a modified Huzinaga operator is constructed which includes the projector of the inactive virtual orbitals as well. Note that the subsequent correlation calculations will only use the active virtual subspace. See also examples below.

project

The projector-based embedding approach of Manby and co-workers [84] will be used. The embedded atoms and the low-level DFT approach can be specified as described above.

Default:

embed=off

Examples:

1.

CCSD(T)-in-PBE embedding with the Huzinaga-equation-based approach, atoms 1 and 2 are included in the embedded region, the number of the embedded orbitals is determined automatically, the amul algorithm is used for the selection of the orbitals with the default threshold:
calc=DF-CCSD(T)
embed=huzinaga
1-2
PBE
0

2.

The same as example 1, but the amul algorithm is used with a threshold of 0.25:
calc=DF-CCSD(T)
embed=huzinaga
1-2
PBE
0 amul 0.25

3.

The same as example 1, but the bopu algorithm is used with 0.95 MO completeness criteria:
calc=DF-CCSD(T)
embed=huzinaga
1-2
PBE
0 bopu 0.95

4.

Same as example 1, but a mixed basis set is used, cc-pVDZ for the environment and cc-pVTZ for the embedded subsystem:
calc=DF-CCSD(T)
basis=embed
cc-pVDZ
cc-pVTZ
embed=huzinaga
1-2
PBE
0

5.

dRPA@PBE-in-PBE embedding with the Huzinaga-equation-based approach, atoms 1, 2, 3, and 5 as well as 10 orbitals are included in the active region:
calc=dRPA
dft=PBE
embed=huzinaga
1-3,5
PBE
10

6.

B3LYP-in-BLYP embedding with the Huzinaga-equation-based approach, the number of the embedded orbitals will be the same as the number of valance orbitals. Note that the active atoms are not specified because of the ecore algorithm, and a blank line is used in the second line after the keyword embed:
calc=B3LYP
embed=huzinaga

BLYP
0 ecore

7.

B3LYP-in-BLYP embedding with the Huzinaga-equation-based approach, the number of the embedded orbitals will be the 4 MOs with the highest orbital energies:
calc=B3LYP
embed=huzinaga

BLYP
4 ecore

8.

B3LYP-in-BLYP embedding with the Huzinaga-equation-based approach, orbitals with the 1, 2, 3, 4, and 13 serial numbers are selected manually as active orbitals. Again, note that the list of active atoms are not required in this case:
calc=B3LYP
embed=huzinaga

BLYP
0 serialno 1,2-4,13

9.

CCSD(T)-in-PBE embedding with the Huzinaga-equation-based approach, atoms 1 and 2 are included in the embedded region. The spade algorithm is used for the automatic selection of the active occupied orbitals, while 4 active virtual orbitals are selected by the nmul scheme. Note that the embedded occupied MOs of the second SCF run are only allowed to mix with the 4 selected virtual MOs, and subsequently, the CCSD(T) calculation is carried out with the active occupied and active virtual MOs:
calc=DF-CCSD(T)
orbloce=special
spade
spade
spade
embed=huzinaga
1-2
PBE
0
4 nmul

10.

Same as example 9, but after the embedded HF solution is obtained, projected atomic orbitals (PAO) are constructed for the correlation calculation. Note that the atomic orbitals of atoms 1 and 2 will be used to calculate the norm of the PAOs, and those PAOs that have a norm lower than pao_subsys_tol will be omitted in the subsequent correlation calculation. Note the blank line below orblocv.
calc=DF-CCSD(T)
orblocv=pao-subsys

orbloce=special
spade
spade
spade
embed=huzinaga
1-2
PBE
0
4 nmul

11.

Same as example 10, but this time, the norm of the PAOs are calculated using an extended number of atoms thus generating more virtual orbitals.
calc=DF-CCSD(T)
orblocv=pao-subsys
1-2,8-10
orbloce=special
spade
spade
spade
embed=huzinaga
1-2
PBE
0
4 nmul

12.

Same as example 11, except that all virtual orbitals are used in the high-level SCF run, and only the CCSD(T) calculation utilizes a reduced number of virtual orbitals. Again, note the blank line below orblocv, which can be used to override the atom list which is used for the norm calculation of PAOs. Here, the atom list is not overridden.
calc=DF-CCSD(T)
orblocv=pao-subsys

orbloce=special
spade
spade
off
embed=huzinaga
1-2
PBE
0

epert

Use this option to add an external perturbation to the Hamiltonian, e.g., an external electric dipole field.

Options:

none

No perturbations are added.

any integer in the [0,9] interval$\mathrm{>}$

the number of the operators added to the Hamiltonian. The operators and the corresponding coefficients (in a.u.) should be specified in the subsequent lines as follows:
operator 1$\mathrm{>}$ coefficient 1$\mathrm{>}$
operator 2$\mathrm{>}$ coefficient 2$\mathrm{>}$
operator 3$\mathrm{>}$ coefficient 3$\mathrm{>}$
…
where the operator can be x, y, z, xx, yy, zz, xy, xz, yz, xxx, xxy, xxz, xyy, xyz, xzz, yyy, yyz, yzz, zzz.

Note:

The symmetry of the perturbation is not taken care of automatically. If the perturbation lowers the symmetry of the system, you must change the computational point group (keyword cmpgrp) or turn off symmetry (symm=off).

Default:

epert=none

Example:

to add the $\widehat{y}$ and $\widehat{z}$ dipole length operators to the Hamiltonian with coefficients 0.01 and 0.001 a.u., respectively, the input should include the following lines
epert=2
y 0.01
z 0.001

eps

Threshold for the cumulative populations of MP2 natural orbitals (NOs) or optimized virtual orbitals (OVOs), to be used together with keyword ovirt. The cumulative population for an MO is calculated by summing up the occupation number of that particular MO and all the MOs with larger occupation numbers, and then this number is divided by the number of electrons. If unset, keyword lnoepsv is used as the threshold for MP2 NOs. The use of keyword lnoepsv is preferred instead of keyword eps. See Ref. 136 for more details.

Options:

any real number in the [0,1] interval$\mathrm{>}$

Virtual orbitals with cumulative populations of higher than this number will be dropped.

Default:

None. By default keyword lnoepsv is used.

Notes:

1.

This keyword can not be used with explicitly correlated calculations.

2.

If eps is specified, the spatial symmetry is not used in correlation calculations.

Example:

to set a threshold of 0.95 type eps=0.95

espcharge

Select the desired method for calculating atomic charges based on the electrostatic potential around the molecule.

Options:

off

No atomic charge calculation based on electrostatic potential.

chelpg

Calculate CHELPG charges [breneman1990determining].

mk

Calculate Merz–Singh–Kollman charges [singh1984approach].

Default:

espcharge=off

Notes:

1.

If espcharge$\mathrm{\ne }$off and dens=0, then it will be changed to dens=1.

2.

Atomic radii used for the determination of the charges are listed in Table LABEL:radii. The values are based on the original articles and the Multiwfn implementation. For atoms not shown, the UFF radii divided by 1.2 are utilized.

Example:

to calculate CHELPG charges use espcharge=chelpg

excrad

Sets the radius of local fitting domains for the exchange contribution in direct density-fitting SCF calculations [127, 107]. In direct DF-SCF calculations, in each iteration step, the MOs are localized. For each localized MO Löwdin atomic charges are computed, and all atoms are selected which have a charge greater than 0.05. All further atoms will be included in the fitting domain of the MO for which the electron repulsion integrals including the corresponding AOs and the basis functions residing on the atoms selected in the first step are estimated to be greater than a threshold.

Options:

any positive real number$\mathrm{>}$

Threshold for the integrals (in E${}_h$).

0

A threshold of zero will be applied, i.e., a conventional direct DF-SCF calculation will be executed.

Notes:

1.

Local fitting domains are available for RHF, UHF, ROHF, RKS, UKS, and ROKS calculations.

2.

For average organic molecules with localized electronic structure excrad=1.0 is a good choice. For more complicated systems other thresholds may be necessary. For excrad=1.0 excrad_fin is set to ${10}^{-3}$, which is fine with basis sets excluding diffuse functions. For basis sets with diffuse functions excrad_fin=1e-5 or tighter is recommended.

Default:

excrad=1.0 if scfalg=locfit1 or scfalg=locfit2, excrad=0 otherwise

Example:

to set a threshold of 0.1 E${}_h$ type excrad=0.1

excrad_fin

In density-fitting SCF calculations, if excrad and excrad_fin differ, an extra iteration is performed to get an accurate SCF energy. excrad_fin specifies the radius of local fitting domains for the exchange contribution in this iteration step. See also notes for keyword excrad.

Options:

See the description of keyword excrad.

Default:

excrad_fin=excrad/1000

Example:

to avoid the use of local fitting domains in the extra iteration step give
excrad_fin=0.0

fitting

Specifies the fitting metric for direct DF-SCF calculations.

Options:

Coulomb

Coulomb-metric DF-SCF calculation.

Overlap

Overlap-metric DF-SCF calculation.

Default:

fitting=Coulomb

Example:

to use the overlap metric, set fitting=Overlap

fmm

Controls the multipole method for three-center Coulomb integrals for density fitting SCF calculations. See also keyword fmmord.

Options:

off

No multipole approximation is used for the integrals.

on

The exchange contribution will be evaluated using multipole approximations.

Coulomb

Both the Coulomb and the exchange contributions will be evaluated using multipole approximations.

Note:

The multipole method can be employed either with or without local fitting approximations (see keyword scfalg). If no local fitting is used, the speedup is quite good, the computation time can roughly be halved. With local fitting approximations, the speedup is moderate.

Default:

fmm=off

Example:

To use the multipole method to speed up a DF-HF calculation, set fmm=on

fmmord

The keyword controls the order of the multipole approximation if the multipole method is used for three-center Coulomb integrals (see also keyword fmm). If the multipole approximation is invoked to calculate an integral of the product of two Gaussians, the contribution of multipole moments up to order $l_1$ $+$ $l_2$ $+$ fmmord will be considered, where $l_1$ and $l_2$ are the angular momentum quantum numbers of the Gaussians.

Options:

any positive integer$\mathrm{>}$

Default:

fmmord=8

Example:

for lower accuracy but increased speed, give fmmord=6

freq

Requests harmonic vibrational frequency calculation (numerical). Ideal gas thermodynamic properties will also be evaluated in the rigid-rotor harmonic-oscillator approximation. If geometry optimization is also carried out, i.e., gopt $\ne$ off, the frequencies are calculated at the optimized geometry.

Options:

on or off

Note:

You should also set this keyword if you are interested in thermodynamic properties of atoms.

Default:

freq=off

Example:

for a frequency calculation set freq=on

gamma

Exponent for the Slater-type correlation factor ($\gamma$) used in explicitly correlated calculations [CorrFactTew, MP2-F12_TM].

Options:

any positive real number$\mathrm{>}$

Value of the correlation factor in bohr${}^{-1}$.

Note:

In Mrcc, six Gaussians are used to fit the Slater-type correlation factor. The exponents and coefficients were taken from Ref. CorrFactTew.

Default:

gamma=0.9 for cc-pVDZ-F12, gamma=1.1 for cc-pVQZ-F12 or aug-cc-pVTZ, gamma=1.4 for aug-cc-pVQZ or aug-cc-pV5Z, gamma=1.0 otherwise.

Example:

to set an exponent of 1.3 bohr${}^{-1}$ give gamma=1.3

gauss

Specifies whether spherical harmonic or Cartesian Gaussian basis functions will be used.

Options:

spher

Spherical harmonic Gaussians will be used

cart

Cartesian Gaussians will be used

Notes:

1.

For calculations using the density fitting (DF) approximation, if intalg=os or intalg=auto, the Coulomb integrals are evaluated by algorithms [2, 139] which only enable the use of spherical harmonic Gaussians. Consequently, Cartesian Gaussians are only available with intalg=rys in DF calculations (see the description of keyword intalg).

2.

The derivative integrals are evaluated by the solid-harmonic Hermite scheme [131] (see the description of keyword intalg), consequently, differentiated integrals, and thus energy derivatives cannot be evaluated with Cartesian Gaussian basis sets.

Default:

gauss=spher

Example:

for Cartesian Gaussians the user should set gauss=cart

geom

Specifies the format of molecular geometry. The geometry must be given in the corresponding format in the subsequent lines.

Options:

zmat

Usual Z-matrix format. In the Z-matrix the geometrical parameters can only be specified as variables, and the variables must be defined after the matrix, following a blank line. Another blank line is required after the variables. This Z-matrix format is compatible to that of Cfour and nearly compatible to that for Gaussian and Molpro. Z-matrices can be generated by Molden (see also Sect. 14.1), then the Gaussian-style Z-matrix format must be chosen. The symbol for dummy atoms is “X”.

xyz

Cartesian coordinates in xyz format, that is, the number of atoms, a blank line, then for each atom the atomic symbol or atomic number and the $x$, $y$, and $z$ components of Cartesian coordinates. Cartesian coordinates in xyz format can also be generated by Molden (see also Sect. 14.1).

tmol

Cartesian coordinates in a format similar to that used by the Turbomole package, that is, the number of atoms, a blank line, then for each atom the $x$, $y$, and $z$ components of Cartesian coordinates and the atomic symbol or atomic number.

mol

Cartesian coordinates and connectivity in .mol format, that is, the number of atoms and number of bonds in the first line, then for each atom the $x$, $y$, and $z$ components of Cartesian coordinates and the atomic symbol, then for each bond the serial number of the atoms connected by the bond and the type of the bond (1 for single bond, etc.). This geometry specifications is needed if the specified method requires the connectivity.

Note:

For the use of ghost atoms see the description of keyword ghost.

Default:

geom=zmat, which is equivalent to geom, i.e., if it is not specified whether the geometry is supplied in Z-matrix format or in other formats, Z-matrix format is supposed. Nevertheless, the coordinates must be given in the subsequent lines in any case.

Examples:

the following five geometry inputs for H${}_2$O${}_2$ are equivalent

1.

Z-matrix format, bond lengths in Å:
geom
H
O 1 R1
O 2 R2 1 A
H 3 R1 2 A 1 D

R1=0.967
R2=1.456
A=102.32
D=115.89

2.

xyz format, coordinates in bohr, atoms are specified by atomic symbols:
unit=bohr
geom=xyz
4

H 0.00000000 0.00000000 0.00000000
O 1.82736517 0.00000000 0.00000000
O 2.41444411 2.68807873 0.00000000
H 3.25922198 2.90267673 1.60610134

3.

xyz format, coordinates in bohr, atoms are specified by atomic numbers:
unit=bohr
geom=xyz
4

1 0.00000000 0.00000000 0.00000000
8 1.82736517 0.00000000 0.00000000
8 2.41444411 2.68807873 0.00000000
1 3.25922198 2.90267673 1.60610134

4.

Turbomole format, coordinates in bohr, atoms are specified by atomic symbols:
unit=bohr
geom=tmol
4

0.00000000 0.00000000 0.00000000 H
1.82736517 0.00000000 0.00000000 O
2.41444411 2.68807873 0.00000000 O
3.25922198 2.90267673 1.60610134 H

4.

.mol format, coordinates in bohr:
unit=bohr
geom=mol
4 3
0.00000000 0.00000000 0.00000000 H
1.82736517 0.00000000 0.00000000 O
2.41444411 2.68807873 0.00000000 O
3.25922198 2.90267673 1.60610134 H
1 2 1
2 3 1
3 4 1

ghost

Ghost atoms can be specified using this keyword, e.g., for the purpose of basis set superposition error (BSSE) calculations with the counterpoise method.

Options:

none

There are no ghost atoms.

serialno

Using this option one can select the ghost atoms specifying their serial numbers. The latter should be given in the subsequent line as ,,…,-,…, where $n_i$’s are the serial numbers of the atoms. Serial numbers separated by dash mean that through are ghost atoms. Note that the numbering of the atoms must be identical to that used in the Z-matrix or Cartesian coordinate specification, but dummy atoms must be excluded.

Default:

ghost=none

Examples:

1.

Rectangular HF dimer, the atoms of the second HF molecule are ghost atoms:
geom
H
F 1 R1
H 2 R2 1 A
F 3 R1 2 A 1 D

R1=0.98000000
R2=2.00000000
A=90.00000000
D=0.000000000

ghost=serialno
3-4

2.

Ammonia, the third hydrogen is a ghost atom (note that the serial number of the hydrogen is 4 instead of 5 because of the dummy atom):
geom
X
N 1 R
H 2 NH 1 AL
H 2 NH 1 AL 3 A
H 2 NH 1 AL 3 B

R=1.00000000
NH=1.01000000
AL=115.40000000
A=120.00000000
B=-120.00000000

ghost=serialno
4

gopt

Requests geometry optimization. Currently only the full geometry optimization is supported, geometrical parameters cannot be frozen.

Options:

off

no geometry optimization.

full

full geometry optimization.

Notes:

1.

The coordinates in the MINP file are replaced by the converged ones at the end of the geometry optimization. The initial MINP file is saved as MINP.init.

2.

The Abelian symmetry of the molecule is utilized at the calculation of gradients and update of the coordinates, thus, the computational point group is preserved during the optimization.

Default:

gopt=off

Example:

to carry out a full geometry optimization set gopt=full

grdens

This keyword is useful for the analysis of HF, KS, or correlated (MP2, CI, CC, …) one-electron density and its derivatives. The one-electron density, its gradient, and Laplacian will be calculated on a grid used for DFT calculations (see keywords agrid and rgrid) and saved for external use. In the case of correlated calculations the densities are evaluated using the relaxed density matrices.

Options:

off

Densities are not evaluated.

on

The one-electron density and its derivatives are calculated in the grid points. These values together with the grid are written to the unformatted Fortran file DENSITY. If a correlation calculation is performed the densities calculated with the correlation method are stored in the DENSITY file, while the SCF densities are saved to the file DENSITY.SCF. For restricted orbitals the files use the following format:

$N$
${𝐫}_1$ $w_1$ $\rho ({𝐫}_1)$ $\nabla \rho ({𝐫}_1)$ ${\nabla }^2\rho ({𝐫}_1)$
${𝐫}_2$ $w_2$ $\rho ({𝐫}_2)$ $\nabla \rho ({𝐫}_2)$ ${\nabla }^2\rho ({𝐫}_2)$
 ⋮
${𝐫}_N$ $w_N$ $\rho ({𝐫}_N)$ $\nabla \rho ({𝐫}_N)$ ${\nabla }^2\rho ({𝐫}_N)$

where $N$ is the number of grid points, ${𝐫}_i$ = ($x_i$, $y_i$, $z_i$) is the Cartesian coordinate of grid point $i$ with $w_i$ as the corresponding weight, and $\rho ({𝐫}_i)$ is the density in point $i$. For unrestricted calculations the corresponding $\alpha$ and $\beta$ quantities are stored separately, and the lines of the files change as
${𝐫}_i$ $w_i$ ${\rho }_{\alpha }({𝐫}_i)$ ${\rho }_{\beta }({𝐫}_i)$ $\nabla {\rho }_{\alpha }({𝐫}_i)$ $\nabla {\rho }_{\beta }({𝐫}_i)$ ${\nabla }^2{\rho }_{\alpha }({𝐫}_i)$ ${\nabla }^2{\rho }_{\beta }({𝐫}_i)$

Default:

grdens=off

Example:

to save the densities give grdens=on

grid

Specifies the integration grid for DFT calculations. The grid construction follows the design principles of Becke [6] in any case.

