References

• [1] Mihály Kállay, Péter R. Nagy, Dávid Mester, Zoltán Rolik, Gyula Samu, József Csontos, József Csóka, P. Bernát Szabó, László Gyevi-Nagy, Bence Hégely, István Ladjánszki, Lóránt Szegedy, Bence Ladóczki, Klára Petrov, Máté Farkas, Pál D. Mezei, and Ádám Ganyecz: The MRCC program system: Accurate quantum chemistry from water to proteins, J. Chem. Phys. 152, 074107 (2020).
• [2] Dávid Mester, Péter R. Nagy, József Csóka, László Gyevi-Nagy, P. Bernát Szabó, Réka A. Horváth, Klára Petrov, Bence Hégely, Bence Ladóczki, Gyula Samu, Balázs D. Lőrincz, and Mihály Kállay: Overview of developments in the MRCC program system, J. Phys. Chem. A 129, 2086 (2025).
• [3] Mihály Kállay and Péter R. Surján: Higher excitations in coupled-cluster theory, J. Chem. Phys. 115, 2945 (2001).
• [4] Mihály Kállay, Péter G. Szalay, and Péter R. Surján: A general state-selective coupled-cluster algorithm, J. Chem. Phys. 117, 980 (2002).
• [5] Mihály Kállay, Jürgen Gauss, and Péter G. Szalay: Analytic first derivatives for general coupled-cluster and configuration interaction models, J. Chem. Phys. 119, 2991 (2003).
• [6] Mihály Kállay and Jürgen Gauss: Analytic second derivatives for general coupled-cluster and configuration interaction models, J. Chem. Phys. 120, 6841 (2004).
• [7] Mihály Kállay and Jürgen Gauss: Calculation of excited-state properties using general coupled-cluster and configuration-interaction models, J. Chem. Phys. 121, 9257 (2004).
• [8] Yannick J. Bomble, John F. Stanton, Mihály Kállay, and Jürgen Gauss: Coupled cluster methods including non-iterative approximate quadruple excitation corrections, J. Chem. Phys. 123, 054101 (2005).
• [9] Mihály Kállay and Jürgen Gauss: Approximate treatment of higher excitations in coupled-cluster theory, J. Chem. Phys. 123, 214105 (2005).
• [10] Jürgen Gauss, Attila Tajti, Mihály Kállay, John F. Stanton, and Péter G. Szalay: Analytic calculation of the diagonal Born–Oppenheimer correction within configuration-interaction and coupled-cluster theory, J. Chem. Phys. 125, 144111 (2006).
• [11] Mihály Kállay and Jürgen Gauss: Calculation of frequency-dependent polarizabilities using general coupled-cluster models, J. Mol. Struct.:THEOCHEM 768, 71 (2006).
• [12] Jürgen Gauss, Kenneth Ruud, and Mihály Kállay: Gauge-origin independent calculation of magnetizabilities and rotational $g$ tensors at the coupled-cluster level, J. Chem. Phys. 127, 074101 (2007).
• [13] Darragh P. O’Neill, Mihály Kállay, and Jürgen Gauss: Calculation of frequency-dependent hyperpolarizabilities using general coupled-cluster models, J. Chem. Phys. 127, 134109 (2007).
• [14] Darragh P. O’Neill, Mihály Kállay, and Jürgen Gauss: Analytic evaluation of Raman intensities in coupled-cluster theory, Mol. Phys. 105, 2447 (2007).
• [15] Mihály Kállay and Jürgen Gauss: Approximate treatment of higher excitations in coupled-cluster theory. II. Extension to general single-determinant reference functions and improved approaches for the canonical Hartree–Fock case, J. Chem. Phys. 129, 144101 (2008).
• [16] Jürgen Gauss, Mihály Kállay, and Frank Neese: Calculation of electronic g-tensors using coupled-cluster theory, J. Phys. Chem. A 113, 11541 (2009).
• [17] Sanghamitra Das, Debashis Mukherjee, and Mihály Kállay: Full implementation and benchmark studies of Mukherjee’s state-specific multi-reference coupled-cluster ansatz, J. Chem. Phys. 132, 074103 (2010).
• [18] Huliyar S. Nataraj, Mihály Kállay, and Lucas Visscher: General implementation of the relativistic coupled-cluster method, J. Chem. Phys. 133, 234109 (2010).
• [19] Sanghamitra Das, Mihály Kállay, and Debashis Mukherjee: Inclusion of selected higher excitations involving active orbitals in the state-specific multi-reference coupled-cluster theory, J. Chem. Phys. 133, 234110 (2010).
• [20] Mihály Kállay, Huliyar S. Nataraj, Bijaya K. Sahoo, Bhanu P. Das, and Lucas Visscher: Relativistic general-order coupled-cluster method for high-precision calculations: Application to the Al⁺ atomic clock, Phys. Rev. A 83, 030503(R) (2011).
• [21] Zoltán Rolik and Mihály Kállay: Cost-reduction of high-order coupled-cluster methods via active-space and orbital transformation techniques, J. Chem. Phys. 134, 124111 (2011).
• [22] Zoltán Rolik and Mihály Kállay: A general-order local coupled-cluster method based on the cluster-in-molecule approach, J. Chem. Phys. 135, 104111 (2011).
• [23] Sanghamitra Das, Mihály Kállay, and Debashis Mukherjee: Superior performance of Mukherjee’s state-specific multi-reference coupled-cluster theory at the singles and doubles truncation scheme with localized active orbitals, Chem. Phys. 392, 83 (2012).
• [24] Zoltán Rolik, Lóránt Szegedy, István Ladjánszki, Bence Ladóczki, and Mihály Kállay: An efficient linear-scaling CCSD(T) method based on local natural orbitals, J. Chem. Phys. 139, 094105 (2013).
• [25] Zoltán Rolik and Mihály Kállay: A quasiparticle-based multireference coupled-cluster method, J. Chem. Phys. 141, 134112 (2014).
• [26] Mihály Kállay: A systematic way for the cost reduction of density fitting methods, J. Chem. Phys. 141, 244113 (2014).
• [27] Dávid Mester, József Csontos, and Mihály Kállay: Unconventional bond functions for quantum chemical calculations, Theor. Chem. Acc. 134, 74 (2015).
• [28] Pál D. Mezei, Gábor I. Csonka, Adrienn Ruzsinszky, and Mihály Kállay: Construction and application of a new dual-hybrid random phase approximation, J. Chem. Theory Comput. 11, 4615 (2015).
• [29] Bence Hégely, Ferenc Bogár, György G. Ferenczy, and Mihály Kállay: A QM/MM program using frozen localized orbitals and the Huzinaga equation, Theor. Chem. Acc. 134, 132 (2015).
• [30] Mihály Kállay: Linear-scaling implementation of the direct random-phase approximation, J. Chem. Phys. 142, 204105 (2015).
• [31] Péter R. Nagy, Gyula Samu, and Mihály Kállay: An integral-direct linear-scaling second-order Møller–Plesset approach, J. Chem. Theory Comput. 12, 4897 (2016).
• [32] Pál D. Mezei, Gábor I. Csonka, Adrienn Ruzsinszky, and Mihály Kállay: Construction of a spin-component scaled dual-hybrid random phase approximation, J. Chem. Theory Comput. 13, 796 (2017).
• [33] Bence Hégely, Péter R. Nagy, György G. Ferenczy, and Mihály Kállay: Exact density functional and wave function embedding schemes based on orbital localization, J. Chem. Phys. 145, 064107 (2016).
• [34] Gyula Samu and Mihály Kállay: Efficient evaluation of three-center Coulomb integrals, J. Chem. Phys. 146, 204101 (2017).
• [35] Dávid Mester, Péter R. Nagy, and Mihály Kállay: Reduced-cost linear-response CC2 method based on natural orbitals and natural auxiliary functions, J. Chem. Phys. 146, 194102 (2017).
• [36] Péter R. Nagy and Mihály Kállay: Optimization of the linear-scaling local natural orbital CCSD(T) method: Redundancy-free triples correction using Laplace transform, J. Chem. Phys. 146, 214106 (2017).
• [37] Dávid Mester, Péter R. Nagy, and Mihály Kállay: Reduced-cost second-order algebraic-diagrammatic construction method for excitation energies and transition moments, J. Chem. Phys. 148, 094111 (2018).
• [38] Péter R. Nagy, Gyula Samu, and Mihály Kállay: Optimization of the linear-scaling local natural orbital CCSD(T) method: Improved algorithm and benchmark applications, J. Chem. Theory Comput. 14, 4193 (2018).
