Manual for the MRCC
Program System
Release date: February 9, 2019
Department of Physical Chemistry and Materials Science
Budapest University of Technology and Economics
http://www.mrcc.hu/
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. 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, environmental variables, and input records of the input file. These must be typed as shown. Variables, that is, numbers, options, etc. which must by 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.
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)
local correlation methods and multi-level approaches (drpa); closed-shell coupled-cluster singles and doubles with perturbative triples [CCSD(T)] code (ccsd)
integral transformation and orbital optimization code (ovirt); domain construction for local correlation calculations (mulli)
excited-state approaches (cis), bond functions (integ)
density-fitting integrals (integ)
installation script (build.mrcc), geometry optimization, basis set optimization, the Mrcc homepage
quadratic and multi-configurational self-consistent field algorithms (scf)
open-shell CCSD(T) code (uccsd)
closed-shell CCSD(T) code (ccsd)
Hartree–Fock self-consistent field code (scf)
closed-shell CCSD(T) code (ccsd)
four-center atomic orbital integral code (integ)
orbital relaxation contribution to gradients for density-fitting methods, density-fitting MP2 gradient (prop)
orbital relaxation contribution to gradients for coupled-cluster methods (prop)
double hybrid and van der Waals density functionals (dft)
QM/MM and embedding approaches (qmmod)
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, an
appropriate citation would be:
“Mrcc, a quantum chemical program suite written by M. Kállay,
P. R. Nagy, Z. Rolik, D. Mester, G. Samu, J. Csontos, J. Csóka,
B. P. Szabó, L. Gyevi-Nagy, I. Ladjánszki, L. Szegedy,
B. Ladóczki, K. Petrov, M. Farkas, P. D. Mezei, and B. Hégely.
See also
Z. Rolik, L. Szegedy, I. Ladjánszki, B. Ladóczki, and M. Kállay,
J. Chem. Phys. 139, 094105 (2013),
as well as: www.mrcc.hu.”
In addition, credit must be given to the corresponding papers which
describe the underlying methodological developments. The corresponding
references are given in Sect. 6 of the manual.
If Mrcc is used combined with other program systems, 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 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, 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.
Most of the implemented features are available via the Cfour interface using RHF, ROHF, and UHF orbitals: single-point energy calculations, geometry optimizations, first-, second-, and third-order property calculations, electronic excitation energies, excited-state and transition properties, diagonal Born–Oppenheimer correction (DBOC) calculations. Most of the properties implemented in Cfour are also available with Mrcc. The interface also enables the use of several relativistic Hamiltonians.
The Cfour interface is very user-friendly. You only have to prepare the input file ZMAT for Cfour with the keyword CC_PROG=MRCC, and run Cfour. The Mrcc input file is then written automatically and Mrcc is called directly by Cfour, and you do not need to write any input file for Mrcc. Most of the features of Mrcc can be controlled by the corresponding Cfour keyword, see Cfour’s homepage at www.cfour.de. If you use the Cfour interface, you can safely ignore the rest of this manual.
You also have the option to turn off the automatic construction of the Mrcc input file by giving INPUT_MRCC=OFF in the Cfour input file ZMAT. However, it is only recommended for expert users.
Single-point energies, equilibrium geometries, ground- and excited-state first-order properties, and transition moments can be computed with RHF, ROHF, and MCSCF reference states using the Columbus interface. Evaluation of harmonic vibrational frequencies is also possible via numerically differentiated analytical gradients.
Running Mrcc with Columbus requires three additional programs, colto55, coldens, and runc_mrcc, which are available for Columbus licensees from the authors of Mrcc upon request.
To use this interface for single-point energy calculations first prepare input files for Columbus using the colinp script. It is important to set a calculation in the input file which requires a complete integral transformation (e.g., CISD and not just MCSCF). Execute Columbus. If you do not need the results of the Columbus calculations, you can stop them after completing the integral transformation. Run the colto55 program in the WORK directory created by Columbus. This will convert the Columbus integral files to the Mrcc format. Prepare input file MINP for Mrcc as described in Sect. 11. Run dmrcc as described in Sect. 9. It is recommended to execute first some inexpensive calculation (e.g., CISD) with Mrcc and compare the HF and CISD energies in order to test your input files.
For property calculations create the Columbus and the Mrcc input files. In the Columbus input set the corresponding MRCI property calculation. Copy the Mrcc input file MINP to the WORK directory of Columbus. If the directory does not exist, create it. Then execute the runc_mrcc script.
The interface to the Dirac code enables four-component relativistic calculations with the full Dirac–Coulomb Hamiltonian and several approximate variants thereof. Single-point energy calculations are possible with all the methods implemented in Mrcc using Kramers-paired Dirac–Fock orbitals. First-order property (unrelaxed) calculations are available with iterative CC and CI methods. See Refs. 115 and 74 for more details.
If you use Dirac, you should first prepare input files for
Dirac (see http://diracprogram.org/).
It is important to run a full integral transformation with Dirac
(see the description of the MOLTRA keyword in Dirac’s
manual), and to use Abelian symmetry (that is, the
${D}_{2h}$ group and its subgroups).
Execute the pam script saving the MRCONEE and
MDCINT files, e.g., running it as
pam --get="MRCONEE MDCINT" --inp=Y.inp --mol=X.mol
where X.mol and Y.inp should be replaced by your input files
as appropriate. Then run the dirac_mointegral_export interface
program, which generates the files needed by Mrcc.
It also creates a sample input file MINP for Mrcc, which
contains the input for a closed-shell CCSD calculation.
If you intend to run another type of
calculation, please edit the file as described in Sect. 11.
Please also note that you may need to modify the occupation vector
under the refdet keyword (see the description of the keyword on
page 12), and you should set hamilton=x2c if exact
2-component Hamiltonians are used.
Then run dmrcc as described in Sect. 9.
For relativistic property calculations define the corresponding
operator in the Dirac input file (see the description of the
PROPERTIES and MOLTRA keywords in Dirac’s manual).
Then execute the pam script as
pam --get="MRCONEE MDCINT MDPROP" --inp=Y.inp --mol=X.mol
and edit the MINP file, in particular, set the dens
keyword (page 12). The CC property code currently does not
work with double-group symmetry, and you need to turn off symmetry for
CC property calculations, that is, set symm=off in the MINP
file. Finally run dmrcc.
With Molpro single-point energy calculations are available using RHF, UHF, ROHF, and MCSCF orbitals. The interface also enables the use of Douglas–Kroll–Hess Hamiltonians as well as effective core potentials.
The Molpro interface is very user-friendly. You only have to prepare the input file for Molpro with a line starting with the mrcc label followed by the corresponding keywords, and run Molpro. The Mrcc input file is then written automatically and Mrcc is called directly by Molpro, and you do not need to write any input file for Mrcc. Most of the features of Mrcc can be controlled by the corresponding Molpro keywords. If you use Molpro, you also have the option to install Mrcc with the makefile of Molpro.
For a detailed description of the interface point your browser to the Molpro User’s Manual at www.molpro.net and then click “27 The MRCC program of M. Kallay (MRCC)”.
If you use the Molpro interface, you can safely ignore the rest of this manual.
The Amber/Mrcc interface enables QM/MM and other multiscale calculations. The interface of the Amber MD code and Mrcc is based on the work of Götz et al. [45], which facilitates the integration of QM codes into Amber as external modules. The detailed description of the Amber/Mrcc interface is documented in Ref. 57. Currently for the separation of the QM and MM subsystems only the link atom approach is supported.
With the Amber/Mrcc program the Huzinaga equation-based embedding approaches [58] can also be employed for the QM region. The latter approaches enables the embedding of wave function theory (WFT) or density functional theory (DFT) methods into lower-level WFT or DFT methods and also the combinations thereof (DFT-in-DFT, WFT-in-DFT, WFT-in-WFT, and WFT-in-WFT-in-DFT). Consequently, with the Amber interface you can also define three (QM/QM/MM) or four (QM/QM/QM/MM) layers for the multilevel calculations. At the present stage of development, the multilevel methods with three or four layers are only available for single point energy calculations.
To use the Amber/Mrcc interface you need a properly installed version of Amber (version 2017 or later), see the Amber homepage at ambermd.org. The detailed description of the usage of the interface is well documented in the Amber manual, see section “10.2.6.6. AMBER/MRCC” in the manual.
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.
conventional and density-fitting (resolution-of-identity) Hartree–Fock SCF (Ref. 146): restricted HF (RHF), unrestricted HF (UHF), and restricted open-shell HF (ROHF)
conventional and density-fitting (resolution-of-identity) multi-configurational SCF (MCSCF)
conventional and density-fitting (resolution-of-identity) Kohn–Sham (KS) density functional theory (DFT) (Ref. 78): restricted KS (RKS) and unrestricted KS (UKS); local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA (depending on kinetic-energy density and/or the Laplacian of the density), hybrid, and double-hybrid (DH) functionals (for the available functionals see the description of keyword dft); dispersion corrections
time-dependent HF (TD-HF), time-dependent DFT (TD-DFT), TD-DFT in the Tamm–Dancoff approximation (TDA); currently only for closed-shell molecules with RHF/RKS reference using density-fitting, for LDA and GGA functionals and their hybrids (Ref. 100)
density-fitting (resolution-of-identity) MP2, spin-component scaled MP2 (SCS-MP2), and scaled opposite-spin MP2 (SOS-MP2); currently only for RHF and UHF references (Ref. 78)
density-fitting (resolution-of-identity) random-phase approximation (RPA, also known as ring-CCD, rCCD), direct RPA (dRPA, also known as direct ring-CCD, drCCD), second-order screened exchange (SOSEX), and approximate RPA with exchange (RPAX2); currently the dRPA, SOSEX, and RPAX2 methods are available for RHF/RKS and UHF/UKS references, while the RPA method is only implemented for RHF/RKS (Refs. 78 and 79)
density-fitting (resolution-of-identity) second-order coupled-cluster singles and doubles (CC2), iterative doubles correction to configuration interaction singles [CIS(D${}_{\mathrm{\infty}}$)], and second-order algebraic diagrammatic construction [ADC(2)] approaches; spin-component scaled CC2, CIS(D${}_{\mathrm{\infty}}$), and ADC(2) [SCS-CC2, SCS-CIS(D${}_{\mathrm{\infty}}$), and SCS-ADC(2)]; scaled opposite-spin CC2, CIS(D${}_{\mathrm{\infty}}$), and ADC(2) [SOS-CC2, SOS-CIS(D${}_{\mathrm{\infty}}$), and SOS-ADC(2)] (Refs. 101 and 102)
arbitrary single-reference coupled-cluster methods (Ref. 76): CCSD, CCSDT, CCSDTQ, CCSDTQP, …, CC($n$)
arbitrary single-reference configuration-interaction methods (Ref. 76): CIS, CISD, CISDT, CISDTQ, CISDTQP, …, CI($n$), …, full CI
arbitrary perturbative coupled-cluster models (Refs. 71, 15, and 73):
CCSD[T], CCSDT[Q], CCSDTQ[P], …, CC($n-1$)[$n$]
CCSDT[Q]/A, CCSDTQ[P]/A, …, CC($n-1$)[$n$]/A
CCSDT[Q]/B, CCSDTQ[P]/B, …, CC($n-1$)[$n$]/B
CCSD(T), CCSDT(Q), CCSDTQ(P), …, CC($n-1$)($n$)
CCSDT(Q)/A, CCSDTQ(P)/A, …, CC($n-1$)($n$)/A
CCSDT(Q)/B, CCSDTQ(P)/B, …, CC($n-1$)($n$)/B
CCSD(T)${}_{\mathrm{\Lambda}}$, CCSDT(Q)${}_{\mathrm{\Lambda}}$, CCSDTQ(P)${}_{\mathrm{\Lambda}}$, …, CC($n-1$)($n$)${}_{\mathrm{\Lambda}}$
CCSDT-1a, CCSDTQ-1a, CCSDTQP-1a, …, CC($n$)-1a
CCSDT-1b, CCSDTQ-1b, CCSDTQP-1b, …, CC($n$)-1b
CC2, CC3, CC4, CC5, …, CC$n$
CCSDT-3, CCSDTQ-3, CCSDTQP-3, …, CC($n$)-3
multi-reference CI approaches (Ref. 77)
multi-reference CC approaches using a state-selective ansatz (Ref. 77)
arbitrary single-reference linear-response (equation-of-motion, EOM) CC methods (Ref. 70): LR-CCSD (EOM-CCSD), LR-CCSDT (EOM-CCSDT), LR-CCSDTQ (EOM-CCSDTQ), LR-CCSDTQP (EOM-CCSDTQP), …, LR-CC($n$) [EOM-CC($n$)]
linear-response (equation-of-motion) MRCC schemes (Ref. 70)
DFT/WFT embedding (Ref. 58): DFT-in-DFT, WFT-in-DFT, WFT-in-WFT, and WFT-in-WFT-in-DFT embedding (where WFT stands for wave function theory); currently embedding is only available for closed-shell systems using density-fitting; LDA, GGA, meta-GGA, or hybrid functionals can be used as the DFT method; any WFT method implemented in Mrcc can by used in WFT-in-DFT type embedding calculations; WFT-in-WFT multi-level methods (via keyword corembed) is only available for local correlation methods.
The CI and CC approaches listed above are available with RHF, UHF, standard/semi-canonical ROHF, MCSCF orbitals. Density-fitting with CI or high-order CC is currently enabled only for RHF references. For the perturbative CC approaches with ROHF reference determinant, for theoretical reasons, semi-canonical orbitals are used (see Ref. 73).
The CI and CC approaches listed above are also available with the following interfaces and references.
Cfour, Columbus, and Molpro
Cfour, Columbus, and Molpro
Cfour
Cfour, and Molpro
Columbus and Molpro
QM/MM calculations can be performed by the Amber interface using any method implemented in Mrcc for the QM region.
Single-point calculations are also possible with several types of relativistic Hamiltonians and reference functions, see Sect. 6.7 for more details.
CC$n$ calculations with ROHF orbitals are not possible for theoretical reasons, see Ref. 73 for explanation.
Single-point CI and CC calculations are, in principle, possible with RKS and UKS orbitals.
Geometry optimizations and first-order property calculations can be performed using analytic gradient techniques with the following methods.
conventional and DF (RI) HF-SCF (Ref. 146): RHF and UHF
conventional and DF (RI) DFT (Ref. 78): RKS and UKS with LDA, GGA, meta-GGA (depending only on kinetic-energy density), and hybrid functionals as well as dispersion corrections
double hybrid density functional methods (Ref. 78), such as B2PLYP, B2PLYP-D3, B2GPPLYP, etc. (current limitations: only MP2 correlation, closed shell RKS, no spin-component scaling, no meta-GGA functionals, only DH functionals for which the DFT contribution to the energy is stationary with respect to the variation of the MO coefficients)
DF-MP2 (RI-MP2), currently only for RHF references (Ref. 78)
Currently only unrestricted geometry optimizations are possible, and electric dipole, quadrupole, and octapole moments as well as the electric field at the atomic centers can be evaluated. In addition, Mulliken, Löwdin, and intrinsic atomic orbital (IAO) atomic charges, and Mayer bond orders can be computed using the SCF wave functions. Analytic gradients for the CI and CC methods listed above are available with RHF, UHF, and standard ROHF orbitals without density fitting.