Options:

auto

An automatically constructed adaptive integration grid will be used. The adaptive scheme is motivated by Ref. 77. The important difference is that the grids are optimized for each atom separately to avoid discontinuous potential energy surfaces. Both the angular and the radial grids are selected automatically to ensure the accuracy of the angular and the radial integrations as described at keywords agrid and rgrid. See also the description of keyword grtol. The smoothing function for the Voronoi polyhedra are adopted from Ref. 104 with $m_{\mu }$ = 10.

TMn$\mathrm{>}$

Grid no. $n$ of Treutler–Ahlrichs [AhlrichsGrid] using the Log3 radial quadrature of Mura and Knowles [103].

Default:

grid=TA3 for KS-DFT calculations with non-hybrid LDA and GGA functionals, grid=auto otherwise

Example:

to use grid 2 of Treutler–Ahlrichs, set grid=TA2

grid_sm

If this keyword is set and different from keyword grid, a dual grid DFT calculation will be carried out. The SCF iterations will be performed using the grid specified by grid_sm, and an extra iteration will be carried out with a larger grid set by grid. A first-order correction is also evaluated [DualDF]. This can also be combined with dual (auxiliary) basis, dual metric, etc. approximations, see keywords dual and dual_df.

Options:

see keyword grid.

Default:

grid_sm=grid

Examples:

1.

To use grid 1 and 3 of Treutler–Ahlrichs in the SCF cycles and in the final iteration, respectively, (recommended for KS-DFT calculations with non-hybrid functionals) set:
grid_sm=TA1
grid=TA3

2.

To use grid 1 of Treutler–Ahlrichs and a Coulomb fitting basis in the SCF cycles and the default adaptive grid and a Coulomb-exchange fitting basis in the final iteration (recommended for DFT calculations with a hybrid functional; note that for the latter, you do not need to set dfbasis_scf with def2-type AO basis sets, because this is the default) set:
grid_sm=TA1
dual_df=DAB
dfbasis_scf_sm=def2-QZVPP-RI-J
dfbasis_scf=def2-QZVPP-RI-JK

grtol

The keyword controls the fineness of the angular and radial integration grids employed in DFT calculations. The tolerance for the accuracy of angular integrals will be ${10}^{-\mathrm{𝚐𝚛𝚝𝚘𝚕}}$, while the number of radial grid points increases linearly with grtol. See also the description of keywords agrid and rgrid.

Options:

any positive integer$\mathrm{>}$

Note:

meta-GGA functionals or molecules with special bonding characteristics may require larger integration grids, and it is recommended to run test calculations to decide if the default value of grtol is sufficient.

Default:

grtol=10

Example:

for a fine integration grid give grtol=12

gtol

Threshold for automatic point group recognition. Two atoms will be considered symmetry-equivalent if the difference in any component of their Cartesian coordinates after the symmetry operation is less than ${10}^{-\mathrm{𝚐𝚝𝚘𝚕}}$ bohr.

Options:

any integer$\mathrm{>}$

Default:

gtol=7

Example:

for a tolerance of ${10}^{-4}$ bohr give gtol=4

guido_ct

Use this keyword to calculate the Guido-type $\mathrm{\Delta }𝐫$ charge-transfer descriptor (see Ref. [Guido_CT]).

Options:

on

Calculate the corresponding descriptor.

off

The calculation of the descriptor is turned off.

Default:

guido_ct=off

Example:

To calculate the descriptor use guido_ct=on

hamilton

Specifies what type of Hamiltonian is used in relativistic calculations. This keyword has only effect if iface=Dirac.

Options:

X2Cmmf

exact 2-component molecular-mean-field Hamiltonian [143]

DC

other types of relativistic Hamiltonians such as the full Dirac–Coulomb Hamiltonian or the exact 2-component Hamiltonian

Default:

hamilton=DC

Example:

if you use the exact 2-component molecular-mean-field Hamiltonian, set
hamilton=X2Cmmf

iface

Specifies whether Mrcc is used together with another program system. In this case the transformed MO integrals are calculated by that program and not by Mrcc. See Sect. 5 for the description of various interfaces.

Options:

none

Transformed MO integrals are calculated by Mrcc.

Cfour

Mrcc is interfaced to Cfour.

Columbus

Mrcc is interfaced to Columbus.

Dirac

Mrcc is interfaced to Dirac.

Molpro

Mrcc is interfaced to Molpro.

Notes:

1.

If you use Mrcc together with Cfour or Molpro, you do not need to use this keyword. The Mrcc input file is automatically written and Mrcc is automatically called by these program systems. The user is not required to write the Mrcc input file, most of the features of Mrcc can be controlled from the input files of these programs. With Cfour the user has the option to turn off the automatic construction of the Mrcc input file by giving INPUT_MRCC=OFF in the Cfour input file ZMAT. In the latter case one should use this keyword.

2.

If you use Mrcc together with Columbus or Dirac, this keyword must be always given.

Default:

iface=none, that is, all calculations will be performed by Mrcc.

Example:

to carry out four-component relativistic calculations using the Dirac interface give iface=Dirac

intalg

Specifies the algorithm used for the evaluation of two-electron integrals over primitive Gaussian-type orbitals.

Options:

os

The $(\mathrm{𝐞𝟎}|\mathrm{𝐟𝟎})$ integrals are evaluated by the Obara–Saika procedure using the vertical and transfer recurrence relations [115, 82].

rys

The $(\mathrm{𝐞𝟎}|\mathrm{𝐟𝟎})$ integrals are evaluated by the Rys quadrature scheme [75, 82, 25].

auto

Depending on the angular momenta the program automatically determines which of the two algorithms is executed. For integrals of low angular momentum functions the Rys procedure is used, while the Obara–Saika algorithm is executed otherwise.

herm

The integrals over contracted Gaussians are evaluated by the solid-harmonic Hermite scheme of Reine et al. [131].

Notes:

1.

For calculations using the density fitting (DF) approximation intalg=auto is equivalent intalg=os since the Obara–Saika algorithm is more efficient for any integrals.

2.

For DF methods option herm is not available.

3.

For DF methods, if intalg=os or intalg=auto the Coulomb integrals are evaluated by the algorithm of Ref. 139, which only enables the use of spherical harmonic Gaussians. Consequently, Cartesian Gaussians are only available with intalg=rys in DF calculations (see the description of keyword gauss).

4.

The derivative integrals are evaluated by the solid-harmonic Hermite scheme even if another option is used for the undifferentiated integrals. Consequently, differentiated integrals, and thus energy derivatives cannot be evaluated with Cartesian Gaussian basis sets.

Default:

intalg=auto

Example:

to use the Obara–Saika scheme for all angular momenta add intalg=os

ip_ea

Specifies whether standard excitation energies, ionization potentials, or electron affinities are calculated. This option is available at the ADC(2) and CIS(D) levels, as well as for the corresponding TDDFT functionals [IP_EA].

Options:

off

Standard excited-state calculations are carried out.

ip

Ionization potentials are calculated.

ea

Electron affinities are calculated.

Default:

ip_ea=off

Example:

for ionization potentials, the user should set ip_ea=ip

itol

Threshold for integral calculation. Integrals less than ${10}^{-\mathrm{𝚒𝚝𝚘𝚕}}$ E${}_h$ will be neglected.

Options:

any integer$\mathrm{>}$

Default:

itol=max(10, scftol+4, scfdtol), but itol is changed to itol+1 if basis functions are dropped because of linear dependence (see keyword ovltol)

Example:

for an accuracy of ${10}^{-15}$ E${}_h$ one must give itol=15

laptol

Specifies the accuracy of the numerical Laplace transform in the (T) correlation energy term of local CCSD(T) calculations with localcc$\mathrm{\ge }$2016. See also the description of keyword talg and Ref. 105.

Options:

any positive real number$\mathrm{>}$

The (T) energy denominator will be approximated using its numerical Laplace transform. The number of quadrature points ($n_{\mathrm{q}}$), and hence the accuracy is determined by this number. The minimum value of $n_{\mathrm{q}}$ is also set by this number as $n_{\mathrm{q}}>|{\log }_{10}(\text{𝚕𝚊𝚙𝚝𝚘𝚕})|$.

Default:

laptol=${\mathrm{10}}^{\mathrm{-}\mathrm{2}}$, but laptol=${\mathrm{10}}^{\mathrm{-}\mathrm{3}}$ is set if lcorthr=tight. See also the description of lcorthr for further details.

Example:

to use a threshold of ${10}^{-3}$ type laptol=1e-3

lccoporder

Specifies the order of operations in LNO-CC calculations.

Options:

lccfirst

The integral transformation steps yielding the LNO integral lists of a LIS are immediately followed by the CC calculation in the same LIS. The three-center LNO integrals are stored in memory and passed directly to the ccsd program (unless ccsdalg=disk was requested). Hence, in combination with the default ccsdalg=dfdirect, the LNO integrals can be kept in memory throughout the entire LNO-CC calculation, and disk I/O is completely avoided in these steps. This option is only available with localcc$\mathrm{\ge }$2018 and ccprog=ccsd.

trffirst

The integral transformation steps to the LNO bases of the LISs are completed first for all LISs, which is followed by the CC calculations performed for each LIS in their respective LNO basis. This option requires storing the integral lists of all LISs on disk. It is usually not limiting to store the three-center LNO integrals required for ccprog=ccsd or the four-center LNO integrals required for ccprog=mrcc.

Default:

lccoporder=lccfirst for localcc$\mathrm{\ge }$2018,
lccoporder=trffirst for localcc2018 or ccprog=mrcc.

Example:

to force storing the integrals on disk for localcc$\mathrm{\ge }$2018 set lccoporder=trffirst

lccrest

Use this keyword to restart local CC calculations in the case of localcc$\mathrm{\ge }$2015, e.g., after power failure. If localcc$\mathrm{\ge }$2018 (and lccoporder=lccfirst) the calculation can be restarted at any stage of the local correlation calculation via lccrest=restart. In this case all the intermediate files located in the folder of execution have to be kept intact, and only the updated MINP file (containing lccrest=restart) should be overwritten before the calculation is restarted. The HF calculation and the orbital localization is skipped via the scfiguess=off and the orblocguess=read options, therefore it is important not to modify the VARS, SCFDENSITIES, FOCK, and MOCOEF* files either. Note that the beginning of the computation up to the pair energy evaluation is repeated in the restarted run, and the loop over the extended domains will continue from the index of the first unfinished domain.

For the restart with lccrest=on, compatible with options localcc=2015, localcc=2016, or localcc$\mathrm{\ge }$2018 and lccoporder=trffirst, the LMP2 calculation and the integral transformations have to be completed, and for the remaining domains the localcc.restart, DFINT_AI.*, DFINT_AB.*, DFINT_IJ.*, ajb.*, 55.*, 56, and VARS files are required, and only the updated MINP file (containing lccrest=on) should be overwritten before the calculation is restarted. In the case of localcc$\mathrm{\ge }$2016, talg=lapl or topr, and lccoporder=trffirst the laplbas.* files are also needed.

In the case of an LMP2 calculation or the LMP2 part of an LNO-CC calculation with lccoporder=trffirst and localcc$\mathrm{\ge }$2016, if the loop for the extended domains is started but not finished, the calculation can be restarted with the lccrest= domain option. In this case all the intermediate files located in the folder of execution have to be kept intact, and only the updated MINP file (containing lccrest=domain) should be overwritten before the calculation is restarted. Note that the beginning of the computation up to the pair energy evaluation is repeated in the restarted run, and the loop over the extended domains will continue from the index of the first unfinished domain.

In the case of restricted open-shell local correlation computations, the FOCK.OD file is also needed. For qro=on, the MOCOEF.QRO file should also be preserved.

Options:

restart, on, off, or domain.

Default:

lccrest=off

Example:

to restart a local CCSD(T) calculation set lccrest=restart if localcc$\mathrm{\ge }$2018 (and lccoporder=lccfirst). In the case of localcc<2018 and/or
lccoporder=trffirst set lccrest=on or lccrest=domain depending on the point of interruption.

lcorthr

Controls the accuracy of local correlation calculations by setting the relevant thresholds: bp*, lnoepso, lnoepsv, laptol, naf_cor, osveps, wpairtol, spairtol (see also Refs. 72, 107, and 108 for details).

Options:

vLoose

Very loose thresholds will be used, see Table 2.

Loose

Relatively loose thresholds will be used, see Tables 1 and 2.

Normal

Default threshold set if localcc$\mathrm{\ge }$2018. lcorthr=Normal is a synonym for lcorthr=Loose if localcc=2015 or 2016. See Tables 1 and 2.

Tight

Tight thresholds will be used, see Tables 1 and 2.

vTight

Very Tight thresholds will be used, see Table 1.

vvTight

Even tighter or very very Tight thresholds will be used, see Table 1.

0

The truncation thresholds will be set so that the canonical energy be reproduced, it is only useful for testing.

Notes:

1.

The values of the thresholds controlled by lcorthr are summarized in Table 1 for the localcc$\mathrm{\ge }$2018 case and in Table 2 for the previous schemes. The performance of lcorthr=Loose to vTight settings for localcc=2018 is extensively benchmarked in Ref. 106. The vLoose and vvTight settings may be employed for convergence studies but their accuracy/cost performance is mostly not practical for production calculations.

2.

Expected accuracy. Using the Normal settings for local MP2 and CCSD(T), if localcc$\mathrm{\ge }$2018, 1 kJ/mol (1 kcal/mol) average (maximum) errors are expected in energy differences even for relatively complicated or sizable systems (see Refs. 107, 108, and 106). Note that molecules with complicated electronic structure can exhibit slower convergence with the local approximations and higher local errors [106, L7CCDMC]. Thus, converge tests with increasingly tighter lcorthr settings are suggested at least for some representative systems to determine appropriate local correlation settings and for the robust estimation of the local approximation errors [106]. In the case of monotonic convergence with respect to lcorthr, the corresponding LNO approximations of Ref. 106 are also recommended to further increase the accuracy.
In the case of localcc=2015, considering local dRPA and dRPA related methods, the expected average (maximum) errors for energy differences are 2 kJ/mol (2 kcal/mol) with Loose and 1 kJ/mol (1 kcal/mol) with Tight settings (see Ref. 72).

3.

The restricted open-shell local MP2 approach is available via localcc$\mathrm{\ge }$2021 [ROLocalMP2]. Currently, only MP2 and the corresponding double-hybrid DFT computations are available with our local approximations. ROHF, ROKS, and in combination with unrestricted references, also QRO references can be employed. With UHF (UKS) references, qro=on is set for localcc$\mathrm{\ge }$2021.

4.

For localcc>2018, the NAF approximation is not employed for the local MP2 correlation energy of calc=LMP2, thus this local MP2 result is exactly the same as the byproduct local MP2 energy of an LNO-CCSD(T) computation with localcc>2018. The NAF approximation was employed in Ref. 107, thus naf_cor=2e-3 is set in combination with localcc=2018 and calc=LMP2, leading to a slightly different local MP2 correlation energy than the one obtained within a localcc=2018 type LNO-CCSD(T) computation (where the NAF approach is only employed at the CC level but not for MP2). For local MP2 naf_cor=off, is set if localcc=2015. Keywords lnoepso, lnoepsv, and laptol are irrelevant for local MP2 calculations.

5.

The closed-shell localcc=2018 and localcc=2021 variants are very close but not always identical. In the case of off-center atomic orbitals employed via the ghost keyword, the domain construction scheme was improved, and the localcc=2021 version is considerably more accurate than localcc=2018.

Table 1: Keyword values set by lcorthr if localcc=2018 or 2021.

calc	LMP2${}^a$ or LNO-CC						all
localcc	2018 or 2021
lcorthr	vLoose	Loose	Normal	Tight	vTight	vvTight	0
bpedo	0.9999	0.9999	0.9999	0.99995	0.99999	0.99999	1.0
wpairtol	1e-4	3e-5	1e-5	3e-6	1e-6	3e-7	0.0
lnoepso	1e-4	3e-5	1e-5	3e-6	1e-6	3e-7	0.0
lnoepsv	1e-5	3e-6	1e-6	3e-7	1e-7	3e-8	0.0
laptol	1e-1	1e-1	1e-2	1e-3	1e-3	1e-3	1e-6
naf_cor	1e-2	1e-2	1e-2	1e-2	1e-3	1e-3	off
bpcompo	0.985	0.985	0.985	0.985	0.985	0.985	1.0
bpcompv	0.98	0.98	0.98	0.98	0.98	0.98	1.0
bppdo	0.999	0.999	0.999	0.999	0.999	0.999	1.0
bppdv	0.98	0.98	0.98	0.98	0.98	0.98	1.0
bpedv	0.995	0.995	0.995	0.995	0.995	0.995	1.0
osveps	off	off	off	off	off	off	off
spairtol	off	off	off	off	off	off	off

^a See note 4 for lcorthr for additional details of LMP2.

Table 2: Keyword values set by lcorthr for localcc=2015 or 2016. Note that identical settings are used for both lcorthr=Normal and lcorthr=Loose if localcc=2015 or 2016.

calc	MP2, dRPA, CC		MP2		CC		all
localcc	2015		2016		2016
lcorthr	Normal	Tight	Normal	Tight	Normal	Tight	0
bpedo	-	-	0.9998	0.9999	0.9999	0.99995	1.0
wpairtol	1e-6	1e-7	1.5e-5	1e-5	1e-5	3e-6	0.0
spairtol	1e-4	1e-5	off	off	off	off	0.0
osveps	1e-3	1e-4	off	off	off	off	0.0
lnoepso	3e-5	1e-5	-	-	2e-5	1e-5	0.0
lnoepsv	1e-6	3e-7	-	-	1e-6	5e-7	0.0
laptol	-	-	-	-	1e-2	1e-3	-
naf_cor	1e-2	8e-3	2e-3	2e-3	1e-2	1e-2	off
bpcompo	0.985	0.985	0.985	0.985	0.985	0.985	1.0
bpcompv	0.98	0.98	-	-	-	-	1.0
bppdo	-	-	0.999	0.999	0.999	0.999	1.0
bppdv	-	-	0.98	0.98	0.98	0.98	1.0
bpedv	-	-	0.995	0.995	0.995	0.995	1.0

Default:

lcorthr=Normal

Example:

to use tight thresholds set lcorthr=Tight

lmp2dens

Determines whether the MP2 density matrix fragments are calculated using the “correct” expressions derived for the general type of orbitals, or using the expressions derived for the canonical case (as described in Ref. 135).

Options:

on

The MP2 density matrix fragments are calculated using the correct, non-canonical expressions.

off

The MP2 density matrix fragments are calculated using the approximate canonical expressions (as defined in Ref. 135).

Notes:

1.

To reproduce the method described in Ref. 135 use lmp2dens=off.

2.

The use of lmp2dens=on is recommended since in this case the local CC energy can be corrected by the difference of the local MP2 energy and the approximate local MP2 energy calculated in the local interacting subspaces (see Total CC… energy + correction in the output). This correction usually improves the local CC energy.

Default:

lmp2dens=on

Example:

to use the canonical expressions give lmp2dens=off

lnoepso

Threshold for the occupation numbers of occupied local natural orbitals (LNOs) in the case of local correlation calculations, for state-averaged MP2/CIS(D) occupied natural orbitals for reduced-cost excited-state calculations, or for MP2 occupied natural orbitals for reduced-cost correlation calculations, see also keyword lnoepsv. See Ref. 138 as well as Refs. 93 and 94 for more details.

Options:

any real number in the [0,1] interval$\mathrm{>}$

Orbitals with occupation numbers greater than 1-lnoepso will be frozen.

Notes:

1.

For default settings with options other than lcorthr=Normal, see the description of lcorthr.