• [39] Bence Hégely, Péter R. Nagy, and Mihály Kállay: Dual basis set approach for density functional and wave function embedding schemes, J. Chem. Theory Comput. 14, 4600 (2018).
• [40] Dávid Mester and Mihály Kállay: Reduced-scaling approach for configuration interaction singles and time-dependent density functional theory calculations using hybrid functionals, J. Chem. Theory Comput. 15, 1690 (2019).
• [41] Dávid Mester and Mihály Kállay: Combined density functional and algebraic-diagrammatic construction approach for accurate excitation energies and transition moments, J. Chem. Theory Comput. 15, 4440 (2019).
• [42] Péter R. Nagy and Mihály Kállay: Approaching the basis set limit of CCSD(T) energies for large molecules with local natural orbital coupled-cluster methods, J. Chem. Theory Comput. 15, 5275 (2019).
• [43] Dávid Mester, Péter R. Nagy, and Mihály Kállay: Reduced-scaling correlation methods for the excited states of large molecules: Implementation and benchmarks for the second-order algebraic-diagrammatic construction approach, J. Chem. Theory Comput. 15, 6111 (2019).
• [44] Pál D. Mezei, Adrienn Ruzsinszky, and Mihály Kállay: Reducing the many-electron self-interaction error in the second-order screened exchange method, J. Chem. Theory Comput. 15, 6607 (2019).
• [45] Pál D. Mezei and Mihály Kállay: Construction of a range-separated dual-hybrid direct random phase approximation, J. Chem. Theory Comput. 15, 6678 (2019).
• [46] László Gyevi-Nagy, Mihály Kállay, and Péter R. Nagy: Integral-direct and parallel implementation of the CCSD(T) method: Algorithmic developments and large-scale applications, J. Chem. Theory Comput. 16, 366 (2020).
• [47] József Csóka and Mihály Kállay: Speeding up density fitting Hartree–Fock calculations with multipole approximations, Mol. Phys. 118, e1769213 (2020).
• [48] László Gyevi-Nagy, Mihály Kállay, and Péter R. Nagy: Accurate reduced-cost CCSD(T) energies: Parallel implementation, benchmarks, and large-scale applications, J. Chem. Theory Comput. 17, 860 (2021).
• [49] Dávid Mester and Mihály Kállay: A simple range-separated double-hybrid density functional theory for excited states, J. Chem. Theory Comput. 17, 927 (2021).
• [50] József Csóka and Mihály Kállay: Speeding up Hartree–Fock and Kohn–Sham calculations with first-order corrections, J. Chem. Phys. 154, 164114 (2021).
• [51] P. Bernát Szabó, József Csóka, Mihály Kállay, and Péter R. Nagy: Linear scaling open-shell MP2 approach: algorithm, benchmarks, and large-scale applications, J. Chem. Theory Comput. 17, 2886 (2021).
• [52] Dávid Mester and Mihály Kállay: Spin-scaled range-separated double-hybrid density functional theory for excited states, J. Chem. Theory Comput. 17, 4211 (2021).
• [53] Mihály Kállay, Réka A. Horváth, László Gyevi-Nagy, and Péter R. Nagy: Size-consistent explicitly correlated triple excitation correction, J. Chem. Phys. 155, 034107 (2021).
• [54] Bence Hégely and Mihály Kállay: Multilevel approach to the initial guess for self-consistent field calculations, Int. J. Quantum Chem. 122, e26782 (2021).
• [55] Péter R. Nagy, László Gyevi-Nagy, and Mihály Kállay: Basis set truncation corrections for improved frozen natural orbital CCSD(T) energies, Mol. Phys. 119, e1963495 (2021).
• [56] Ádám Ganyecz and Mihály Kállay: Implementation and optimization of the embedded cluster reference interaction site model, J. Phys. Chem. A 126, 2417 (2022).
• [57] Dávid Mester and Mihály Kállay: Accurate spectral properties within double-hybrid density functional theory: A spin-scaled range-separated second-order algebraic-diagrammatic construction-based approach, J. Chem. Theory Comput. 18, 865 (2022).
• [58] Dávid Mester and Mihály Kállay: Charge-transfer excitations within density functional theory: How accurate are the most recommended approaches?, J. Chem. Theory Comput. 18, 1646 (2022).
• [59] Péter R. Nagy, László Gyevi-Nagy, Balázs D. Lőrincz, and Mihály Kállay: Pursuing the basis set limit of CCSD(T) non-covalent interaction energies for medium-sized complexes: case study on the S66 compilation, Mol. Phys. 121, e2109526 (2023).
• [60] Mihály Kállay, Réka A. Horváth, László Gyevi-Nagy, and Péter R. Nagy: Basis set limit CCSD(T) energies for extended molecules via a reduced-cost explicitly correlated approach, J. Chem. Theory Comput. 19, 174 (2023).
• [61] Bence Hégely, Ádám B. Szirmai, Dávid Mester, Attila Tajti, Péter G. Szalay, and Mihály Kállay: Performance of multilevel methods for excited states, J. Phys. Chem. A 126, 6548 (2022).
• [62] Dávid Mester and Mihály Kállay: Double-hybrid density functional theory for core excitations: Theory and benchmark calculations, J. Chem. Theory Comput. 19, 1310 (2023).
• [63] Dávid Mester and Mihály Kállay: Reduced-cost second-order algebraic-diagrammatic construction method for core excitations, J. Chem. Theory Comput. 19, 2850 (2023).
• [64] József Csóka and Mihály Kállay: Analytic gradients for local density fitting Hartree–Fock and Kohn–Sham methods, J. Chem. Phys. 158, 024110 (2023).
• [65] Dávid Mester and Mihály Kállay: Vertical ionization potentials and electron affinities at the double-hybrid density functional level, J. Chem. Theory Comput. 19, 3982 (2023).
• [66] P. Bernát Szabó, József Csóka, Mihály Kállay, and Péter R. Nagy: Linear-scaling local natural orbital CCSD(T) approach for open-shell systems: algorithm, benchmarks, and large-scale applications, J. Chem. Theory Comput. 19, 8166 (2023).
• [67] Dávid Mester and Mihály Kállay: Basis set limit of CCSD(T) energies: Explicit correlation versus density-based basis-set correction, J. Chem. Theory Comput. 19, 8210 (2023).
• [68] Réka A. Horváth and Mihály Kállay: Basis set limit MP2 energies for extended molecules via a reduced-cost explicitly correlated approach, Mol. Phys. 122, e2304103 (2024).
• [69] József Csóka, Bence Hégely, Péter R. Nagy, and Mihály Kállay: Development of analytic gradients for the Huzinaga quantum embedding method and its applications to large-scale hybrid and double hybrid DFT forces, J. Chem. Phys. 160, 124113 (2024).
• [70] Klára Petrov, József Csóka, and Mihály Kállay: Analytic gradients for density fitting MP2 using natural auxiliary functions, J. Phys. Chem. A 128, 6566 (2024).
• [71] Dávid Mester, Péter R. Nagy, and Mihály Kállay: Basis-set limit CCSD(T) energies for large molecules with local natural orbitals and reduced-scaling basis-set corrections, J. Chem. Theory Comput. 20, 7453 (2024).
• [72] Dávid Mester and Mihály Kállay: Higher-order coupled-cluster calculations with basis-set corrections, Chem. Phys. Lett. 861, 141780 (2025).
• [73] Bence Ladóczki, László Gyevi-Nagy, Péter R. Nagy, and Mihály Kállay: Enabling accurate and large-scale explicitly correlated CCSD(T) computations via a reduced-cost and parallel implementation, J. Chem. Theory Comput. 21, 2432 (2025).
• [74] Jan Řezáč: Cuby: An integrative framework for computational chemistry, J. Comput. Chem. 37, 1230 (2016).
• [75] Thomas Weymuth, Jan P. Unsleber, Paul L. Türtscher, Miguel Steiner, Jan-Grimo Sobez, Charlotte H. Müller, Maximilian Mörchen, Veronika Klasovita, Stephanie A. Grimmel, Marco Eckhoff, Katja-Sophia Csizi, Francesco Bosia, Moritz Bensberg, and Markus Reiher: SCINE-software for chemical interaction networks, J. Chem. Phys. 160, 222501 (2024).
• [76] P. Salvador, E. Ramos-Cordoba, M. Montilla, L. Pujal, and M. Gimferrer: APOST-3D: Chemical concepts from wavefunction analysis, J. Chem. Phys. 160, 172502 (2024).
• [77] https://ash.readthedocs.io/en/latest/index.html, Accessed Jan 1, 2025.
• [78] https://cuby4.molecular.cz/, Accessed Jan 1, 2025.