The following keywords are available to control the optimization process
– to select an algorithm for the optimization
– maximum number of iterations allowed
– convergence criterion for energy change
– convergence criterion for the gradient change
– convergence criterion for the step-size
The optimization will be terminated and regarded as successful when the maximum gradient component becomes less than optgtol and either an energy change from the previous step is less than optetol or the maximum displacement from the previous step is less than optstol. For their detailed description see Sect. 12.
The implemented analytic gradients for the CI and CC approaches listed above can also be utilized via the Cfour and Columbus interfaces with the following references.
Cfour and Columbus
Cfour and Columbus
Cfour
Columbus
In addition to geometries, most of the first-order properties (dipole moments, quadrupole moments, electric field gradients, relativistic contributions, etc.) implemented in Cfour and Columbus can be calculated with Mrcc.
QM/MM geometry optimizations and MD calculations can be performed by the Amber interface using any method implemented in Mrcc for which analytic gradients are available.
Geometry optimizations and first-order property calculations can also be performed via numerical differentiation for all methods available in Mrcc using the Cfour interface.
Analytic gradients are are also available with several types of relativistic Hamiltonians and reference functions, see Sect. 6.7 for more details.
Harmonic vibrational frequencies, infrared (IR) intensities, and ideal gas thermodynamic properties can be evaluated using numerically differentiated analytic gradients for all the methods listed in Sect. 6.2.
CC and CI harmonic frequency and second-order property calculations for RHF and UHF references can also be performed using analytic second derivatives (linear response functions) with the aid of the Cfour interface. Analytic Hessians (LR functions) are available for the following approaches.
In addition to harmonic vibrational frequencies [69], the analytic Hessian code has been tested for NMR chemical shifts [69], static and frequency-dependent electric dipole polarizabilities [72], magnetizabilities and rotational $g$-tensors [41], electronic $g$-tensors [40], spin-spin coupling constants, and spin rotation constants. These properties are available via the Cfour interface.
Using the Cfour interface harmonic frequency calculations are also possible via numerical differentiation of energies for all implemented methods with RHF, ROHF, and UHF orbitals.
Using the Cfour or the Columbus interface harmonic frequency calculations are also possible via numerical differentiation of analytic gradients for all implemented methods for which analytic gradients are available (see Sect. 6.2 for a list of these methods). With Cfour the calculation of static polarizabilities is also possible using numerical differentiation.
NMR chemical shifts can be computed for closed-shell molecules using gauge-including atomic orbitals and RHF reference function.
Third-order property calculations can be performed using analytic third derivative techniques (quadratic response functions) invoking the Cfour interface for the following methods with RHF and UHF orbitals.
The analytic third derivative code has been tested for static and frequency-dependent electric-dipole first (general, second-harmonic-generation, optical-rectification) hyperpolarizabilities [119] and Raman intensities [118]. Please note that the orbital relaxation effects are not considered for the electric-field. These properties are available via the Cfour interface.
Using the Cfour interface anharmonic force fields and the corresponding spectroscopic properties can be computed using numerical differentiation techniques together with analytic first and/or analytic second derivatives at all computational levels for which these derivatives are available (see Sect. 6.2 and 6.3 for a list of these methods).
Diagonal Born-Oppenheimer correction (DBOC) calculations can be performed using analytic second derivative techniques via the Cfour interface for the following methods with RHF and UHF references.
Excitation energies, first-order excited-state properties, and ground to excited-state transition moments can be computed as well as excited-state geometry optimizations can be performed using linear response theory and analytic gradients with the following methods.
Excitation energy and property calculations for the aforementioned methods are available with RHF, UHF, and standard ROHF orbitals. Density-fitting is only possible for RHF-based single point calculations. So far electric and magnetic dipole transition moments, both in the length and the velocity gauge, as well as the corresponding oscillator and rotator strengths have been implemented. For the list of implemented first-order properties see Sect. 6.2.
Excitation energies can also be computed for closed-shell systems using the density-fitting approximation and RHF (RKS) orbitals with the following methods (Refs. 101, 102, and 100).
time-dependent HF (TD-HF), Tamm–Dancoff approximation (TDA), time-dependent DFT (TD-DFT)
second-order coupled-cluster singles and doubles (CC2) method
iterative doubles correction to configuration interaction singles [CIS(D${}_{\mathrm{\infty}}$)] method
second-order algebraic diagrammatic construction [ADC(2)] approach
spin-scaled versions of the latter approaches: SCS-CC2, SCS-CIS(D${}_{\mathrm{\infty}}$), SCS-ADC(2), SOS-CC2, SOS-CIS(D${}_{\mathrm{\infty}}$), and SOS-ADC(2)
Ground to excited-state transition moments are available for TD-HF, TDA, TD-DFT, ADC(2), SCS-ADC(2), and SOS-ADC(2). For the CIS, TD-HF, TDA, TD-DFT, CC2, CIS(D${}_{\mathrm{\infty}}$), ADC(2), SCS-CC2, SCS-CIS(D${}_{\mathrm{\infty}}$), SCS-ADC(2), SOS-CC2, SOS-CIS(D${}_{\mathrm{\infty}}$), and SOS-ADC(2) methods efficient reduced-cost approaches are also implemented, see Sect. 6.8 for details.
Excitation energies, first-order excited-state properties, and ground to excited-state transition moments can also be calculated as well as excited-state geometry optimizations can also be carried out using the following interfaces and reference states.
Cfour, Columbus, and Molpro (only excitation energy)
Cfour, Columbus, and Molpro (only excitation energy)
Cfour and Molpro (only excitation energy)
Columbus and Molpro (only excitation energy)
Please note that for excitation energies and geometries LR-CC methods are equivalent to the corresponding EOM-CC models. It is not true for first-order properties and transition moments.
With CI methods excited to excited-state transition moments can also be evaluated.
Excited-state harmonic frequencies can be evaluated for the above methods with the help of numerical differentiation of analytical gradients, see Sect. 6.3.
Excited-state harmonic frequencies can also be calculated for the above methods via numerical differentiation using the Cfour or Columbus interface.
Excited-state harmonic frequencies and second-order properties can be evaluated for CI methods using analytic second derivatives and the Cfour interface.
Treatment of special relativity in single-point energy calculations is possible for all the CC and CI methods listed in Sect. 6.1 using various relativistic Hamiltonians with the following interfaces (Refs. 115 and 74).
With Molpro relativistic calculations can be performed with Douglas-Kroll-Hess Hamiltonians using RHF, UHF, ROHF, and MCSCF orbitals. The interface also enables the use of effective core potentials (see Molpro’s manual for the specification of the Hamiltonian and effective core potentials).
With Cfour exact two-component (X2C) and spin-free Dirac–Coulomb (SF-DC) calculations can be performed. The evaluation of mass-velocity and Darwin corrections is also possible using analytic gradients for all the methods and reference functions listed in Sect. 6.2. (See the description of the RELATIVISTIC keyword in the Cfour manual for the specification of the Hamiltonian.)
Treatment of special relativity in analytic gradient calculations is possible for all the CC and CI methods listed in Sect. 6.2 using various relativistic Hamiltonians with the following interfaces.
With Cfour analytic gradient calculations can be performed with the exact two-component (X2C) treatment.
The computational expenses of the CC and CI methods listed in Sect. 6.1 can be reduced via orbital transformation techniques (Ref. 144). In this framework, to reduce the computation time the dimension of the properly transformed virtual one-particle space is truncated. Currently optimized virtual orbitals (OVOs) or MP2 natural orbitals (NOs) can be chosen. This technique is recommended for small to medium-size molecules. This scaling reduction approach is available using RHF or UHF orbitals. See the description of keywords ovirt, eps, and ovosnorb for more details.
The cost of density-fitting methods can be reduced using natural auxiliary functions (NAFs) introduced in Ref. 78. The approach is very efficient for dRPA, but considerable speedups can also be achieved for MP2, CC2, and ADC(2). See the description of keywords naf_cor and naf_scf for more details.
The computational expenses of CIS, TD-HF, TDA, TD-DFT, CC2, CIS(D${}_{\mathrm{\infty}}$), ADC(2), SCS-CC2, SCS-CIS(D${}_{\mathrm{\infty}}$), SCS-ADC(2), SOS-CC2, SOS-CIS(D${}_{\mathrm{\infty}}$), and SOS-ADC(2) excited-state calculations can be efficiently reduced using local fitting domains as well as state-averaged NOs and NAFs (Refs. 101, 102, and 100). See the description of keywords redcost_exc and redcost_tddft for more details.
The cost of MP2, dRPA, SOSEX as well as single-reference iterative and perturbative coupled-cluster calculations can be reduced for large molecules by the local natural orbital CC (LNO-CC) approach (Refs. 143, 146, 79, 113, 111, and 114). This method combines ideas from the cluster-in-molecule approach of Li and co-workers [92], the incremental approach of Stoll et al. [155], domain- and pair approximations introduced first by Pulay et al. (see, e.g., Ref. 139) with frozen natural orbital, natural auxiliary function, and Laplace transform techniques. It is currently available only for closed-shell molecules using RHF (RKS) orbitals. See the description of keywords localcc, lnoepso, lnoepsv, domrad, lmp2dens, dendec, nchol, osveps, spairtol, wpairtol, laptol, lccrest, and lcorthr for further details.
Utilizing the above local correlation techniques a multi-level scheme is defined in which the LMOs are classified as active or environment (Ref. 58, 59). The contributions of these LMOs to the total correlation energy are evaluated using different models for the two subsystems, for instance, one can choose a LNO-CC model for the active subsystem and LMP2 for the environment. See the description of keyword corembed for further details.
The optimization of basis set’s exponents and contraction coefficients can be performed with any method for which single-point energy calculations are available (see Sect. 6.1). The implementation is presented in Ref. 99. The related keywords are
– to turn on/off basis set optimization
– to select an algorithm for the optimization
– maximum number of iterations allowed
– convergence criterion for energy change
– convergence criterion for parameter (exponent, contraction coefficient) change
For their detailed description see Sect. 12.
For the optimization of basis sets it is important to know the format for the storage of the basis set parameters. In Mrcc the format used by the Cfour package is adapted. The format is communicated by the following example.
actual lines | description | |||
---|---|---|---|---|
C:6-31G | $\hookleftarrow $ Carbon atom:basis name | |||
Pople’s Gaussian basis set | $\hookleftarrow $ comment line | |||
$\hookleftarrow $ blank line | ||||
2 | $\hookleftarrow $ number of angular momentum types | |||
0 | 1 | $\hookleftarrow $ 0$\to $s , 1$\to $p | ||
3 | 2 | $\hookleftarrow $ number of contracted functions | ||
10 | 4 | $\hookleftarrow $ number of primitives | ||
$\hookleftarrow $ blank line | ||||
3047.5249 | 457.36952 | … | $\hookleftarrow $ exponents for s functions | |
$\hookleftarrow $ blank line | ||||
0.0018347 | 0.0000000 | 0.0000000 | $\hookleftarrow $ contraction coefficients | |
0.0140373 | 0.0000000 | 0.0000000 | for s functions | |
0.0688426 | 0.0000000 | 0.0000000 | ||
0.2321844 | 0.0000000 | 0.0000000 | ||
0.4679413 | 0.0000000 | 0.0000000 | ||
0.3623120 | 0.0000000 | 0.0000000 | ||
0.0000000 | 0.1193324 | 0.0000000 | ||
0.0000000 | 0.1608542 | 0.0000000 | ||
0.0000000 | 1.1434564 | 0.0000000 | ||
0.0000000 | 0.0000000 | 1.0000000 | ||
$\hookleftarrow $ blank line | ||||
7.8682724 | 1.8812885 | … | $\hookleftarrow $ exponents for p functions | |
$\hookleftarrow $ blank line | ||||
0.0689991 | 0.0000000 | $\hookleftarrow $ contraction coefficients | ||
0.3164240 | 0.0000000 | for p functions | ||
0.7443083 | 0.0000000 | |||
0.0000000 | 1.0000000 |
In a basis set optimization process you need two files in the working directory: the appropriate MINP file with the basopt keyword set and a user supplied GENBAS file that contains the basis set information in the above format. You do not need to write the GENBAS file from scratch, you can use the files in the BASIS directory of Mrcc to generate one or you can use the Environmental Molecular Sciences Laboratory (EMSL) Basis Set Library [31, 33, 150] to download a basis in the appropriate form (AcesII format). Note that you can optimize several basis sets at a time: all the basis sets which are added to the GENBAS file will be optimized.
You can perform unconstrained optimization when all the exponents and contraction coefficients are optimized except the ones which are exactly 0.0 or 1.0. Alternatively, you can run constrained optimizations when particular exponents/coefficients or all exponents and coefficients for a given angular momentum quantum number are kept fixed during the optimization. The parameters to be optimized can be specified in the GENBAS file as follows.
Unconstrained optimization: no modifications are needed—by default all exponents and contraction coefficients will be optimized except the ones which are exactly 0.0 or 1.0.
Constrained optimization: by default all the exponents and coefficients will be optimized just as for the unconstrained optimization. To optimize/freeze particular exponents or coefficients special marks should be used:
use the “--” mark (without quotes) if you want to keep an exponent or coefficient fixed during the optimization. You should put this mark right after the fixed parameter (no blank space is allowed). If this mark is attached to an angular momentum quantum number, none of the exponents/coefficients of the functions in the given shell will be optimized except the ones which are marked by “++”.
use the “++” mark (without quotes) if you want a parameter to be optimized. Then you should put this mark right after it (no blanks are allowed). You might wonder why this is needed if the default behavior is optimization. Well, this makes life easier. If you want to optimize just a few parameters, it is easier to constrain all parameters first then mark those, which are needed to be optimized (see the example below).
Examples:
To reoptimize all parameters in the above basis set but the exponents
and coefficients of s-type functions you should copy the basis set to
the GENBAS file and put mark “--” after the angular
momentum quantum number of 0. The first lines of the GENBAS file:
C:6-31G
Pople’s Gaussian basis set
2
0--
1
3
2
10
4
3047.5249
457.36952
…
Both s- and p-type functions are fixed but the first s-exponent:
C:6-31G
Pople’s Gaussian basis set
2
0--
1--
3
2
10
4
3047.5249++
457.36952
…
During the optimization the GENBAS file is continuously updated, and if the optimization terminated successfully, it will contain the optimized values (in this case it is equivalent to the GENBAS.opt file, see below, the only difference is that the file GENBAS.opt may contain the special marks, i.e., “++”, “--”). Further files generated in the optimization are:
GENBAS.init – the initial GENBAS file saved
GENBAS.tmp – temporary file, updated after each iteration, can be used to restart conveniently a failed optimization process
GENBAS.opt – this file contains the optimized parameters after a successful optimization.
After registration at the Mrcc homepage pre-built,
statically-complied binaries are available in the download area. To
install these executables Linux operating system and the 2.5 or later version of the GNU C Library (glibc) is required.
The binaries are provided in a gzipped tar file,
mrcc.YYYY-MM-DD.binary.tar.gz, where YYYY-MM-DD is the
release date of the program. Note that you will
find several program versions on the homepage. Unless there are
overriding reasons not to do so, please always download the last
version. To unpack the file type
tar xvzf mrcc*.binary.tar.gz
Please do not forget to add the name of the directory where the
executables are placed to your PATH environmental variable.
