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Oueis Y, Staroverov VN. Reconstruction of Exchange-Correlation Potentials from Their Matrix Representations. J Chem Theory Comput 2022; 18:6092-6098. [PMID: 36094818 DOI: 10.1021/acs.jctc.2c00655] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Within a basis set of one-electron functions that form linearly independent products (LIPs), it is always possible to construct a unique local (multiplicative) real-space potential that is precisely equivalent to an arbitrary given operator. Although standard basis sets of quantum chemistry rarely form LIPs in a numerical sense, occupied and low-lying virtual canonical Kohn-Sham orbitals often do so, at least for small atoms and molecules. Using these principles, we construct atomic and molecular exchange-correlation potentials from their matrix representations in LIP basis sets of occupied canonical Kohn-Sham orbitals. The reconstructions are found to imitate the original potentials in a consistent but exaggerated way. Since the original and reconstructed potentials produce the same ground-state electron density and energy within the associated LIP basis set, the procedure may be regarded as a rigorous solution to the Kohn-Sham inversion problem within the subspace spanned by the occupied Kohn-Sham orbitals.
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Affiliation(s)
- Yan Oueis
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
| | - Viktor N Staroverov
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
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Affiliation(s)
- Bence Hégely
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Péter R. Nagy
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Mihály Kállay
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
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Mao Y, Horn PR, Mardirossian N, Head-Gordon T, Skylaris CK, Head-Gordon M. Approaching the basis set limit for DFT calculations using an environment-adapted minimal basis with perturbation theory: Formulation, proof of concept, and a pilot implementation. J Chem Phys 2016; 145:044109. [DOI: 10.1063/1.4959125] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yuezhi Mao
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Paul R. Horn
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Narbe Mardirossian
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Teresa Head-Gordon
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, USA
- Department of Bioengineering, University of California, Berkeley, California 94720, USA
- Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Chris-Kriton Skylaris
- School of Chemistry, University of Southampton, Highfield, Southampton, SO17 1BJ, United Kingdom
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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Affiliation(s)
- Ryan P. Steele
- Department of Chemistry and
Henry Eyring Center for Theoretical Chemistry, University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112, United States
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Affiliation(s)
- Jia Deng
- Research
School of Chemistry, The Australian National University, Canberra, Australian Capital Territory 2601, Australia
| | - Andrew T. B. Gilbert
- Research
School of Chemistry, The Australian National University, Canberra, Australian Capital Territory 2601, Australia
| | - Peter M. W. Gill
- Research
School of Chemistry, The Australian National University, Canberra, Australian Capital Territory 2601, Australia
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Shao Y, Gan Z, Epifanovsky E, Gilbert AT, Wormit M, Kussmann J, Lange AW, Behn A, Deng J, Feng X, Ghosh D, Goldey M, Horn PR, Jacobson LD, Kaliman I, Khaliullin RZ, Kuś T, Landau A, Liu J, Proynov EI, Rhee YM, Richard RM, Rohrdanz MA, Steele RP, Sundstrom EJ, Woodcock HL, Zimmerman PM, Zuev D, Albrecht B, Alguire E, Austin B, Beran GJO, Bernard YA, Berquist E, Brandhorst K, Bravaya KB, Brown ST, Casanova D, Chang CM, Chen Y, Chien SH, Closser KD, Crittenden DL, Diedenhofen M, DiStasio RA, Do H, Dutoi AD, Edgar RG, Fatehi S, Fusti-Molnar L, Ghysels A, Golubeva-Zadorozhnaya A, Gomes J, Hanson-Heine MW, Harbach PH, Hauser AW, Hohenstein EG, Holden ZC, Jagau TC, Ji H, Kaduk B, Khistyaev K, Kim J, Kim J, King RA, Klunzinger P, Kosenkov D, Kowalczyk T, Krauter CM, Lao KU, Laurent AD, Lawler KV, Levchenko SV, Lin CY, Liu F, Livshits E, Lochan RC, Luenser A, Manohar P, Manzer SF, Mao SP, Mardirossian N, Marenich AV, Maurer SA, Mayhall NJ, Neuscamman E, Oana CM, Olivares-Amaya R, O’Neill DP, Parkhill JA, Perrine TM, Peverati R, Prociuk A, Rehn DR, Rosta E, Russ NJ, Sharada SM, Sharma S, Small DW, Sodt A, Stein T, Stück D, Su YC, Thom AJ, Tsuchimochi T, Vanovschi V, Vogt L, Vydrov O, Wang T, Watson MA, Wenzel J, White A, Williams CF, Yang J, Yeganeh S, Yost SR, You ZQ, Zhang IY, Zhang X, Zhao Y, Brooks BR, Chan GK, Chipman DM, Cramer CJ, Goddard WA, Gordon MS, Hehre WJ, Klamt A, Schaefer HF, Schmidt MW, Sherrill CD, Truhlar DG, Warshel A, Xu X, Aspuru-Guzik A, Baer R, Bell AT, Besley NA, Chai JD, Dreuw A, Dunietz BD, Furlani TR, Gwaltney SR, Hsu CP, Jung Y, Kong J, Lambrecht DS, Liang W, Ochsenfeld C, Rassolov VA, Slipchenko LV, Subotnik JE, Van Voorhis T, Herbert JM, Krylov AI, Gill PM, Head-Gordon M. Advances in molecular quantum chemistry contained in the Q-Chem 4 program package. Mol Phys 2014. [DOI: 10.1080/00268976.2014.952696] [Citation(s) in RCA: 1769] [Impact Index Per Article: 176.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
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Abstract