• [79] https://github.com/qcscine, Accessed Jan 1, 2025.
• [80] https://github.com/mgimferrer/apost3d.git, Accessed Jan 1, 2025.
• [81] A. Götz, M. A. Clack, and R. C. Walker: An extensible interface for QM/MM molecular dynamics simulations with amber, J. Comput. Chem. 35, 95 (2014).
• [82] Frederick R. Manby, Martina Stella, Jason D. Goodpaster, and Thomas F. Miller III: A simple, exact density-functional-theory embedding scheme, J. Chem. Theory Comput. 8, 2564 (2012).
• [83] F. Maseras and K. Morokuma: IMOMM – A new integrated ab-initio plus molecular mechanics geometry optimization scheme of equilibrium structures and transition-states, J. Comput. Chem. 16, 1170 (1995).
• [84] Thomas Kloss, Jochen Heil, and Stefan M. Kast: Quantum chemistry in solution by combining 3D integral equation theory with a cluster embedding approach, J. Phys. Chem. B 112, 4337 (2008).
• [85] Stefan M. Kast, Jochen Heil, Stefan Güssregen, and K. Friedemann Schmidt: Prediction of tautomer ratios by embedded-cluster integral equation theory, J. Comput. Aided Mol. Des. 24, 343 (2010).
• [86] C. Bannwarth, E. Caldeweyher, S. Ehlert, A. Hansen, P. Pracht, J. Seibert, S. Spicher, and S. Grimme: Extended tight-binding quantum chemistry methods, Wiley Interdiscip. Rev.: Comput. Mol. Sci. 11, e1493 (2020).
• [87] S. Grimme, C. Bannwarth, and P. Shushkov: A robust and accurate tight-binding quantum chemical method for structures, vibrational frequencies, and noncovalent interactions of large molecular systems parametrized for all spd-block elements (Z = 1-86), J. Chem. Theory Comput. 13, 1989 (2017).
• [88] C. Bannwarth, S. Ehlert, and S. Grimme: GFN2-xTB—An accurate and broadly parametrized self-consistent tight-binding quantum chemical method with multipole electrostatics and density-dependent dispersion contributions, J. Chem. Theory Comput. 15, 1652 (2019).
• [89] S. Spicher and S. Grimme: Robust atomistic modeling of materials, organometallic, and biochemical systems, Angew. Chem. Int. Ed. 59, 15665 (2020).
• [90] S. Ehlert, M. Stahn, S. Spicher, and S. Grimme: Robust and efficient implicit solvation model for fast semiempirical methods, J. Chem. Theory Comput. 17, 4250 (2021).
• [91] Mopac2016, James J. P. Stewart, Stewart Computational Chemistry, web: http://OpenMOPAC.net.
• [92] Dávid Mester and Mihály Kállay: Near-basis-set-limit double-hybrid DFT energies with exceptionally low computational costs, J. Phys. Chem. Lett. 16, 2136–2143 (2025).
• [93] S. Humbel, S. Sieber, and K. Morokuma: The IMOMO method: Integration of different levels of molecular orbital approximations for geometry optimization of large systems: Test for $n$-butane conformation and S_N2 reaction: RCl+Cl^-, J. Chem. Phys. 105, 1959 (1996).
• [94] Jacopo Tomasi, Benedetta Mennucci, and Roberto Cammi: Quantum mechanical continuum solvation models, Chem. Rev. 105, 2999 (2005).
• [95] Roberto Di Remigio, Krzysztof Mozgawa, Hui Cao, Ville Weijo, and Luca Frediani: A polarizable continuum model for molecules at spherical diffuse interfaces, J. Chem. Phys. 144, 124103 (2016).
• [96] Roberto Di Remigio, Arnfinn Hykkerud Steindal, Krzysztof Mozgawa, Ville Weijo, Hui Cao, and Luca Frediani: PCMSolver: An open-source library for solvation modeling, Int. J. Quantum Chem. 119, e25685 (2019).
• [97] PCMSolver, an open-source library for the polarizable continuum model electrostatic problem, written by R. Di Remigio, L. Frediani and contributors (see http://pcmsolver.readthedocs.io/), Accessed Jan 1, 2025.
• [98] A. Szabo and N. S. Ostlund, Modern Quantum Chemistry, McGraw-Hill: New York: 1989.
• [99] C. C. J. Roothaan: Self-consistent field theory for open shells of electronic systems, Rev. Mod. Phys. 32, 179 (1960).
• [100] T. Helgaker, P. Jørgensen, and J. Olsen, Molecular Electronic Structure Theory, Wiley: Chichester: 2000.
• [101] József Csóka and Mihály Kállay, to be published, 2020.
• [102] W. Kohn and L. J. Sham: Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133 (1965).
• [103] Michael Filatov and Sason Shaik: Spin-restricted density functional approach to the open-shell problem, Chem. Phys. Lett. 288, 689 (1998).
• [104] Andreas Savin and Heinz-Jürgen Flad: Density functionals for the Yukawa electron-electron interaction, Int. J. Quantum Chem. 56, 327 (1995).
• [105] Stefan Grimme: Semiempirical hybrid density functional with perturbative second-order correlation, J. Chem. Phys. 124, 034108 (2006).
• [106] János G. Ángyán, Iann C. Gerber, Andreas Savin, and Julien Toulouse: van der Waals forces in density functional theory: Perturbational long-range electron-interaction corrections, Phys. Rev. A 72, 012510 (2005).
• [107] Cairedine Kalai and Julien Toulouse: A general range-separated double-hybrid density-functional theory, J. Chem. Phys. 148, 164105 (2018).
• [108] C. Møller and M. S. Plesset: Note on an approximation treatment for many-electron systems, Phys. Rev. 46, 618 (1934).
• [109] Stefan Grimme: Improved second-order Møller–Plesset perturbation theory by separate scaling of parallel- and antiparallel-spin pair correlation energies, J. Chem. Phys. 118, 9095 (2003).
• [110] Yousung Jung, Rohini C. Lochan, Anthony D. Dutoi, and Martin Head-Gordon: Scaled opposite-spin second order Møller–Plesset correlation energy: An economical electronic structure method, J. Chem. Phys. 121, 9793 (2004).
• [111] Stanislav Kedžuch, Matúš Milko, and Jozef Noga: Alternative formulation of the matrix elements in MP2-R12 theory, Int. J. Quantum Chem. 105, 929 (2005).
• [112] Rafał A. Bachorz, Florian A. Bischoff, Andreas Glöß, Christof Hättig, Sebastian Höfener, Wim Klopper, and David P. Tew: The MP2-F12 method in the turbomole program package, J. Comput. Chem. 32, 2492 (2011).
• [113] Filipp Furche: Molecular tests of the random phase approximation to the exchange-correlation energy functional, Phys. Rev. B 64, 195120 (2001).
• [114] Andreas Grüneis, Martijn Marsman, Judith Harl, Laurids Schimka, and Georg Kresse: Making the random phase approximation to electronic correlation accurate, J. Chem. Phys. 131, 154115 (2009).
• [115] Xinguo Ren, Patrick Rinke, Gustavo E. Scuseria, and Matthias Scheffler: Renormalized second-order perturbation theory for the electron correlation energy: Concept, implementation, and benchmarks, Phys. Rev. B 88, 035120 (2013).
• [116] A. Szabo and N. S. Ostlund: The correlation energy in the random phase approximation: Intermolecular forces between closed-shell systems, J. Chem. Phys. 67, 4351 (1977).
• [117] Andreas Heßelmann: Random-phase-approximation correlation method including exchange interactions, Phys. Rev. A 85, 012517 (2012).
• [118] O. Christiansen, H. Koch, and P. Jørgensen: The second-order approximate coupled cluster singles and doubles model CC2, Chem. Phys. Lett. 243, 409 (1995).
• [119] Arnim Hellweg, Sarah A. Grün, and Christof Hättig: Benchmarking the performance of spin-component scaled CC2 in ground and electronically excited states, Phys. Chem. Chem. Phys. 10, 4119 (2008).
• [120] Nina O. C. Winter and Christof Hättig: Scaled opposite-spin CC2 for ground and excited states with fourth order scaling computational costs, J. Chem. Phys. 134, 184101 (2011).
• [121] Rodney J Bartlett and David M Silver: Many-body perturbation theory applied to electron pair correlation energies. I. Closed-shell first-row diatomic hydrides, J. Chem. Phys. 62, 3258 (1975).
• [122] J. Čížek: On the correlation problem in atomic and molecular systems. Calculation of wavefunction components in Ursell-type expansion using quantum-field theoretical methods, J. Chem. Phys. 45, 4256 (1966).