2.

For FNO-CC calculations, occupied NOs are only implemented for closed-shell references with density fitting.

3.

Frozen occupied NOs are not implemented for explicitly correlated methods.

Default:

lnoepso=1e-5 for local correlation, lnoepso=0 for excited-states

Example:

to set a threshold of $5\cdot {10}^{-6}$ type lnoepso=5e-6

lnoepsv

Threshold for the occupation numbers of virtual local natural orbitals (LNOs) in the case of local correlation calculations, for state-averaged MP2/CIS(D) virtual natural orbitals for reduced-cost excited-state calculations, or for MP2 virtual natural orbitals for reduced-cost correlation calculations, see also keyword lnoepso. See Ref. 138 as well as Refs. 93, 94, FNONAF, and RedCostF12 for more details.

Options:

any real number in the [0,1] interval$\mathrm{>}$

Orbitals with occupation numbers smaller than this number will be dropped.

Note:

For default settings with options other than lcorthr=Normal, see the description of lcorthr.

Default:

lnoepsv=1e-6 for local correlation; lnoepsv=7.5e-5 for excited states if no spin scaling is applied; lnoepsv=3e-5 for spin-scaled excited-state models (such as SCS-CC2, SOS-CC2, …); lnoepsv=5e-5 for reduced-cost (FNO) ground-state calculations if no explicit correlation is used. For explicitly correlated CC calculations, lnoepsv=1e-4 with the cc-pVDZ-F12 and aug-cc-pVDZ bases, lnoepsv=1e-6 with cc-pVQZ-F12 and aug-cc-pVQZ, and lnoepsv=1e-5 otherwise.

Example:

to set a threshold of $5\cdot {10}^{-7}$ type lnoepsv=5e-7

localcc

Specifies if local correlation calculation is performed. See Refs. 135, 138, 72, 107, 105, and 108 for more details.

Options:

off

No local correlation calculation is performed.

2013

The algorithm of Ref. 138 is used.

2015

An algorithm based on Ref. 72 is used.

2016

The local MP2 algorithm of Ref. 107 or the local CC algorithm of Ref. 105 is used.

2018

The local MP2 algorithm of Ref. 107 (with tighter settings) or the local CC algorithm of Refs. 108 and 106 is used.

2021

The local MP2 algorithms of Refs. 107 (with tighter settings) and ROLocalMP2 (for restricted open-shell references) or the closed-shell local CC algorithm of Refs. 108 and 106 are used.

on

Equivalent to localcc=2021 in the case of MP2 or CC, and equivalent to localcc= 2015 otherwise

Note:

Local correlation methods can also be run if the prefix “L” (or “LNO-” in the case of CC methods) is added to the corresponding option of keyword calc, see the description of calc. Local SCS-MP2 (SOS-MP2) calculations can be run with calc=LSCS-MP2 (calc=LSOS-MP2).

Default:

localcc=off

Example:

for local correlation calculations give localcc=on

localcorrsymm

Controls the point group symmetry recognition feature of ground-state local correlation methods with localcc$\mathrm{\ge }$2018 as discussed in Sect. 3.4 of Ref. 108.

Options:

off

Point group symmetry is not exploited for the local correlation computation.

on

The symmetry equivalent domains are recognized by analyzing both the diagonal and off-diagonal elements of the Fock matrix transformed to the localized MO basis.

diag

The symmetry equivalent domains are determined only based on the diagonal Fock matrix elements. This is a less strict criterion than localcorrsymm=on.

read

The degeneracy levels of each localized MO can be read from the MINP input file. The domain correlation energy contribution of each localized MO will be multiplied by the positive integer degeneracy level in the MO order determined by the MO localization program. Orbitals without symmetry equivalent MOs should have a degeneracy level of 1. Negative integers denote that the correlation energy contribution of the corresponding MO is already accounted for in the domain of a symmetry equivalent MO. The correctness of these degeneracy levels is not checked by the program. The orblocguess=read or restart setting is recommended with the option to retain the order of the localized MOs.

Default:

localcorrsymm=off

Notes:

1.

While Abelian point group symmetry is recognized and exploited by the HF/KS-DFT programs, the orbital localization algorithms are not yet symmetry adapted. Hence the localized MOs may not exhibit (all of) the symmetry properties of the molecular structure and canonical MOs. Because of that, the localcorrsymm feature is turned off by default even if localcc$\mathrm{\ne }$off. If localcorrsymm$\mathrm{\ne }$off is set, it is recommended to manually check the degeneracy level determination in the output section “Determine symmetry equivalent LMO lists”.

2.

This point group symmetry identification approach [108] can also take advantage of non-Abelian symmetry if the canonical and localized MOs retain the corresponding symmetry properties even if (non-Abelian) symmetry is not enforced by the SCF and localization algorithms.

Example:

to read the list of symmetry-equivalent MOs for $C_{2v}$ water:
localcorrsymm=read
2 -2 2 -2

mact

Specifies the number of active orbitals in an MCSCF calculation. See also the description of keyword docc.

Options:

The number of active orbitals per irrep should be given in the following format:
mact=
where is the number of active orbitals in irrep $i$, and $N_{ir}$ is the number of irreps.

Default:

There is no default, the active orbitals must be given in the case of an MCSCF calculation.

Example:

See the description of keyword docc for examples.

maxact

Maximum number of inactive labels. One can impose restrictions on the cluster operator using this keyword. The maximum number of virtual/occupied inactive labels on the singly, doubly, … excited clusters can be specified.

Options:

on or off. If maxact=on, the maximum number of virtual and occupied inactive labels must be specified in the subsequent line as an integer vector. The integers must be separated by spaces. The vector should contain as many elements as the excitation rank of the highest excitation in the cluster operator. The integers are maximum number of virtual/occupied inactive labels allowed on amplitudes of single, double, … excitations, respectively.

Default:

maxact=off

Example:

Suppose that we have up to quadruple excitations, and the single, double, triple, and quadruple excitations are allowed to have maximum of 1, 2, 2, and 1 inactive virtual and occupied labels, respectively. Then the input file should include the following lines:
maxact=on
1 2 2 1

maxdim

Maximum number of trial vectors in the Davidson procedure in the case of CIS, TDA, TD-HF, and TD-DFT calculations. The procedure will be restarted if the dimension of the reduced subspace reaches maxdim.

Options:

any positive integer$\mathrm{>}$

Default:

maxdim=max(200, 3*max(ntrip, nsing))

Example:

for a maximum of 50 expansion vectors set maxdim=50

maxex

Level of highest excitation included in the cluster operator in the case of MRCI/CC calculations. In an MR calculation all single, double (or higher) excitations out of the reference determinants are included in the cluster operator (see the description of keyword nacto), however, the very high excitations are frequently irrelevant. Using this option the latter can be dropped. If maxex is set to a positive integer $n$, only up to $n$-fold excitations will be included in the cluster operator. The excitation manifold can be further selected by imposing constrains on the number of active/inactive labels of the excitations (see keyword maxact). See Refs. 70 and 60 for more details.

Options:

0

The excitation manifold is not truncated.

any positive integer$\mathrm{>}$

The excitation manifold is truncated at $n$-fold excitations, see above.

Default:

maxex=0

Example:

to truncate the excitation manifold at triple excitations set maxex=3

maxmicroit

Maximum number of microiterations in a Newton step in the case quadratic SCF calculations (see keyword qscf).

Options:

any positive integer$\mathrm{>}$

Default:

maxmicroit=100

Example:

to increase the maximum number of microiterations to 200 give maxmicroit=200

mcscfiguess

Initial guess for the MCSCF calculation.

Options:

The sad, ao, core, mo, and restart options can be used as described for keyword scfiguess. In addition, there is one further option:

HF

An RHF or ROHF calculation is run before the MCSCF calculation, and the HF MOs will be used as initial guess in the MCSCF calculation.

Note:

To restart the MCSCF calculation using MOs from a previous MCSCF run, e.g., when calculating potential energy surfaces, use mcscfiguess=mo

Default:

mcscfiguess=HF

Example:

set mcscfiguess=sad to start the MCSCF calculation from SAD initial guess.

mem

Specifies the core memory used.

Options:

any positive integer$\mathrm{>}$MB

The amount of memory to allocate is specified in megabytes

any positive integer$\mathrm{>}$GB

The amount of memory to allocate is specified in gigabytes

Default:

mem=256MB

Example:

to allocate 8 GB core memory the user should set mem=8GB

mmprog

Specifies the molecular mechanics program to be used for ONIOM calculations. See the description below for the supported methods and programs. Currently, it is not necessary to specify the keyword as Mrcc automatically checks the program availability for the specified molecular mechanics method.

Options:

off

molecular mechanics method is not requested.

xtb

The xTB package of Grimme [xtbprog].

Default:

The default for GFN-FF is xtb, otherwise mmprog=off.

Example:

to select the xTB program for a calculation, set mmprog=xtb.

molden

Specifies whether input file for the Molden program and an xyz-file containing the Cartesian coordinates are written (see also Sect. 14).

Options:

on

Cartesian coordinates, basis set information, and MO coefficients are saved to file MOLDEN. This file can be opened by Molden and used to visualize the structure of the molecule and the MOs. In addition, Cartesian coordinates are also written to file COORD.xyz in xyz (XMol) format, which can be processed by many molecular visualization programs.

off

The construction of the MOLDEN input and the COORD.xyz file is turned off.

Default:

molden=on

Example:

if you do not need Molden input and the COORD.xyz file, add molden=off

mpitasks

Specifies the number of MPI tasks spawned by dmrcc. Currently only executables scf, mrcc, and ccsd can be spawned for MPI parallel execution. All of the current MPI implementations replicate all arrays stored in memory for each MPI task. The mem keyword sets the available memory for a single MPI task. Hence, mem should be set to the total available memory of the compute node divided by the number of MPI tasks used on a single compute node.

Options:

any positive integer$\mathrm{>}$

Default:

mpitasks=1

Note:

For optimal performance, please set mpitasks to the total number of available CPUs/NUMA nodes/nodes/cores, etc., as the additional number of processes on top of mpitasks are driver processes running mostly in the background and do not require dedicated resources.

Example:

to run an MPI-parallel CC calculation using $2$ MPI tasks set mpitasks=2

mulmet

Specifies the multipole approximation used for the evaluation of pair energies of distant pairs.

Options:

0

The simplified dipole-dipole estimate of Ref. 134 will be used.

1

Full dipole-dipole estimate [125].

2

All the terms are included in the multipole expansion up to the contributions of the quadrupole moment [107].

3

All the terms are included in the multipole expansion up to the contributions of the octapole moment [107].

Default:

mulmet=3 if localcc$\mathrm{\ge }$2016, mulmet=0 otherwise

Example:

to use the octapole approximation set mulmet=3

mult

Spin multiplicity ($2S+1$) of the Hartree–Fock or Kohn–Sham wave function. If a CI or CC calculation is also performed, the same multiplicity is supposed for the ground-state wave function. For excited states the multiplicity will be arbitrary, only $M_S$ is conserved. For closed-shell reference determinants the multiplicity (strictly speaking the parity of $S$) can be controlled by keywords nsing and ntrip, see below.

Options:

any positive integer$\mathrm{>}$

Default:

for atoms the corresponding experimental multiplicity is set, for molecules mult=1 (singlet) for an even number of electrons, mult=2 (doublet) otherwise

Example:

for a triplet state one should give mult=3

nab

Specifies whether the natural auxiliary basis (NAB) approximation will be used for explicitly correlated CC calculations and also specifies the threshold for the occupation numbers of NAB functions (see Ref. RedCostF12).

Options:

off

the NAB approach will not be used.

any real number in the [0,1] interval$\mathrm{>}$

A NAB will be constructed and auxiliary functions with occupation numbers smaller than this number will be dropped.

on

Sets nab=0.1

Default:

nab=0.1 for reduced-cost explicitly correlated calculations (that is, if the FNO- prefix is added to the acronym of the selected method), nab=off otherwise.

Example:

to use the NAB approximation and set a threshold of $0.2$, type nab=0.2

nacto

Number of active occupied spinorbitals for multi-reference (active-space) CI/CC calculations. By default, nacto pieces of spinorbitals under the Fermi level are supposed to be active. This can be overwritten using keyword active, which enables the user to select the active orbitals manually (see the description of keyword active). In a MRCI/CC calculation a complete active space (CAS) is supposed defined by keywords nacto and nactv (or alternatively by active) and up to $n$-fold excitations from the reference determinants of this space are included in the excitation manifold, where $n$ is determined by keyword calc (2 for CCSD, 3 for CCSDT, …). See Ref. 70 for more details. See also keywords nactv, maxex, and maxact. Note also that this keyword only sets the active orbitals for the post-SCF calculation, the MCSCF active orbitals can be specified by keyword mact.

Options:

any positive integer$\mathrm{>}$ or 0

Default:

If MCSCF reference is used, nacto is set so that the MCSCF active orbitals (given by keyword mact) will also be the active orbitals in the post-SCF calculation. nacto=0 in the general case.

Example:

for two active occupied spin-orbitals give nacto=2

nactv

Number of active virtual spinorbitals for multi-reference (active-space) CI/CC calculations. By default, nactv pieces of spinorbitals above the Fermi level are supposed to be active, which can be overwritten using keyword active. For a detailed description see keyword nacto.

Options:

any positive integer$\mathrm{>}$ or 0

Default:

If MCSCF reference is used, nactv is set so that the MCSCF active orbitals (given by keyword mact) will also be the active orbitals in the post-SCF calculation. nactv=0 in the general case.

Example:

for two active virtual spin-orbitals give nactv=2

nafalg

Specifies how natural auxiliary functions (NAFs) will be constructed in the case spin-unrestricted MOs. NAFs can be calculated by diagonalizing (${𝐖}^{\alpha }$ $+$ ${𝐖}^{\beta }$)/2 or ${𝐖}^{\alpha }$ (see Ref. 71 for the definitions). The latter option is somewhat more efficient but can be dangerous for processes involving atoms.

Options:

albe

NAFs are constructed from (${𝐖}^{\alpha }$ $+$ ${𝐖}^{\beta }$)/2.

alpha

NAFs are constructed from ${𝐖}^{\alpha }$.

Default:

nafalg=albe

Example:

to use ${𝐖}^{\alpha }$, set nafalg=alpha

nafdens

This keyword can be used to control the state-averaged density construction for local ADC(2) calculations. See Ref. 92 for further details.

Options:

off

The NAF approximation is not used for the density construction.

on

A fast, local domain-based algorithm is used for the density construction invoking the NAF approximation.

Default:

nafdens=off

Notes:

1.

If redcost_exc=on and localcc=2016 settings are used, nafdens=on is set by default.

2.

If local CVS-ADC(2) calculations are carried out, all the NAFs are retrieved during the density construction.

Example:

to switch on the NAF approximation at the construction of density matrices, set nafdens=on

naf_cor

Specifies whether natural auxiliary functions (NAFs) will be used for density-fitting correlated calculations and also specifies the threshold for the occupation numbers of NAFs (see Ref. 71).

Options:

off

NAFs will not be constructed.

any real number in the [0,1] interval$\mathrm{>}$

A NAF basis will be constructed and NAFs with occupation numbers smaller than this number will be dropped.

on

Sets naf_cor=5e-2 when ccprog=ccsd is set or naf_cor=5e-3 in other cases if the use of NAFs is not specified as default. If NAFs are used as default, e.g., in the cases of certain local correlation and reduced-cost excited-state approaches, naf_cor=on should not be written to the input file.

Note:

If ccprog=mrcc or dfbasis_cor=none, no correction for the dropped NAFs is calculated.

Default:

according to the value of lcorthr for local correlation methods; naf_cor=0.1 for the reduced-cost excited-state approaches of Refs. 93 and 94 (see keyword redcost_exc) without spin scaling; naf_cor=0.075 for the spin-scaled version of the latter methods (such as SCS-CC2, SOS-CC2, …); naf_cor=0.05 for reduced-cost ground-state calculations (that is, if theFNO- prefix is added to the acronym of the selected method); naf_cor=off otherwise.

Example:

to use NAFs and set a threshold of ${10}^{-2}$, type naf_cor=1e-2

naf_f12

Specifies whether natural auxiliary functions (NAFs) will be used for explicitly correlated CC calculations at the calculation of the F12-dependent intermediates and also specifies the threshold for the occupation numbers of NAFs (see Ref. RedCostF12).

Options:

off

NAFs will not be constructed.

any real number in the [0,1] interval$\mathrm{>}$

A NAF basis will be constructed and NAFs with occupation numbers smaller than this number will be dropped.

on

Sets naf_f12=5e-2

Default:

naf_f12=5e-2 for reduced-cost explicitly correlated calculations (that is, if the FNO- prefix is added to the acronym of the selected method), naf_f12=off otherwise.

Example:

to use NAFs and set a threshold of ${10}^{-2}$, type naf_f12=1e-2

naf_scf

Specifies whether NAFs will be used for density-fitting SCF calculations and also specifies the threshold for the occupation numbers of NAFs (see Ref. 71). The syntax is analogous with that for keyword naf_cor.

naftyp

Specifies how NAFs will be constructed in the case of local correlation calculations. NAFs are constructed by diagonalizing the $𝐖={𝐉}^{\mathrm{T}}𝐉$ matrix where $𝐉$ is a particular block of the three-center Coulomb integral matrix (see Refs. 71 and 108 for details).

Options:

Jai

NAFs are constructed from $J_{ai}^P$

Jpi

NAFs are constructed from $J_{pi}^P$

Jpq

NAFs are constructed from $J_{pq}^P$ using the $p\ge q$ values.

Jpq_inv

NAFs are constructed from all $J_{pq}^P$ integrals. This option generates NAFs invariant to orbital rotations among the MOs but it overweighs the $p\ne q$ integrals compared to the diagonal $p=q$ integrals, leading to a minor numerical deviation compared to the naftyp=Jpq option.

Jmi

NAFs are constructed from $J_{\mu i}^P$

Default:

naftyp=Jpq for local CC and localcc$\mathrm{\ge }$2016 as well as for the reduced-cost excited-state approaches of Refs. 93 and 94 (see keyword redcost_exc), naftyp=Jai for local MP2 and localcc$\mathrm{\ge }$2016

Example:

to construct NAFs using $J_{pq}^P$ set naftyp=Jpq

nchol

Number of Cholesky vectors/quadrature points for the Laplace integral in the case methods based on the decomposition of energy denominators. See also the description of keyword dendec.

Options:

auto

The number of Cholesky vectors/quadrature points will be automatically determined to achieve the required precision.

any positive integer$\mathrm{>}$

The number of Cholesky vectors/quadrature points will also be automatically determined but the maximum number of the vectors cannot exceed this number.

Default:

nchol=auto

Example:

to use ten Cholesky vectors/quadrature points give nchol=10

ndeps

Step size for the numerical differentiation in atomic units.

Options:

any positive real number$\mathrm{>}$

Default:

ndeps=1e-3

Example:

for a step size of $5\cdot {10}^{-4}$ a.u. for numerical Hessian evaluation set ndeps=5e-4

nstate

Number of electronic states including the ground state and excited states. In non-relativistic calculations, for closed-shell reference determinants nstate is supposed to be the number of singlet states. See also keywords nsing, ntrip, and optex.

Options:

any positive integer$\mathrm{>}$

Default:

nstate=max(1, nsing+ntrip)

Example:

for three states give nstate=3

nsing

Number of singlet electronic states (strictly speaking the number of of states with $M_S=0$ and $S$ is even) including the ground state and excited states. Use this option only for non-relativistic calculations and closed-shell reference determinants, it should be zero otherwise. In the case of closed-shell reference determinants a partial spin-adaptation is possible, see Ref. 69. This enables us to search for singlet and triplet roots separately. See also keywords nstate and ntrip.