To install Mrcc from source code some version of the Unix operating system, Fortran 90 and C++ compilers as well as BLAS (basic linear algebra subprograms) and LAPACK (linear algebra package) libraries are required. Optionally, Mrcc can also be linked with the Libxc library of density functionals [96, 65]. Please be sure that the directories where the compilers are located are included in your PATH environmental variable. Please also check your LD_LIBRARY_PATH environmental variable, which must include the directories containing the BLAS and LAPACK libraries.
After registration at the Mrcc homepage the program can be
downloaded as a gzipped tar file, mrcc.YYYY-MM-DD.tar.gz, where
YYYY-MM-DD is the release date of the program. Note that you will
find several program versions on the homepage. Unless there are
overriding reasons not to do so, please always download the last
version. To unpack the file type
tar xvzf mrcc*.tar.gz
To install Mrcc run the build.mrcc script as
build.mrcc [$$compiler$\mathrm{>}$] [-i$$option1$\mathrm{>}$] [-p$$option2$\mathrm{>}$] [-g] [-d]
[-f$$folder$\mathrm{>}$]
[-l$$library$\mathrm{>}$]
$$compiler$\mathrm{>}$ specifies the compiler to be used.
Currently the supported compiler systems are:
Intel
Intel compiler
GNU
GNU compiler (g77 or gfortran)
PGF
Portland Group Fortran compiler
G95
G95 Fortran 95 compiler
PATH
Pathscale compiler
HP
HP Fortran Compiler
DEC
Compaq Fortran Compiler (DEC machines)
XLF
XL Fortran Compiler (IBM machines)
Solaris10
Sun Solaris10 and Studio10 Fortran Compiler (AMD64)
If the build.mrcc script is invoked without specifying the
$$compiler$\mathrm{>}$ variable, a help message is displayed.
Optional arguments:
specifies if 32- or 64-bit integer variables are used.
Accordingly, $$option1$\mathrm{>}$ can take the value of 32 or
64. The 32-bit integer version is not supported any more.
Default: 64 for 64-bit machines, 32 otherwise.
generates parallel code using message passing interface
(MPI) or OpenMP technologies. Accordingly, $$option2$\mathrm{>}$ can take
the MPI or OMP values. MPI parallelization is available
with the PGF, Intel, GNU, and Solaris10 compilers, while OpenMP
parallelization has been tested with PGF, Intel, GNU, and HP compilers.
Please note that currently the two
parallelization schemes cannot be combined.
Default: no parallelization.
source codes are compiled with debugging option
(use this for development purposes)
Default: no debugging option.
source codes are compiled for development, no
optimization is performed (use this for development purposes)
Default: codes are compiled with highest level optimization.
specifies the installation folder. Executables, basis set libraries, and test jobs will be copied to directory $$folder$\mathrm{>}$. If this flag is not used, you will find the executables, etc. in the directory where you perform the installation.
Mrcc is linked with an external library, currently the only option for $$library$\mathrm{>}$ is libxc, which requires the installation of the Libxc library, see notes below.
Notes:
After the installation please do not forget to add the directory where the Mrcc executables are located to your PATH environmental variable. This is the $$folder$\mathrm{>}$ directory if you used the -f flag at the installation, otherwise the directory where you executed the build.mrcc script.
The build.mrcc script has been tested on several platforms with several versions of the supported compilers and libraries. Nevertheless you may need to customize the compiler flags, names of libraries, etc. These data can be found in the build.mrcc.config file, please edit this file if necessary. Please do not change build.mrcc.
To ensure the best performance of the software the use of Intel compiler is recommended.
If you use Mrcc together with Molpro, you can also use the Molpro installer to install Mrcc, please follow the instructions in the Molpro manual (www.molpro.net).
If Mrcc is linked with the Libxc library, Libxc must be installed before starting the installation of Mrcc. Note that you must compile Libxc with the same Fortran compiler as used for the installation of Mrcc. At the installation of Libxc it is recommended to set the installation path of Libxc (--prefix option of configure) to the directory where the installation of Mrcc is carried out, otherwise please set the LIBS_LIBXC environmental variable to the installation path of Libxc before running build.mrcc. See the manual for the Libxc project for details [65], as well as the examples below. The current release of Mrcc has been tested with the 4.2.3 version of Libxc.
Examples:
Compile Mrcc for OpenMP parallel execution with the Intel compiler
(recommended):
build.mrcc Intel -pOMP
Compile Mrcc for OpenMP parallel execution with the Intel compiler
and install it to the /prog/mrcc directory (recommended):
build.mrcc Intel -pOMP -f/prog/mrcc
Compile Mrcc for OpenMP parallel execution with the Intel compiler
and link with the Libxc library supposing that Mrcc is
compiled in the /prog/mrcc directory (recommended):
Download the Libxc library (libxc*.tar.gz) from the homepage
of the Libxc project [65].
tar xvzf libxc*.tar.gz
cd libxc*
./configure --prefix=/prog/mrcc/ FC=ifort
make
make check
make install
cd /prog/mrcc
build.mrcc Intel -pOMP -llibxc
Compile Mrcc for serial execution with the Intel compiler:
build.mrcc Intel
Compile Mrcc for parallel execution using MPI environment
with the Intel compiler for 32-bit machines:
build.mrcc Intel -i32 -pMPI
Under the Windows operating system the pre-built binaries cannot be directly executed, and the direct compilation of the source code has not been attempted so far. For Windows users we recommend the use of virtualization software packages, such as VirtualBox, which allow Linux as a guest operating system. In that environment Mrcc can be installed in the normal way as described in the previous subsections.
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 environmental 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). If you run these test jobs with OpenMP-parallelized executables (i.e., the build.mrcc script was run with the -pOMP switch) on more than two cores, some of them will fail since the memory requirement for OpenMP-parallel runs grows with the number of cores. In this case the failure of these tests does not indicate a problem with your installation.
We note that currently the mtest script does not support MPI. The MPI jobs stop at some point and require the manual execution of mrcc with mpirun (see Sect. 9.3). The mtest script is not prepared for such jobs and will return with an error message. To test your installation you should collect a couple of such jobs and run them manually.
If you do not use Libxc, the test jobs requiring the library (jobs *Libxc*) will fail. You can ignore this or, to avoid it, delete files *Libxc* from the MTEST directory before running the mtest script.
Please also 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 environmental 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 environmental 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.
To run Mrcc in serial the user must invoke the driver of the
package by simply typing
dmrcc
on a Unix console. To redirect the input one should execute dmrcc
as
dmrcc $\mathrm{>}$ out
where out is the output file.
Several executables of the package can be run in OpenMP parallel mode, hence it is recommended to use this option on multiprocessor machines.
The pre-built binaries available at the Mrcc homepage support OpenMP-parallel execution. If you prefer source-code installation, to compile the program for OpenMP parallel execution you need to invoke the build.mrcc script with the -pOMP option at compilation (see Sect. 7). The OpenMP parallelization has been tested with PGF, Intel, GNU, and HP compilers. Please be careful with other compilers, run, e.g., our test suite (see Sect. 8) with the OpenMP-complied executables before production calculations.
To run the code with OpenMP
you only need to set the environmental variable OMP_NUM_THREADS
to the number of cores you want to use. E.g., under Bourne shell (bash):
export OMP_NUM_THREADS=4
Then the program should be executed as described above.
Currently only executable mrcc can be run in parallel using MPI technology. To compile the program for MPI parallel execution you need to invoke the build.mrcc script with the -pMPI option at compilations (see Sect. 7). It has been tested with the PGF, Intel, GNU, and Solaris compilers as well as the Open MPI and local area multicomputer MPI (LAM/MPI) environments.
To execute mrcc using MPI you should follow the following steps.
Prepare input files as usual. Execute dmrcc. The program will stop
after some time with the message “Now launch mrcc in parallel
mode!”. Then copy files fort.1* and fort.5* to the
compute nodes, and execute mrcc using mpirun.
E.g. (with Open MPI):
for i in ‘cat myhosts‘
do
scp fort.1* fort.5* $i:/scr/$USER/
done
mpirun --nolocal --hostfile myhosts -wdir /scr/$USER/ -np 10 mrcc
In the above script it is supposed that the user has a file
named myhosts with the names of the compute nodes, and
that the user has a temporary directory, /scr/$USER/, on each
node. The script will execute mrcc on 10 nodes specified in
myhosts, no program is executed on the submit node.
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.
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.
Input reader and analyzer. This program reads the input file MINP, checks keywords, options, and dependencies; sets default values for keywords.
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.
Hartree–Fock and Kohn–Sham SCF code. It solves the RHF, UHF, ROHF, RKS, or UKS equations using either conventional or direct SCF techniques. It also performs the semi-canonicalization of orbitals (if requested) for ROHF wave functions.
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.
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.
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.
A very fast, hand-coded, MO-integral-based (DF) CCSD and CCSD(T) code. The code has been optimized for local CC calculations but can also be used for conventional CC calculations. Currently it only functions for closed-shell systems, and the spatial symmetry is not utilized.
A very fast, hand-coded, integral direct DF CIS, TDA, TD-DFT, ADC(2), CIS(D${}_{\mathrm{\infty}}$), and CC2 code. Currently it only works for closed-shell systems, and the spatial symmetry is not utilized.
This program solves the CPHF/KS equations, constructs relaxed density matrices, calculates first-order molecular properties and Cartesian gradients.
Interface program for QM/MM and embedding calculations.
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.
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):
Minimal and optimal memory for double-precision (real*8) arrays.
Memory allocated by mrcc for integer arrays.
(= 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).
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.
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.
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.
All orbitals are inactive (i.e., single-reference calculation).
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.
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.
active=none
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
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
Specifies the angular integration grid for DFT calculations. The grid construction follows the design principles of Becke [7], the smoothing function for the Voronoi polyhedra are adopted from Ref. 110 with ${m}_{\mu}$ = 10. 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 [7] 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.
For the selection of the angular grids, by default, an adaptive scheme motivated by Ref. 88 is used. The angular grids are selected for each radial point so that the error in the angular integrals will not be larger than ${10}^{-\mathrm{\U0001d690\U0001d69b\U0001d69d\U0001d698\U0001d695}}$. The important difference is that the grids are optimized for each atom separately to avoid discontinuous potential energy surfaces. For the construction of the radial integration grid see the description of keyword rgrid. See also the description of keyword grtol.
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.
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 is MMMM and NNNN, respectively.
agrid=LD0006-LD0590
for a 974-point Lebedev grid set agrid=LD0974
to use an adaptive grid with at least 110 and at most 974 angular points set agrid=LD0110-LD0974
for a very fine grid use
agrid=LD0110-LD0974
grtol=12
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.
If the same basis set is used for all atoms, the label of the basis set must be given.
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 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.
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).
It is the same as embed, but the partitioning defined by keyword corembed will be used.
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.
By default the following basis sets are available for elements H to Kr in Mrcc:
the def2 Gaussian basis sets of Weigend and Ahlrichs [164]: def2-SV(P), def2-SVP, def2-TZVP, def2-TZVPP, def2-QZVP, def2-QZVPP
the augmented def2 Gaussian basis sets of Rappoport and Furche [140]: def2-SVPD, def2-TZVPD, def2-TZVPPD, def2-QZVPD, def2-QZVPPD
F12 basis sets for explicitly correlated wave functions developed by Peterson et al. [131]: cc-pV$X$Z-F12 ($X$ = D, T, Q)
the Gaussian basis sets of Dunning and Hay (LANL2DZ) [28]
the auxiliary basis sets of Hellweg and Rappoport for the augmented def2 Gaussian basis sets [62]: 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 [167]: cc-pV$X$Z-RI-JK, aug-cc-pV$X$Z-RI-JK ($X$ = D, T, Q, 5), def2-QZVPP-RI-JK
From Na to La and from Hf to Rn the following basis sets are available, which must be used together with the corresponding ECP (see also the description of keyword ECP):
the def2 Gaussian basis sets of Weigend and Ahlrichs [164]: def2-SV(P), def2-SVP, def2-TZVP, def2-TZVPP, def2-QZVP, def2-QZVPP
the augmented def2 Gaussian basis sets of Rappoport and Furche [140]: def2-SVPD, def2-TZVPD, def2-TZVPPD, def2-QZVPD, def2-QZVPPD
the auxiliary basis sets of Hellweg and Rappoport for the augmented def2 Gaussian basis sets [62]: def2-SVPD-RI, def2-TZVPD-RI, def2-TZVPPD-RI, def2-QZVPD-RI, def2-QZVPPD-RI
the auxiliary basis sets of Hättig for correlation calculations with the PP basis sets: cc-pV$X$Z-PP-RI and aug-cc-pV$X$Z-PP-RI ($X$ = D, T, Q, 5)
Please note that some of the above basis sets are not available for all elements.
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.
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.
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.
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.
Only the conventional AO basis set can be specified with this keyword. For the fitting basis sets used in density-fitting approximations see the description of keywords dfbasis_*.
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.
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.
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.
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.
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).
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
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
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
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
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
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.
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.
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
Specifies the small basis set used in dual basis-set calculations as well as for generating SCF initial guess (scfiguess=small).
the options are the same as for keyword basis, but there is an additional one, none, which means that no small basis is defined.
basis_sm=none
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
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
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.
on, off, or $$any real number$\mathrm{>}$
basopt=off
To optimize a basis set variationally set basopt=on
To optimize a basis set minimizing the difference of the calculated energy and -76.287041 E${}_{h}$ set basopt=-76.287041
Specifies the bond function (BF) basis (see Ref. 99 for details).
No BFs are used.
name of the BF basis to be used.
The format of the name of the BF basis, $$BF basis name$\mathrm{>}$, is $$AO basis name$\mathrm{>}$-$$BF type$\mathrm{>}$. E.g., 6-31G-1s1p is a BF basis optimized for the 6-31G AO basis and one s and one p function set are placed on the corresponding bonds.
The BF basis sets are stored in the BASIS/Bond file but the BF basis can also be specified in the GENBAS file similar to the AO basis sets (see the description of keyword basis). The format of the label of the BF basis in the file is B$$bond name$\mathrm{>}$:$$BF basis name$\mathrm{>}$. E.g., BCH:6-31G-1s1p is 6-31G-1s1p BF basis optimized for the C–H bond.
If BF bases are used, the geometry must be given in mol format (see the description of keyword geom)
bfbasis=none
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
Boughton–Pulay completeness criterion [16] 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.
This number will be used as the completeness criterion.
bpcompo=0.985
Atom domains determined by bpcompo are also utilized to construct local fitting domains in the case of localcc=2016 or 2018 according to Ref. 113.
to set a threshold of 0.99 type bpcompo=0.99
Boughton–Pulay completeness criterion [16] for virtual orbitals (projected atomic orbitals). See also keyword bpcompo.
This number will be used as the completeness criterion.
bpcompv=0.98
to set a threshold of 0.95 type bpcompv=0.95
Boughton–Pulay completeness criterion [16] for the occupied orbitals of an extended domain. See also keyword bpcompo.