• [123] G. D. Purvis III and R. J. Bartlett: A full coupled-cluster singles and doubles model: The inclusion of disconnected triples, J. Chem. Phys. 76, 1910 (1982).
• [124] J. Noga and R. J. Bartlett: The full CCSDT model for molecular electronic structure, J. Chem. Phys. 86, 7041 (1987).
• [125] S. A. Kucharski and R. J. Bartlett: The coupled-cluster single, double, triple, and quadruple excitation method, J. Chem. Phys. 97, 4282 (1992).
• [126] K. Raghavachari, G. W. Trucks, J. A. Pople, and M. Head-Gordon: A fifth-order perturbation comparison of electron correlation theories, Chem. Phys. Lett. 157, 479 (1989).
• [127] M. Urban, J. Noga, S. J. Cole, and R. J. Bartlett: Towards a full CCSDT model for electron correlation, J. Chem. Phys. 83, 4041 (1985).
• [128] S. A. Kucharski and R. J. Bartlett: An efficient way to include connected quadruple contributions into the coupled cluster method, J. Chem. Phys. 108, 9221 (1998).
• [129] S. A. Kucharski and R. J. Bartlett: Noniterative energy corrections through fifth-order to the coupled cluster singles and doubles method, J. Chem. Phys. 108, 5243 (1998).
• [130] T. D. Crawford and J. F. Stanton: Investigation of an asymmetric triple-excitation correction for coupled-cluster energies, Int. J. Quantum Chem. 70, 601 (1998).
• [131] Y. S. Lee, S. A. Kucharski, and R. J. Bartlett: A coupled cluster approach with triple excitations, J. Chem. Phys. 81, 5906 (1984).
• [132] H. Koch, O. Christiansen, P. Jørgensen, A. M. Sánchez de Merás, and T. Helgaker: The CC3 model: An iterative coupled cluster approach including connected triples, J. Chem. Phys. 106, 1808 (1997).
• [133] Christof Hättig, David P. Tew, and Andreas Köhn: Accurate and efficient approximations to explicitly correlated coupled-cluster singles and doubles, CCSD-F12, J. Chem. Phys. 132, 231102 (2010).
• [134] G. Knizia, T. B. Adler, and H.-J. Werner: Simplified CCSD(T)-F12 methods: Theory and benchmarks, J. Chem. Phys. 130, 054104 (2009).
• [135] Emmanuel Giner, Barthélémy Pradines, Anthony Ferté, Roland Assaraf, Andreas Savin, and Julien Toulouse: Curing basis-set convergence of wave-function theory using density-functional theory: A systematically improvable approach, J. Chem. Phys. 149, 194301 (2018).
• [136] Pierre-François Loos, Barthélémy Pradines, Anthony Scemama, Julien Toulouse, and Emmanuel Giner: A density-based basis-set correction for wave function theory, J. Phys. Chem. Lett. 10, 2931 (2019).
• [137] N. Oliphant and L. Adamowicz: Multireference coupled-cluster method using a single-reference formalism, J. Chem. Phys. 94, 1229 (1991).
• [138] P. Piecuch, N. Oliphant, and L. Adamowicz: A state-selective multireference coupled-cluster theory employing the single-reference formalism, J. Chem. Phys. 99, 1875 (1993).
• [139] R. J. Buenker and S. D. Peyerimhoff: Individualized configuration selection in CI calculations with subsequent energy extrapolation, Theor. Chem. Acc. 35, 33 (1974).
• [140] Stephen R. Langhoff and Ernest R. Davidson: Configuration interaction calculations on the nitrogen molecule, Int. J. Quantum Chem. 8, 61 (1974).
• [141] J. B. Foresman, M. Head-Gordon, J. A. Pople, and M. J. Frisch: Toward a systematic molecular orbital theory for excited states, J. Phys. Chem. 96, 135 (1992).
• [142] A. D. McLachlan and A. M. Ball: Time-dependent Hartree–Fock theory for molecules, Rev. Mod. Phys. 36, 844 (1964).
• [143] M. E. Casida, Recent advances in density functional methods, in Computational Chemistry: Reviews of Current Trends, edited by D. P. Chong: volume 1: World Scientific: Singapore: 1999.
• [144] So Hirata and Martin Head-Gordon: Time-dependent density functional theory within the Tamm–Dancoff approximation, Chem. Phys. Lett. 314, 291 (1999).
• [145] Takeshi Yanai, David P Tew, and Nicholas C Handy: A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP), Chem. Phys. Lett. 393, 51 (2004).
• [146] Yoshihiro Tawada, Takao Tsuneda, Susumu Yanagisawa, Takeshi Yanai, and Kimihiko Hirao: A long-range-corrected time-dependent density functional theory, J. Chem. Phys. 120, 8425 (2004).
• [147] Stefan Grimme and Frank Neese: Double-hybrid density functional theory for excited electronic states of molecules, J. Chem. Phys. 127, 154116 (2007).
• [148] Marcos Casanova-Páez, Michael B. Dardis, and Lars Goerigk: $\omega$B2PLYP and $\omega$B2GPPLYP: The first two double-hybrid density functionals with long-range correction optimized for excitation energies, J. Chem. Theory Comput. 15, 4735 (2019).
• [149] M. Head-Gordon, R. J. Rico, M. Oumi, and T. J. Lee: A doubles correction to electronic excited states from configuration interaction in the space of single substitutions, Chem. Phys. Lett. 219, 21 (1994).
• [150] Stefan Grimme and Ekaterina I. Izgorodina: Calculation of 0–0 excitation energies of organic molecules by CIS(D) quantum chemical methods, Chem. Phys. 305, 223 (2004).
• [151] Young Min Rhee and Martin Head-Gordon: Scaled second-order perturbation corrections to configuration interaction singles: Efficient and reliable excitation energy methods, J. Phys. Chem. A 111, 5314 (2007).
• [152] Martin Head-Gordon, Manabu Oumi, and David Maurice: Quasidegenerate second-order perturbation corrections to single-excitation configuration interaction, Mol. Phys. 96, 593 (1999).
• [153] Jochen Schirmer: Beyond the random-phase approximation: A new approximation scheme for the polarization propagator, Phys. Rev. A 26, 2395 (1982).
• [154] P. Piecuch, S. A. Kucharski, and R. J. Bartlett: Coupled-cluster methods with internal and semi-internal triply and quadruply excited clusters: CCSDt and CCSDtq approaches, J. Chem. Phys. 110, 6103 (1999).
• [155] WanZhen Liang and Martin Head-Gordon: Approaching the basis set limit in density functional theory calculations using dual basis sets without diagonalization, J. Phys. Chem. A 108, 3206 (2004).
• [156] R. B. Murphy, Y. Cao, M. D. Beachy, M. N. Ringnalda, and R. A. Friesner: Efficient pseudospectral methods for density functional calculations, J. Chem. Phys. 112, 10131 (2000).
• [157] F. Neese, F. Wennmohs, A. Hansen, and U. Becker: Efficient, approximate and parallel Hartree–Fock and hybrid DFT calculations. A ‘chain-of-spheres’ algorithm for the Hartree–Fock exchange, Chem. Phys. 356, 98 (2009).
• [158] Robert Polly, Hans-Joachim Werner, Frederick R. Manby, and Peter J. Knowles: Fast Hartree–Fock theory using local fitting approximations, Mol. Phys. 102, 2311 (2004).
• [159] Samuel Manzer, Paul R. Horn, Narbe Mardirossian, and Martin Head-Gordon: Fast, accurate evaluation of exact exchange: The occ-RI-K algorithm, J. Chem. Phys. 143, 024113 (2015).
• [160] S. Li, J. Ma, and Y. Jiang: Linear scaling local correlation approach for solving the coupled cluster equations of large systems, J. Comput. Chem. 23, 237 (2002).
• [161] H. Stoll: Correlation energy of diamond, Phys. Rev. B 46, 6700 (1992).
• [162] P. Pulay and S. Saebø: Orbital-invariant formulation and second-order gradient evaluation in Møller–Plesset perturbation theory, Theor. Chem. Acc. 69, 357 (1986).
• [163] Yasmine S. Al-Hamdani, Péter R. Nagy, Dennis Barton, Mihály Kállay, Jan Gerit Brandenburg, and Alexandre Tkatchenko: Interactions between large molecules pose a puzzle for reference quantum mechanical methods, Nat. Commun. 12, 3927 (2021).