Options:

any positive integer$\mathrm{>}$

Default:

nsing=1 for closed-shell reference determinants, nsing=0 otherwise

Example:

for two singlet states give nsing=2

ntrip

Number of triplet electronic states (strictly speaking the number of of states with $M_S=0$ and $S$ is odd) including the ground state and excited states. Use this option only for non-relativistic calculations and closed-shell reference determinants, it should be zero otherwise. See the description of keywords nstate and ntrip.

Options:

any positive integer$\mathrm{>}$

Default:

ntrip=0

Example:

for two triplet states give ntrip=2

nto

If set, natural transition orbitals (NTOs) or state-averaged natural orbitals (NOs) are written (see also Sect. 14).

Options:

on

NTOs or NOs are saved to the corresponding files (see Notes). These files can be handled using the same programs as file MOLDEN can (see keyword molden).

off

The construction of the corresponding NTO or NO files is turned off.

Notes:

1.

For the reduced-cost CC2, CIS(D${}_{\mathrm{\infty }}$), and ADC(2), methods of Refs. 93 and 94, and for their spin-scaled versions, the pseudo-canonicalized state-averaged NOs will be saved to files MOLDEN_NO.$\mathrm{n}$, where $n$ is the serial number of the excited state.

2.

For the NTOs, in the case of CIS/TDHF/TDDFT/TDA-TDDFT calculations, the MOLDEN_CIS_NTO.$\mathrm{n}$ files are generated for each state, where $n$ is the serial number of the excited state according to energy order.

3.

For the NTOs, in the case of ADC(2)/CC2/CIS(D${}_{\mathrm{\infty }}$) calculations, the
MOLDEN_CORR_NTO.$\mathrm{n}$ files are generated. For a canonical calculation, the files are labeled according to the order of the excitation energies of the second-order method. In contrast, if a state-specific, for example, reduced-cost calculation is performed, the files are labeled according to the order of the CIS excitation energies. Note that the ADC(2) and CIS roots can be swapped. You can check at the end of the output in the summary if such rearrangement occurred.

4.

For the NTOs, in the case of double hybrid calculations, the MOLDEN_DH_NTO.$\mathrm{n}$ files are generated. In the case of the
ADC(2)-based ansatz, the files are labeled according to the order of the excitation energies. In contrast, if the CIS(D)-based ansatz is used, the files are labeled according to the order of the TDA excitation energies.

5.

For the second-order methods, NTOs are calculated using only single excitation coefficients.

Default:

nto=off

Example:

if you need the NTO or NO files, add nto=on

numgrad

This keyword controls the calculation of the numerical gradient of the energy with respect to nuclear positions.

Options:

on

Calculates the numerical gradient with a four point central difference scheme with step size of $0.01$ bohr. Please note that these settings may not be suitable for all types of calculations and molecules. Currently there is no way to control the step size or the numerical stencil from the input file.

off

Mrcc does not calculate numerical gradients.

Default:

numgrad=off

occ

Specifies the occupation of the Hartree–Fock determinant.

Options:

1.

If this keyword is not given, the occupation is automatically determined in the SCF calculations.

2.

For RHF calculations the occupation should be given in the following format:
occ=
where is the number of occupied orbitals in irrep $i$, and $N_{ir}$ is the number of irreps.

3.

For ROHF and UHF calculations the occupation should be given as
occ=/
where is the number of occupied $\sigma$ spinorbitals in irrep $i$.

Default:

occ is not specified, that is, the occupation is set by the SCF program.

Examples:

1.

Water, RHF calculation:
occ=3,1,1,0

2.

Water, UHF calculation:
occ=3,1,1,0/3,1,1,0

3.

Carbon atom, ROHF or UHF calculation:
occ=2,0,0,0,0,1,0,1/2,0,0,0,0,0,0,0

occri

Turns on the OCC-RI-K [occri, DualDF] algorithm. It can be used together with local and non-local direct DF-SCF calculations. It is available for both Coulomb- and overlap-metric DF-SCF methods. The desired fitting metric can be selected with the fitting and dual_df keywords.

Options:

on

Turns on the OCC-RI-K algorithm.

off

Turns off the OCC-RI-K algorithm.

Default:

It is turned off except for overlap-metric SCF calculations.

Example:

to turn of the OCC-RI-K algorithm, set occri=on

oniom

Initiates an ONIOM calculation [86, 57] and specifies the number of layers. In an ONIOM calculation, the system is split up into several layers described at different levels of theory. Both mechanical and electronic embeddings are supported. In the case of the mechanical embedding, the presence of the lower layers are omitted in upper-layer calculations, while a point charge representation of the lower layers is used in electrostatic embedding. The top layer (model system, active subsystem) is treated at the highest level, and the corresponding method, basis set, …are set by the other keywords in the MINP file, calc, basis, …, as usual. The atoms and the boundary handling schemes of the upper layers, and the methods of the lower layers must be specified in the subsequent lines as follows, starting from the lowest-level layer. For each layer three lines are required.

The atoms of the layer must be given by their serial numbers in the first line as ,,…,-,…, where $n_i$’s are the serial numbers of the atoms. Serial numbers separated by dash mean that atoms through are part of the layer. Note that the numbering of the atoms must be identical to that used in the Z-matrix or Cartesian coordinate specification, but dummy atoms must be excluded. Atoms of an upper-level layer have to be a subset of the lower-level layers.

The method for the lower-level layer must be specified in the second line using the corresponding options of keyword calc, or the supported methods of external programs (see keywords sqmprog and mmprog). The highest-level method is specified by keyword calc (or keywords calc and dft if a KS reference is used in a correlation calculation). The specification of the basis set (for the low-level method), charge, and multiplicity of the lower-level layer is optional but can be given in the second line separated by forward slashes and spaces, e.g., as PBE / cc-pVDZ / -1 / 1. See keywords basis, charge, and mult for the available options, respectively. Note that keywords basis, charge, and mult specify the basis of the last calculation, the charge, and the multiplicity of the top layer, respectively. If the basis set is not specified under oniom, the basis set of the upper-level layer will be used, while the default options will be applied for the charge and the multiplicity if they are not set here.

In the third line, an integer should be given which specifies the border handling scheme: the automatic (0), the semi-automatic (1), and the manual (2) border handling schemes are supported.

In the case of the automatic handling of layer borders, the following procedure is executed if the method of the lowest layer is not calculated by an external program. The MOs are localized after the first, full-system calculation (see orbloce for the available options for the localization scheme), and the localized MOs are assigned to maximum of two atoms by the Boughton–Pulay algorithm [9]. If the completeness criteria of a truncated LMO is greater than 0.8, the bond order between the corresponding two atoms is increased by one. The borders of the layers are then determined by those bonds which are located on a layer and a non-layer atom. Depending on their integer bond order, a hydrogen, an oxygen, or a nitrogen atom is selected as link atom. The bond distance is set based on the type of the link atom and the layer atom (see the average bond distances at https://cccbdb.nist.gov/expbondlengths1.asp), and the link atom is placed in the direction of the original bond. Note that the implementation follows the convention of the Amber program, where the distances between the link atoms and the layer atoms are fixed independently of the geometry. Note also that quadruple bonds are not separable automatically, and the separation of aromatic structures should be avoided. If the method of the lowest-level layer is handled by an external program, the same procedure is executed except that the the bonding table is not built by using the Boughton–Pulay algorithm. Instead, the bond table is based on the bond order table of the external program.

In the case of the manual border handling, the user has to specify the atom pairs of the borders, the link atoms, and the distance between the link atoms and the layer atoms. These specifications can be given in three input sections separated by forward slashes and spaces on the same line as follows:
,
where $B_n$, $x_n$, $y_n$, $L_n$, and $R_n$ are the serial number of the border, the layer atom of the border bond, the non-layer atom of the border bond, the atomic symbol of the link atom, and the distance between the layer atom and the link atom, respectively. Note that the serial numbers of the borders are always followed by a colon, different specifications of the same section are separated by a comma, and different specifications of the same border hold the same border serial number in all input sections. All the border parameters have to be specified in the case of manual border handling, and $B_n$ and $n$ have to be positive integers smaller than the number of the atoms in the system. Note that the unit of $R_n$ has to match that set by keyword unit as there are no consistency checks in this handling scheme. Note also that, currently, the manual border handling scheme is the only option if one considers using the GFN-FF method via the Mrcc-xtb interface.

The semi-automatic border handling (1) is the combination of the automatic and manual schemes: the borders are selected and set by the automatic approach, but these selections can be modified manually. Any automatically selected $B_m$ border can be deleted by writing a colon and an $X$ after the serial number of the border in the border atom pair section: . New borders can also be defined in the same manner as in the case of the manual border handling, however, all the parameters of the newly defined borders have to be specified. Please be aware that the simple overwriting of single parameters of the automatic approach is not supported by this scheme.

The ONIOM implementation allows arbitrary number of layers, thus the input requirement of an ONIOM calculation with $N$ layers is $(N-1)*3$ lines: the atoms of the second layer are specified in the first line, while atoms of the third layer are specified in the fourth line after the keyword oniom, and so on. To allow full control over the keywords of the subcalculations, the subminp keyword is advised for use. Note that that projection-based embedding and multi-level local correlation are supported as the top-level calculations (see the keywords embed and corembed for the description). Note also that the restart of the ONIOM procedure is controlled by the comprest keyword. See also the examples below.

Options:

off

No ONIOM calculation is performed.

any positive integer$\mathrm{>}$-me

An ONIOM calculation with mechanical embedding will be carried out with this integer specifying the number of layers. The further parameters should be given in the subsequent lines as described above.

any positive integer$\mathrm{>}$-ee

An ONIOM calculation with electronic embedding will be carried out with this integer specifying the number of layers. The further parameters should be given in the subsequent lines as described above. See also keywords oniom_eechg and oniom_qcorr for options of the point charge representation of the lower layers.

Default:

oniom=off, while mechanical embedding is used if only a positive integer is given as input.

Examples:

1.

A two-layer ONIOM calculation is requested where the model system (layer 2) consists of atoms 8 and 9 (using the automatic border handling scheme). The subcalculations will be executed in the following order: PBE/STO-3G (full system), PBE/STO-3G (model system), and CCSD/aug-cc-pVDZ (model system):
basis=aug-cc-pVDZ
calc=CCSD
oniom=2
8-9
PBE / STO-3g
0

2.

The same settings are applied as in the previous case except that the borders are selected manually: layer 2 will have two borders between atoms 8-5 and 8-1. The first (second) link atom is a hydrogen (fluorine), which will be placed 1.09 Å (1.01 Å) away from atom 8 in the direction of atom 5 (1):
basis=aug-cc-pVDZ
calc=CCSD
oniom=2
8-9
PBE / STO-3g
2 / 1:8-5,2:8-1 / 1:H,2:F / 1:1.09,2:1.01

3.

The same settings are applied as in the previous case except that the borders are selected semi-automatically: the first border of the automatic selection is deleted and an additional third border is specified which is located between atoms 8 and 2. In this case, chlorine will be used as link atom, and it will be placed 1.01 Å away from atom 5 in the direction of atom 2:
basis=aug-cc-pVDZ
calc=CCSD
oniom=2
8-9
PBE / STO-3G
1 / 1:X,3:8-2 / 3:Cl / 3:1.01

4.

Four-layer ONIOM calculation, LNO-CCSD(T):LMP2:PBE:LDA (aug-cc-pVDZ:cc-pVDZ:6-31G*:STO-3G). Each layer uses automatic border handling scheme and has a different negative charge, except the top layer, which has zero charge:
basis=aug-cc-pVDZ
calc=LNO-CCSD(T)
charge=0
mult=1
oniom=4
1-8
LDA / STO-3G / -3 / 1
0
1-5
PBE / 6-31G* / -2 / 1
0
1-2
LMP2 / cc-pVDZ / -1 / 1
0

5.

Two-layer ONIOM calculation, LNO-CCSD(T)-in-LMP2:PBE (aug-cc-pVTZ:6-31G*). The automatic border handling scheme is utilized. The multilevel local correlation approach is used as the top-level calculation with an automatic selection of active occupied molecular orbitals.
basis=aug-cc-pVTZ
calc=LNO-CCSD(T)
corembed=on
1-4
LMP2
0
charge=0
mult=1
oniom=2
1-8
PBE / 6-31G* / 0 / 1
0

6.

Two-layer ONIOM calculation, LNO-CCSD(T)-in-PBE0:PBE (aug-cc-pVTZ:6-31G*). The automatic border handling scheme is utilized. The projection-based embedding is used as the top-level calculation with an automatic selection of active occupied molecular orbitals.
basis=aug-cc-pVTZ
calc=LNO-CCSD(T)
embed=huzinaga
1-4
PBE0
0
charge=0
mult=1
oniom=2
1-8
PBE / 6-31G* / 0 / 1
0

7.

Two-layer ONIOM calculation, PBE0:PM6-D3H4 (aug-cc-pVTZ:minimal basis). The automatic border handling scheme is utilized. The Mopac semi-empirical program is used for the PM6-D3H4 calculations.
basis=aug-cc-pVTZ
calc=PBE0
charge=0
mult=1
sqmprog=mopac2016
oniom=2
1-8
PM6-D3H4 / / 0 / 1
0

8.

Two-layer ONIOM calculation, LNO-CCSD(T)-in-LMP2-in-PBE-D3:GFN2-xTB (aug-cc-pVTZ:minimal basis). The automatic border handling scheme is utilized for the ONIOM calculation, while the amul scheme is used for the selection of occupied orbitals in the embedding and multilevel local correlation calculations. The xTB semi-empirical program is used for the GFN2-xTB calculations.
basis=aug-cc-pVTZ
calc=LNO-CCSD(T)
charge=0
mult=1
orbloce=pm
sqmprog=xtb
corembed=on
1-4
0
embed=huzinaga
1-8
PBE-D3
0
oniom=2
1-12
GFN2-xTB / / 0 / 1
0

oniom_eechg

Specifies the type of atomic charges used in the ONIOM calculations with electronic embedding. Note that in the case of the mulli, lowdin, iao, chelpg , and mk options, the atomic charges are generated after the first ONIOM subcalculation. Note also that in the cases where gopt$\mathrm{\ne }$off and freq$\mathrm{\ne }$off, these charges will be used in all calculations.

Options:

off

No embedding charges. This is equivalent with mechanical embedding.

mulli

Mulliken atomic charges are used as embedding charges.

lowdin

Löwdin atomic charges are used as embedding charges.

iao

Intrinsic atomic orbital (IAO) atomic charges atomic charges are used as embedding charges.

chelpg

CHELPG atomic charges are used as embedding charges.

mk

Merz–Singh–Kollman atomic charges are used as embedding charges.

external

The charges are obtained by an external program if the same program is used in the first calculation. Currently, only the xTB program is supported.

amber

Perturbation-independent charges are obtained from the topology file of the Amber program. See the manual of Amber how to generate such files and the example below how to use them with Mrcc. If oniom_eechg=amber and qmmm=off, then it is assumed that the serial numbers of the atoms are the same in the topology file and in MINP.

user

Those atomic charges will be used that are specified after the line of oniom_eechg. Note that each given atomic charge must be in a new line, the order of the charges must be the same as the order of the corresponding atoms in the specification of the geometry, and the charge of all atoms must be specified.

Default:

oniom_eechg=lowdin, if oniom$\mathrm{\ne }$off and electronic embedding is utilized,
oniom_eechg=off otherwise.

Example:

1.

Two-layer ONIOM calculation is requested with electronic embedding for a system with 9 atoms. The upper layer consists of atoms 8 and 9, while the layer borders are handled automatically. The subcalculations will be executed in the following order: PBE/STO-3G (full system), PBE/STO-3G (model system, in the presence of the IAO atomic charges of atoms 1-7), and CCSD/aug-cc-pVDZ (model system, in the presence of the IAO atomic charges of atoms 1-7).
basis=aug-cc-pVDZ
calc=CCSD
oniom_eechg=iao
oniom=2-ee
8-9
PBE / STO-3G
0

2.

The same settings are applied to a 2-atom system, except that user-defined charges will be used:
basis=aug-cc-pVDZ
calc=CCSD
charge=-1
oniom_eechg=user
1.00
-1.00
oniom=2-ee
2
PBE / STO-3G
0

3.

A two-layer ONIOM calculation is requested with electronic embedding, PBE0:GFN2-xTB (6-31G*:minimal basis). After the full system calculation, a GFN2-xTB and a PBE0 calculation are executed using the point charges obtained from the xTB program.
basis=6-31G*
calc=PBE0
oniom_eechg=external
oniom=2-ee
2
GFN2-xTB / / 0 / 1
0

4.

A two-layer ONIOM calculation is requested with electronic embedding, PBE0:GFN2-xTB (6-31G*:minimal basis). After the full system calculation, a GFN2-xTB and a PBE0 calculation are executed using the point charges obtained from the topology file example.prmtop of the Amber program.
basis=6-31G*
calc=PBE0
oniom_eechg=amber
example.prmtop
oniom=2-ee
2
GFN2-xTB / / 0 / 1
0

oniom_pcm

Specifies the PCM scheme for ONIOM calculations [101, 149].

Options:

off

ONIOM subcalculations will not use PCM.

c

PCM is utilized only in the first calculation, i.e., in the lowest-level calculation performed for the entire system.

x

PCM will be used in all subcalculations. The cavity of the upper layer calculation will be the same as in the first calculation. The wall of the cavity is repolarized by the density of the subcalculation.

Notes:

1.

If the lowest-level calculation is handed by an external program, the implicit solvent model of the external program can be utilized with oniom_pcm=c.

2.

If the Mopac program is utilized in the first calculation and pcm=solvent$\mathrm{>}$, then the eps and rsolv keywords are set for Mopac. The corresponding static permittivity and probe radius values of the given solvent are taken from the PCMSolver library.

Default:

oniom_pcm=x if oniom$\mathrm{\ne }$off and pcm$\mathrm{\ne }$off and mechanical embedding is used, oniom_pcm=c if oniom$\mathrm{\ne }$off and pcm$\mathrm{\ne }$off and electronic embedding is used and the lowest-level calculation is handled by an external program, oniom_pcm=off otherwise.

Examples:

1.

Two-layer ONIOM calculation is requested using the IEFPCM solvent model utilizing water for the medium. The upper layer consists of atoms 8 and 9, while the layer borders are handled automatically. The subcalculations will be executed in the following order: PBE/STO-3G (full system, in the cavity of the full system), PBE/STO-3G (model system, in the cavity of the full system), and CCSD/aug-cc-pVDZ (model system, in the cavity of the full system). Note that the interface is repolarized in all subcalculations.
basis=aug-cc-pVDZ
calc=CCSD
pcm=water
oniom_pcm=x
oniom=2
8-9
PBE / STO-3G
0

2.

The same settings are applied as in example 1, except that PCM is only utilized in the first calculation:
basis=aug-cc-pVDZ
calc=CCSD
pcm=water
oniom_pcm=c
oniom=2
8-9
PBE / STO-3G
0

3.

The same settings are applied as in example 2 except that the implicit solvent model is only utilized in the first calculation by an external program:
basis=aug-cc-pVDZ
calc=CCSD
pcm=water
oniom_pcm=c
oniom=2
8-9
PM6-D3H4 / / 0 / 1
0

oniom_qcorr

Specifies the point charge correction scheme for ONIOM calculations to avoid the overpolarization of the electron density by those classical point charges that are saptially close to the quantum mechanical system. This feature also guarantees integer net charges for the subsystems.

