Kohn–Sham Density in a Slater Orbital Basis Set

Rask, Alan E.; Li, Liying; Zimmerman, Paul M.

doi:10.1021/acs.jpca.3c08303

Title: Kohn–Sham Density in a Slater Orbital Basis Set

Journal Article · 11 April 2024 · Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory

DOI: https://doi.org/10.1021/acs.jpca.3c08303 · OSTI ID:2409383

^[1];

^[2];

^[3]

SandboxAQ, Palo Alto, CA (United States); University of Michigan, Ann Arbor, MI (United States); University of Michigan
University of Michigan, Ann Arbor, MI (United States); Southern University of Science and Technology, Guangdong (China)
University of Michigan, Ann Arbor, MI (United States)

Finite, atom-centered Slater basis sets are used to determine approximate Kohn–Sham molecular orbitals. This is achieved by minimizing the kinetic energy plus the sum-squared difference between the Kohn–Sham density and the full configuration interaction density. As a result of the finite basis, a weight factor is introduced to balance the two minimization components. Results herein show that this can be done systematically, without sensitive dependence on the choice of scaling factor. In addition, the algorithm is applied to the LiH diatomic for fractional electron counts, where stretching the bond introduces significant reorganization of the electron density. As a result, the analysis will show the correct KS orbital structure and reveal the effects of correlation and electron locality on the KS solutions.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: University of Michigan, Ann Arbor, MI (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0022241

OSTI ID:: 2409383

Journal Information:: Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory, Journal Name: Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory Journal Issue: 16 Vol. 128; ISSN 1089-5639

Publisher:: American Chemical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (61)