• [164] Tamás Földes, Ádám Madarász, Ágnes Révész, Zoltán Dobi, Szilárd Varga, Andrea Hamza, Péter R. Nagy, Petri M. Pihko, and Imre Pápai: Stereocontrol in diphenylprolinol silyl ether catalyzed michael additions: Steric shielding or Curtin–Hammett scenario?, J. Am. Chem. Soc. 139, 17052 (2017).
• [165] Sanim Rahman, Vered Wineman-Fisher, Péter R. Nagy, Yasmine Al-Hamdani, Alexandre Tkatchenko, and Sameer Varma: Methyl-induced polarization destabilizes the noncovalent interactions of N-methylated lysines, Chem. Eur. J. 27, 11005 (2021).
• [166] Péter R. Nagy: State-of-the-art local correlation methods enable accurate and affordable gold standard quantum chemistry up to a few hundred atoms, Chem. Sci. 15, 14556 (2024).
• [167] Basis Set Exchange, https://www.basissetexchange.org/.
• [168] David J. Feller: The role of databases in support of computational chemistry calculations, J. Comput. Chem. 17, 1571 (1996).
• [169] K. L. Schuchardt, B. T. Didier, T. Elsethagen, L. Sun, V. Gurumoorthi, J. Chase, J. Li, and T. L. Windus: Basis set exchange: A community database for computational sciences, J. Chem. Inf. Model. 47, 1045 (2007).
• [170] Benjamin P. Pritchard, Doaa Altarawy, Brett Didier, Tara D. Gibson, and Theresa L. Windus: A new basis set exchange: An open, up-to-date resource for the molecular sciences community, J. Chem. Inf. Model. 59, 4814 (2019).
• [171] Miguel A. L. Marques, Micael J. T. Oliveira, and Tobias Burnus: Libxc: A library of exchange and correlation functionals for density functional theory, Comput. Phys. Commun. 183, 2272 (2012).
• [172] Susi Lehtola, Conrad Steigemann, Micael J. T. Oliveira, and Miguel A. L. Marques: Recent developments in libxc – A comprehensive library of functionals for density functional theory, SoftwareX 7, 1 (2018).
• [173] https://libxc.gitlab.io/, Accessed Jan 1, 2025.
• [174] Axel D. Becke: A multicenter numerical integration scheme for polyatomic molecules, J. Chem. Phys. 88, 2547 (1988).
• [175] Oliver Treutler and Reinhart Ahlrichs: Efficient molecular numerical integration schemes, J. Chem. Phys. 102, 346 (1995).
• [176] Thom H. Dunning Jr.: Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen, J. Chem. Phys. 90, 1007 (1989).
• [177] Rick A. Kendall, Thom H. Dunning Jr., and Robert J. Harrison: Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions, J. Chem. Phys. 96, 6796 (1992).
• [178] David E. Woon and Thom H. Dunning Jr.: Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon, J. Chem. Phys. 98, 1358 (1993).
• [179] David E. Woon and Thom H. Dunning Jr.: Gaussian basis sets for use in correlated molecular calculations. V. Core-valence basis sets for boron through neon, J. Chem. Phys. 103, 4572 (1995).
• [180] Kirk A. Peterson and Thom H. Dunning Jr.: Accurate correlation consistent basis sets for molecular core-valence correlation effects: The second row atoms Al-Ar, and the first row atoms B-Ne revisited, J. Chem. Phys. 117, 10548 (2002).
• [181] Thom H. Dunning Jr., Kirk A. Peterson, and Angela K. Wilson: Gaussian basis sets for use in correlated molecular calculations. X. The atoms aluminum through argon revisited, J. Chem. Phys. 114, 9244 (2001).
• [182] P. C. Hariharan and J. A. Pople: The influence of polarization functions on molecular orbital hydrogenation energies, Theor. Chem. Acc. 28, 213 (1973).
• [183] R. Krishnan, J. S. Binkley, R. Seeger, and J. A. Pople: Self-consistent molecular orbital methods. XX. A basis set for correlated wave functions, J. Chem. Phys. 72, 650 (1980).
• [184] W. J. Hehre, R. Ditchfield, and J. A. Pople: Self-consistent molecular orbital methods. XII. Further extensions of Gaussian-type basis sets for use in molecular orbital studies of organic molecules, J. Chem. Phys. 56, 2257 (1972).
• [185] J. D. Dill and J. A. Pople: Self-consistent molecular orbital methods. XV. Extended Gaussian-type basis sets for lithium, beryllium, and boron, J. Chem. Phys. 62, 2921 (1975).
• [186] M. M. Francl, W. J. Petro, W. J. Hehre, J. S. Binkley, M. S. Gordon, D. J. DeFrees, and J. A. Pople: Self-consistent molecular orbital methods. XXIII. A polarization-type basis set for second-row elements, J. Chem. Phys. 77, 3654 (1982).
• [187] J. S. Binkley, J. A. Pople, and W. J. Hehre: Self-consistent molecular orbital methods. 21. Small split-valence basis sets for first-row elements, J. Am. Chem. Soc. 102, 939 (1980).
• [188] M. S. Gordon, J. S. Binkley, J. A. Pople, W. J. Pietro, and W. J. Hehre: Self-consistent molecular-orbital methods. 22. Small split-valence basis sets for second-row elements, J. Am. Chem. Soc. 104, 2797 (1983).
• [189] A. D. McLean and G. S. Chandler: Contracted Gaussian basis sets for molecular calculations. I. Second row atoms, Z=11-18, J. Chem. Phys. 72, 5639 (1980).
• [190] T. Clark, J. Chandrasekhar, G.W. Spitznagel, and P. v. R. Schleyer: Efficient diffuse function-augmented basis sets for anion calculations. III. The 3-21+G basis set for first-row elements, Li-F, J. Comput. Chem. 4, 294 (1983).
• [191] Florian Weigend and Reinhart Ahlrichs: Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy, Phys. Chem. Chem. Phys. 7, 3297 (2005).
• [192] Dmitrij Rappoport and Filipp Furche: Property-optimized Gaussian basis sets for molecular response calculations, J. Chem. Phys. 133, 134105 (2010).
• [193] Kirk A. Peterson, Thomas B. Adler, and Hans-Joachim Werner: Systematically convergent basis sets for explicitly correlated wavefunctions: The atoms H, He, B-Ne, and Al-Ar, J. Chem. Phys. 128, 084102 (2008).
• [194] Thom H. Dunning Jr. and P. Jeffrey Hay, Gaussian basis sets for molecular calculations, in Methods of Electronic Structure Theory, edited by Henry F. Schaefer III: volume 2: Plenum: New York: 1977.
• [195] Florian Weigend, Marco Häser, Holger Patzelt, and Reinhart Ahlrichs: RI-MP2: optimized auxiliary basis sets and demonstration of efficiency, Chem. Phys. Lett. 294, 143 (1998).
• [196] Florian Weigend, Andreas Köhn, and Christof Hättig: Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations, J. Chem. Phys. 116, 3175 (2002).
• [197] Arnim Hellweg and Dmitrij Rappoport: Development of new auxiliary basis functions of the Karlsruhe segmented contracted basis sets including diffuse basis functions (def2-SVPD, def2-TZVPPD, and def2-QVPPD) for RI-MP2 and RI-CC calculations, Phys. Chem. Chem. Phys. 17, 1010 (2015).
• [198] Florian Weigend: Hartree–Fock exchange fitting basis sets for H to Rn, J. Comput. Chem. 29, 167 (2008).
• [199] Florian Weigend: Accurate Coulomb-fitting basis sets for H to Rn, Phys. Chem. Chem. Phys. 8, 1057 (2006).
• [200] Kazim E. Yousaf and Kirk A. Peterson: Optimized auxiliary basis sets for explicitly correlated methods, J. Chem. Phys. 129, 184108 (2008).
• [201] Kazim E. Yousaf and Kirk A. Peterson: Optimized complementary auxiliary basis sets for explicitly correlated methods: aug-cc-pVnZ orbital basis sets, Chem. Phys. Lett. 476, 303 (2009).
• [202] J. Grant Hill, Shivnath Mazumder, and Kirk A. Peterson: Correlation consistent basis sets for molecular core-valence effects with explicitly correlated wave functions: The atoms B–Ne and Al–Ar, J. Chem. Phys. 132, 054108 (2010).
• [203] J. Grant Hill and Kirk A. Peterson: Explicitly correlated coupled cluster calculations for molecules containing group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) elements: Optimized complementary auxiliary basis sets for valence and core-valence basis sets, J. Chem. Theory Comput. 8, 518 (2012).
• [204] P. Jeffrey Hay and Willard R. Wadt: Ab initio effective core potentials for molecular calculations. Potentials for the transition metal atoms Sc to Hg, J. Chem. Phys. 82, 270 (1985).