A new electronic structure model is developed in which the ground state energy of a molecular system is given by a Hartree-Fock-like expression with parametrized one- and two-electron integrals over an extended (minimal + polarization) set of orthogonalized atom-centered basis functions, the variational equations being solved formally within the minimal basis but the effect of polarization functions being included in the spirit of second-order perturbation theory. It is designed to yield good dipole polarizabilities and improved intermolecular potentials with dispersion terms. The molecular integrals include up to three-center one-electron and two-center two-electron terms, all in simple analytical forms. A method to extract the effective one-electron Hamiltonian of nonlocal-exchange Kohn-Sham theory from the coupled-cluster one-electron density matrix is designed and used to get its matrix representation in a molecule-intrinsic minimal basis as an input to the parametrization procedure--making a direct link to the correlated wavefunction theory. The model has been trained for 15 elements (H, Li-F, Na-Cl, 720 parameters) on a set of 5581 molecules (including ions, transition states, and weakly bound complexes) whose first- and second-order properties were computed by the coupled-cluster theory as a reference, and a good agreement is seen. The model looks promising for the study of large molecular systems, it is believed to be an important step forward from the traditional semiempirical models towards higher accuracy at nearly as low a computational cost.
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Affiliation(s)
- Dimitri N Laikov
- Chemistry Department, Moscow State University, 119992 Moscow, Russia.
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Affiliation(s)
- Liguo Kong
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Florian A. Bischoff
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
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Deng J, Gilbert ATB, Gill PMW. Communication: Efficient counterpoise corrections by a perturbative approach. J Chem Phys 2011; 135:081105. [DOI: 10.1063/1.3632054] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
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Kong L, Valeev EF. Perturbative correction for the basis set incompleteness error of complete-active-space self-consistent field. J Chem Phys 2010; 133:174126. [DOI: 10.1063/1.3499600] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
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Marshall MS, Sears JS, Burns LA, Brédas JL, Sherrill CD. An Error and Efficiency Analysis of Approximations to Møller−Plesset Perturbation Theory. J Chem Theory Comput 2010. [DOI: 10.1021/ct100468f] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Michael S. Marshall
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, and School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States, and Center for Computational Molecular Science and Technology, Center for Organic Photonics and Electronics, and School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States
| | - John S. Sears
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, and School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States, and Center for Computational Molecular Science and Technology, Center for Organic Photonics and Electronics, and School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States
| | - Lori A. Burns
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, and School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States, and Center for Computational Molecular Science and Technology, Center for Organic Photonics and Electronics, and School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States
| | - Jean-Luc Brédas
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, and School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States, and Center for Computational Molecular Science and Technology, Center for Organic Photonics and Electronics, and School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States
| | - C. David Sherrill
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, and School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States, and Center for Computational Molecular Science and Technology, Center for Organic Photonics and Electronics, and School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States
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Abstract
We discuss several measures of the quality of a molecular orbital. Each requires only that the orbital be associated with a well-defined Fock operator and is thus applicable to both Hartree–Fock and density functional orbitals. One of the measures, the γ diagnostic, ranges from γ = 0 (perfect) to γ = π/2 (poor) and is conceptually simple. We illustrate its usefulness by applying it to a number of small atoms and ions.
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Affiliation(s)
- Jia Deng
- Research School of Chemistry, Australian National University, ACT 0200, Australia
| | - Andrew T.B. Gilbert
- Research School of Chemistry, Australian National University, ACT 0200, Australia
| | - Peter M.W. Gill
- Research School of Chemistry, Australian National University, ACT 0200, Australia
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Köhn A, Tew DP. Towards the Hartree–Fock and coupled-cluster singles and doubles basis set limit: A study of various models that employ single excitations into a complementary auxiliary basis set. J Chem Phys 2010; 132:024101. [DOI: 10.1063/1.3291040] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
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