Options:

0

The correct integer charge of the subsystems is guaranteed. The point charges of the upper-layer atoms are summed, the integer charge of the upper-layer is subtracted from the sum, and the residual charge is distributed equally among those atoms that were not counted in the summation.

1

Same as option 0, but moreover, the point charges of the lower-layer host atoms are added to the point charge summation, and then they are zeroed.

special

Same as option 1, but moreover, user-defined point charges of the lower-layer host atoms are added to the point charge summation, and then they are zeroed. The serial numbers of the additional atoms have to be specified in the subsequent lines after the keyword oniom_qcorr for each layer. See the examples below.

off

No charge correction scheme is utilized. The initial input point charges will be used throughout the subcalculations, thus the sum of the point charges may differ from the integer charge of the environment subsystem.

Notes:

1.

In the case of options 0, 1, and special, the integer charges are guaranteed for each sublayer, thus a unique charge correction is utilized for each layer.

2.

Option 1 only differs from option 0 if the subsystems are covalently bound.

Default:

oniom_qcorr=off if oniom=off, and oniom_qcorr=1 otherwise.

Example:

1.

A CCSD:PBE (aug-cc-pVDZ:STO-3G) calculation is performed for the system that consists of 6 atoms. The manual border handling scheme is employed: a hydrogen link atom is positioned to the layer border, which is between atoms 2 and 5. No charge correction is utilized, thus the input point charges will be employed for the model system calculations. Note that the sum of point charges of the environmental subsystem ($-$1.1) differs from the integer charge of the subsystem ($-$1), that is, the charge of the total system (0) minus the charge of the model system ($+$1)
basis=aug-cc-pVDZ
calc=CCSD
charge=1
oniom_qcorr=off
oniom_eechg=user
0.85
-0.60
0.85
0.20
-1.5
0.20
oniom=2-ee
1-3
PBE / STO-3G / 0 / 1
2 / 1:2-5 / 1:H / 1:1.09

2.

The same settings are applied as in the previous example except that the integer charge of the subsystem is guaranteed with oniom_qcorr=0. In this case, the sum of point charges of atoms 1-3 is summed ($+$1.1), the charge of the model system ($+$1) is subtracted, and the difference (0.1) is distributed equally among the rest of the charges, which results in point charges $+$0.233, $-$1.467, and $+$0.233 for atoms 4, 5, and 6, respectively. Note that the point charge representation of the environmental subsystem matches the integer charge of the subsystem.

3.

The same settings are applied as in the previous example except that oniom_qcorr=1. In addition to the previous example, the point charge of the lower-layer host atom, which is atom 5, is included in the summation. After the integer charge of the subsystem ($+$1) is subtracted from the resulting point charge sum ($-$0.4), the residual charge ($-$1.4) is distributed equally among the rest of the point charges, which results in $-$0.5 and $-$0.5 for atoms 4 and 6, respectively. Note that the point charge representation of the environmental subsystem matches the integer charge of the subsystem.

4.

A CCSD:PBE0:PBE (aug-cc-pVDZ:6-31G*:STO-3G) calculation is carried out for a system which consists of 12 atoms, and manual border handling scheme is employed. The same charge correction procedure is utilized as in the previous example, except that additional point charges are used in the summation procedure and then they are zeroed. In the case of the second layer calculations, atoms 7 and 8 are added to the charge correction procedure. In the case of the last layer calculations, the point charge of atoms 5-9 will also be used in the summation and then zeroed.
basis=aug-cc-pVDZ
calc=CCSD
charge=1
oniom_qcorr=special
7,8
5-9
oniom_eechg=lowdin
oniom=2-ee
1-6
PBE / STO-3G / 0 / 1
2 / 1:6-9 / 1:H / 1:1.09
1-3
PBE0 / 6-31G⁢ / 0 /1
2 / 1:1-4 / 1:H / 1:1.09

optalg

Specifies the optimization algorithm used for geometry and basis set optimizations. For basis set optimization, at the moment, the downhill simplex method of Nelder and Mead [111] is the only available option. A geometry optimization can be carried out by either the Broyden–Fletcher–Goldfarb–Shanno (BFGS) or the simplex algorithm.

Options:

simplex

the simplex method of Nelder and Mead.

BFGS

the BFGS algorithm.

Default:

optalg=simplex for basis set optimization, optalg=BFGS otherwise.

Example:

To run a geometry optimization with the simplex algorithm set optalg=simplex

optmaxit

Maximum number of iteration steps allowed in a geometry or basis set optimization. If the simplex algorithm is used, i.e., optalg=simplex, the maximum number of function evaluations is also controlled by the parameter optmaxit: it is set to 15$\times$optmaxit. If the optimization is terminated with a message “the maximum number of function evaluation is exceeded”, then you can increase the value of optmaxit appropriately.

Options:

any positive integer$\mathrm{>}$

Default:

optmaxit=50

Example:

to allow 60 iteration steps set optmaxit=60

optetol

Convergence threshold for geometry or basis set optimization. If the simplex algorithm is used, i.e., optalg=simplex, the optimization is terminated when the energy difference (in E${}_h$) becomes less then this value and the optstol criterion is also fulfilled. In addition to the criterion for the gradient (optgtol) and the step-size (optstol) the energy change between the cycles is also monitored. For a successful geometry optimization it is required that the optgtol criterion is satisfied and either the energy difference between the last two steps becomes less than this value (in E${}_h$) or the optstol criterion is met.

Options:

any positive real number$\mathrm{>}$

Default:

optetol=1e-6

Example:

for a convergence threshold of $5\cdot {10}^{-6}$ E${}_h$ set optetol=5e-6

optex

Serial number of the excited state (excluding the ground state) for which the geometry optimization or property calculation is performed. See also keywords nsing, ntrip, and nstate.

Options:

any positive integer$\mathrm{>}$ that is smaller than the total number of states set by keywords nsing, ntrip, and nstate.

Default:

optex=nstate-1, that is, the geometry optimization will be performed for the highest excited state considered.

Example:

if you set
calc=CIS
nsing=3
optex=1
for a closed-shell molecule, the ground-state and two excited-state roots will be determined in each geometry optimization step, but the gradients will be calculated for the lowest singlet excited state.

optgtol

Convergence threshold for geometry optimization, upper limit (in E${}_h$/bohr) for the maximum gradient component. For a successful geometry optimization this criterion must be fulfilled.

Options:

any positive real number$\mathrm{>}$

Default:

optgtol=1e-4

Example:

for a convergence threshold of $3\cdot {10}^{-4}$ E${}_h$/bohr set optgtol=3e-4

optstol

Convergence threshold for geometry or basis set optimization. For the latter the optimization is terminated when the maximum change in the parameters becomes less then this value and the optetol criterion is also fulfilled, for the former this criterion is met when the maximum step-size from the previous step (in bohr) is lower than this value. The geometry optimization is terminated successfully if, in addition to the optgtol criterion obeyed, either this criterion is met or the energy difference between the last two steps becomes less than optetol.

Options:

any positive real number$\mathrm{>}$

Default:

optstol=1e-3 for a basis set optimization, optstol=1e-4 otherwise.

Example:

to set a threshold of ${10}^{-5}$ bohr for a geometry optimization type optstol=1e-5

orblocc

Specifies what type of orbital localization is performed for the core molecular orbitals.

Options:

All the options introduced for keyword orbloco also work for orblocc, see the description of keyword orbloco for details.

Default:

orblocc=orbloco if localcc=2013, or core=corr and
localcc$\mathrm{\ne }$off; orblocc=off otherwise

Example:

to localize of core orbitals with the Pipek–Mezey algorithm specify orblocc=on

orbloce

Specifies what type of orbital localization is performed for the molecular orbitals in the case of localization-based embedding calculations.

Options:

All the options introduced for keyword orbloco also work for orbloce, see the description of keyword orbloco for details. An additional option is orbloce=special, where one must specify orblocc, orbloco, and orblocv, respectively, in the three subsequent lines after orbloce.

Notes:

1.

Except for orbloce=special, the same option is set for the core and valance orbitals.

2.

The keyword also controls the orbital localization in the case of automated link atom handling of ONIOM calculations.

3.

orbloce=special is the only option to allow the selection of virtual orbitals in the subsequent projector constructions, where all options of orblocv can be used, except pao-subsys. Note that it is allowed to utilize the full virtual subspace in the high-level SCF run but to use different virtual orbitals during the correlation calculations. See examples 10 and 11 for keyword embed.

4.

If orbloce=spade is utilized, the atoms specified under the keyword embed are used to construct the projector.

Default:

orbloce=spade if embed$\mathrm{\ne }$off and oniom=off,
orbloce=pm if oniom$\mathrm{\ne }$off,
orbloce=off otherwise

Examples:

1.

to localize the orbitals with the Pipek–Mezey algorithm specify orbloce=pm

2.

to use Pipek–Mezey localization for the occupied orbitals and SPADE localization for the virtual orbitals, type
orbloce=special
pm
pm
spade
note that this setup allows the selection of active virtual orbitals, thus the projector of the embedding calculations will contain frozen virtual orbitals during the high-level SCF run.

orblocguess

Initial guess for the orbital localization.

Options:

cholesky

Guess orbitals are calculated by the Cholesky decomposition of the one-particle density matrix [4].

restart

Guess orbitals for the localization are read from the
MOCOEF.LOC file produced in a previous run where orbital localization was performed.

read

Orbitals are read from the MOCOEF.LOC file and directly employed at later steps of the calculation without any change. The locality of the orbitals is not checked and the orbital localization is skipped entirely.

Note:

The combination of orblocguess=restart (or orblocguess=read) with scfiguess= off can be particularly useful if the result files of the converged SCF iteration and orbital localization steps are available and only the local correlation step should be repeated with different settings. See also the description of scfiguess=off for this option.

Default:

orblocguess=cholesky

Example:

to speed up the orbital localization by using the localized orbitals of a previous calculation as guess specify orblocguess=restart.

orbloco

Specifies what type of orbital localization is performed for occupied molecular orbitals.

Options:

off

No orbital localization.

boys

Boys localization is performed [27].

pm

Pipek–Mezey localization is performed [126].

IBO

intrinsic bond orbitals of Knizia are constructed [76].

gboysm$\mathrm{>}$

generalized Boys localization by Jansík et al. [58], where $m$ is a positive integer defining the power of orbital variance. Note that for $m=1$, the Boys localization is retrieved.

cholesky

localized orbitals are calculated by the Cholesky decomposition of the one-particle density matrix [4].

spade

the SPADE fragment localization of Claudino and Mayhall [12].

Default:

orbloco=off in the general case, orbloco=boys for local correlation calculations

Note:

In the case of orbloco=spade, a list of atoms is read after the line orbloco in the following format: ,,…,-,…, where $n_i$’s are the serial numbers of the atoms. Serial numbers separated by dash mean that the atomic orbitals of atoms through are used in the projector construction. Note that the numbering of the atoms must be identical to that used in the Z-matrix or Cartesian coordinate specification, but dummy atoms must be excluded.

Examples:

1.

to carry out Pipek–Mezey localization for the occupied orbitals, type orbloco=pm

2.

to carry out generalized Boys localization with $m=2$ for the occupied orbitals, type orbloco=gboys2

3.

Consider three water molecules, denoted by A, B, and C, whose atoms have identifiers of 1-3, 4-6, and 7-9, respectively. To obtain orbitals that are localized on molecule B, type
orbloco=spade
4,5-6
Note that simultaneously one obtains occupied orbitals which are localized on molecules A and C.

orblocv

Specifies what type of orbital localization is performed for virtual molecular orbitals.

Options:

All the options introduced for keyword orbloco excepting IBO also work for orblocv, see the description of keyword orbloco for details. In addition, two more options are available:

pao

Projected atomic orbitals (PAO)

pao-subsys

Subsystem-specific projected atomic orbitals

Notes:

1.

orblocv=pao is only an available option for local correlation calculations.

2.

orblocv=pao-subsys generates virtual orbitals that are localized on a specified list of atoms. In this case, a list of atoms is read after the line orblocv in the following format: ,,…,-,…, where $n_i$’s are the serial numbers of the atoms. Serial numbers separated by dash mean that the atomic orbitals of atom through atom are used to calculate the norm of the PAOs. Note that the numbering of the atoms must be identical to that used in the Z-matrix or Cartesian coordinate specification, but dummy atoms must be excluded. Note also that those PAOs whose norm is below pao_subsys_tol are dropped.

3.

If orblocv=pao-subsys and embed$\mathrm{\ne }$off, then the required atom list is read under the keyword embed, but this can be overridden if a list of atoms under the keyword orblocv is specified. See examples 10 and 11 for keyword embed.

4.

If orblocv=pao-subsys and molden$\mathrm{\ne }$off, then the constructed PAOs are written to the end of the MOLDEN file, while the coefficients of the rest of the virtual orbitals are filled with zeros. Note that the number of the latter orbitals equals with the number of dropped PAOs.

Default:

orblocv=off in the general case, orblocv=pao for local correlation calculations

Examples:

1.

to carry out Boys localization for the virtual orbitals type orblocv=boys

2.

To use projected atomic orbitals that are localized on atoms 2, 4 and 6-10, type
orblocv=pao-subsys
2,4,6-10

3.

To partition the virtual space of the water molecules in the 3rd example of orbloco, type
orblocv=spade
4,5-6

osveps

Threshold for the occupation numbers of orbital specific virtual orbitals (OSVs) used at the evaluation of pair correlation energies in local MP2 and dRPA calculations. See the description of keyword wpairtol for more details.

Options:

off

OSVs are not constructed and not dropped

any real number in the [0,1] interval$\mathrm{>}$

Orbitals with occupation numbers smaller than this number will be dropped.

Default:

osveps=1e-3 for localcc=2015, osveps=off for localcc$\mathrm{\ge }$2016

Example:

to set a threshold of ${10}^{-4}$ type osveps=1e-4

ovirt

This keyword controls the cost reduction approaches based on natural orbital (NO) or optimized virtual orbitals (OVOs) techniques. For a ground-state correlation calculation, if this keyword is set, the virtual MOs will be transformed to MP2 NOs or OVOs [112]. Subsequently the virtual space will be truncated on the basis of the populations of the orbitals, which can be controlled by keywords eps, lnoepsv, and ovosnorb. See Ref. 136 for more details.

Options:

off

The virtual MOs are not changed.

MP2

MP2 NOs will be used.

OVOS

Optimized virtual orbitals will be used.

PPL

MP2 NOs are used and the PPL+ and (T+) corrections [FNOExt] are calculated.

Note:

If ccprog=mrcc no correction for the dropped NOs is calculated.

Default:

ovirt=MP2 for reduced-cost correlated calculations (that is, if the FNO- prefix is added to the acronym of the selected method), ovirt=off otherwise

Example:

to use MP2 NOs for a ground-state CC calculation give ovirt=MP2

ovltol

Tolerance for the eigenvalues of the AO overlap matrix. Eigenvectors corresponding to the eigenvalues lower that ovltol will be removed to cure the linear dependence of the AO basis set.

Options:

any positive real number or zero$\mathrm{>}$

This number will be used as the threshold for the eigenvalues of the overlap matrix.

Default:

ovltol=1e-7

Example:

to keep all the basis functions set ovltol=0.0

ovosnorb

Specifies the retained percentage of virtual orbitals in an optimized virtual orbitals (OVOs) calculations. ovosnorb % of virtual orbitals will be retained.

Options:

any number between 0 and 100$\mathrm{>}$

Default:

ovosnorb=80.0

Example:

to retain only 70 % of the virtuals give ovosnorb=70.0

pao_subsys_tol

This keyword sets the threshold on the norm of the retained projected atomic orbitals (PAO) during the PAO construction. The norm of the PAOs are calculated using the atomic orbitals of a list of specified atoms, and PAOs whose norm is lower than pao_subsys_tol are dropped. See also keyword orblocv.

Options:

any positive real number in the [0,1] interval $\mathrm{>}$

Default:

pao_subsys_tol=1e-3

Example:

To keep a fewer number of virtual PAOs, use pao_subsys_tol=1e-2

pcm

If this keyword is set, solvent effects will be considered employing the polarizable continuum model (PCM) [147] via an interface to the PCMSolver library [16, 17, 1]. See also keywords pcm_* below.

Options:

off

No solvent effects will be considered

solvent$\mathrm{>}$

Solvent effects will be considered with the corresponding solvent. The name of the solvent should be given as defined in PCMSolver, such as Water, Methanol, Acetonitrile, …, see the manual of the PCMSolver [1]. Spaces in the names must be replaced by underscores, e.g., Propylene_Carbonate instead of Propylene Carbonate.

Default:

pcm=off

Examples:

1.

To perform a calculation with water as solvent set pcm=Water

2.

To perform a calculation with a manually set permittivity of 78.39, add the following lines:
pcm=explicit
pcm_green_eps=78.39

pcm_*

These keywords control the PCM calculation and correspond to the keywords of the PCMSolver library. See the documentation of the PCMSolver library for a detailed description [16, 17, 1]. These keywords will be passed to PCMSolver without any sanity check. The keywords and the corresponding default values are as follows (Å and Å${}^2$ are used for length and area, respectively).

   PCM_Cavity_Type=GePol

   PCM_Cavity_Area=0.3

   PCM_Cavity_Scaling=False

   PCM_Cavity_RadiiSet=UFF

   PCM_Cavity_NpzFile=empty string$\mathrm{>}$

   PCM_Cavity_MinRadius=100.0

   PCM_Medium_SolverType=IEFPCM

   PCM_Medium_Correction=0.0

   PCM_Medium_ProbeRadius=1.0

   PCM_Green_Eps=1.0

   PCM_Green_Type=UniformDielectric

Note:

In particular cases the average area of the surface partition for the cavity
(PCM_Cavity_Area) is not appropriate, and you get an error message. In this case, you should change the value of PCM_Cavity_Area.

Example:

to change the cavity surface area partition to 0.2 Å${}^2$ set PCM_Cavity_Area=0.2

popul

This keyword controls the wave function analysis. See also keyword nto for the generation of natural transition orbitals (NTOs) and the keyword espcharge to generate CHELPG and Merz–Singh–Kollman atomic charges.

Options:

off

No wave function analysis is performed.

Mulli

A population analysis is also performed, and Mulliken and Löwdin atomic charges as well as Mayer bond orders are computed [102, 87].

IAO

In addition to the above parameters, intrinsic atomic orbitals (IAOs) are constructed and IAO partial charges are calculated [76].

deco

In addition to the parameters listed for Mulli, the atomic decomposition of the energy is also computed.

Default:

popul=Mulli if dens $\ne$ 0, popul=off otherwise

Example:

to calculate IAO charges set popul=IAO

pressure

The pressure in Pa at which the thermodynamic properties are evaluated (see also keyword freq).

Options:

any positive integer$\mathrm{>}$

Default:

pressure=100000

Example:

for 1 atm set pressure=101325

pssp

Turns on pseudo-spectral (COSX) exchange matrix build for SCF calculations. It uses DFT grids as integration grid (see keywords agrid and agrid_pssp). By default, a smaller grid (specified with agrid_pssp_sm) is used to get a self-consistent density which is then used to get a more accurate result on the larger grid (specified with agrid_pssp). The result is further enhanced with a first order correction [DualDF]. The COSX algorithm can be used for both Hartree–Fock and hybrid DFT calculations.