This number will be used as the completeness criterion.
bpedo=bpcompo is set if bpedo is not specified and not employed in the local correlation calculation
to set a threshold of 0.9998 type bpedo=0.9998
Boughton–Pulay completeness criterion [16] for the virtual orbitals (projected atomic orbitals) of an extended domain. See also keyword bpcompo.
This number will be used as the completeness criterion.
bpedv=0.995 is set as default in the case of localcc=2016 or 2018 according to Ref. 113.
bpedv=bpcompv is set if bpedv is not specified and not employed in the local correlation calculation
to set a threshold of 0.99 type bpedv=0.99
Boughton–Pulay completeness criterion [16] for the occupied orbital of a primary domain. See also keyword bpcompo.
This number will be used as the completeness criterion.
bppdo=0.999 is set as default in the case of localcc=2016 or 2018 according to Ref. 113.
bppdo=bpcompo is set if bppdo is not specified and not employed in the local correlation calculation
to set a threshold of 0.99 type bppdo=0.99
Boughton–Pulay completeness criterion [16] for virtual orbitals (projected atomic orbitals) of a primary domain. See also keywords bppdo and bpcompo.
This number will be used as the completeness criterion.
bppdv=bpcompv
to set a threshold of 0.99 type bppdv=0.99
Specifies the type of the calculation.
Hartree–Fock SCF calculation, the type of the Hartree–Fock wave function can be controlled by keyword scftype (see also keyword scftype).
Restricted, unrestricted, restricted open-shell Hartree–Fock SCF calculation, or multi-configurational SCF, respectively. The type of the Hartree–Fock/MCSCF wave function 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.
Kohn–Sham SCF calculation with the specified density functional. The type of the Kohn–Sham procedure (i.e., RKS of UKS) can be controlled by keyword scftype (see also keyword scftype). The options are identical to those of keyword dft (except for off, user, and userd), 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.
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.
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.
TD-DFT in the Tamm–Dancoff approximation (TDA). For HF reference it is equivalent to CIS. It is only available with density fitting.
Second-order Møller–Plesset (MP2) calculation, the spin-component scaled MP2 (SCS-MP2) [48] and the scaled opposite-spin MP2 (SOS-MP2) [67] energy will also be computed (see also keywords scsps and scspt). Note that efficient MP2 calculations are only possible with the density-fitting (resolution-of-identity) approximation, and, by default, a DF-MP2 ($\equiv $ RI-MP2) calculation is performed (that is, options MP2, DF-MP2, and RI-MP2 are synonyms). If you are still interested in the MP2 energy without DF, you can, e.g., run a CCSD calculation (without DF), where the MP2 energy is also calculated.
Scaled opposite-spin second-order Møller–Plesset (SOS-MP2) calculation [67] 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).
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.
Direct random-phase approximation (dRPA) calculation (see Eqs. 7 and 8 in Ref. 160). 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).
Random-phase approximation (RPA) calculation (see Eqs. 10 and 13 in Ref. 160, 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).
Second-order screened exchange (SOSEX) [50] calculation (see Eqs. 7 and 9 in Ref. 160), the dRPA energy is 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).
RPAX2 calculation (see Eqs. 17 to 19 in Ref. 63). 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).
Configuration interaction singles (CIS) calculation [100]. 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.
Iterative doubles correction to configuration interaction singles [CIS(D${}_{\mathrm{\infty}}$)] calculation [56, 101, 102]. 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].
Second-order algebraic diagrammatic construction [ADC(2)] calculation [149, 53, 101, 102]. 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].
Second-order coupled-cluster singles and doubles (CC2) calculation [18, 53, 101, 102]. 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.
Scaled opposite-spin CC2, CIS(D${}_{\mathrm{\infty}}$), and ADC(2) [SOS-CC2, SOS-CIS(D${}_{\mathrm{\infty}}$), SOS-ADC(2)] calculation [18, 168, 101, 102]. An ${N}^{4}$-scaling algorithm based on the Cholesky decomposition/Laplace transform of energy denominators is executed. It is only available with density fitting. See also keywords scsps and scspt.
The corresponding single-reference CC calculation with perturbative corrections (see Ref. 71).
The corresponding single-reference CC calculation with perturbative corrections (see Ref. 71).
The corresponding CCSD(T)${}_{\mathrm{\Lambda}}$, CCSDT(Q)${}_{\mathrm{\Lambda}}$, etc. calculation (see Ref. 71).
The corresponding iterative approximate single-reference CC calculation (see Ref. 71).
The corresponding iterative approximate single-reference CC calculation (see Ref. 71).
The corresponding iterative approximate single-reference CC calculation (see Ref. 71).
The corresponding iterative approximate single-reference CC calculation (see Ref. 71).
The corresponding single-reference CC calculation with perturbative corrections using ansatz A (see Ref. 73).
The corresponding single-reference CC calculation with perturbative corrections using ansatz B (see Ref. 73).
The corresponding single-reference CC calculation with perturbative corrections using ansatz A (see Ref. 73).
The corresponding single-reference CC calculation with perturbative corrections using ansatz B (see Ref. 73).
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).
For excited-state calculations with the TD-HF, TDA, TD-DFT, CIS, 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.
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.
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.
Local correlation methods can be run if the prefix “L” is added to the corresponding option of the keyword, e.g., as LMP2, LdRPA, LCCSD(T), 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. Both options are equivalent to setting localcc=on.
For the dRPA, RPA, and SOSEX methods the use of PBE orbitals is recommended.
For the RPAX2 method the use of PBEx orbitals is recommended.
calc=SCF
To run a CCSD(T) calculation the user should set calc=CCSD(T)
For DF-HF (RI-HF) calculations type:
calc=DF-HF
which is equivalent to the following input:
calc=SCF
dfbasis_scf=auto
For a local CCSD(T) calculation using the local natural orbital approximation set calc=LCCSD(T) or calc=LNO-CCSD(T)
For a RI-MP2 calculation set calc=MP2
For a DFT calculation with the B3LYP functional set calc=B3LYP
Direct RPA calculation with Kohn–Sham orbitals calculated with the
PBE functional:
calc=dRPA
dft=PBE
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
Maximum number of iteration steps in correlated calculations (CC, CI, RPA, …).
$$any positive integer$\mathrm{>}$
ccmaxit=50
to increase the maximum number of CC iterations to 100 give ccmaxit=100
Specifies the CC program to be used.
The automated, string-based CC program mrcc will be called.
The very fast, hand-coded CCSD(T) codes, ccsd or uccsd, will be executed (currently the spatial symmetry cannot be utilized).
The very fast, hand-coded, integral direct DF-CIS code cis will be executed (currently the spatial symmetry cannot be utilized).
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.
ccprog=ccsd for CCSD and CCSD(T) calculations, ccprog=cis for CIS, CIS(D${}_{\mathrm{\infty}}$), ADC(2), and CC2 calculations, ccprog=mrcc otherwise.
to use the mrcc code for CCSD or CCSD(T) calculations give ccprog=mrcc
Specifies the CCSD algorithm employed in the ccsd program if ccprog=ccsd.
An MO-based, hand-coded, OpenMP-parallel CCSD algorithm is invoked [146]. 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. 51).
A highly-optimized, hand-coded, OpenMP-parallel, extremely low-memory, in-core, integral-direct ${t}_{1}$-transformed DF-CCSD algorithm is invoked [51]. The necessary four-center integrals and intermediates are constructed completely in memory via an integral direct manner in each iteration, 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.
ccsdalg=dfdirect if density fitting is employed 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.
The dfdirect algorithm is currently only available with the ccsd program, i.e., via ccprog=ccsd.
ccsdalg=disk switches to the CCSD algorithm that stores the four-center integrals on disk.
Convergence threshold for the energy in correlated calculations (CC, CI, dRPA, RPA, etc.). The energy will be accurate to ${10}^{-\mathrm{\U0001d68c\U0001d68c\U0001d69d\U0001d698\U0001d695}}$ E${}_{h}$.
$$any integer$\mathrm{>}$
cctol=8 for property calculations,
cctol=[-${\mathrm{log}}_{10}$(optetol)]+2 for geometry optimizations,
cctol=5 for localcc=2016 and
localcc=2018,
cctol=6 otherwise
for an accuracy of ${10}^{-8}$ E${}_{h}$ one must give cctol=8
Charge of the system.
$$any integer$\mathrm{>}$
charge=0
for the Cl${}^{-}$ ion one should give charge=-1
Specifies what type of algorithm is to be used in CIS, TDA, TD-HF, and TD-DFT calculations.
Conventional algorithm, two-electron integrals are stored on disk
Completely I/O-free, integral-direct algorithm, two-electron integrals are recalculated in each iteration step.
Partially I/O-free, integral-direct algorithm; recommended if the I/O is fast and/or few states are required.
Variant of direct2, but usually slower.
Based on the size of the molecule the program will automatically select the most efficient one from the above options.
cialg=auto
to use disk-based algorithm set cialg=disk
The initial guess vectors for CI and LR-CC calculations can be specified using this keyword.
The initial trial vectors are supplied by the user and
should be given in the subsequent lines as follows. For each state
the corresponding initial guess vector must given by the number of
non-zero elements of the vector on the first line, followed by as many
lines as the number of non-zero elements. In each line the
corresponding excitation operator and the value for this element of the
vector must be provided in the following format:
$$
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.
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.
ciguess=off
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.
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.
The guess vector is not required to be normalized, it is done automatically.
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).
Specifies the computational point group. All calculations will use the specified Abelian group. See Sect. 13 for more details.
The molecular symmetry is automatically recognized.
Schönflies symbol of the Abelian point group such as C1, Ci, Cs, C2, C2v, C2h, D2, D2h
cmpgrp=C1 is equivalent to symm=off
cmpgrp=auto
to use ${C}_{2v}$ point group for benzene set cmpgrp=C2v
Specifies whether the core electrons are correlated.
Frozen core approximation
All core electrons are correlated
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.
core=frozen
to correlate all core electrons set core=corr or core=0
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.
Conventional case, a single model defined by calc is used for the entire system.
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.
corembed=off
Local correlation methods available with localcc=2015,
localcc=2016, and localcc=2018 (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. 58). Note that models with KS-DFT
reference, such as dRPA, SOSEX, etc., are not available for multi-level
local correlation calculations.
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 for previous versions according to lcorthr=loose and localcc=2015 or localcc=2016) are employed for the low-level model of the environment.
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
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
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
Diagonal Born–Oppenheimer correction (DBOC) (available only with Cfour).
on or off
dboc=off
for a DBOC calculation set dboc=on
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${}_{\mathrm{\infty}}$), and SOS-ADC(2) as well as for local MP2 and dRPA calculations. The dRPA calculation is performed using the modified algorithm of Heßelmann [63] 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. 79). 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.
for SOS-CC2, 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 decomposition will be used
Laplace transform will be used
dendec=Laplace for SOS-MP2, SOS-CC2, SOS-CIS(D${}_{\mathrm{\infty}}$), and SOS-ADC(2); dendec=Cholesky otherwise
The algorithms based on the Laplace-transformed technique use minimax quadratures obtained from Ref. 158.
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. 158). The subsequent NN lines must contain, respectively, the weights and quadrature points.
to use Laplace transform give dendec=Laplace
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. 68, 69, 70, 72, 118, 119 for more details.
Density-matrix calculation (for geometry optimizations, first-order properties, etc.)
Density-matrix first derivatives (for second-order property calculations, available only with Cfour)
Transition density matrices (for transition moment calculations)
Second and third derivatives of the density-matrix (for third-order property calculations, available only with Cfour)
dens=2 for geometry optimizations and QM/MM calculations, dens=0 otherwise
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).
If dens $\ne $ 0, a population analysis is also performed, and Mulliken and Löwdin atomic charges as well as Mayer bond orders are computed.
for the calculation of both one- and two-particle density matrices set dens=2
Specifies how the inverse of the two-center Coulomb integral matrix is decomposed in density fitting direct SCF calculations.
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.
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 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.
dfalg=InvSqrt for property calculations, dfalg=LinEq otherwise
to use Cholesky decomposition set dfalg=Cholesky
Specifies whether the density fitting approximation will be used in the correlated calculations and also specifies the fitting basis set.
The density fitting approximation is not used for the correlated calculation.
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.
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.
For the available fitting basis sets see the notes for keyword basis on page 12.
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.
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.
To use the cc-pVTZ-RI fitting basis in the correlated calculation for all atoms the input must include dfbasis_cor= cc-pVTZ-RI
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
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
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
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.
dfbasis_scf=auto if dfbasis_cor$\mathrm{\ne}$none and for DFT calculations, dfbasis_scf=none otherwise.
Specifies the integral transformation program to be used for the transformation of three-center Coulomb integrals.
the drpa program will be called
the ovirt program will be called
dfintran=ovirt if ovirt$\mathrm{\ne}$off, dfintran=drpa otherwise.
to use the ovirt code set dfintran=ovirt
Use this keyword to perform DFT calculations and to specify the functional.
No DFT calculation is carried out.
The name of the functional, see Table 1 for the available functionals.
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 [65]).
User-defined functional. Any combination of the following contributions can be defined:
the available standalone functionals, see column “User” in Table 1.
the functionals available in the Libxc library (if installed), use simply the Libxc identifier of the functionals (see the homepage of the Libxc project [65]).
the HF exchange, denoted by HFx
the MP2, dRPA, and SOSEX correlation, denoted, respectively, by MP2, 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.
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$\mathrm{>}$ $$functional name 3$\mathrm{>}$
…
User-defined functional, but different functionals
are used for the calculation of the density and the energy. It is useful
for defining special double-hybrid functionals.
The combination should be specified in the
subsequent lines as follows (see also the examples below):
$$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.