• [205] Willard R. Wadt and P. Jeffrey Hay: Ab initio effective core potentials for molecular calculations. Potentials for main group elements Na to Bi, J. Chem. Phys. 82, 284 (1985).
• [206] P. Jeffrey Hay and Willard R. Wadt: Ab initio effective core potentials for molecular calculations. Potentials for K to Au including the outermost core orbitals, J. Chem. Phys. 82, 299 (1985).
• [207] Kirk A. Peterson: Systematically convergent basis sets with relativistic pseudopotentials. I. Correlation consistent basis sets for the post-d group 13-15 elements, J. Chem. Phys. 119, 11099 (2003).
• [208] Kirk A. Peterson, Detlev Figgen, Erich Goll, Hermann Stoll, and Michael Dolg: Systematically convergent basis sets with relativistic pseudopotentials. II. Small-core pseudopotentials and correlation consistent basis sets for the post-d group 16-18 elements, J. Chem. Phys. 119, 11113 (2003).
• [209] Kirk A Peterson and Cristina Puzzarini: Systematically convergent basis sets for transition metals. II. Pseudopotential-based correlation consistent basis sets for the group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) elements, Theor. Chem. Acc. 114, 283 (2005).
• [210] Kirk A. Peterson, Detlev Figgen, Michael Dolg, and Hermann Stoll: Energy-consistent relativistic pseudopotentials and correlation consistent basis sets for the 4d elements Y-Pd, J. Chem. Phys. 126, 124101 (2007).
• [211] Detlev Figgen, Kirk A. Peterson, Michael Dolg, and Hermann Stoll: Energy-consistent pseudopotentials and correlation consistent basis sets for the 5d elements Hf-Pt, J. Chem. Phys. 130, 164108 (2009).
• [212] Kirk A. Peterson and Kazim E. Yousaf: Molecular core-valence correlation effects involving the post-d elements Ga-Rn: Benchmarks and new pseudopotential-based correlation consistent basis sets, J. Chem. Phys. 133, 174116 (2010).
• [213] Christof Hättig: Optimization of auxiliary basis sets for RI-MP2 and RI-CC2 calculations: Core-valence and quintuple-$\zeta$ basis sets for H to Ar and QZVPP basis sets for Li to Kr, Phys. Chem. Chem. Phys. 7, 59 (2005).
• [214] J. Grant Hill: Auxiliary basis sets for density-fitting second-order Møller–Plesset perturbation theory: Weighted core-valence correlation consistent basis sets for the 4d elements Y-Pd, J. Comput. Chem. 34, 2168 (2013).
• [215] Stella Kritikou and J. Grant Hill: Auxiliary basis sets for density fitting in explicitly correlated calculations: The atoms H–Ar, J. Chem. Theory Comput. 11, 5269 (2015).
• [216] A correlation consistent basis sets repository, http://www.grant-hill.group.shef.ac.uk/ccrepo/, Accessed Jan 1, 2025.
• [217] James W. Boughton and Peter Pulay: Comparison of the Boys and Pipek–Mezey localizations in the local correlation approach and automatic virtual basis selection, J. Comput. Chem. 14, 736 (1993).
• [218] Julien Toulouse, Wuming Zhu, Andreas Savin, Georg Jansen, and János G. Ángyán: Closed-shell ring coupled cluster doubles theory with range separation applied on weak intermolecular interactions, J. Chem. Phys. 135, 084119 (2011).
• [219] Christof Hättig and Florian Weigend: CC2 excitation energy calculations on large molecules using the resolution of the identity approximation, J. Chem. Phys. 113, 5154 (2000).
• [220] Nisha Mehta and Jan M. L. Martin: Explicitly correlated double-hybrid DFT: A comprehensive analysis of the basis set convergence on the GMTKN55 database, J. Chem. Theory Comput. 18, 5978 (2022).
• [221] Sonia Coriani and Henrik Koch: Communication: X-ray absorption spectra and core-ionization potentials within a core-valence separated coupled cluster framework, J. Chem. Phys. 143, 181103 (2015).
• [222] L. S. Cederbaum, W. Domcke, and J. Schirmer: Many-body theory of core holes, Phys. Rev. A 22, 206 (1980).
• [223] Akio Takatsuka, Seiichiro Ten-no, and Wolfgang Hackbusch: Minimax approximation for the decomposition of energy denominators in Laplace-transformed Møller–Plesset perturbation theories, J. Chem. Phys. 129, 044112 (2008).
• [224] Alejandro J. Garza, Ireneusz W. Bulik, Thomas M. Henderson, and Gustavo E. Scuseria: Range separated hybrids of pair coupled cluster doubles and density functionals, Phys. Chem. Chem. Phys. 17, 22412 (2015).
• [225] Functionals were obtained from the Density Functional Repository as developed and distributed by the Quantum Chemistry Group, CCLRC Daresbury Laboratory, Daresbury, Cheshire, WA4 4AD United Kingdom. Contact Huub van Dam (h.j.j.vandam@dl.ac.uk) or Paul Sherwood for further information.
• [226] R. Strange, F. R. Manby, and P. J. Knowles: Automatic code generation in density functional theory, Comput. Phys. Commun. 136, 310 (2001).
• [227] Stefan Grimme, Jens Antony, Stephan Ehrlich, and Helge Krieg: A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys. 132, 154104 (2010).
• [228] Stefan Grimme, Stephan Ehrlich, and Lars Goerigk: Effect of the damping function in dispersion corrected density functional theory, J. Comput. Chem. 32, 1456 (2011).
• [229] P. A. M. Dirac: Quantum mechanics of many-electron systems, Proc. R. Soc. London A 123, 714 (1929).
• [230] J. C. Slater: A simplification of the Hartree–Fock method, Phys. Rev. 81, 385 (1951).
• [231] S. H. Vosko, L. Wilk, and M. Nusair: Accurate spin-dependent electron liquid correlation energies for local spin density calculations: A critical analysis, Can. J. Phys. 58, 1200 (1980).
• [232] J. P. Perdew and A. Zunger: Self-interaction correction to density-functional approximations for many-electron systems, Phys. Rev. B 23, 5048 (1981).
• [233] J. P. Perdew and Y. Wang: Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B 45, 13244 (1992).
• [234] Axel D. Becke: Density-functional exchange-energy approximation with correct asymptotic-behavior, Phys. Rev. A 38, 3098 (1988).
• [235] John P. Perdew, Kieron Burke, and Matthias Ernzerhof: Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
• [236] M. Ernzerhof and J. P. Perdew: Generalized gradient approximation to the angle- and system-averaged exchange hole, J. Chem. Phys. 109, 3313 (1998).
• [237] J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais: Atoms, molecules, solids and surfaces: Applications of the generalized gradient approximation for exchange and correlation, Phys. Rev. B 46, 6671 (1992).
• [238] C. Adamo and V. Barone: Exchange functionals with improved long-range behavior and adiabatic connection methods without adjustable parameters: The mPW and mPW1PW models, J. Chem. Phys. 108, 664 (1998).
• [239] Javier Carmona-Espíndola, José L. Gázquez, Alberto Vela, and S. B. Trickey: Generalized gradient approximation exchange energy functional with near-best semilocal performance, J. Chem. Theory Comput. 15, 303 (2019).
• [240] C. Lee, W. Yang, and R. G. Parr: Development of the Colle–Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B 37, 785 (1988).
• [241] John P. Perdew: Density-functional approximation for the correlation energy of the inhomogeneous electron gas, Phys. Rev. B 33, 8822 (1986).
• [242] A. Daniel Boese, Nikos L. Doltsinis, Nicholas C. Handy, and Michiel Sprik: New generalized gradient approximation functionals, J. Chem. Phys. 112, 1670 (2000).
• [243] A. Daniel Boese and Nicholas C. Handy: A new parametriztion of exchange-correlation generalized gradient approximation functionals, J. Chem. Phys. 114, 5497 (2001).
• [244] Xin Xu and William A. Goddard III: The X3LYP extended density functional for accurate descriptions of nonbond interactions, spin states, and thermochemical properties, Proc. Natl. Acad. Sci. U.S.A. 101, 2673 (2004).
• [245] E. E. Dahlke and D. G. Truhlar: Improved density functionals for water, J. Phys. Chem. B 109, 15677 (2005).
• [246] Axel D. Becke: A new mixing of Hartree–Fock and local density-functional theories, J. Chem. Phys. 98, 1372 (1993).
• [247] Axel D. Becke: Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys. 98, 5648 (1993).