Options:

on

The pseudo-spectral algorithm is used for exchange matrix formation.

off

The pseudo-spectral algorithm is turned off.

Default:

pssp=off

Notes:

One can perform a single grid COSX calculation by setting dual_df=off. For more information, see keyword dual_df and the examples below. The radial grid of the integration grid can be specified by rgrid, while the accuracy of the grid can be tuned by the grtol keyword. Keep in mind, however, that these keywords control the DFT grid as well.

Examples:

1.

DFT calculation with the PBE0 functional and COSX:
basis=cc-pVTZ
calc=PBE0
scfalg=direct
pssp=on

2.

DFT calculation with the PBE0 functional and COSX using a single grid:
basis=cc-pVTZ
calc=PBE0
scfalg=direct
pssp=on
dual_df=off

3.

DFT calculation with the PBE0 functional and COSX using custom grid options:
basis=cc-pVTZ
calc=PBE0
scfalg=direct
pssp=on
agrid_pssp=LD0006-LD0350
agrid_pssp_sm=LD0006-LD0110

ptfreq

Frequency of the perturbation for frequency-dependent properties in atomic units (available only with Cfour). See Refs. 64 and 114 for more details.

Options:

any real number$\mathrm{>}$

Default:

ptfreq=0.0

Example:

to set a frequency of 0.1 a.u. give ptfreq=0.1

ptthreads

Sets the number of outer OpenMP threads in program ccsd while calculating the (T) correction.

Options:

any positive integer$\mathrm{>}$

Default:

ptthreads=2

Example:

to reduce the memory requirement of a CCSD(T) calculation by turning off nested OpenMP parallelization set ptthreads=1

qmmm

This keyword tells Mrcc that a QM/MM calculation is performed and the point charges included in the input file must be processed. This keyword is automatically added to the MINP file by the MM program conducting the QM/MM calculations, and you do not need to bother with it. Use this keyword in the only case if you want to add point charges manually.

Options:

off

QM/MM calculation is not performed and no point charges are added.

Amber

Currently this is the only option, the Amber MD code will be used for the QM/MM calculation or point charges will be added.

Note:

Point charges can be manually added to the end of the input file in the following format:
pointcharges
number of point charges$\mathrm{>}$


 ⋮
where $x_i$, $y_i$, and $z_i$ are the Cartesian coordinates and $q_i$ is the charge for point charge $i$. The charge must be given in a.u., while for the coordinates the same unit must be used as for the specification of the molecular geometry.

Default:

qmmm=off

Example:

to add two point charges with coordinates (0, 0, 1) and (0, 1, 0) a.u. (provided that the geometry is also given in bohr) and charges of 0.5 and -0.5 a.u. qmmm=Amber should be set anywhere in the MINP file, and the following lines should be added to the end the file:
pointcharges
2
0.0 0.0 1.0 0.5
0.0 1.0 0.0 -0.5

qro

Switches on the computation of quasi-restricted orbitals (QROs) determined from UHF/UKS orbitals [QRO, ROLocalMP2]. QROs are useful for the cases where the convergence of the ROHF/ROKS iterations is problematic but restricted open-shell orbitals are desired/needed, such as in the case of our open-shell local correlation methods. The starting point of determining the QROs is an UHF/UKS solution, which may be simpler to find than the ROHF/ROKS one. The QROs are constructed as the eigenvectors of the total density matrix of the unrestricted computation [QRO, ROLocalMP2]. The QROs obtained in this way with occupation numbers close to 2, 1, and 0 are selected to be doubly, singly, and not occupied in the QRO determinant, respectively, which becomes an eigenfunction of ${\widehat{S}}^2$ by construction.

Options:

on or off

Default:

qro=on for localcc$\mathrm{\ge }$2021 and UHF/UKS computation, and qro=off otherwise.

Note:

The scfguessdens=uhf option can also be useful to utilize satisfactory UHF/UKS densities for the initial guess construction of ROHF/ROKS computations.

qscf

Use this option to carry out quadratic RHF, UHF, ROHF, RKS, and UKS SCF calculations and also to select the algorithm used for MCSCF calculations. One can use either (quasi-)Newton or trust region iterations with optional line search.

Options:

off

No quadratic SCF, conventional SCF algorithm will be

on

Equivalent to AugHessG executed.

Newton

Simple Newton iteration.

NewtonL

Simple Newton iteration with line search.

AugHess

Trust region method with augmented Hessian algorithm without line search. The trust radius is updated according to the scheme described in Ref. 51.

AugHessM

Trust region method with augmented Hessian algorithm using line search. The trust radius update scheme is similar to the above one but uses different coefficients.

AugHessL

Trust region method with augmented Hessian algorithm using line search. The trust radius is updated as described in Ref. 51, but this method takes into account the step length found by the line search.

AugHessG

Trust region method with augmented Hessian algorithm using line search. The trust radius update scheme takes into account the change of the gradient in the consecutive iterations.

BFGS

Quasi-Newton method utilizing the BFGS algorithm (see also keywords bfgsmem and bfgstol).

Note:

The simple (quasi-)Newton iteration schemes are only efficient in the vicinity of a minimum and not recommended in the general case. We recommend the use of the AugHessG or AugHessL options in difficult cases.

Default:

qscf=AugHessG for MCSCF calculations, qscf=off otherwise

Example:

UKS calculation with the B3LYP functional using the AugHessG algorithm:
calc=B3LYP
scftype=UHF
qscf=AugHessG

redcost_exc

This keyword controls the cost reduction approaches based on natural orbital (NO) and natural auxiliary function (NAF) techniques for excited states. For a (spin-scaled) CIS(D${}_{\mathrm{\infty }}$), ADC(2), and CC2 calculation, if redcost_exc$\mathrm{\ne }$off, the reduced-cost approach of Refs. 93 and 94 is invoked, and truncated state-averaged MP2/CIS(D) NOs as well as NAFs will be used. The lnoepso, lnoepsv, naf_cor, and naftyp keywords will be automatically set depending on the selected option for redcost_exc. For CIS, TD-HF, TDA, TD-DFT calculations the NAF approximation will be invoked if redcost_exc=8.

Options:

off

The cost reduction techniques will not be used.

on

Reduced-cost calculation will be executed with default settings (see also Table LABEL:RedCostTab).

cust

Reduced-cost calculation will be executed with customized truncation thresholds. The threshold for the complete MO space NAFs (CS-NAFs), CIS coefficients, orbital energies, and linear dependency must be specified in the subsequent line, respectively, as
threshold 1$\mathrm{>}$ threshold 2$\mathrm{>}$ threshold 3$\mathrm{>}$ threshold 4$\mathrm{>}$
The default values of these thresholds are 0.1 a.u., 0.35, 0.15 a.u., ${10}^{-7}$, respectively. These are used with if any other option is chosen. See Ref. 94 for the detailed description of these parameters.

positive integers from 1 to 10$\mathrm{>}$

See Table LABEL:RedCostTab.

Default:

redcost_exc=off

Examples:

1.

Reduced-cost ADC(2) calculation for the lowest singlet excited state with the default settings proposed in Ref. 94:
calc=ADC(2)
nsing=2
redcost_exc=on

2.

Reduced-cost TD-DFT calculation with the PBE0 functional for the lowest 3 singlet excited states of a molecule:
calc=PBE0
redcost_exc=8
nstate=4

redcost_tddft

This keyword controls the use of local fitting domains for reduced-scaling density fitting CIS, TD-HF, and TD-DFT calculations. See Ref. 91 for more details.

Options:

off

The scaling reduction techniques will not be used.

on

Reduced-scaling calculation will be executed with a completeness criterion of 0.985 for the wave function truncation.

any real number in the [0,1] interval$\mathrm{>}$

This number will be used as the completeness criterion.

Default:

redcost_tddft=off

Example:

to set a completeness criterion of 0.99 type redcost_tddft=0.99

refdet

The reference determinant (Fermi-vacuum) for CI/CC calculations can be specified using this keyword. By default the reference determinant is identical to the HF determinant, but sometimes it is necessary to change this.

Options:

none

The reference determinant is identical to the HF determinant.

serialno

Using this option one can define the occupation of the correlated orbitals in the reference determinant specifying their serial numbers. This option requires three more lines. In the first line the serial numbers of the doubly-occupied orbitals must be given, while in the second and third lines those orbitals should be specified which are singly-occupied by an alpha or a beta electron, respectively. For the format of these lines see the description of the serialno option of the active keyword. For relativistic calculations the occupation of the spinors (i.e., not that of the Kramers-pairs) should be given. For technical reasons all electrons are treated as alpha electrons and the serial numbers of the occupied spinors must be given in the second line, the first and third lines must be left blank.

vector

Using this option one can set the occupation numbers for each correlated orbital. In the subsequent line an integer vector should be supplied with as many elements as the number of correlated orbitals (correlated spinors for relativistic calculations, not Kramers-pairs!). The integers must be separated by spaces. In the case of non-relativistic calculations type 2 for doubly-occupied orbitals, 1 for open-shell orbitals with alpha electron, -1 for open-shell orbitals with beta electron, 0 otherwise. In the case of relativistic calculations type 1 for each occupied spinor, 0 otherwise.

Notes:

1.

Frozen orbitals must not be considered here in any case.

2.

If the MO integrals are taken over from another program, the numbering of orbitals may be different from that of the parent program. Here the order of MOs: doubly occupied, open shell, virtual; and in each of this blocks the MOs are reordered according to the orbital energies (natural orbital occupations in the case of active MCSCF orbitals).

3.

If the MO integrals are taken over from another program, and this line is omitted, the program will fill the orbitals with electrons from the bottom automatically. In this manner we do not need this line for closed shells or a doublet reference determinant, but, e.g., for high-spin states the Fermi vacuum must be defined here.

4.

For relativistic calculations (Dirac interface) this line is always required. The spinors are symmetry-blocked according to the Fermion irreps of the corresponding double group. Complex conjugate irreps follow each other. Within each irrep the spinors are numbered according to orbital energies. Please note that this line is automatically printed by the dirac_mointegral_export program, and you do not have to do it by hand. However, for technical reasons, always a closed-shell occupation is generated, and you may need to remove or add some electrons.

Default:

refdet=none, that is, the reference determinant is identical to the HF determinant.

Examples:

1.

We have 20 correlated orbitals, 10 electrons, and we are interested in a high-spin triplet state. Suppose that orbitals 1 to 4 are doubly-occupied while orbitals 5 and 6 are singly occupied by alpha electrons. Using the serialno option the input should include the following four lines (note the blank line at the end):
refdet=serialno
1-4
5,6

2.

The same using the vector option:
refdet=vector
2 2 2 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0

3.

We perform a relativistic calculation for the Be atom with 20 correlated spinors. We have 6, 6, 4, and 4 spinors in the four Fermion irreps, E${}_{1/2g}$, E${}_{-1/2g}$, E${}_{1/2u}$, and E${}_{-1/2u}$ of the $C_{2h}^{*}$ double group, respectively, and two occupied spinors in both of the gerade irreps. Thus using the vector option the occupation vector should be given as:
refdet=vector
1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0

4.

The same using the serialno option (note the blank lines):
refdet=serialno

1,2,7,8

rest

Use this keyword to restart canonical (i.e., not local) CI and CC calculations from previously calculated wave function parameters (cluster amplitudes, CI coefficients, $\lambda$ amplitudes, etc.) if ccprog=mrcc. For restarting local correlation calculations see keyword lccrest.

Options:

1

The program restarts from the previously calculated parameters.

2

The program executes automatically the lower-level calculations of the same type consecutively (e.g., CCSD, CCSDT, and CCSDTQ if CCSDTQ is requested) and restarts each calculation from the previous one (this is only available for energy calculations).

3

Same as rest=1, however, only selected roots from the previous calculation will be used as initial guess. The serial number of the roots must be specified in the subsequent line as

where is the serial number of the states. The number of states given here must be equal to nstate or nsing + ntrip. Please note that the ground state solution is not automatically selected, it should also be given here if needed. It is recommended to use root following (diag=follow) together with this option.

4

Same as rest=2 but the initial vectors are selected as in the case of rest=3.

Notes:

use the restart option, e.g.,

1.

after system crash.

2.

if the iteration procedure did not converge in the given number of steps.

3.

for geometry optimization.

4.

for potential curve calculations.

5.

if you are interested in high-order CC/CI energies. Then it is worth restarting the calculations with higher excitations using the converged vectors of the same method including lower excitations, e.g., CCSDT using the converged CCSD amplitudes, CCSDTQ using the CCSDT amplitudes, and so on. With this trick 1-3 iteration steps can be saved usually, but more ones in the case of strong static correlation (i.e., large cluster amplitudes). Use exclusively rest=2 for this purpose (that is, not rest=1)!

6.

if you are interested in calculating the energies for all methods in a hierarchy (e.g., executing all CC methods up to CCSDTQP). Use exclusively rest=2 for this purpose (that is, not rest=1)!

7.

to generate brute-force initial guess for excited-state calculations (rest=3 or 4). That is, if you do not want to bother with the initial guess for excited states, but you know approximately the energy of the excited states, then execute a low-level method for many roots. Use LR-CCS (calc=CCS) and CIS (calc=CIS), respectively, for higher-order LR-CC and CI calculations. Select the desired roots on the basis of their energies, and use them as initial guess in high-level calculations. (For other options for the initial guess for excited-state calculations see keyword ciguess.)

8.

Please note that the program always needs the file fort.16 from the previous calculation for the restart and also fort.17, if more than one root is sought or for geometry optimization.

Default:

rest=0

Examples:

1.

to restart a CC calculation after power failure set rest=1

2.

to restart a LR-CCSD calculation using the first, third, and fifth roots of a previous LR-CCS calculation the input should include the following two lines:
rest=3
1 3 5

rgrid

Specifies the radial integration grid for DFT calculations. See also the description of keywords grid, agrid, and grtol.

Options:

Log3

the Log3 quadrature of Mura and Knowles [103]

GC

Gauss–Chebyshev quadrature. A modified version of the mapping function of Ref. 77 is employed: the function is scaled by the atomic scaling parameters of Becke [6].

GCTA

Gauss–Chebyshev quadrature of Treutler and Ahlrichs (M4 quadrature of Ref. AhlrichsGrid)

EM

Euler–Maclaurin quadrature [104]

Note:

For the grids of Treutler–Ahlrichs (grid=TA*), the number of grid points is fixed (see Ref. AhlrichsGrid). Otherwise, the number of grid points is calculated by the
max{20, 5*(3*grtol/2+$i$+10)} formula with $i$ as the number of the row in the periodic table where the atom is located [77]. To change the number of radial integration points, set the value of grtol. If an adaptive grid is used (see keyword grid), the number of radial grid points is determined automatically so that the error in the radial integrals will not be larger than ${10}^{1-\mathrm{𝚐𝚛𝚝𝚘𝚕}}$. In this case, the above value is just the maximum allowed number of points.

Default:

rgrid=Log3

Examples:

1.

to use the Euler–Maclaurin scheme set rgrid=EM

2.

to use the default Log3 grid with more points set grtol=12

rism

Specifies the 3D-RISM settings of an EC-RISM calculation.

Options:

off

No EC-RISM calculation.

on

EC-RISM with default settings (TIP3P water, PSE-3 closure, gridspace=0.3 Å, buffer=15 Å, CHELPG charge, see Ref. RISM for further details).

any options of the rism3d.snglpnt program$\mathrm{>}$

Other 3D-RISM settings can be used by simply passing the rism3d.snglpnt commands to this keyword. For example, the above default setting written in this mode is rism=--xvv
solvent.xvv --grdspc 0.3,0.3,0.3 --tolerance 1E-5 --closure pse3
--buffer 15 --maxstep 10000, where solvent.xvv is the solvent susceptibility file provided by the user from an earlier 1D-RISM calculation with TIP3P water and PSE-3 closure. The --pdb, --prmtop, --rst, --volfmt, --chgdist, --pc+, and --gf settings are automatically set by Mrcc, and passing them to the keyword could cause problems. --xvv must be defined in these cases, while the --closure, --grdspc, and --buffer settings should be considered, because these can alter the results substantially. See the AmberTools manual for further details on the various rism3d.snglpnt settings.

Default:

rism=off

Notes:

1.

If rism$\mathrm{\ne }$off, and no espcharge is specified, espcharge=chelpg is the default setting.

2.

The solvent susceptibility file (solvent.xvv) can be created by modifying the automatically created rism1d input of a default EC-RISM run (solvent.inp). In this case, an mdl file of the solvent is required, either from the Amber library or from the user. See the AmberTools manual for further details on the solvent susceptibility file preparation with rism1d.

3.

The EC-RISM calculation can be restarted by providing an ATCHARGE.GUESS file, containing only the corresponding atomic charges in one column. In this case, for the first 3D-RISM calculation, the provided charges will be used, not the ones determined from the gas-phase calculation.

4.

If the studied system has atoms without GAFF2 force field parameters, you must provide a file called FRCMOD which contains the missing Lennard–Jones parameters by listing each atom with their van der Waals radius ($r*$) and well-depth ($ϵ$). Here is an example for the file structure (the values are not recommendations):
NONBON
Si 1.778 0.015
Fe 1.800 0.010

Examples:

1.

to use EC-RISM with default settings give rism=on

2.

to use EC-RISM with Kovalenko–Hirata closure (KH), ethanol solvent (ethanol.xvv), 10 Å buffer and 0.5 Å gridspace set rism=-xvv ethanol.xvv --closure KH --buffer 10 --grdspc 0.5,0.5,0.5, where the solvent susceptibility file of the ethanol (ethanol.xvv) is in the same folder as the MINP file.

rohfcore

Specifies the type of the frozen ROHF or ROKS orbitals if rohftype=semicanonical and core=frozen. See also the description of keyword rohftype.

Options:

standard

The orbitals will be frozen before the semi-canonicalization of the orbitals, that is, standard ROHF (ROKS) orbitals will be frozen.

semicanonical

The orbitals will be frozen after the semi-canonicalization of the orbitals, that is, semicanonical ROHF (ROKS) orbitals will be frozen.

Notes:

1.

For ROHF-based correlation calculations Cfour and Molpro use semicanonical and standard frozen orbitals, respectively. If you want to compare the results computed with Mrcc to those obtained with the above programs, use this keyword to select the same type of frozen ROHF orbitals.

2.

In the case of local correlation calculations standard ROHF (ROKS) orbitals are frozen for theoretical reasons. If results of local and canonical correlation calculations are compared, standard ROHF (ROKS) orbitals should be frozen in the canonical calculations as well.

Default:

rohfcore=standard for local correlation calculations,
rohfcore=semicanonical otherwise.

Example:

to use standard ROHF core orbitals for canonical correlation methods set rohfcore=semicanonical

rohftype

Specifies the type of the ROHF or ROKS orbitals. See also the description of keyword scftype.

Options:

standard

Standard ROHF (ROKS) orbitals obtained by diagonalizing the ROHF (ROKS) Fock-matrix.

semicanonical

Semicanonical ROHF (ROKS) orbitals obtained by separately diagonalizing the alpha and beta UHF (UKS) Fock-matrices constructed using the converged ROHF (ROKS) orbitals.

Notes:

1.

rohftype=semicanonical is required for perturbative CC methods if ROHF orbitals are used, otherwise the expressions for the perturbative corrections are not correct. Iterative CC and CI methods are invariant to the choice of ROHF orbitals (if all electrons are correlated).

2.

It is very important to give this keyword if Mrcc is used together with another code and ROHF orbitals are used since this keyword tells Mrcc what type of ROHF orbitals are taken over from the other code.