Functional | Description | User |
LDA exchange functionals | ||
LDA | Slater–Dirac exchange (local density approximation) [27, 152, 85] | Yes |
LDA correlation functionals | ||
VWN1 | functional I of Vosko, Wilk, and Nusair [161] | Yes |
VWN2 | functional II of Vosko, Wilk, and Nusair [161] | Yes |
VWN3 | functional III of Vosko, Wilk, and Nusair [161] | Yes |
VWN4 | functional IV of Vosko, Wilk, and Nusair [161] | Yes |
VWN5 | functional V of Vosko, Wilk, and Nusair [161] | Yes |
PZ | Perdew–Zunger 1981 correlation functional [125] | Yes |
PW | Perdew–Wang 1992 correlation functional [124] | Yes |
GGA exchange functionals | ||
B88 | Becke’s 1988 exchange functional [8] | Yes |
PBEx | functional of Perdew, Burke, and Ernzerhof [126] | Yes |
PBEh | 1988 revision of PBEx by Ernzerhof and Perdew [32] | Yes |
PW91x | Perdew–Wang 1991 exchange functional [122] | Yes |
G96 | exchange functional of Gill [126] | Yes |
mPW91x | modified PW91x functional of Adamo and Barone [2] | Yes |
GGA correlation functionals | ||
LYP | correlation functional of Lee, Yang, and Parr [90] | Yes |
P86 | Perdew’s 1986 correlation functional [128] | Yes |
PBEc | functional of Perdew, Burke, and Ernzerhof [126] | Yes |
PW91c | Perdew–Wang 1991 correlation functional [122] | Yes |
GGA exchange-correlation functionals | ||
BLYP | Becke’s 1988 exchange functional [8] and the correlation functional of Lee, Yang, and Parr (B88 + LYP) [90] | No |
BP86 | BP86 exchange-correlation functional (B88 + P86) [8, 128] | No |
PBE | exchange-correlation functional of Perdew, Burke, and Ernzerhof (PBEx + PBEc) [126] | No |
PW91 | Perdew and Wang 1991 exchange-correlation functional (PW91x + PW91c) [122] | No |
HCTH120 | HCTH120 exchange-correlation functional of Boese and co-workers [13] | Yes |
HCTH147 | HCTH147 exchange-correlation functional of Boese and co-workers [13] | Yes |
HCTH407 | HCTH407 exchange-correlation functional of Boese and Handy [14] | Yes |
XLYP | exchange-correlation functional of Xu and Goddard [171] | Yes |
mPWLYP1w | exchange-correlation functional of Dahlke and Truhlar optimized for water [22] | Yes |
Hybrid GGA exchange-correlation functionals | ||
BHLYP | Becke’s half-and-half exchange in combination with the LYP correlation functional (0.5 B88 + 0.5 HF exchange + LYP) [8, 90, 9] | No |
B3LYP | Becke’s three-parameter hybrid functional including the correlation functional of Lee, Yang, and Parr (0.08 LDA + 0.72 B88 + 0.2 HF exchange + 0.19 VWN5 + 0.81 LYP) [8, 27, 152, 161, 10, 90] | No |
B3LYP3 | Becke’s three-parameter hybrid functional including the correlation functional of Lee, Yang, and Parr (0.8 LDA + 0.72 B88 + 0.2 HF exchange + 0.19 VWN3 + 0.81 LYP) [8, 27, 152, 161, 10, 90, 154]. Note that this is equivalent to the B3LYP functional of the Gaussian package. | Yes |
B3PW91 | Becke’s three-parameter hybrid functional including the 1991 correlation functional of Perdew and Wang (0.08 LDA + 0.72 B88 + 0.2 HF exchange + 0.19 VWN5 + 0.81 PW91c) [8, 27, 152, 161, 10, 122] | No |
B1LYP | modified B3LYP functional of Adamo and Barone [1] | Yes |
O3LYP | modified B3LYP functional of Cohen and Handy [20] | Yes |
B97 | Becke’s 1997 exchange-correlation functional (including 0.1943 HF exchange) [11] | Yes |
PBE0 | hybrid functional of Perdew, Burke, and Ernzerhof (0.75 PBEx + 0.25 HF exchange + PBEc) [126, 127] | No |
X3LYP | hybrid functional of Xu and Goddard [171] | Yes |
Meta-GGA exchange functionals | ||
TPSSx | exchange functional of Tao, Perdew, Staroverov, and Scuseria [159] | Yes |
revTPSSx | revised TPSS exchange of Perdew et al. [123] | Yes |
SCANx | exchange functional of Sun, Ruzsinszky, and Perdew [157] | Yes |
Meta-GGA correlation functionals | ||
B95 | Becke’s 1995 correlation functional [6] | Yes |
TPSSc | correlation functional of Tao, Perdew, Staroverov, and Scuseria [159] | Yes |
revTPSSc | revised TPSS correlation of Perdew et al. [123] | Yes |
SCANc | correlation functional of Sun, Ruzsinszky, and Perdew [157] | Yes |
revSCANc | revised SCAN correlation functional of Mezei, Csonka, and Kállay [105] | Yes |
Meta-GGA exchange-correlation functionals | ||
TPSS | exchange-correlation functional of Tao, Perdew, Staroverov, and Scuseria [159] | No |
revTPSS | revised TPSS functional of Perdew et al. [123] | No |
M06-L | 2006 exchange-correlation functional of Zhao and Truhlar [176, 175] | No |
B97M-V | exchange-correlation functional of Mardirossian and Head-Gordon [95] | Yes |
SCAN | exchange-correlation functional of Sun, Ruzsinszky, and Perdew [157] | No |
revSCAN | revised SCAN exchange-correlation functional of Mezei, Csonka, and Kállay [105] | No |
Hybrid meta-GGA exchange-correlation functionals | ||
M06-2X | 29-parameter exchange-correlation functional of Zhao and Truhlar including 0.54 HF exchange [176] | No |
M06-HF | hybrid meta-GGA functional of Zhao and Truhlar including 100% HF exchange [178] | No |
M08-HX | 47-parameter exchange-correlation functional of Zhao and Truhlar including 0.5223 HF exchange [177] | Yes |
M08-SO | 44-parameter exchange-correlation functional of Zhao and Truhlar including 0.5679 HF exchange [177] | Yes |
TPSSh | hybrid version of TPSS including 0.1 HF exchange [153] | Yes |
revTPSSh | revised TPSSh of Csonka, Perdew, and Ruzsinszky including 0.1 HF exchange [153, 21] | Yes |
mPW1B95 | mixture of mPW91x and B95 by Zhao and Truhlar [173] | Yes |
PW6B95 | mixture of PW91x and B95 by Zhao and Truhlar [174] | Yes |
SCAN0 | hybrid version of SCAN including 0.25 HF exchange [157, 66] | No |
revSCAN0 | hybrid version of revised SCAN including 0.25 HF exchange [105] | No |
Double hybrid functionals | ||
B2PLYP | Grimme’s two-parameter double hybrid functional including MP2 correction (0.47 B88 + 0.53 HF exchange + 0.73 LYP + 0.27 MP2 correlation) [49] | No |
B2GPPLYP | two-parameter double hybrid functional including MP2 correction of Martin and co-workers (0.35 B88 + 0.65 HF exchange + 0.64 LYP + 0.36 MP2 correlation) [80] | No |
DSDPBEP86 | dispersion corrected, spin-component scaled double hybrid functional of Kozuch and Martin (0.30 PBEx + 0.70 HF exchange + 0.43 P86 + 0.53 MP2 antiparallel-spin correlation + 0.25 MP2 parallel-spin correlation) [86, 87]. Note that the dispersion correction is only included if the -D3 postfix is added (see the note below). | No |
DSDPBEhB95 | dispersion corrected, spin-component scaled double hybrid functional of Kozuch and Martin (0.34 PBEh + 0.66 HF exchange + 0.55 B95 + 0.47 MP2 antiparallel-spin correlation + 0.09 MP2 parallel-spin correlation) [87]. Note that the dispersion correction is only included if the -D3 postfix is added (see the note below). | No |
XYG3 | double hybrid functional of Zhang, Xu, and Goddard (0.2107 B88 - 0.014 LDA + 0.8033 HF exchange + 0.6789 LYP + 0.3211 MP2 correlation evaluated with B2LYP orbitals) [172, 43] | No |
SCAN0-2 | SCAN-based double-hybrid of Hui and Chai (0.793701 HF exchange + 0.206299 SCANx + 0.5 SCANc + 0.5 MP2 correlation [157, 66] | No |
dRPA75 | the dual-hybrid random phase approximation (dRPA75) method of Mezei et al. [106]. The KS orbitals are obtained with the “0.25 PBEx + 0.75 HF exchange + PBEc” functional, while the energy is calculated using the “0.25 PBEx + 0.75 HF exchange + dRPA correlation” expression. Dispersion correction [17] can be included if the -D3 postfix is added. | No |
SCS-dRPA75 | the spin-component scaled dual-hybrid random phase approximation (SCS-dRPA75) method of Mezei et al. [106, 107]. The KS orbitals are obtained with the “0.25 PBEx + 0.75 HF exchange + PBEc” functional, while the energy is calculated using the “0.25 PBEx + 0.75 HF exchange + 1.5 dRPA antiparallel-spin correlation + 0.5 dRPA parallel-spin correlation” expression. | No |
van der Waals density functionals | ||
VV10NL | the nonlocal part (the $\beta N$ term is ignored) of the 2010 van der Waals density functional of Vydrov and Van Voorhis [162], both self-consistent and non-self-consistent implementations are available, see also the the comment below | Yes |
dft=off
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 [46, 47] 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,
dRPA75-D3,
HF-D3.
See also the description of keyword edisp.
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).
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.
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.
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.
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.
For the VV10 van der Waals functional you can modify parameters $b$ and $C$ (see Ref. 162) if it is used with the user or userd options. For that purpose the two parameters should be specified after the VV10NL flag separated by spaces, see the example below. If the parameters are not set, those of Ref. 162 will be used.
To perform a DFT calculation with the B3LYP functional give dft=B3LYP or calc=B3LYP
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
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
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
SOSEX calculation with Kohn–Sham orbitals calculated with the
LDA exchange functional:
calc=SOSEX
dft=LDA
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
B2PLYP calculation, the MP2 contribution is evaluated using local
MP2 approximation:
calc=LB2PLYP
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
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
Local dRPA calculation with Kohn–Sham orbitals calculated with the
PBE functional:
calc=LdRPA
dft=PBE
To perform a DFT calculation with the B3LYP functional using its Libxc implementation set calc=HYB_GGA_XC_B3LYP5
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
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 VV10NL 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 VV10NL 8.0 0.0093
Type of diagonalization algorithm used for the CI and LR-CC calculations.
Standard Davidson diagonalization
Davidson diagonalization with root-following, recommended for excited-state calculations if the initial guess is given manually or the calculation is restarted
diag=david
for root-following type diag=follow
Specifies the number of doubly occupied orbitals in an MCSCF calculation. See also the description of keyword mact.
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.
There is no default, the occupation must be set in the case of an MCSCF calculation.
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
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
Radius of atom domains for the local correlation method of Ref. 146 (localcc=2013). For each localized MO (LMO), using the Boughton–Pulay procedure [16], 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.
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.
Infinite radius will be applied, i.e., there is only one atom domain including all atoms.
domrad=10.0
To use the local CC methods as defined in Ref. 143 set domrad=inf, that is, use only one atom domain including all atoms.
to set a threshold of 12.0 bohr type domrad=12.0
Specifies the type of the algorithm for the solution of the dRPA equations or the calculation of SOS-MP2 energies. See Ref. 79 for more details.
The algorithm of Ref. 63 will be used, the fitting of integral lists will be performed before the dRPA iterations (SOS-MP2 calculation).
The algorithm of Ref. 79 will be executed, the fitting of the integrals is not performed. This algorithm is efficient for large molecules.
The dRPA correlation energy is calculated using the plasmon formula.
The algorithm is automatically selected on the basis of the size of the molecule (canonical dRPA) or the HOMO-LUMO gap (local dRPA).
For SOSEX calculations drpaalg=fit is the only option, which is forced by the program.
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.
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}$.
drpaalg=fit and drpaalg=auto for canonical and local dRPA, respectively.
to set the second option give drpaalg=nofit
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. 59 for more details.
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. 59. 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. 59. Similar to e1, but there is also an iterative step with the large basis.
dual=off
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
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
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
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.
No ECPs will be used.
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.
If the same ECP is used for all atoms, the label of the ECP can be given here.
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{>}$ .
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.
By default the following ECP are available for elements Na to Rn in Mrcc:
Please note that some of the above ECPs are not available for all elements.
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.
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.
ecp=auto
To use the MCDHF-ECP-10 pseudopotential for all atoms the input must include ecp=MCDHF-ECP-10
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
This keyword controls the calculation of empirical dispersion corrections for DFT and HF calculations using the DFT-D3 approach of Grimme and co-workers [46, 47]. 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 environmental variable.
No dispersion correction will be computed.
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).
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.
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 [47].
edisp=off
to calculate the D3 dispersion correction including BJ damping to the B3LYP energy give calc=B3LYP-D3
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
This keyword controls DFT embedding calculations. Currently it is only available for closed-shell systems using density-fitting.
No embedding.
The Huzinaga-equation-based embedding approach [58, 59] 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). 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 should be given which is the number of the embedded orbitals or zero if the latter is 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 and bopu, which mean the Mulliken population- and the Boughton–Pulay algorithm-based schemes of Refs. 58 and 59, respectively. For aMul you can also specify the Mulliken population threshold (see the appendix of Ref. 59). The threshold for the bopu algorithm can be controlled by the bpcompo keyword. The default is aMul with a threshold of 0.3. See also examples below.
The projector-based embedding approach of Manby and co-workers [94] will be used. The embedded atoms and the low-level DFT approach can be specified as described above.
embed=off
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
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
The same as example 1, but the bopu algorithm is
used:
calc=DF-CCSD(T)
embed=huzinaga
1-2
PBE
0 bopu
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
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
Use this option to add an external perturbation to the Hamiltonian, e.g., an external electric dipole field.
No perturbations are added.
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.
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).
epert=none
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
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. See Ref. 144 for more details.
Virtual orbitals with cumulative populations of higher than this number will be dropped.
eps=0.975
to set a threshold of 0.95 type eps=0.95
Sets the radius of local fitting domains for the exchange contribution in direct density-fitting SCF calculations [138, 113]. 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.
Threshold for the integrals (in E${}_{h}$).
A threshold of zero will be applied, i.e., a conventional direct DF-SCF calculation will be executed.
Local fitting domains are available for RHF, UHF, ROHF, RKS, and UKS calculations.
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.
excrad=1.0 if scfalg=locfit1 or scfalg=locfit2, excrad=0 otherwise
to set a threshold of 0.1 E${}_{h}$ type excrad=0.1
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.
See the description of keyword excrad.
excrad_fin=excrad/1000
to avoid the use of local fitting domains in the extra iteration step give excrad_fin=0.0
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.
on or off
You should also set this keyword if you are interested thermodynamic properties of atoms.
freq=off
for a frequency calculation set freq=on
Specifies whether spherical harmonic or Cartesian Gaussian basis functions will be used.
Spherical harmonic Gaussians will be used
Cartesian Gaussians will be used
For calculations using the density fitting (DF) approximation, if intalg=os or intalg=auto, the Coulomb integrals are evaluated by algorithms [3, 147] 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).
The derivative integrals are evaluated by the solid-harmonic Hermite scheme [141] (see the description of keyword intalg), consequently, differentiated integrals, and thus energy derivatives cannot be evaluated with Cartesian Gaussian basis sets.
gauss=spher
for Cartesian Gaussians the user should set gauss=cart
Specifies the format of molecular geometry. The geometry must be given in the corresponding format in the subsequent lines.
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”.
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).
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.
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.
For the use of ghost atoms see the description of keyword ghost.
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.
the following five geometry inputs for H${}_{2}$O${}_{2}$ are equivalent
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
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
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
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
.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 atoms can be specified using this keyword, e.g., for the purpose of basis set superposition error (BSSE) calculations with the counterpoise method.
There are no ghost atoms.
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 $$ are ghost atoms. Note that the numbering of the atoms must be identical to that used in the Z-matrix or Cartesian coordinate specification, but dummy atoms must be excluded.
ghost=none
Rectangular HF dimer, the atoms of the second HF molecule
are ghost atoms:
geom
H
F 1 R1
H 2 R2 1 A
F 3 R1 2 A 1 D
R1=0.98000000
R2=2.00000000
A=90.00000000
D=0.000000000
ghost=serialno
3-4
Ammonia, the third hydrogen is a ghost atom (note that the
serial number of the hydrogen is 4 instead of 5 because of the dummy
atom:
geom
X
N 1 R
H 2 NH 1 AL
H 2 NH 1 AL 3 A
H 2 NH 1 AL 3 B
R=1.00000000
NH=1.01000000
AL=115.40000000
A=120.00000000
B=-120.00000000
ghost=serialno
4
Requests geometry optimization. Currently only the full geometry optimization is supported, geometrical parameters cannot be frozen.
no geometry optimization.
full geometry optimization.