• [248] P. J. Stephens, F. J. Devlin, C. F. Chabalowski, and M. J. Frisch: Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields, J. Phys. Chem. 98, 11623 (1994).
• [249] C. Adamo and V. Barone: Toward reliable adiabatic connection models free from adjustable parameters, Chem. Phys. Lett. 274, 242 (1997).
• [250] A. J. Cohen and N. C. Handy: Dynamic correlation, Mol. Phys. 99, 607 (2001).
• [251] Axel D. Becke: Density-functional thermochemistry. V. Systematic optimization of exchange-correlation functionals, J. Chem. Phys. 107, 8554 (1997).
• [252] John P. Perdew, Matthias Ernzerhof, and Kieron Burke: Rationale for mixing exact exchange with density functional approximations, J. Chem. Phys. 105, 9982 (1996).
• [253] J. Tao, J. P. Perdew, V. N. Staroverov, and G. E. Scuseria: Climbing the density functional ladder: Nonempirical meta-generalized gradient approximation designed for molecules and solids, Phys. Rev. Lett. 91, 146401 (2003).
• [254] J. P. Perdew, A. Ruzsinszky, G. I. Csonka, L. A. Constantin, and J. Sun: Workhorse semilocal density functional for condensed matter physics and quantum chemistry, Phys. Rev. Lett. 103, 026403 (2009).
• [255] Jianwei Sun, Adrienn Ruzsinszky, and John P. Perdew: Strongly constrained and appropriately normed semilocal density functional, Phys. Rev. Lett. 115, 036402 (2015).
• [256] A. D. Becke: Density-functional thermochemistry. IV. A new dynamical correlation functional and implications for exact-exchange mixing, J. Chem. Phys. 104, 1040 (1996).
• [257] Pál D. Mezei, Gábor I. Csonka, and Mihály Kállay: Simple modifications of the SCAN meta-generalized gradient approximation functional, J. Chem. Theory Comput. 14, 2469 (2018).
• [258] Y. Zhao and D. G. Truhlar: The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals, Theor. Chem. Acc. 120, 215 (2006).
• [259] Y. Zhao and D. G. Truhlar: A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions, J. Chem. Phys. 125, 194101 (2006).
• [260] Narbe Mardirossian and Martin Head-Gordon: Mapping the genome of meta-generalized gradient approximation density functionals: The search for B97M-V, J. Chem. Phys. 142, 074111 (2015).
• [261] Yan Zhao and Donald G. Truhlar: Density functional for spectroscopy: No long-range self-interaction error, good performance for Rydberg and charge-transfer states, and better performance on average than B3LYP for ground states, J. Phys. Chem. A 110, 13126 (2006).
• [262] Y. Zhao and D. G. Truhlar: Exploring the limit of accuracy of the global hybrid meta density functional for main-group thermochemistry, kinetics, and noncovalent interactions, J. Chem. Theory Comput. 4, 1849 (2008).
• [263] V. N. Staroverov, G. E. Scuseria, J. Tao, and J. P. Perdew: Comparative assessment of a new nonempirical density functional: Molecules and hydrogen-bonded complexes, J. Chem. Phys. 119, 12129 (2003).
• [264] G. I. Csonka, J. P. Perdew, and A. Ruzsinszky: Global hybrid functionals: A look at the engine under the hood, J. Chem. Theory Comput. 6, 3688 (2010).
• [265] Y. Zhao and D. G. Truhlar: Hybrid meta density functional theory methods for thermochemistry, thermochemical kinetics, and noncovalent interactions: The MPW1B95 and MPWB1K models and comparative assessments for hydrogen bonding and van der Waals interactions, J. Phys. Chem. A 108, 6908 (2004).
• [266] Y. Zhao and D. G. Truhlar: Design of density functionals that are broadly accurate for thermochemistry, thermochemical kinetics, and nonbonded interactions, J. Phys. Chem. A 109, 5656 (2005).
• [267] Haoyu S. Yu, Xiao He, Shaohong L. Li, and Donald G. Truhlar: MN15: A Kohn–Sham global-hybrid exchange-correlation density functional with broad accuracy for multi-reference and single-reference systems and noncovalent interactions, Chem. Sci. 7, 5032 (2016).
• [268] Kerwin Hui and Jeng-Da Chai: SCAN-based hybrid and double-hybrid density functionals from models without fitted parameters, J. Chem. Phys. 144, 044114 (2016).
• [269] Erich Goll, Hans-Joachim Werner, and Hermann Stoll: A short-range gradient-corrected density functional in long-range coupled-cluster calculations for rare gas dimers, Phys. Chem. Chem. Phys. 7, 3917 (2005).
• [270] Jochen Heyd, Gustavo E. Scuseria, and Matthias Ernzerhof: Hybrid functionals based on a screened Coulomb potential, J. Chem. Phys. 118, 8207 (2003).
• [271] Aliaksandr V. Krukau, Oleg A. Vydrov, Artur F. Izmaylov, and Gustavo E. Scuseria: Influence of the exchange screening parameter on the performance of screened hybrid functionals, J. Chem. Phys. 125, 224106 (2006).
• [272] Oleg A. Vydrov and Gustavo E. Scuseria: Assessment of a long-range corrected hybrid functional, J. Chem. Phys. 125, 234109 (2006).
• [273] Jeng-Da Chai and Martin Head-Gordon: Systematic optimization of long-range corrected hybrid density functionals, J. Chem. Phys. 128, 084106 (2008).
• [274] Narbe Mardirossian and Martin Head-Gordon: $\omega$B97X-V: A 10-parameter, range-separated hybrid, generalized gradient approximation density functional with nonlocal correlation, designed by a survival-of-the-fittest strategy, Phys. Chem. Chem. Phys. 16, 9904 (2014).
• [275] Roberto Peverati and Donald G. Truhlar: Improving the accuracy of hybrid meta-GGA density functionals by range separation, J. Phys. Chem. Lett. 2, 2810 (2011).
• [276] Roberto Peverati and Donald G. Truhlar: Screened-exchange density functionals with broad accuracy for chemistry and solid-state physics, Phys. Chem. Chem. Phys. 14, 16187 (2012).
• [277] Narbe Mardirossian and Martin Head-Gordon: $\omega$B97M-V: A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation, J. Chem. Phys. 144, 214110 (2016).
• [278] Amir Karton, Alex Tarnopolsky, Jean-Francois Lamère, George C. Schatz, and Jan M. L. Martin: Highly accurate first-principles benchmark data sets for the parametrization and validation of density functional and other approximate methods. Derivation of a robust, generally applicable, double-hybrid functional for thermochemistry and thermochemical kinetics, J. Phys. Chem. A 112, 12868 (2008).
• [279] Sebastian Kozuch and Jan M. L. Martin: DSD-PBEP86: in search of the best double-hybrid DFT with spin-component scaled MP2 and dispersion corrections, Phys. Chem. Chem. Phys. 13, 20104 (2011).
• [280] Sebastian Kozuch and Jan M. L. Martin: Spin-component-scaled double hybrids: An extensive search for the best fifth-rung functionals blending DFT and perturbation theory, J. Comput. Chem. 34, 2327 (2013).
• [281] Ying Zhang, Xin Xu, and William A. Goddard III: Doubly hybrid density functional for accurate descriptions of nonbond interactions, thermochemistry, and thermochemical kinetics, Proc. Natl. Acad. Sci. U.S.A. 106, 4963 (2009).
• [282] Lars Goerigk and Stefan Grimme: Efficient and accurate double-hybrid-meta-GGA density functionals – Evaluation with the extended GMTKN30 database for general main group thermochemistry, kinetics, and noncovalent interactions, J. Chem. Theory Comput. 7, 291 (2011).
• [283] Brina Brauer, Manoj K. Kesharwani, Sebastian Kozuch, and Jan M. L. Martin: The S66x8 benchmark for noncovalent interactions revisited: explicitly correlated ab initio methods and density functional theory, Phys. Chem. Chem. Phys. 18, 20905 (2016).
• [284] Oleg A. Vydrov and Troy Van Voorhis: Nonlocal van der Waals density functional: The simpler the better, J. Chem. Phys. 133, 244103 (2010).
• [285] Golokesh Santra, Emmanouil Semidalas, and Jan M. L. Martin: Surprisingly good performance of XYG3 family functionals using a scaled KS-MP3 correlation, J. Phys. Chem. Lett. 12, 9368 (2021).
• [286] Golokesh Santra, Emmanouil Semidalas, and Jan M. L. Martin: Exploring avenues beyond revised DSD functionals: II. Random-phase approximation and scaled MP3 corrections, J. Phys. Chem. A 125, 4628 (2021).