Default:

for ccprog=ccsd rohftype=semicanonical; for ccprog=mrcc
rohftype=standard for iterative CC and CI methods,
rohftype=semicanonical for perturbative methods.

Example:

to use semicanonical ROHF orbitals for iterative CC methods give
rohftype=semicanonical

scf_conv

Specifies the parameter set for SCF acceleration techniques, which includes Pulay’s DIIS algorithm, the level shifting of orbital energies, and the density matrix damping schemes. See also Table 3 for the specific parameters.

Options:

normal

initiates the normal set of SCF acceleration parameters

fast

initiates the fast set of SCF acceleration parameters

Table 3: Parameter table for SCF acceleration techniques

Keyword	fast	normal (DFT)	normal (HF)
scfdiis_start	2	2	2
scfdiis_end	scfmaxit	scfmaxit	scfmaxit
scfdiis_dtol	0.2	0	0
scfdiis_watch	off	off	off
scfext	10	10	10
scfdiis_step	1	1	1
scfdamp_mode	3	1	off
scfdamp	0.5	0.7	0
scfdamp_maxfact	0.9	0.7	0
scfdamp_minfact	0.1	0.7	0
scfdamp_dampstep	0.1	0	0
scfdamp_dtol	0.5	0	0
scfdamp_end	scfmaxit	3	scfmaxit
scflshift	0.1	0.2	0.2
scflshift_gaptol	0.1	0.2	0.2
scflshift_dtol	1d-2	0	0
scflshift_end	scfmaxit	8	8

Notes:

1.

In the case of scf_conv=normal, damping is turned off for Hartree–Fock calculations.

2.

The SCF acceleration parameters can be overwritten manually by specifying the above keywords regardless of the options of scf_conv.

Default:

scf_conv=normal

Example:

if the SCF convergence may be less problematic to reach, type scf_conv=fast

scfalg

Specifies what type of SCF algorithm is to be used.

Options:

disk

Conventional SCF algorithm, two-electron integrals are stored on disk.

direct

Direct SCF algorithm, two-electron integrals are recalculated in each iteration step.

auto

Based on the size and geometry of the molecule the program will automatically select the more efficient one from the above options.

locfit1

Density-fitting direct SCF algorithm using local fitting domains for the exchange contribution [127, 107]. See also keyword excrad.

locfit2

Same as locfit1 but, in addition to the auxiliary functions, domains are also constructed for the AOs and MOs. This is efficient only for very large molecules.

Default:

scfalg=auto

Notes:

In the case of locfit1 and locfit2 calculations, the orbital localization method can be specified with the scfloc keyword.

Example:

to run direct SCF, add scfalg=direct

scfdamp

Specifies whether damping of the SCF density matrices is performed.

Options:

off

No damping.

any real number in the [0,1] interval$\mathrm{>}$

In each SCF iteration cycle the new and old SCF density matrices are mixed by factors (1-scfdamp) and scfdamp, respectively.

on

Equivalent to scfdamp=0.7

Default:

scfdamp=off for Hartree–Fock, and scfdamp=0.7 for DFT calculations, and scfdamp=0.7 when a damping scheme is specified using scfdamp_mode.

Notes:

In the case of dynamic dampig schemes (scfdamp_mode=2 or scfdamp_mode=3), the keyword scfdamp sets the initial damping factor.

Example:

to use a damping factor of $0.8$ type scfdamp=0.8

scfdamp_dtol

Specifies the tolerance in the RMS of the difference density matrix where the SCF damping is turned off. See also the notes for scfdamp_mode if scfdamp_end is used with scfdamp_dtol.

Options:

any positive real number$\mathrm{>}$ or 0

Default:

scfdamp_dtol=0, that is, the SCF damping is independent of the RMS of the difference density matrix.

Example:

to use a density-dependent damping approach, set scfdamp_dtol=1d-3, which means that the density damping is switched off when the RMS of difference density matrix is below 1d-3.

scfdamp_dampstep

Specifies the constant change in scfdamp if scfdamp_mode=2 or scfdamp_mode=3 is used.

Options:

any positive real number$\mathrm{>}$ or 0

Default:

scfdamp_dampstep=0, that is, scfdamp is not changed in any iteration. If scfdamp_mode=2 or scfdamp_mode=3, then scfdamp_dampstep=0.05

Example:

to use larger steps in the scfdamp, type scfdamp_dampstep=0.1

scfdamp_end

Specifies the last iteration step in which the SCF damping is applied. See also the notes for scfdamp_mode if scfdamp_end is used with scfdamp_dtol.

Options:

any positive integer$\mathrm{>}$

Default:

scfdamp_end=3 for DFT calculations, that is, the SCF damping is turned off after the third SCF iteration, scfdamp_end=scfmaxit otherwise.

Example:

to turn off the SCF damping after iteration step 20, give scfdamp_end=20

scfdamp_minfact

Specifies the smallest value that scfdamp can take if scfdamp_mode=2 or scfdamp_mode=3 is used.

Options:

any real number in the [0,scfdamp] interval$\mathrm{>}$

Default:

scfdamp_minfact=scfdamp in the case of scfdamp_mode=1, that is, an unchanged damping factor for the static damping approach. If a dynamic damping scheme is specified (scfdamp_mode=2 or scfdamp_mode=3), then scfdamp_minfact=0.1, that is, scfdamp cannot take a smaller value than 0.1.

Example:

to use a minimum factor for scfdamp, type scfdamp_minfact=0.2

scfdamp_maxfact

Specifies the largest value that scfdamp can take if scfdamp_mode=2 or scfdamp_mode=3 is used.

Options:

any real number in the [scfdamp,1.0] interval$\mathrm{>}$

Default:

scfdamp_maxfact=scfdamp in the case of scfdamp_mode=1, that is, an unchanged damping factor for the static damping approach. If a dynamic damping scheme is specified (scfdamp_mode=2 or scfdamp_mode=3), then scfdamp_maxfact=0.95, that is, scfdamp cannot take a larger value than 0.95.

Example:

to restrict the scfdamp parameter to a smaller maximum value in the case of dynamic damping, type scfdamp_maxfact=0.85

scfdamp_mode

Specifies which SCF damping scheme is performed.

Options:

off

No damping.

1

Static damping. The damping factor set by scfdamp is unchanged in any iterations.

2

Steadily decreasing damping scheme. The damping factor, which is initialized by scfdamp, is decreased by scfdamp_dampstep in every iteration if the RMS of the gradient decreases. The smallest possible damping factor is scfdamp_minfact.

3

Dynamically adjusted damping scheme. The damping factor, which is initialized by scfdamp, is increased by scfdamp_dampstep if the RMS of the gradient increases and it is decreased otherwise by the same magnitude. The damping factor cannot take a larger value than scfdamp_maxfact or a lower one than scfdamp_minfact.

on

Equivalent to scfdamp_mode=3

Notes:

1.

The damping schemes are applied from the first iteration. The damping can be turned off by specifying an iteration step (scfdamp_end), or using a tolerance in the RMS of difference density matrix (scfdamp_dtol).

2.

If scfdamp_end and scfdamp_dtol are used together, damping is activated if the iteration number is lower than scfdamp_end or the RMS of difference density is larger than scfdamp_dtol.

3.

Note that when scfdamp_mode=3 and scfdamp_dtol is set, the damping can be switched on again if a larger change in the density matrix occurs. When the damping is re-activated, scfdamp is set to scfdamp_minfact. The re-activation of the damping of the SCF density matrix is forbidden in the case of scfdamp_mode=1 and scfdamp_mode=2.

Default:

scfdamp_mode=1 for DFT, and scfdamp_mode=off for HF calculations, respectively.

Example:

to use a steadily decreasing damping factor, set scfdamp_mode=2

scfdiis

Specifies if DIIS convergence acceleration is used in the SCF calculations.

Options:

on or off

Default:

scfdiis=on

Example:

to turn off DIIS convergence accelerator add scfdiis=off

scfdiis_delmax

Specifies the number of times when the DIIS error vector is allowed to be deleted (i.e., the DIIS is restarted) by the scfdiis_watch algorithm. See also the description of scfdiis_watch.

Options:

any positive integer$\mathrm{>}$

Default:

scfdiis_delmax=2, that is, scfdiis_watch turns off if the DIIS error vectors have already deleted twice.

Example:

to increase the allowed number of DIIS restarts, type scfdiis_delmax=5

scfdiis_dtol

Specifies the tolerance in the RMS of difference density matrix when the DIIS convergence acceleration is turned on. Note that scfdiis_start has higher priority.

Options:

any positive real number$\mathrm{>}$ or 0

Default:

scfdiis_dtol=0, that is, the DIIS procedure is independent from the RMS of difference density matrix.

Notes:

Once the RMS of the difference density is lower than scfdiis_dtol, the DIIS procedure is applied and it is not switched off even if the SCF density matrix changes significantly.

Example:

to turn on the DIIS convergence accelerator after the deviation of the density matrix is small, type scfdiis_dtol=1d-3

scfdiis_end

Specifies the last iteration step in which the DIIS convergence acceleration is applied.

Options:

any positive integer$\mathrm{>}$

Default:

scfdiis_end=scfmaxit, that is, the DIIS procedure is not turned off.

Example:

to turn off the DIIS convergence accelerator after iteration step 20 give
scfdiis_end=20

scfdiis_start

Specifies the first iteration step in which the DIIS convergence acceleration is applied.

Options:

any positive integer$\mathrm{>}$

Default:

scfdiis_start=2, that is, the DIIS procedure is active from the second iteration.

Example:

to turn on the DIIS convergence accelerator in iteration step 5 give
scfdiis_start=5

scfdiis_step

Specifies the frequency of DIIS extrapolations. The extrapolation will be carried out in every scfdiis_step’th iteration cycle.

Options:

any positive integer$\mathrm{>}$

Default:

scfdiis_step=1, that is, the DIIS extrapolation is performed in each iteration step.

Example:

to carry out DIIS extrapolation only in every second iteration step give
scfdiis_step=2

scfdiis_watch

Specifies if the DIIS error vectors are deleted when the DIIS error raises at least scfdiis_wlimit times in the previous scfdiis_wrange iterations. Note that the deletion of error vectors can happen at most scfdiis_delmax times.

Options:

off

The DIIS error vectors will not be deleted.

on

The DIIS error vectors will be deleted if the above conditions are met.

Default:

scfdiis_watch=off

Example:

to turn on the DIIS error watch algorithm type scfdiis_watch=on

scfdiis_wlimit

Specifies the number of times when the DIIS error is allowed to rise in the previous scfdiis_wrange iterations before the vectors are deleted if scfdiis_watch=on.

Options:

any positive integer$\mathrm{>}$

Default:

scfdiis_wlimit=scfext/2 if scfext is an even number and
scfdiis_watch=(scfext+1)/2 otherwise.

Example:

to increase the number of iterations in which the DIIS error is allowed to raise, type scfdiis_wlimit=20

scfdiis_wrange

Specifies the number of SCF iterations in which the DIIS error is checked by the “scfdiis_watch” algorithm.

Options:

any positive integer$\mathrm{>}$

Default:

scfdiis_wrange=scfext

Example:

to increase the number of iterations in which the DIIS error is checked by the scfdiis_watch algorithm, type scfdiis_wrange=15

scfdtol

Convergence threshold for the density matrix in SCF calculations. The RMS change in the density matrix will be smaller than ${10}^{-\mathrm{𝚜𝚌𝚏𝚍𝚝𝚘𝚕}}$.

Options:

any integer$\mathrm{>}$

Default:

scfdtol=scftol+2 for frequency calculations, otherwise
scfdtol=scftol+1 for correlation calculations, scfdtol=scftol for SCF calculations

Example:

for an accuracy of ${10}^{-8}$ one must give scfdtol=8

scfext

Specifies the maximum number of Fock-matrices used for the DIIS extrapolation in SCF calculations.

Options:

any positive integer$\mathrm{>}$

Default:

scfext=10

Example:

to increase the maximum number of DIIS vectors to 15 give scfext=15

scfguessdens

Communicates the format of the initial guess density stored in the
SCFDENSITIES file, which is used for scfiguess=restart. Upon the completion of the SCF job step in the cases of unrestricted SCF computations and restricted open-shell SCF computations followed by the construction of semi-canonical orbitals, the SCFDENSITIES file format is different from that of standard restricted open-shell computations. The scfguessdens keyword can be used to perform a restricted open-shell SCF computation using the density matrices of an unrestricted computation in the SCFDENSITIES file as an initial guess and vice versa.

Options:

uhf

The program assumes for scfiguess=restart that the SCFDENSITIES file is a result of an unrestricted SCF job.

rhf

The program assumes for scfiguess=restart that the SCFDENSITIES file is a result of a restricted SCF job.

rohfscn

The program assumes for scfiguess=restart that the SCFDENSITIES file is a result of a restricted open-shell computation ended with the construction of semi-canonical orbitals.

rohfstd

The program assumes for scfiguess=restart that the SCFDENSITIES file is a result of a standard restricted open-shell computation (without the construction of semi-canonical orbitals).

Default:

scfguessdens is not set by default assuming that the SCFDENSITIES file structure is the same for the job that produced the initial guess density and the job to be restarted from that initial guess density.

scfiguess

Initial guess for the SCF calculation.

Options:

sad

Superpositions of atomic densities. For each atom a density-fitting UHF calculation is performed, and the initial one-particle density matrix is constructed from the averaged alpha and beta atomic densities.

ao

Atomic density initial guess. The initial one-particle density matrix is constructed from diagonal atomic densities derived from the occupation of the atoms. It is efficient for Dunning’s basis sets.

core

Core Hamiltonian initial guess. The initial MOs are obtained by diagonalizing the one-electron integral matrix.

mo

The SCF calculation will use the MO coefficients obtained in a previous calculation and stored in the MOCOEF file. The calculation can only be restarted from the MOs computed with the same basis set.

restart

The SCF calculation will use the density matrices obtained in a previous calculation and stored in the SCFDENSITIES file. If the calculation is restarted from the densities obtained with another basis set, the VARS file is also required. See also note 1 below.

off

No SCF calculation will be performed, but the Fock-matrix and the MO coefficients obtained in a previous calculation will be used in the correlation calculations. This requires the FOCK, MOCOEF, and VARS files from the previous calculation. See also note 1 below.

min

A density fitting SCF calculation will be performed using the cc-pVTZ-min minimal basis set (see the description of keyword basis), and the resulting density will be used as initial guess. In the minimal-basis SCF calculation the AO basis set is used as the auxiliary basis, and loose convergence thresholds are employed, consequently, the energy is unreliable and should not be used for any purpose.

small

A density fitting SCF calculation will be performed using a smaller basis set which must be specified by keyword basis_sm (see the description of keyword basis_sm), and the resulting density will be used as initial guess.

gfn1

A GFN1-xTB calculation will be performed if the xTB program is available, and the resulting density is used as an initial guess for the valence electrons. The sad technology is utilized to get an initial guess for the core electrons.

gfn2

It is the same as gfn1, except that a GFN2-xTB is used by the xTB program.

Notes:

1.

If your SCF calculation is killed for some reason, e.g., by a power failure, but if you have all the files created by the program, you can simply continue the SCF calculation. To that end you should just execute program scf in the directory where Mrcc was running. The SCF program will continue from the iteration step where it crashed. If you also want to run a post-SCF calculation, just restart the entire run with scfiguess=off after the SCF has converged.

2.

Restarting from densities obtained with a bigger basis set is not allowed.

3.

To restart SCF runs from the results of DFT embedding calculations with the Huzinaga-equation- or projector-based approaches use MO coefficients, i.e.,
scfiguess=mo, since only the subsystem densities are stored at the end of the embedding calculation but the MOs are available for the entire system.

Default:

scfiguess=sad

Examples:

1.

For a core Hamiltonian initial guess set scfiguess=core

2.

For restarting the SCF calculation from the results of a calculation performed with the same basis set type scfiguess=restart. Note that you need the SCFDENSITIES file from the previous run.

3.

You would like to generate a good initial guess for an aug-cc-pVTZ SCF calculation. First, run a calculation with the cc-pVTZ basis set (cc-pVTZ-min is also a good option), that is, your input file should contain the
basis=cc-pVTZ
line. Then, restart your aug-cc-pVTZ calculation from the cc-pVTZ density matrix. To that end the MINP file should include the following lines:
basis=aug-cc-pVTZ
scfiguess=restart
Note that the SCFDENSITIES and the VARS files from the cc-pVTZ run must be copied to the directory where the aug-cc-pVTZ calculation is executed.

4.

The calculations in the previous example can be run more simply, in one step using the small option and the basis_sm keyword as
basis=aug-cc-pVTZ
basis_sm=cc-pVTZ
scfiguess=small

scfloc

Specifies the localization type used for local density fitting SCF calculations. For more information on local SCF calculations, see the scfalg keyword.

Options:

boys

Boys–Foster localization.

pm

Pipek–Mezey localization with Löwdin charges.

pmm

Pipek–Mezey localization with Mulliken charges.

gboysm$\mathrm{>}$

generalized Boys localization by Jansík et al. [58], where $m$ is a positive integer defining the power of orbital variance. Note that for $m=1$, the Boys localization is retrieved.

Default:

scfloc=pm

Example:

to use Boys localization in the SCF cycles, set scfloc=boys

scflshift

Level shift parameter for the SCF calculation.

Options:

off

No level shifting.

any real positive number $\mathrm{>}$

The value of the level shift parameter in a.u.

on

Equivalent to scflshift=0.2

Default:

scflshift=0.2

Notes:

• 1.

  scflshift is turned off in the first diagonalization by default.

• 2.

  scflshift_gaptol and scflshift_end have equal priority in shutting down level shifting. This means that the HOMO-LUMO gap has to be smaller than scflshift_gaptol and the iteration number has to be lower than scflshift_end to perform level shifting. However, if the HOMO-LUMO gap is lower than scflshift_gaptol and the iteration number is lower than scflshift_end, the level shifting is still switched off if the RMS of difference density is lower than scflshift_dtol.

Example:

To use a level shift value of 0.5 a.u. give scflshift=0.5

scflshift_dtol

Specifies the tolerance in the RMS of the difference density matrix where the SCF level shifting is turned off.

Options:

any positive real number$\mathrm{>}$ or 0

Default:

scflshift_dtol=0, that is, the SCF level shifting is independent of the RMS of the difference density matrix.

Note:

the scflshift_dtol criterion of level shifting is only checked if the HOMO-LUMO gap is smaller than scflshift_gaptol and the number of SCF iterations is lower than scflshift_end.

Example:

to use a level shifting scheme that depends on the RMS of the difference density matrix, set scflshift_dtol=1d-4, that is, the level shifting is turned off after the RMS of difference density is lower than 0.0001 (regardless of the iteration step and the HOMO-LUMO gap).

scflshift_end

Specifies the last iteration step in which the SCF level shifting is applied.

Options:

any positive integer$\mathrm{>}$

Default:

scflshift_end=8, that is, the SCF level shifting is turned off after iteration step 8.

Notes:

scflshift_gaptol and scflshift_end have equal priority in shutting down level shifting. See also scflshift_dtol and the notes of scflshift for more details.

Example:

to turn off the SCF level shifting after iteration step 20, give scflshift_end=20

scflshift_gaptol

Specifies the tolerance (in a.u.) in the gap between the HOMO and the LUMO where the SCF level shifting is turned off.

Options:

any positive real number$\mathrm{>}$ or 0

Default:

scflshift_gaptol=0.2, that is, the SCF level shifting is turned off after the HOMO-LUMO gap is larger than the given value.