The coordinates in the MINP file are replaced by the converged ones at the end of the geometry optimization. The initial MINP file is saved as MINP.init.
The Abelian symmetry of the molecule is utilized at the calculation of gradients and update of the coordinates, thus, the computational point group is preserved during the optimization.
gopt=off
to carry out a full geometry optimization set gopt=full
Threshold for automatic point group recognition. Two atoms will be considered symmetry-equivalent if the difference in any component of their Cartesian coordinates after the symmetry operation is less than ${10}^{-\mathrm{\U0001d690\U0001d69d\U0001d698\U0001d695}}$ bohr.
$$any integer$\mathrm{>}$
gtol=7
for a tolerance of ${10}^{-4}$ bohr give gtol=4
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.
Densities are not evaluated.
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:
$N$
${\mathbf{r}}_{1}$ ${w}_{1}$ $\rho ({\mathbf{r}}_{1})$ $\nabla \rho ({\mathbf{r}}_{1})$ ${\nabla}^{2}\rho ({\mathbf{r}}_{1})$
${\mathbf{r}}_{2}$ ${w}_{2}$ $\rho ({\mathbf{r}}_{2})$ $\nabla \rho ({\mathbf{r}}_{2})$ ${\nabla}^{2}\rho ({\mathbf{r}}_{2})$
⋮
${\mathbf{r}}_{N}$ ${w}_{N}$ $\rho ({\mathbf{r}}_{N})$ $\nabla \rho ({\mathbf{r}}_{N})$ ${\nabla}^{2}\rho ({\mathbf{r}}_{N})$
where $N$ is the number of grid points, ${\mathbf{r}}_{i}$ = (${x}_{i}$, ${y}_{i}$,
${z}_{i}$) is the Cartesian coordinate of grid point $i$ with ${w}_{i}$ as
the corresponding weight, and $\rho ({\mathbf{r}}_{i})$ 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
${\mathbf{r}}_{i}$ ${w}_{i}$ ${\rho}_{\alpha}({\mathbf{r}}_{i})$ ${\rho}_{\beta}({\mathbf{r}}_{i})$ $\nabla {\rho}_{\alpha}({\mathbf{r}}_{i})$ $\nabla {\rho}_{\beta}({\mathbf{r}}_{i})$ ${\nabla}^{2}{\rho}_{\alpha}({\mathbf{r}}_{i})$ ${\nabla}^{2}{\rho}_{\beta}({\mathbf{r}}_{i})$
grdens=off
to save the densities give grdens=on
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 ${10}^{-\mathrm{\U0001d690\U0001d69b\U0001d69d\U0001d698\U0001d695}}$, while the number of radial grid points increases linearly with grtol. See also the description of keywords agrid and rgrid.
$$any positive integer$\mathrm{>}$
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.
grtol=10
for a fine integration grid give grtol=12
Specifies what type of Hamiltonian is used in relativistic calculations. This keyword has only effect if iface=Dirac.
exact 2-component molecular-mean-field Hamiltonian [151]
other types of relativistic Hamiltonians such as the full Dirac–Coulomb Hamiltonian or the exact 2-component Hamiltonian
hamilton=DC
if you use the exact 2-component molecular-mean-field Hamiltonian, set hamilton=X2Cmmf
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.
Transformed MO integrals are calculated by Mrcc.
Mrcc is interfaced to Cfour.
Mrcc is interfaced to Columbus.
Mrcc is interfaced to Dirac.
Mrcc is interfaced to Molpro.
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.
If you use Mrcc together with Columbus or Dirac, this keyword must be always given.
iface=none, that is, all calculations will be performed by Mrcc.
to carry out four-component relativistic calculations using the Dirac interface give iface=Dirac
Specifies the algorithm used for the evaluation of two-electron integrals over primitive Gaussian-type orbitals.
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.
The integrals over contracted Gaussians are evaluated by the solid-harmonic Hermite scheme of Reine et al. [141].
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.
For DF methods option herm is not available.
For DF methods, if intalg=os or intalg=auto the Coulomb integrals are evaluated by the algorithm of Ref. 147, 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).
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.
intalg=auto
to use the Obara–Saika scheme for all angular momenta add intalg=os
Threshold for integral calculation. Integrals less than ${10}^{-\mathrm{\U0001d692\U0001d69d\U0001d698\U0001d695}}$ E${}_{h}$ will be neglected.
$$any integer$\mathrm{>}$
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)
for an accuracy of ${10}^{-15}$ E${}_{h}$ one must give itol=15
Specifies the accuracy of the numerical Laplace transform in the (T) correlation energy term of local CCSD(T) calculations with localcc=2016 or 2018. See also the description of keyword talg and Ref. 111.
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 ${n}_{\mathrm{q}}>|{\mathrm{log}}_{10}(\text{\U0001d695\U0001d68a\U0001d699\U0001d69d\U0001d698\U0001d695})|$.
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.
to use a threshold of ${10}^{-3}$ type laptol=1e-3
Specifies the order of operations in LNO-CC calculations.
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}$2018 and ccprog=ccsd.
The integral transformation steps to the LNO bases of the LISs are completed first for all LISs, which is followed by the CC calculations performed for each LIS in their respective LNO basis. This option requires storing the integral lists of all LISs on disk. It is usually not limiting to store the three-center LNO integrals required for ccprog=ccsd or the four-center LNO integrals required for ccprog=mrcc.
lccoporder=lccfirst for localcc$\mathrm{\ge}$2018,
lccoporder=trffirst for localcc$$2018 or ccprog=mrcc.
to force storing the integrals on disk for localcc$\mathrm{\ge}$2018 set lccoporder=trffirst
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=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=2016 or localcc=2018 and 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=2016 or localcc=2018, 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.
restart, on, off, or domain.
lccrest=off
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.
Controls the accuracy of local correlation calculations by setting the relevant thresholds: bp*, lnoepso, lnoepsv, laptol, naf_cor, osveps, wpairtol, spairtol (see also Refs. 79, 113, and 114 for details).
The truncation thresholds will be set so that the canonical energy be reproduced, it is only useful for testing.
Expected accuracy. Using the Normal settings for local MP2 and CCSD(T), if localcc=2018, 1 kJ/mol (1 kcal/mol) average (maximum) errors are expected in energy differences even for relatively complicated or sizable systems (see Refs. 113 and 114). 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. 79).
For local MP2 naf_cor=off is set if localcc=2015. Keywords lnoepso, lnoepsv, and laptol are irrelevant for local MP2 calculations.
calc | MP2 | CC | all | ||||
---|---|---|---|---|---|---|---|
localcc | 2018 | 2018 | |||||
lcorthr | Loose | Normal | Tight | Loose | Normal | Tight | 0 |
bpedo | 0.9999 | 0.9999 | 0.99995 | 0.9999 | 0.9999 | 0.99995 | 1.0 |
wpairtol | 3e-5 | 1e-5 | 3e-6 | 3e-5 | 1e-5 | 3e-6 | 0.0 |
lnoepso | - | - | - | 3e-5 | 1e-5 | 3e-6 | 0.0 |
lnoepsv | - | - | - | 3e-6 | 1e-6 | 3e-7 | 0.0 |
laptol | - | - | - | 1e-1 | 1e-2 | 1e-3 | - |
naf_cor | 2e-3 | 2e-3 | 2e-3 | 1e-2 | 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 | 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 |
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 |
lcorthr=Normal
to use tight thresholds set lcorthr=Tight
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. 143).
The MP2 density matrix fragments are calculated using the correct, non-canonical expressions.
The MP2 density matrix fragments are calculated using the approximate canonical expressions (as defined in Ref. 143).
To reproduce the method described in Ref. 143 use lmp2dens=off.
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.
lmp2dens=on
to use the canonical expressions give lmp2dens=off
Threshold for the occupation numbers of occupied local natural orbitals (LNOs) in the case of local correlation calculations, or for state-averaged MP2/CIS(D) occupied natural orbitals for reduced-cost excited-state calculations, see also keyword lnoepsv. See Ref. 146 as well as Refs. 101 and 102 for more details.
Orbitals with occupation numbers greater than 1-lnoepso will be frozen.
For default settings with options other than localcc=2018 and lcorthr=Normal, see the description of lcorthr.
lnoepso=1e-5 for local correlation, lnoepso=0 for excited-states
to set a threshold of $5\cdot {10}^{-6}$ type lnoepso=5e-6
Threshold for the occupation numbers of virtual local natural orbitals (LNOs) in the case of local correlation calculations, or for state-averaged MP2/CIS(D) virtual natural orbitals for reduced-cost excited-state calculations, see also keyword lnoepso. See Ref. 146 as well as Refs. 101 and 102 for more details.
Orbitals with occupation numbers smaller than this number will be dropped.
For default settings with options other than localcc=2018 and lcorthr=Normal, see the description of lcorthr.
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, …)
to set a threshold of $5\cdot {10}^{-7}$ type lnoepsv=5e-7
Specifies if local correlation calculation is performed. See Refs. 143, 146, 79, 113, 111, and 114 for more details.
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).
localcc=off
for local correlation calculations give localcc=on
Specifies the number of active orbitals in an MCSCF calculation. See also the description of keyword docc.
The number of active orbitals per irrep should be given in the
following format:
mact=$$
where $$ is the number of active orbitals in irrep $i$,
and ${N}_{ir}$ is the number of irreps.
There is no default, the active orbitals must be given in the case of an MCSCF calculation.
See the description of keyword docc for examples.
Maximum number of inactive labels. One can impose restrictions on the cluster operator using this keyword. The maximum number of virtual/occupied inactive labels on the singly, doubly, … excited clusters can be specified.
on or off. If maxact=on, the maximum number of virtual and occupied inactive labels must be specified in the subsequent line as an integer vector. The integers must be separated by spaces. The vector should contain as many elements as the excitation rank of the highest excitation in the cluster operator. The integers are maximum number of virtual/occupied inactive labels allowed on amplitudes of single, double, … excitations, respectively.
maxact=off
Suppose that we have up to quadruple excitations,
and the single, double, triple, and quadruple excitations are allowed to
have maximum of 1, 2, 2, and 1 inactive virtual and occupied labels,
respectively. Then the input file should include the following lines:
maxact=on
1 2 2 1
Maximum number of trial vectors in the Davidson procedure in the case of CIS, TDA, TD-HF, and TD-DFT calculations. The procedure will be restarted if the dimension of the reduced subspace reaches maxdim.
$$any positive integer$\mathrm{>}$
maxdim=max(100, 3*max(ntrip, nsing))
for a maximum of 50 expansion vectors set maxdim=50
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. 77 and 68 for more details.
The excitation manifold is not truncated.
The excitation manifold is truncated at $n$-fold excitations, see above.
maxex=0
to truncate the excitation manifold at triple excitations set maxex=3
Initial guess for the MCSCF calculation.
The sad, ao, core, mo, and restart options can be used as described for keyword scfiguess. In addition, there is one further option:
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.
To restart the MCSCF calculation using MOs from a previous MCSCF run, e.g., when calculating potential energy surfaces, use mcscfiguess=mo
mcscfiguess=HF
set mcscfiguess=sad to start the MCSCF calculation from SAD initial guess.
Specifies the core memory used.
The amount of memory to allocate is specified in megabytes
The amount of memory to allocate is specified in gigabytes
mem=256MB
to allocate 8 GB core memory the user should set mem=8GB
Specifies whether input file for the Molden program and an xyz-file containing the Cartesian coordinates are written (see also Sect. 14).
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.
The construction of the MOLDEN input and the COORD.xyz file is turned off.
For the reduced-cost CC2, CIS(D${}_{\mathrm{\infty}}$), and ADC(2), methods of Refs. 101 and 102, and for their spin-scaled versions, if molden=on and verbosity$\mathrm{\ge}$3, the pseudo-canonicalized state-averaged natural orbitals will be saved to files MOLDEN_NO.$\mathrm{n}$, where $n$ is the serial number of the excited state.
molden=on
if you do not need Molden input and the COORD.xyz file, add molden=off
Specifies the multipole approximation used for the evaluation of pair energies of distant pairs.
The simplified dipole-dipole estimate of Ref. 142 will be used.
Full dipole-dipole estimate [136].
All the terms are included in the multipole expansion up to the contributions of the quadrupole moment [113].
All the terms are included in the multipole expansion up to the contributions of the octapole moment [113].
mulmet=3 if localcc=2016 or 2018,
mulmet=0 otherwise
to use the octapole approximation set mulmet=3
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.
$$any positive integer$\mathrm{>}$
for atoms the corresponding experimental multiplicity is set, for molecules mult=1 (singlet) for an even number of electrons, mult=2 (doublet) otherwise
for a triplet state one should give mult=3
Number of active occupied spinorbitals for multi-reference (active-space) CI/CC calculations. By default, nacto pieces of spinorbitals under the Fermi level are supposed to be active. This can be overwritten using keyword active, which enables the user to select the active orbitals manually (see the description of keyword active). In a MRCI/CC calculation a complete active space (CAS) is supposed defined by keywords nacto and nactv (or alternatively by active) and up to $n$-fold excitations from the reference determinants of this space are included in the excitation manifold, where $n$ is determined by keyword calc (2 for CCSD, 3 for CCSDT, …). See Ref. 77 for more details. See also keywords nactv, maxex, and maxact. Note also that this keyword only sets the active orbitals for the post-SCF calculation, the MCSCF active orbitals can be specified by keyword mact.
$$any positive integer$\mathrm{>}$ or 0
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.
for two active occupied spin-orbitals give nacto=2
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.
$$any positive integer$\mathrm{>}$ or 0
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.
for two active virtual spin-orbitals give nactv=2
Specifies how natural auxiliary functions (NAFs) will be constructed in the case spin-unrestricted MOs. NAFs can be calculated by diagonalizing (${\mathbf{W}}^{\alpha}$ $+$ ${\mathbf{W}}^{\beta}$)/2 or ${\mathbf{W}}^{\alpha}$ (see Ref. 78 for the definitions). The latter option is somewhat more efficient but can be dangerous for processes involving atoms.
NAFs are constructed from (${\mathbf{W}}^{\alpha}$ $+$ ${\mathbf{W}}^{\beta}$)/2.
NAFs are constructed from ${\mathbf{W}}^{\alpha}$.
nafalg=albe
to use ${\mathbf{W}}^{\alpha}$ set nafalg=alpha
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. 78).
NAFs will not be constructed.
A NAF basis will be constructed and NAFs with occupation numbers smaller than this number will be dropped.
Sets naf_cor=5e-3 if the use of NAFs is not set 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.
according to the value of lcorthr for local correlation methods; naf_cor=0.1 for the reduced-cost excited-state approaches of Refs. 101 and 102 (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=off otherwise.
to use NAFs and set a threshold of ${10}^{-2}$ type naf_cor=1e-2
Specifies whether NAFs will be used for density-fitting SCF calculations and also specifies the threshold for the occupation numbers of NAFs (see Ref. 78). The syntax is analogous with that for keyword naf_cor.