• [287] Jeppe Olsen, Poul Jørgensen, and Jack Simons: Passing the one-billion limit in full configuration-interaction (FCI) calculations, Chem. Phys. Lett. 169, 463 (1990).
• [288] Mihály Kállay and Péter R. Surján: Computing coupled-cluster wave functions with arbitrary excitations, J. Chem. Phys. 113, 1359 (2000).
• [289] D. Andrae, U. Häußermann, M. Dolg, H. Stoll, and H. Preuß: Energy-adjusted ab initio pseudopotentials for the second and third row transition elements, Theor. Chem. Acc. 77, 123 (1990).
• [290] M. Kaupp, P. v. R. Schleyer, H. Stoll, and H. Preuss: Pseudopotential approaches to Ca, Sr, and Ba hydrides. Why are some alkaline earth MX2 compounds bent?, J. Chem. Phys. 94, 1360 (1991).
• [291] Thierry Leininger, Andreas Nicklass, Wolfgang Küchle, Hermann Stoll, Michael Dolg, and Andreas Bergner: The accuracy of the pseudopotential approximation: non-frozen-core effects for spectroscopic constants of alkali fluorides XF (X = K, Rb, Cs), Chem. Phys. Lett. 255, 274 (1996).
• [292] Bernhard Metz, Marcus Schweizer, Hermann Stoll, Michael Dolg, and Wenjian Liu: A small-core multiconfiguration Dirac–Hartree–Fock-adjusted pseudopotential for Tl – application to TlX (X = F, Cl, Br, I), Theor. Chem. Acc. 104, 22 (2000).
• [293] Bernhard Metz, Hermann Stoll, and Michael Dolg: Small-core multiconfiguration-Dirac–Hartree–Fock-adjusted pseudopotentials for post-d main group elements: Application to PbH and PbO, J. Chem. Phys. 113, 2563 (2000).
• [294] K. A. Peterson, B. C. Shepler, D. Figgen, and H. Stoll: On the spectroscopic and thermochemical properties of ClO, BrO, IO, and their anions, J. Phys. Chem. A 110, 13877 (2006).
• [295] Detlev Figgen, Guntram Rauhut, Michael Dolg, and Hermann Stoll: Energy-consistent pseudopotentials for group 11 and 12 atoms: adjustment to multi-configuration Dirac–Hartree–Fock data, Chem. Phys. 311, 227 (2005).
• [296] Daniel Claudino and Nicholas J. Mayhall: Automatic partition of orbital spaces based on singular value decomposition in the context of embedding theories, J. Chem. Theory Comput. 15, 1053 (2019).
• [297] Ádám B. Szirmai, Bence Hégely, Attila Tajti, Mihály Kállay, and Péter G. Szalay: Projected atomic orbitals as optimal virtual space for excited state projection-based embedding calculations, J. Chem. Theory Comput. 20, 3420 (2024).
• [298] Curt M. Breneman and Kenneth B. Wiberg: Determining atom-centered monopoles from molecular electrostatic potentials. The need for high sampling density in formamide conformational analysis, J. Comput. Chem. 11, 361 (1990).
• [299] U. Chandra Singh and Peter A. Kollman: An approach to computing electrostatic charges for molecules, J. Comput. Chem. 5, 129 (1984).
• [300] David P. Tew and Wim Klopper: New correlation factors for explicitly correlated electronic wave functions, J. Chem. Phys. 123, 074101 (2005).
• [301] Reinhart Ahlrichs: Efficient evaluation of three-center two-electron integrals over Gaussian functions, Phys. Chem. Chem. Phys. 6, 5119 (2004).
• [302] S. Reine, E. Tellgren, and T. Helgaker: A unified scheme for the calculation of differentiated and undifferentiated molecular integrals over solid-harmonic Gaussians, Phys. Chem. Chem. Phys. 9, 4771 (2007).
• [303] Matthias Krack and Andreas M. Köster: An adaptive numerical integrator for molecular integrals, J. Chem. Phys. 108, 3226 (1998).
• [304] Christopher W. Murray, Nicholas C. Handy, and Gregory J. Laming: Quadrature schemes for integrals of density functional theory, Mol. Phys. 78, 997 (1993).
• [305] M. E. Mura and P. J. Knowles: Improved radial grids for quadrature in molecular density functional calculations, J. Chem. Phys. 104, 9848 (1996).
• [306] Ciro A. Guido, Pietro Cortona, Benedetta Mennucci, and Carlo Adamo: On the metric of charge transfer molecular excitations: A simple chemical descriptor, J. Chem. Theory Comput. 9, 3118 (2013).
• [307] Jetze Sikkema, Lucas Visscher, Trond Saue, and Miroslav Iliaš: The molecular mean-field approach for correlated relativistic calculations, J. Chem. Phys. 131, 124116 (2009).
• [308] S. Obara and A. Saika: Efficient recursive computation of molecular integrals over Cartesian Gaussian functions, J. Chem. Phys. 84, 3963 (1986).
• [309] R. Lindh, U. Ryu, and B. Liu: The reduced multiplication scheme of the Rys quadrature and new recurrence relations for auxiliary function based two-electron integral evaluation, J. Chem. Phys. 95, 5889 (1991).
• [310] Harry F. King and Michel Dupuis: Numerical integration using Rys polynomials, J. Comput. Phys. 21, 144 (1976).
• [311] N. Flocke: On the use of shifted Jacobi polynomials in accurate evaluation of roots and weights of Rys polynomials, J. Chem. Phys. 131, 064107 (2009).
• [312] Christoph Riplinger and Frank Neese: An efficient and near linear scaling pair natural orbital based local coupled cluster method, J. Chem. Phys. 138, 034106 (2013).
• [313] Peter Pinski, Christoph Riplinger, Edward F. Valeev, and F. Neese: Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals, J. Chem. Phys. 143, 034108 (2015).
• [314] S. J. Mo, T. Vreven, B. Mennucci, K. Morokuma, and J. Tomasi: Theoretical study of the S_N2 reaction of Cl^-(H₂O)+CH₃Cl using our own N-layered integrated molecular orbital and molecular mechanics polarizable continuum model method (ONIOM, PCM), Theor. Chem. Acc. 111, 154 (2004).
• [315] T. Vreven, B. Mennucci, C. O. da Silva, K. Morokuma, and J. Tomasi: The ONIOM-PCM method: Combining the hybrid molecular orbital method and the polarizable continuum model for solvation. Application to the geometry and properties of a merocyanine in solution, J. Chem. Phys. 115, 62 (2001).
• [316] J. A. Nelder and R. Mead: A simplex method for function minimization, Comput. J. 7, 308 (1965).
• [317] Francesco Aquilante, Thomas Bondo Pedersen, Alfredo M. Sánchez de Merás, and Henrik Koch: Fast noniterative orbital localization for large molecules, J. Chem. Phys. 125, 174101 (2006).
• [318] J. M. Foster and S. F. Boys: Canonical configurational interaction procedure, Rev. Mod. Phys. 32, 300 (1960).
• [319] J. Pipek and P. Mezey: A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions, J. Chem. Phys. 90, 4916 (1989).
• [320] Gerald Knizia: Intrinsic atomic orbitals: An unbiased bridge between quantum theory and chemical concepts, J. Chem. Theory Comput. 9, 4834 (2013).
• [321] B. Jansík, S. Høst, K. Kristensen, and P. Jørgensen: Local orbitals by minimizing powers of the orbital variance, J. Chem. Phys. 134, 194104 (2011).
• [322] Pavel Neogrády, Michal Pitoňák, and Miroslav Urban: Optimized virtual orbitals for correlated calculations: An alternative approach, Mol. Phys. 103, 2141 (2005).
• [323] R. S. Mulliken: Electronic population analysis on LCAO-MO molecular wave functions. I, J. Chem. Phys. 23, 1833 (1955).
• [324] I. Mayer: Charge, bond order and valence in the ab initio SCF theory, Chem. Phys. Lett. 97, 270 (1983).
• [325] Frank Neese: Importance of direct spin–spin coupling and spin-flip excitations for the zero-field splittings of transition metal complexes: A case study, J. Am. Chem. Soc. 128, 10213 (2006).
• [326] Georg Hetzer, Peter Pulay, and Hans-Joachim Werner: Multipole approximation of distant pair energies in local MP2 calculations, Chem. Phys. Lett. 290, 143 (1998).
• [327] Gijs Schaftenaar and Jan H. Noordik: Molden: a pre- and post-processing program for molecular and electronic structures, J. Comput.-Aided Mol. Design 14, 123 (2000).