Notes:

• 1.

  scflshift_gaptol and scflshift_end have equal priority in shutting down level shifting. See also scflshift_dtol and the notes for scflshift for more details.

• 2.

  scflshift_gaptol=0 means that the level shifting scheme is independent of the HOMO-LUMO gap.

• 3.

  scflshift_gaptol allows dynamic level shifting, i.e., when the HOMO-LUMO gap is larger than scflshift_gaptol, the level shifting will be switched off, while it is re-activated if the gap becomes lower than scflshift_gaptol (note that the re-activation can be inhibited with scflshift_dtol and scflshift_end).

Example:

to increase the gap criteria to turn the level shifting on type scfdamp_gaptol=0.3

scfmaxit

Maximum number of iteration steps in SCF calculations.

Options:

any positive integer$\mathrm{>}$

Default:

scfmaxit=50

Example:

to increase the maximum number of SCF iterations to 200 give scfmaxit=200

scftol

Convergence threshold for the energy in SCF calculations. The energy will be accurate to ${10}^{-\mathrm{𝚜𝚌𝚏𝚝𝚘𝚕}}$ E${}_h$.

Options:

any integer$\mathrm{>}$

Default:

scftol=max(8,cctol) for property calculations,
scftol=max(6,cctol) otherwise

Example:

for an accuracy of ${10}^{-8}$ E${}_h$ one must give scftol=8

scftype

Specifies the type of the Hartree–Fock/Kohn–Sham/MC SCF procedure, or the type of the molecular orbitals if the MO integrals are computed by other programs. See also the description of keyword rohftype.

Options:

RHF, ROHF, UHF, RKS, ROKS, UKS, or MCSCF

Notes:

1.

It is very important to give this keyword if Mrcc is used together with another code and ROHF or MCSCF orbitals are used since this keyword tells Mrcc that the orbitals are not canonical HF orbitals. Please also set keyword rohftype in this case.

2.

If an SCF calculation is run, the type of the SCF wave function can also be controlled by keyword calc. See the description of calc.

3.

The RKS, UKS, and ROKS options are synonyms for the RHF, UHF, and ROHF options, respectively. That is, for DFT calculations, the RHF, UHF, and ROHF options will instruct the code to run RKS, UKS, and ROKS calculations, respectively, and vice versa.

Default:

scftype=RHF for closed-shell systems, scftype=UHF for open shells.

Example:

to use ROHF or ROKS for open-shell systems type scftype=ROHF

scspe

Scaling factor for the higher-order terms in the dRPA equations for the sedRPA and seSOSEX methods of Ref. 100.

Options:

any real number$\mathrm{>}$

the higher-order terms in the dRPA equations will be scaled by this number.

Default:

scspe=0.8 for the sedRPA and seSOSEX methods, scspe=1.0 otherwise.

Example:

to set a scaling factor of 0.9 type scspe=0.9

scsph

Scaling factor for the higher-order terms in the energy expressions for the dsdRPA and dsSOSEX methods of Ref. 100.

Options:

any real number$\mathrm{>}$

the higher-order terms in the energy expressions will be scaled by this number.

Default:

scsph=0.85 for the dsdRPA and dsSOSEX methods, scsph=1.0 otherwise.

Example:

to set a scaling factor of 0.9 type scsph=0.9

scsps

Scaling factor for the antiparallel-spin component of the correlation energy in spin-scaled correlation calculations [SCS-MP2, SCS-CC2, SCS-CIS(D), SCS-CIS(D${}_{\mathrm{\infty }}$), SCS-ADC(2), SOS-MP2, SOS-CC2, SOS-CIS(D), SOS-CIS(D${}_{\mathrm{\infty }}$), SOS-ADC(2)] [39, 156].

Options:

any real number$\mathrm{>}$

the antiparallel-spin component of the correlation energy will be scaled by this number.

Notes:

1.

In the case of ground-state double hybrid DFT calculations, scsps is overwritten by the corresponding parameter of the DFT functional. To change this parameter, use dft=user or userd and set the value of MP2s. If an excited-state double hybrid DFT calculation is executed, the scaling factor for the antiparallel-spin component is calculated as MP2s*scsps when solving the excited-state equations.

2.

For SCS-CIS(D), in the case of the parameterization of Rhee and Head-Gordon [133], this scaling factor is used for the direct terms.

Default:

scsps=6/5 for the SCS methods, scsps=1.3 for the SOS approaches

Example:

to set a scaling factor of 1.5 type scsps=1.5

scsps_t

Scaling factor for the indirect terms with antiparallel-spin in SCS-CIS(D) calculations (see Ref. 133).

Options:

any real number$\mathrm{>}$

the indirect terms with antiparallel-spin will be scaled by this number.

Note:

In the case of the SCS-CC2 consistent analogue of the SCS-CIS(D) method [52], the direct and indirect terms are scaled by the same factor.

Default:

scsps_t=scsps

Example:

to set a scaling factor of 1.5 type scsps_t=1.5

scspt

Scaling factor for the parallel-spin component of the correlation energy in spin-scaled correlation calculations [SCS-MP2, SCS-CC2, SCS-CIS(D), SCS-CIS(D${}_{\mathrm{\infty }}$), SCS-ADC(2), SOS-MP2, SOS-CC2, SOS-CIS(D), SOS-CIS(D${}_{\mathrm{\infty }}$), SOS-ADC(2)] [39, 156].

Options:

any real number$\mathrm{>}$

the parallel-spin component of the correlation energy will be scaled by this number.

Notes:

1.

In the case of ground-state double hybrid DFT calculations, scspt is overwritten by the corresponding parameter of the DFT functional. To change this parameter, use dft=user or userd and set the value of MP2t. If an excited-state double hybrid DFT calculation is executed, the scaling factor for the parallel-spin component is calculated as MP2t*scspt when solving the excited-state equations.

2.

For SCS-CIS(D) and SOS-CIS(D), in the case of the parameterization of Rhee and Head-Gordon [133], this scaling factor is used for the direct terms.

Default:

scspt=1/3 for the SCS methods, scspt=0.0 for the SOS approaches

Example:

to set a scaling factor of 0.5 type scspt=0.5

scspt_t

Scaling factor for the indirect terms with parallel-spin in SOS-CIS(D) or SCS-CIS(D) calculations (see Ref. 133).

Options:

any real number$\mathrm{>}$

the indirect terms with parallel-spin will be scaled by this number.

Note:

In the case of the SCS-CC2 and SOS-CC2 consistent analogues of the SCS-CIS(D) and SOS-CIS(D) methods [52], the direct and indirect terms are scaled by the same factor.

Default:

scspt_t=scspt

Example:

to set a scaling factor of 0.5, type scspt_t=0.5

spairtol

Threshold for the selection of strong pairs in local MP2, dRPA, and CC methods. For each orbital pair an estimate of the pair correlation energy is calculated (see the description of keyword wpairtol). An orbital pair will be considered as strong pair if the absolute value of the pair correlation energy estimate is greater than spairtol. In the subsequent calculations strong pairs will be treated at a higher level, while for the other pairs (weak and distant) the corresponding pair correlation energy estimates will be added to the correlation energy. See also Refs. 72 and 108 for more details.

Options:

off

the local MP2 or dRPA pair correlation energy estimate is not calculated, an orbital pair will be considered as strong pair in this case if the absolute value of the available pair correlation energy estimate is greater than wpairtol. See also the description of keyword wpairtol and Ref. 107.

any positive real number$\mathrm{>}$

Orbital pairs with pair correlation energy estimates greater than this number (in E${}_h$) will be considered as strong pairs.

Default:

spairtol=1e-4 for localcc=2015, spairtol=off for localcc$\mathrm{\ge }$2016

Example:

to set a threshold of ${10}^{-5}$ E${}_h$ type spairtol=1e-5

sqmprog

Specifies the semi-empirical quantum chemistry program to be used for ONIOM calculations. See the description below for the supported methods and programs. Currently, it is not necessary to specify the keyword as Mrcc automatically checks the program availability for the specified semi-empirical method, and the available techniques are implemented in only one of the supported programs.

Options:

off

Semi-empirical quantum chemistry method is not requested.

mopac2016

The Mopac package of Stewart [MOPAC2016].

xtb

The xTB package of Grimme [xtbprog].

Default:

the default for the AM1, MNDO, MNDOD, PM3, PM6, PM6-D3, PM6-DH+, PM6-DH2, PM6-DH2X, PM6-D3H4, PM6-D3H4X, PM7, PM7TS, and RM1 methods is mopac2016. The default for GFN0-xTB, GFN1-xTB, and GFN2-xTB is xtb. Otherwise sqmprog=off.

Example:

to use the Mopac program for a PM5 calculation, type sqmprog=mopac2016.

subminp

This keyword controls the input handling of ONIOM calculations.

Options:

top

Keywords specified in the MINP file are only used in the last (high level) calculation. For other layers, the default options will be set.

minp

Keywords specified in the MINP file are used in all calculations. The following keywords are not affected by this option as these are handled by the ONIOM algorithm automatically: mem, qmmm, gopt, freq, calc, basis, charge, mult, verbosity, test, qmreg, oniom, geom, subminp, dens, mpitasks, pcm, oniom_pcm, pcm_$\mathrm{\ast }$, oniom_eechg, embed, corembed, orbloce, orblocv.

temp

The use of template files is requested. Before each calculation, a MINP..tpl file is searched, where $X$ is the serial number of the calculation. If any template file is found, its content is used as is, without consistency check, thus the template file should contain keywords excluding those that are listed above for the minp option. Note that the template files are only searched in the directory where dmrcc is executed.

t+t

The top and temp options are used together.

m+t

The minp and temp options are used together.

Notes

1.

The first line of the MINP..tpl file is catanated to the input keyword list of MINP. if the Mopac program is used for the calculation.

2.

The first line of the MINP..tpl file is catanated to the command line if the xTB program is used for the calculation. The rest of MINP..tpl is added to MINP..xtbinp, which is the xcontrol file of the xTB program.

Default:

top

Examples:

1.

The following example is a CCSD:PBE (aug-cc-pVDZ:STO-3G) ONIOM calculation. The MINP file contains the following keywords:
basis=aug-cc-pVDZ
calc=CCSD
scfdtol=10
subminp=top
oniom=2
8-9
PBE / STO-3G / 0 / 1
0
In this case, PBE/STO-3G (full system), PBE/STO-3G (model system), and CCSD/aug-cc-pVDZ (model system) calculations are requested, which are denoted as calculation #1, #2, and #3, respectively. Calculation #1 and #2 are executed with the default scfdtol, while calculation #3 will use scfdtol=10.

2.

The setting are the same as in example 1 except that subminp=minp. In this case, all calculations will use scfdtol=10.

3.

The settings are the same as in example 1 except that subminp=temp, and there are two files (MINP.2.tpl and MINP.3.tpl) in which there is only the following line:
scflshift=0.3
In this case, calculation #1 will use the default options, while in calculations #2 and #3, scflshift=0.3 will be set. Note that all calculations will use the default option for scfdtol.

symm

Spatial symmetry (irreducible representation) of the state. See Sect. 13 for the implemented point groups, conventions for irreps, etc.

Options:

0

No symmetry adaptation, that is, all calculations will use the $C_1$ point group

off

Equivalent to symm=0

1, 2, …, 8

Serial number of the irrep (see Sect. 13).

irrep label$\mathrm{>}$

Label for the irrep (see Sect. 13).

Note:

Irreps can only be specified by their serial numbers if Mrcc is used with another program. In that case please check the manual or output of the other program system for the numbering of irreps.

Default:

by default the state symmetry is determined on the basis of the occupation of the HF determinant.

Examples:

1.

for the second irrep of the point group type symm=2

2.

for the B${}_{1u}$ irrep of the $D_{2h}$ point group type symm=B1u

talg

Specifies the algorithm for the calculation of the (T) correction in the case of the CCSD(T) method.

Options:

occ

The outmost loops run over the occupied indices of the triples amplitudes.

virt

The outmost loops run over the virtual indices of the triples amplitudes.

lapl

Laplace transformed (T) energy expression for localcc$\mathrm{\ge }$2016 according to Ref. 105. See also the laptol keyword to set the accuracy of the numerical Laplace transform.

topr

The T0${}^{\prime }$ semi-canonical approximation of the local (T) expression according to Ref. 105.

Default:

talg=occ for conventional CCSD(T) calculations, talg=lapl for the local CCSD(T) scheme of localcc$\mathrm{\ge }$2016 and talg=virt for local CCSD(T) with localcc=2013 or 2015.

Notes:

1.

For algorithmic reasons in the case of previous local CCSD(T) schemes (localcc=2013 or 2015) talg=virt is the only option. For localcc$\mathrm{\ge }$2016, the default is talg=lapl, and talg=virt is used if lcorthr=0 is set.

2.

For conventional CCSD(T) calculations talg=occ is recommended since the algorithm is somewhat faster than the other one. In turn, if density-fitting is not employed, its memory requirement is higher. The program checks automatically if the available memory is sufficient for the first algorithm (i.e., talg=occ). If this is not the case, talg will be automatically set to virt.

3.

If density-fitting is employed and ccsdalg=dfdirect is set, a highly memory-economic, completely in-core, integral-direct implementation of the talg=occ scheme is invoked [41]. This algorithm assembles the necessary four-center integrals with two and three virtual MO indices on the fly instead of storing the entire integral lists on disk or in memory. The on the fly integral assembly has negligible additional cost compared to the cost of the (T) correlation energy and has better OpenMP parallel scaling due to the elimination of all disk I/O.

4.

In the case of localcc$\mathrm{\ge }$2016 the talg=topr algorithm is approximately three times faster for the (T) contribution than talg=lapl with its default settings but considerably less accurate. For quick exploratory calculations the talg=lapl algorithm is recommended in combination with laptol=0.1.

Example:

to change the default for a conventional CCSD(T) calculation set talg=virt

temp

The temperature in K at which the thermodynamic properties are evaluated (see also keyword freq).

Options:

any positive real number$\mathrm{>}$

Default:

temp=298.15

Example:

for 300 K set temp=300.0

test

A keyword for testing Mrcc. If an energy value is specified using this keyword, it will be compared to the energy calculated last time [e.g., the CCSD(T) energy and not the CCSD or HF energy if calc=CCSD(T)] in the Mrcc run. An error message will be displayed and the program exits with an error code if the test energy and the calculated energy differ. This keyword is mainly used by the developers of the program to create test jobs to check the correctness of the computed energies. (See Sect. 8 for the further details.)

Options:

off

No testing.

any real number$\mathrm{>}$

The energy to be tested.

Default:

test=off

Example:

to set a test energy of -40.38235315 E${}_h$ type test=-40.38235315

tlmo

Threshold for local MO (LMO) completeness for local excited-state calculations. See Ref. 92 for a detailed description of this threshold ($T_{\mathrm{LMO}}$ in the paper).

Options:

any real number in the [0,1] interval$\mathrm{>}$

This number will be used as the completeness criterion.

Default:

tlmo=0.999

Example:

to set a threshold of 0.99 type tlmo=0.99

tpao

Threshold for projected AO (PAO) completeness for local excited-state calculations. See Ref. 92 for a detailed description of this threshold ($T_{\mathrm{PAO}}$ in the paper).

Options:

any real number in the [0,1] interval$\mathrm{>}$

This number will be used as the completeness criterion.

Default:

tpao=0.94

Example:

to set a threshold of 0.9 type tpao=0.9

tprint

Controls the printing of converged cluster amplitudes/CI coefficients if ccprog=mrcc or ccprog=ccsd.

Options:

off

No printing.

any real number$\mathrm{>}$

Cluster amplitudes/CI coefficients whose absolute value is greater than this number will be printed.

Note:

The value of the cluster amplitude/CI coefficient and the corresponding spin-orbital labels (serial number of the orbital + a or b for alpha or beta spin orbitals, respectively) will be printed. The numbering of the orbitals corresponds to increasing orbital energy order. Note that orbital energies are printed at the end of the SCF run if verbosity$\mathrm{\ge }$3. You can also identify the orbitals using Molden (see Sect. 14.1).

Default:

tprint=off

Example:

to set a threshold of 0.01 give tprint=0.01

uncontract

Uncontract contracted basis sets.

Options:

on or off

Default:

uncontract=off

Example:

to uncontract the basis set add uncontract=on

unit

Specifies the units used for molecular geometries.

Options:

angs

Ångströms will be used

bohr

Atomic units will be used

Default:

unit=angs

Example:

to use bohrs rather than ångströms the user should set unit=bohr

usedisk

Controls the memory and disk usage of the domain construction part of the LNO-CC algorithms.

Options:

0, 1, 2. The minimal memory requirement of the domain construction part of the LNO-CC methods decreases, while the size of the arrays stored temporarily on disk increases with increasing value of the option. usedisk=0 prohibits the use of disk I/O in this part and hence requires somewhat more memory. For more details see Ref. 106.

Default:

usedisk=2

Note:

usedisk=0 is only compatible with the in-core DF-CCSD algorithm invoked by ccsdalg=dfdirect.

Example:

to invoke the in-core domain construction algorithm, for instance, if a local hard disk is not available for the executing node, set usedisk=0.

verbosity

Controls the verbosity of the output.

Options:

0, 1, 2, 3. The verbosity of the output increases gradually with increasing value of the option. Error messages are not suppressed at any level.

Default:

verbosity=2

Example:

to increase the amount of information printed out, give verbosity=3

wpairtol

Threshold for the selection of weak pairs in local MP2, RPA, and CC methods. For each orbital pair the estimate of the pair correlation energy is calculated with a multipole approximation [55, 134, 107]. An orbital pair will be considered as distant pair if the absolute value of the multipole-based pair correlation energy estimate is smaller than wpairtol. For the distant pairs the corresponding multipole-based pair correlation energy estimates will be added to the correlation energy, and distant pairs will be neglected in the subsequent calculations.

In the case of localcc=2015, for the remaining pairs a more accurate pair correlation energy estimate will be calculated using orbital specific virtuals (OSVs) controlled by keyword osveps, and these pairs will be further classified as weak and strong pairs controlled by keyword spairtol, see the description of keyword spairtol. The extended domain of an occupied orbital will include those orbitals for which the latter accurate pair correlation energy estimate is greater than spairtol. See also Ref. 72 for more details.

In the case of localcc$\mathrm{\ge }$2016, spairtol=off is set as default, and the extended domain of an occupied orbital will include those orbitals for which the multipole-based pair correlation energy is greater than wpairtol. See also Refs. 107 and 108 for more details.

Note that for closed-shell local CC methods if spairtol$\mathrm{\ne }$off is specified as a non-default option in the case of localcc$\mathrm{\ge }$2016, accurate MP2 pair energies are computed in the extended domains for the remaining non-distant pairs. Then the non-distant pairs are further divided into weak and strong categories according to the value of spairtol, as discussed above. In this case the MP2 pair energies of the weak pairs are added to the correlation energy, and new, somewhat smaller extended domains are constructed to proceed with the higher-level computation as above using solely the strong pair list. See also Ref. 108 for more details.

Options:

any positive real number$\mathrm{>}$

Orbital pairs with multipole-based pair correlation energy estimates smaller than this number (in E${}_h$) will be considered as distant pairs.

Default:

wpairtol=1e-5 for local MP2 and CC if localcc$\mathrm{\ge }$2018,
wpairtol=min(1e-6, 0.01*spairtol) for localcc=2015

Note:

For defaults with other than the above settings, see the description of lcorthr

Example:

to set a threshold of $5\cdot {10}^{-6}$ E${}_h$ type wpairtol=5e-6