Specifies how NAFs will be constructed in the case of local correlation calculations. NAFs are constructed by diagonalizing the $\mathbf{W}={\mathbf{J}}^{\mathrm{T}}\mathbf{J}$ matrix where $\mathbf{J}$ is a particular block of the three-center Coulomb integral matrix (see Refs. 78 and 114 for details).
NAFs are constructed from ${J}_{ai}^{P}$
NAFs are constructed from ${J}_{pi}^{P}$
NAFs are constructed from ${J}_{pq}^{P}$
NAFs are constructed from ${J}_{\mu i}^{P}$
to construct NAFs using ${J}_{pq}^{P}$ set naftyp=Jpq
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.
The number of Cholesky vectors/quadrature points will be automatically determined to achieve the required precision.
The number of Cholesky vectors/quadrature points will also be automatically determined but the maximum number of the vectors cannot exceed this number.
nchol=auto
to use ten Cholesky vectors/quadrature points give nchol=10
Step size for the numerical differentiation in atomic units.
$$any positive real number$\mathrm{>}$
ndeps=1e-3
for a step size of $5\cdot {10}^{-4}$ a.u. for numerical Hessian evaluation set ndeps=5e-4
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 and ntrip.
$$any positive integer$\mathrm{>}$
nstate=max(1, nsing+ntrip)
for three states give nstate=3
Number of singlet electronic states (strictly speaking the number of of states with ${M}_{S}=0$ and $S$ is even) including the ground state and excited states. Use this option only for non-relativistic calculations and closed-shell reference determinants, it should be zero otherwise. In the case of closed-shell reference determinants a partial spin-adaptation is possible, see Ref. 76. This enables us to search for singlet and triplet roots separately. See also keywords nstate and ntrip.
$$any positive integer$\mathrm{>}$
nsing=1 for closed-shell reference determinants, nsing=0 otherwise
for two singlet states give nsing=2
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.
$$any positive integer$\mathrm{>}$
ntrip=0
for two triplet states give ntrip=2
Specifies the occupation of the Hartree–Fock determinant.
If this keyword is not given, the occupation is automatically determined in the SCF calculations.
For RHF calculations the occupation should be given in the following
format:
occ=$$
where $$ is the number of occupied orbitals in irrep $i$, and
${N}_{ir}$ is the number of irreps.
For ROHF and UHF calculations the occupation should be given as
occ=$$/$$
where $$ is the number of occupied $\sigma $ spinorbitals in irrep $i$.
occ is not specified, that is, the occupation is set by the SCF program.
Water, RHF calculation:
occ=3,1,1,0
Water, UHF calculation:
occ=3,1,1,0/3,1,1,0
Carbon atom, ROHF or UHF calculation:
occ=2,0,0,0,0,1,0,1/2,0,0,0,0,0,0,0
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 [116] is the only available option. A geometry optimization can be carried out by either the Broyden–Fletcher–Goldfarb–Shanno (BFGS) or the simplex algorithm.
the simplex method of Nelder and Mead.
the BFGS algorithm.
optalg=simplex for basis set optimization, optalg=BFGS otherwise.
To run a geometry optimization with the simplex algorithm set optalg=simplex
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.
$$any positive integer$\mathrm{>}$
optmaxit=50
to allow 60 iteration steps set optmaxit=60
Convergence threshold for geometry or basis set optimization. If the simplex algorithm is used, i.e., optalg=simplex, the optimization is terminated when the energy difference (in E${}_{h}$) becomes less then this value and the optstol criterion is also fulfilled. In addition to the criterion for the gradient (optgtol) and the step-size (optstol) the energy change between the cycles is also monitored. For a successful geometry optimization it is required that the optgtol criterion is satisfied and either the energy difference between the last two steps becomes less than this value (in E${}_{h}$) or the optstol criterion is met.
$$any positive real number$\mathrm{>}$
optetol=1e-6
for a convergence threshold of $5\cdot {10}^{-6}$ E${}_{h}$ set optetol=5e-6
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.
$$any positive real number$\mathrm{>}$
optgtol=1e-4
for a convergence threshold of $3\cdot {10}^{-4}$ E${}_{h}$/bohr set optgtol=3e-4
Convergence threshold for geometry or basis set optimization. For the latter the optimization is terminated when the maximum change in the parameters becomes less then this value and the optetol criterion is also fulfilled, for the former this criterion is met when the maximum step-size from the previous step (in bohr) is lower than this value. The geometry optimization is terminated successfully if, in addition to the optgtol criterion obeyed, either this criterion is met or the energy difference between the last two steps becomes less than optetol.
$$any positive real number$\mathrm{>}$
optstol=1e-3 for a basis set optimization, optstol=1e-4 otherwise.
to set a threshold of ${10}^{-5}$ bohr for a geometry optimization type optstol=1e-5
Specifies what type of orbital localization is performed for the core molecular orbitals.
All the options introduced for keyword orbloco also work for orblocc, see the description of keyword orbloco for details.
orblocc=orbloco if localcc=2013, or core=corr and
localcc$\mathrm{\ne}$off;
orblocc=off otherwise
to localize of core orbitals with the Pipek–Mezey algorithm specify orblocc=on
Initial guess for the orbital localization.
Guess orbitals are calculated by the Cholesky decomposition of the one-particle density matrix [5].
Guess orbitals for the localization are read from
the
MOCOEF.LOC file produced in a previous run where orbital
localization was performed.
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.
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.
orblocguess=cholesky
to speed up the orbital localization by using the localized orbitals of a previous calculation as guess specify orblocguess=restart.
Specifies what type of orbital localization is performed for occupied molecular orbitals.
orbloco=off in the general case, orbloco=boys for local correlation calculations
to carry out Pipek–Mezey localization for the occupied orbitals type orbloco=pm
Specifies what type of orbital localization is performed for virtual molecular orbitals.
All the options introduced for keyword orbloco excepting IBO also work for orblocv, see the description of keyword orbloco for details. In addition, for local correlation calculations there is one more option:
Projected atomic orbitals.
orblocv=off in the general case, orblocv=pao for local correlation calculations
to carry out Boys localization for the virtual orbitals type orblocv=boys
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.
OSVs are not constructed and not dropped
Orbitals with occupation numbers smaller than this number will be dropped.
osveps=1e-3 for localcc=2015, osveps=off for localcc=2016 or 2018
to set a threshold of ${10}^{-4}$ type osveps=1e-4
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 [117]. Subsequently the virtual space will be truncated on the basis of the populations of the orbitals, which can be controlled by keywords eps and ovosnorb. See Ref. 144 for more details.
The virtual MOs are not changed.
MP2 NOs will be used.
Optimized virtual orbitals will be used.
ovirt=off
to use MP2 NOs for a ground-state CC calculation give ovirt=MP2
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.
This number will be used as the threshold for the eigenvalues of the overlap matrix.
ovltol=1e-7
to keep all the basis functions set ovltol=0.0
Specifies the retained percentage of virtual orbitals in an optimized virtual orbitals (OVOs) calculations. ovosnorb % of virtual orbitals will be retained.
$$any number between 0 and 100$\mathrm{>}$
ovosnorb=80.0
to retain only 70 % of the virtuals give ovosnorb=70.0
This keyword controls the wave function analysis.
No wave function analysis is performed.
In addition to the above parameters, intrinsic atomic orbitals (IAOs) are constructed and IAO partial charges are calculated [84].
popul=Mulli if dens $\ne $ 0, popul=off otherwise
to calculate IAO charges set popul=IAO
The pressure in Pa at which the thermodynamic properties are evaluated (see also keyword freq).
$$any positive integer$\mathrm{>}$
pressure=100000
for 1 atm set pressure=101325
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 need to bother with it. Use this keyword in the only case if you want to add point charges manually.
QM/MM calculation is not performed and no point charges are added.
Currently this is the only option, the Amber MD code will be used for the QM/MM calculation or point charges will be added.
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.
qmmm=off
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
Use this option to carry out quadratic RHF, UHF, RKS, and UKS SCF calculations and also to select the algorithm used for MCSCF calculations. One can use either Newton or trust region iterations with optional line search. For ROHF calculations with quadratic convergence use the MCSCF code.
No quadratic SCF, conventional SCF algorithm will be executed.
Simple Newton iteration.
Simple Newton iteration with line search.
Trust region method with augmented Hessian algorithm without line search. The trust radius is updated according to the scheme described in Ref. 61.
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.
Trust region method with augmented Hessian algorithm using line search. The trust radius is updated as described in Ref. 61, but this method takes into account the step length found by the line search.
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.
The simple 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.
qscf=AugHessG for MCSCF calculations, qscf=off otherwise
UKS calculation with the B3LYP functional using the
AugHessG algorithm:
calc=B3LYP
scftype=UHF
qscf=AugHessG
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. 101 and 102 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.
The cost reduction techniques will not be used.
Reduced-cost calculation will be executed with default settings (see also Table 4).
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. 102 for the detailed description of
these parameters.
See Table 4.
redcost_exc=off
Reduced-cost ADC(2) calculation for the lowest
singlet excited state with the
default settings proposed in Ref. 102:
calc=ADC(2)
nsing=2
redcost_exc=on
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
Option | CS-NAF | NO | Can. | RS-NAF | Note |
off | no | no | no | no | Default |
on | yes/no | yes | yes | yes | Equivalent to 1 or 6 depending on keyword localcc |
cust | yes | yes | yes | yes | Customized thresholds |
1 | yes | yes | yes | yes | The approach presented in Ref. 102, default if localcc=off and redcost_exc=on |
2 | no | yes | no | yes | The approach presented in Ref. 101 |
3 | no | no | no | yes | The approach presented in Ref. 101 without NOs |
4 | no | yes | no | no | The approach presented in Ref. 101 without NAFs |
5 | no | yes | yes | no | |
6 | no | yes | yes | yes | Default if localcc=2016 and redcost_exc=on |
7 | yes | yes | no | yes | |
8 | yes | no | no | no | For reduced-cost CIS, TD-HF, TDA, TD-DFT, … |
9 | yes | yes | yes | no | |
10 | yes | yes | no | no |
This keyword controls the use of local fitting domains for reduced-scaling density fitting CIS, TD-HF, and TD-DFT calculations. See Ref. 100 for more details.
The scaling reduction techniques will not be used.
Reduced-scaling calculation will be executed with a completeness criterion of 0.985 for the wave function truncation.
This number will be used as the completeness criterion.
redcost_tddft=off
to set a completeness criterion of 0.99 type redcost_tddft=0.99
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.
The reference determinant is identical to the HF determinant.
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.
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.
Frozen orbitals must not be considered here in any case.
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).
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.
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.
refdet=none, that is, the reference determinant is identical to the HF determinant.
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
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
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
The same using the serialno option (note the blank
lines):
refdet=serialno
1,2,7,8
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.
The program restarts from the previously calculated parameters.
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).
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.
Same as rest=2 but the initial vectors are selected as in the case of rest=3.
use the restart option, e.g.,
after system crash.
if the iteration procedure did not converge in the given number of steps.
for geometry optimization.
for potential curve calculations.
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)!
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)!
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.)
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.
rest=0
to restart a CC calculation after power failure set rest=1
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
Specifies the radial integration grid for DFT calculations. For the details of the grid construction see the description of keyword agrid. See also the description of keyword grtol.
the number of grid points is calculated by the max{20,5*(3*grtol/2+$i$-8)} formula with $i$ as the number of the row in the periodic table where the atom is located [88]. To change the number of radial integration points set the value of grtol.
rgrid=Log3
to use the Euler–Maclaurin scheme set rgrid=EM
to use the default Log3 grid with more points set grtol=12
Specifies the type of the ROHF orbitals. See also the description of keyword scftype.
Standard ROHF orbitals obtained by diagonalizing the ROHF Fock-matrix.
Semicanonical ROHF orbitals obtained by separately diagonalizing the alpha and beta UHF Fock-matrices constructed using the converged ROHF orbitals.
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).
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.
rohftype=standard for iterative CC and CI
methods,
rohftype=semicanonical for perturbative methods.
to use semicanonical ROHF orbitals for iterative CC methods give rohftype=semicanonical
Specifies what type of SCF algorithm is to be used.
Conventional SCF algorithm, two-electron integrals are stored on disk.
Direct SCF algorithm, two-electron integrals are recalculated in each iteration step.
Based on the size and geometry of the molecule the program will automatically select the more efficient one from the above options.
Same as locfit1 but, in addition to the auxiliary functions, domains are also constructed for the AOs and MOs.
scfalg=auto
to run direct SCF add scfalg=direct
Specifies whether damping of the SCF density matrices is performed.
No damping.
In each SCF iteration cycle the new and old SCF density matrices are mixed by factors (1-scfdamp) and scfdamp, respectively.
Equivalent to scfdamp=0.7
scfdamp=off
to use a damping factor of $0.8$ type scfdamp=0.8
Specifies if DIIS convergence acceleration is used in the SCF calculations.
on or off
scfdiis=on
to turn off DIIS convergence accelerator add scfdiis=off
Specifies the last iteration step in which the DIIS convergence acceleration is applied.
$$any positive integer$\mathrm{>}$
scfdiis_end=scfmaxit, that is, the DIIS procedure is not turned off.
to turn off the DIIS convergence accelerator after iteration step 20 give scfdiis_end=20
Specifies the first iteration step in which the DIIS convergence acceleration is applied.
$$any positive integer$\mathrm{>}$
scfdiis_start=1, that is, the DIIS procedure is active from the first iteration.
to turn on the DIIS convergence accelerator in iteration step 5 give scfdiis_start=5
Specifies the frequency of DIIS extrapolations. The extrapolation will be carried out in every scfdiis_step’th iteration cycle.
$$any positive integer$\mathrm{>}$
scfdiis_step=1, that is, the DIIS extrapolation is performed in each iteration step.
to carry out DIIS extrapolation only in every second iteration step give scfdiis_step=2
Convergence threshold for the density matrix in SCF calculations. The RMS change in the density matrix will be smaller than ${10}^{-\mathrm{\U0001d69c\U0001d68c\U0001d68f\U0001d68d\U0001d69d\U0001d698\U0001d695}}$.
$$any integer$\mathrm{>}$
scfdtol=scftol+2 for frequency calculations,
otherwise
scfdtol=scftol+1 for correlation calculations,
scfdtol=scftol for SCF calculations
for an accuracy of ${10}^{-8}$ one must give scfdtol=8
Specifies the number of Fock-matrices used for the DIIS extrapolation in SCF calculations.
$$any positive integer$\mathrm{>}$
scfext=10
to increase the number of DIIS vectors to 15 give scfext=15
Initial guess for the SCF calculation.
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.
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 Hamiltonian initial guess. The initial MOs are obtained by diagonalizing the one-electron integral matrix.
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.
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.
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.
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.
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.
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.
Restarting from densities obtained with a bigger basis set is not allowed.
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.
scfiguess=sad
For a core Hamiltonian initial guess set scfiguess=core
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.
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.
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
Level shift parameter for the SCF calculation.
No level shifting.
The value of the level shift parameter in a.u.
Equivalent to scflshift=0.2
scflshift=off
To use a level shift value of 0.5 a.u. give scflshift=0.5
Maximum number of iteration steps in SCF calculations.
$$any positive integer$\mathrm{>}$
scfmaxit=50
to increase the maximum number of SCF iterations to 200 give scfmaxit=200
Convergence threshold for the energy in SCF calculations. The energy will be accurate to ${10}^{-\mathrm{\U0001d69c\U0001d68c\U0001d68f\U0001d69d\U0001d698\U0001d695}}$ E${}_{h}$.
$$any integer$\mathrm{>}$
scftol=max(8,cctol) for property
calculations,
scftol=max(6,cctol) otherwise
for an accuracy of ${10}^{-8}$ E${}_{h}$ one must give scftol=8
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.
RHF, ROHF, UHF, or MCSCF
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.
If a HF-SCF calculation is run, the type of the SCF wave function can also be controlled by keyword calc. See the description of calc.
For DFT calculations only the RHF and UHF options can be used, which, in that case, instruct the code to run RKS or UKS calculations, respectively.
scftype=RHF for closed-shell systems, scftype=UHF for open shells.
to use ROHF for open-shell systems type scftype=ROHF
Scaling factor for the antiparallel-spin component of the correlation energy in spin-scaled correlation calculations [SCS-MP2, SCS-CC2, SCS-CIS(D${}_{\mathrm{\infty}}$), SCS-ADC(2), SOS-MP2, SOS-CC2, SOS-CIS(D${}_{\mathrm{\infty}}$), SOS-ADC(2)] [48, 168].
the antiparallel-spin component of the correlation energy will be scaled by this number.
scsps=6/5 for the SCS methods, scsps=1.3 for the SOS approaches
to set a scaling factor of 1.5 type scsps=1.5
Scaling factor for the parallel-spin component of the correlation energy in spin-scaled correlation calculations [SCS-MP2, SCS-CC2, SCS-CIS(D${}_{\mathrm{\infty}}$), SCS-ADC(2), SOS-MP2, SOS-CC2, SOS-CIS(D${}_{\mathrm{\infty}}$), SOS-ADC(2)] [48, 168].
the parallel-spin component of the correlation energy will be scaled by this number.
scspt=1/3 for the SCS methods, scspt=0.0 for the SOS approaches
to set a scaling factor of 0.5 type scspt=0.5
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. 79 and 114 for more details.
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. 113.
Orbital pairs with pair correlation energy estimates greater than this number (in E${}_{h}$) will be considered as strong pairs.
spairtol=1e-4 for localcc=2015, spairtol=off for
localcc=2016 and localcc=2018
to set a threshold of ${10}^{-5}$ E${}_{h}$ type spairtol=1e-5
Spatial symmetry (irreducible representation) of the state. See Sect. 13 for the implemented point groups, conventions for irreps, etc.
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.
by default the state symmetry is determined on the basis of the occupation of the HF determinant.
for the second irrep of the point group type symm=2
for the B${}_{1u}$ irrep of the ${D}_{2h}$ point group type symm=B1u
Specifies the algorithm for the calculation of the (T) correction in the case of the CCSD(T) method.
The outmost loops run over the occupied indices of the triples amplitudes.
The outmost loops run over the virtual indices of the triples amplitudes.
Laplace transformed (T) energy expression for localcc=2016 or 2018 according to Ref. 111. See also the laptol keyword to set the accuracy of the numerical Laplace transform.
The T0${}^{\prime}$ semi-canonical approximation of the local (T) expression according to Ref. 111.
talg=occ for conventional CCSD(T) calculations, talg=lapl for the local CCSD(T) scheme of localcc=2016 or 2018, and talg=virt for local CCSD(T) with localcc=2013 or 2015.
For algorithmic reasons in the case of previous local CCSD(T) schemes (localcc=2013 or 2015) talg=virt is the only option. For localcc=2016 or 2018, the default is talg=lapl, and talg=virt is used if lcorthr=0 is set.
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.
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 [51]. 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.
In the case of localcc=2016 or 2018 the talg=topr algorithm is approximately three times faster 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.
to change the default for a conventional CCSD(T) calculation set talg=virt
The temperature in K at which the thermodynamic properties are evaluated (see also keyword freq).
$$any positive real number$\mathrm{>}$
temp=298.15
for 300 K set temp=300.0
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.)
No testing.
The energy to be tested.
test=off
to set a test energy of -40.38235315 E${}_{h}$ type test=-40.38235315
Controls the printing of converged cluster amplitudes/CI coefficients if ccprog=mrcc.
No printing.
Cluster amplitudes/CI coefficients whose absolute value is greater than this number will be printed.
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).
tprint=off
to set a threshold of 0.01 give tprint=0.01
Uncontract contracted basis sets.
on or off
uncontract=off
to uncontract the basis set add uncontract=on
Specifies the units used for molecular geometries.
Ångströms will be used
Atomic units will be used
unit=angs
to use bohrs rather than ångströms the user should set unit=bohr
Controls the memory and disk usage of the domain construction part of the LNO-CC algorithms.
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. 112.
usedisk=2
usedisk=0 is only compatible with the in-core DF-CCSD algorithm invoked by ccsdalg=dfdirect.
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.
Controls the verbosity of the output.
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.
verbosity=2
to increase the amount of information printed out
give
verbosity=3
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 [64, 142, 113]. 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. 79 for more details.
In the case of localcc=2016 or 2018, 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. 113 and 114 for more details.
Note that for local CC methods if spairtol$\mathrm{\ne}$off is specified as a non-default option in the case of localcc=2016 or 2018, accurate MP2 pair energies are computed in the extended domains for the remaining non-distant pairs. Then the non-distant pairs are further divided into weak and strong categories according to the value of spairtol, as discussed above. In this case the MP2 pair energies of the weak pairs are added to the correlation energy, and new, somewhat smaller extended domains are constructed to proceed with the higher-level computation as above using solely the strong pair list. See also Ref. 114 for more details.
Orbital pairs with multipole-based pair correlation energy estimates smaller than this number (in E${}_{h}$) will be considered as distant pairs.
wpairtol=1e-5 for local MP2 and CC if localcc=2018,
wpairtol=min(1e-6, 0.01*spairtol)
for localcc=2015
For defaults with other than the above settings, see the description of lcorthr
to set a threshold of $5\cdot {10}^{-6}$ E${}_{h}$ type wpairtol=5e-6
The Mrcc program can handle Abelian point group symmetry. The handling of symmetry can be controlled by keywords cmpgrp (see page 12) and symm (see page 12). In the following we give the character tables used by the program. The symmetry of electronic states can be specified by keyword symm using either the serial number of the irrep or its symbol. The serial number of an irrep is given by its position in the below tables as appropriate. To specify the state symmetry by the symbol of the irrep replace the superscripts in the irrep symbol by lowercase letters, e.g., give B2g for B${}_{2g}$. For the A${}^{{}^{\prime}}$ and A${}^{{}^{\prime \prime}}$ irreps of ${C}_{s}$ group use A’ and A", respectively (apostrophe and quotation mark).
Character table for the ${C}_{1}$ point group
$E$ | ||
---|---|---|
A | $1$ | $x$, $y$, $z$, ${R}_{x}$, ${R}_{y}$, ${R}_{z}$, |
${x}^{2}$, ${y}^{2}$, ${z}^{2}$, $xy$, $xz$, $yz$ |
Character table for the ${C}_{i}$ point group
$E$ | $i$ | ||
---|---|---|---|
A${}_{1g}$ | $1$ | $1$ | ${R}_{x}$, ${R}_{y}$, ${R}_{z}$, ${x}^{2}$, ${y}^{2}$, ${z}^{2}$, $xy$, $xz$, $yz$ |
A${}_{1u}$ | $1$ | $-1$ | $x$, $y$, $z$ |
Character table for the ${C}_{s}$ point group
$E$ | ${\sigma}_{h}$ | ||
---|---|---|---|
A${}^{{}^{\prime}}$ | $1$ | $1$ | $x$, $y$, ${R}_{z}$, ${x}^{2}$, ${y}^{2}$, ${z}^{2}$, $xy$ |
A${}^{{}^{\prime \prime}}$ | $1$ | $-1$ | $z$, ${R}_{x}$, ${R}_{y}$, $yz$, $xz$ |
Character table for the ${C}_{2}$ point group
$E$ | ${C}_{2}$ | ||
---|---|---|---|
A | $1$ | $1$ | $z$, ${R}_{z}$, ${x}^{2}$, ${y}^{2}$, ${z}^{2}$, $xy$ |
B | $1$ | $-1$ | $x$, $y$, ${R}_{x}$, ${R}_{y}$, $yz$, $xz$ |
Character table for the ${C}_{2v}$ point group
$E$ | ${C}_{2}$ | ${\sigma}_{h}$ | ${\sigma}_{v}$ | ||
---|---|---|---|---|---|
A${}_{1}$ | $1$ | $1$ | $1$ | $1$ | $z$, ${x}^{2}$, ${y}^{2}$, ${z}^{2}$ |
B${}_{1}$ | $1$ | $-1$ | $1$ | $-1$ | $y$, ${R}_{x}$, $yz$ |
B${}_{2}$ | $1$ | $-1$ | $-1$ | $1$ | $x$, ${R}_{y}$, $xz$ |
A${}_{2}$ | $1$ | $1$ | $-1$ | $-1$ | ${R}_{z}$, $xy$ |
Character table for the ${C}_{2h}$ point group
$E$ | ${C}_{2}(z)$ | $i$ | ${\sigma}_{h}$ | ||
---|---|---|---|---|---|
A${}_{g}$ | $1$ | $1$ | $1$ | $1$ | ${R}_{z}$, ${x}^{2}$, ${y}^{2}$, ${z}^{2}$, $xy$ |
B${}_{g}$ | $1$ | $-1$ | $1$ | $-1$ | ${R}_{x}$, ${R}_{y}$, $xz$, $yz$ |
A${}_{u}$ | $1$ | $1$ | $-1$ | $-1$ | $z$ |
B${}_{u}$ | $1$ | $-1$ | $-1$ | $1$ | $x$, $y$ |
Character table for the ${D}_{2}$ point group
$E$ | ${C}_{2}(z)$ | ${C}_{2}(y)$ | ${C}_{2}(x)$ | ||
---|---|---|---|---|---|
A | $1$ | $1$ | $1$ | $1$ | ${x}^{2}$, ${y}^{2}$, ${z}^{2}$ |
B${}_{1}$ | $1$ | $1$ | $-1$ | $-1$ | $z$, ${R}_{z}$, $xy$ |
B${}_{2}$ | $1$ | $-1$ | $1$ | $-1$ | $y$, ${R}_{y}$, $xz$ |
B${}_{3}$ | $1$ | $-1$ | $-1$ | $1$ | $x$, ${R}_{x}$, $yz$ |
Character table for the ${D}_{2h}$ point group
$E$ | ${C}_{2}(z)$ | ${C}_{2}(y)$ | ${C}_{2}(x)$ | $i$ | ${\sigma}_{xy}$ | ${\sigma}_{xz}$ | ${\sigma}_{yz}$ | ||
---|---|---|---|---|---|---|---|---|---|
A${}_{g}$ | $1$ | $1$ | $1$ | $1$ | $1$ | $1$ | $1$ | $1$ | ${x}^{2}$, ${y}^{2}$, ${z}^{2}$ |
B${}_{1g}$ | $1$ | $1$ | $-1$ | $-1$ | $1$ | $1$ | $-1$ | $-1$ | ${R}_{z}$, $xy$ |
B${}_{2g}$ | $1$ | $-1$ | $1$ | $-1$ | $1$ | $-1$ | $1$ | $-1$ | ${R}_{y}$, $xz$ |
B${}_{3g}$ | $1$ | $-1$ | $-1$ | $1$ | $1$ | $-1$ | $-1$ | $1$ | ${R}_{x}$, $yz$ |
A${}_{u}$ | $1$ | $1$ | $1$ | $1$ | $-1$ | $-1$ | $-1$ | $-1$ | |
B${}_{1u}$ | $1$ | $1$ | $-1$ | $-1$ | $-1$ | $-1$ | $1$ | $1$ | $z$ |
B${}_{2u}$ | $1$ | $-1$ | $1$ | $-1$ | $-1$ | $1$ | $-1$ | $1$ | $y$ |
B${}_{3u}$ | $1$ | $-1$ | $-1$ | $1$ | $-1$ | $1$ | $1$ | $-1$ | $x$ |
For the visualization of molecular structures, molecular orbitals, electron densities, geometry optimization steps, normal modes, and IR spectra an interface has been developed to the Molden program [148]. Cartesian coordinates, basis function information, MO coefficients, etc. are saved to file MOLDEN using Molden format. After the termination of Mrcc, Molden should be started by typing molden MOLDEN. The Molden interface can be controlled by the molden keyword (see page 12 for the description of the keyword).
If the MOs are localized, the MOLDEN file containing the canonical HF orbitals is saved under the name MOLDEN.CAN, and the canonical MOs are replaced by the localized ones in the MOLDEN file. You can use both files to visualize the MOs that you are interested in.
Please note that Molden can also be used for the generation of input molecular structures in Z-matrix or xyz format (see the description of the geom keyword on page 12).
Cartesian coordinates are also written to file COORD.xyz in xyz (XMol) format, which can be processed by many molecular visualization programs. This interface can also be controlled by the molden keyword (see page 12 for the description of the keyword).
The authors of the Mrcc program are very grateful to
Professor Jürgen Gauss (Universität Mainz) for continuous support and discussions, development and maintenance of the Cfour interface, and for the permission to use the basis set format of Cfour.
Dr. Michael Harding (TU Karlsruhe) for continuous support and for his help in the parallelization of the code.
Professor Hans-Joachim Werner (Universität Stuttgart), Professor Peter J. Knowles (Cardiff University), and Dr. Andy May (Cardiff University) for the development and maintenance of the Molpro interface, and many useful suggestions.
Professor Péter G. Szalay (Eötvös University, Budapest) for his continuous support and for the development of the Columbus interface.
Professor Lucas Visscher (VU University Amsterdam) for the development and maintenance of the Dirac interface, and for the permission to distribute the interface code.
Dr. Andreas Götz (University of California San Diego) for the development and maintenance of the Amber interface,
Professor Péter R. Surján (Eötvös University, Budapest) for his support at the early stages of the code development.
János Brátán (TU Budapest) for continuous technical support.
Financial support to the development of the Mrcc suite has been provided by the
Hungarian Scientific Research Fund (OTKA), Grant Agreement Nos. T023052, T035094, T047182, T49718, D048583, NF72194, K108752, and PD108451.
National Research, Development, and Innovation Office (NKFIH), Grant Agreement No. KKP126451.
European Research Council (ERC) under the European Community’s Seventh Framework Programme (FP7/2007-2013), ERC Grant Agreement No. 200639.
Hungarian Science and Technology Foundation, Grant Agreement Nos. IND-5/2001 and IND 04/2006.
Bolyai Research Scholarship of the Hungarian Academy of Sciences, Grant Agreement Nos. BO/00593/07, BO/00199/14, and BO/00558/18.
New Hungary Development Plan, project ID: TÁMOP-4.2.1/B-09/1/KMR-2010-0002.
Lendület Program of the Hungarian Academy of Sciences.
Higher Education Excellence Program of the Ministry of Human Capacities.
New National Excellence Program of the Ministry of Human Capacities, ID: ÚNKP-17-4-BME-55 and ÚNKP-18-4-BME-257.
Hungarian HPC Infrastructure at NIIF Institute, Hungary.