Optimized Slater-type basis sets for the elements 1-118 Van Lenthe, E.; Baerends, E. J. Journal of Computational Chemistry, Vol. 24, Issue 9 https://doi.org/10.1002/jcc.10255	journal	May 2003
An improved algorithm for analytical gradient evaluation in resolution-of-the-identity second-order Møller-Plesset perturbation theory: Application to alanine tetrapeptide conformational analysis Distasio, Robert A.; Steele, Ryan P.; Rhee, Young Min Journal of Computational Chemistry, Vol. 28, Issue 5 https://doi.org/10.1002/jcc.20604	journal	April 2007
Localization of molecular orbitals on fragments Sax, Alexander F. Journal of Computational Chemistry, Vol. 33, Issue 17 https://doi.org/10.1002/jcc.22980	journal	April 2012
The numerical evaluation of Slater integrals on graphics processing units Dang, Duy‐Khoi; Wilson, Leighton W.; Zimmerman, Paul M. Journal of Computational Chemistry, Vol. 43, Issue 25 https://doi.org/10.1002/jcc.26968	journal	July 2022
DFT in a nutshell Burke, Kieron; Wagner, Lucas O. International Journal of Quantum Chemistry, Vol. 113, Issue 2 https://doi.org/10.1002/qua.24259	journal	July 2012
Density and density matrix from optimized linearly independent product basis functions for Be Morrison, Robert C. International Journal of Quantum Chemistry, Vol. 34, Issue S22 https://doi.org/10.1002/qua.560340809	journal	March 1988
Density functionals for exchange and correlation energies: Exact conditions and comparison of approximations Levy, Mel; Perdew, John P. International Journal of Quantum Chemistry, Vol. 49, Issue 4 https://doi.org/10.1002/qua.560490416	journal	February 1994
Delocalization error: The greatest outstanding challenge in density‐functional theory Bryenton, Kyle R.; Adeleke, Adebayo A.; Dale, Stephen G. WIREs Computational Molecular Science https://doi.org/10.1002/wcms.1631	journal	July 2022
Zur Theorie des Wasserstoffatoms Fock, V. Zeitschrift f�r Physik, Vol. 98, Issue 3-4 https://doi.org/10.1007/BF01336904	journal	March 1935
Kohn-Sham potentials corresponding to Slater and Gaussian basis set densities Schipper, P. R. T.; Gritsenko, O. V.; Baerends, E. J. Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 98, Issue 1 https://doi.org/10.1007/s002140050273	journal	October 1997
Density matrices from densities Schwarz, W. H. E.; Müller, B. Chemical Physics Letters, Vol. 166, Issue 5-6 https://doi.org/10.1016/0009-2614(90)87161-J	journal	March 1990
Auxiliary basis sets to approximate Coulomb potentials (Chem. Phys. Letters 240 (1995) 283-290) Eichkorn, K.; Treutler, O.; Öhm, H. Chemical Physics Letters, Vol. 242, Issue 6 https://doi.org/10.1016/0009-2614(95)00838-U	journal	September 1995
Relationship of Kohn–Sham eigenvalues to excitation energies Savin, A.; Umrigar, C. J.; Gonze, Xavier Chemical Physics Letters, Vol. 288, Issue 2-4 https://doi.org/10.1016/S0009-2614(98)00316-9	journal	May 1998
RI-MP2: optimized auxiliary basis sets and demonstration of efficiency Weigend, Florian; Häser, Marco; Patzelt, Holger Chemical Physics Letters, Vol. 294, Issue 1-3 https://doi.org/10.1016/S0009-2614(98)00862-8	journal	September 1998
Resolutions of the Coulomb operator: II. The Laguerre generator Gill, Peter M. W.; Gilbert, Andrew T. B. Chemical Physics, Vol. 356, Issue 1-3 https://doi.org/10.1016/j.chemphys.2008.10.047	journal	February 2009
A benchmark study of Li2+, Li2−, LiH+ and LiH−: Quantum Monte-Carlo and coupled-cluster computations Nasiri, Saeed; Zahedi, Mansour Computational and Theoretical Chemistry, Vol. 1114 https://doi.org/10.1016/j.comptc.2017.05.015	journal	August 2017
Self-interaction error of local density functionals for alkali–halide dissociation Dutoi, Anthony D.; Head-Gordon, Martin Chemical Physics Letters, Vol. 422, Issue 1-3 https://doi.org/10.1016/j.cplett.2006.02.025	journal	April 2006
Reduction of Hartree–Fock Wavefunctions to Kohn–Sham Effective Potentials Using Multiresolution Analysis Stückrath, Julius B.; Bischoff, Florian A. Journal of Chemical Theory and Computation, Vol. 17, Issue 3 https://doi.org/10.1021/acs.jctc.0c01103	journal	February 2021
Reconstruction of Exchange–Correlation Potentials from Their Matrix Representations Oueis, Yan; Staroverov, Viktor N. Journal of Chemical Theory and Computation, Vol. 18, Issue 10 https://doi.org/10.1021/acs.jctc.2c00655	journal	September 2022
Heat-Bath Configuration Interaction: An Efficient Selected Configuration Interaction Algorithm Inspired by Heat-Bath Sampling Holmes, Adam A.; Tubman, Norm M.; Umrigar, C. J. Journal of Chemical Theory and Computation, Vol. 12, Issue 8 https://doi.org/10.1021/acs.jctc.6b00407	journal	August 2016
Conceptual Problem with Calculating Electron Densities in Finite Basis Density Functional Theory Mayer, István; Pápai, Imre; Bakó, Imre Journal of Chemical Theory and Computation, Vol. 13, Issue 9 https://doi.org/10.1021/acs.jctc.7b00562	journal	August 2017
Advances in Parallel Heat Bath Configuration Interaction Dang, Duy-Khoi; Kammeraad, Joshua A.; Zimmerman, Paul M. The Journal of Physical Chemistry A, Vol. 127, Issue 1 https://doi.org/10.1021/acs.jpca.2c07949	journal	December 2022
Local Potentials Reconstructed within Linearly Independent Product Basis Sets of Increasing Size Oueis, Yan; Sizov, Georgii N.; Staroverov, Viktor N. The Journal of Physical Chemistry A, Vol. 127, Issue 11 https://doi.org/10.1021/acs.jpca.3c00119	journal	March 2023
Charge-Transfer Steps in Density Functional Theory from the Perspective of the Exact Electron Factorization Kocák, Jakub; Kraisler, Eli; Schild, Axel The Journal of Physical Chemistry Letters, Vol. 12, Issue 12 https://doi.org/10.1021/acs.jpclett.1c00467	journal	March 2021
Inverse Kohn–Sham Density Functional Theory: Progress and Challenges Shi, Yuming; Wasserman, Adam The Journal of Physical Chemistry Letters, Vol. 12, Issue 22 https://doi.org/10.1021/acs.jpclett.1c00752	journal	June 2021
A Comparison of Exact and Model Exchange–Correlation Potentials for Molecules Kanungo, Bikash; Zimmerman, Paul M.; Gavini, Vikram The Journal of Physical Chemistry Letters, Vol. 12, Issue 50 https://doi.org/10.1021/acs.jpclett.1c03670	journal	December 2021
Noninteracting v-Representable Subspaces of Orbitals in the Kohn–Sham Method Staroverov, Viktor N. The Journal of Physical Chemistry Letters, Vol. 13, Issue 29 https://doi.org/10.1021/acs.jpclett.2c01827	journal	July 2022
The Nature of the Chemical Bond in Lithium Hydride and Hydrogen Fluoride Bader, R. F. W.; Henneker, W. H. Journal of the American Chemical Society, Vol. 88, Issue 2 https://doi.org/10.1021/ja00954a019	journal	January 1966
Design of Density Functionals That Are Broadly Accurate for Thermochemistry, Thermochemical Kinetics, and Nonbonded Interactions Zhao, Yan; Truhlar, Donald G. The Journal of Physical Chemistry A, Vol. 109, Issue 25 https://doi.org/10.1021/jp050536c	journal	June 2005
Exact exchange-correlation potentials from ground-state electron densities Kanungo, Bikash; Zimmerman, Paul M.; Gavini, Vikram Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-12467-0	journal	October 2019
Density functional generalized gradient calculations using Slater basis sets Cohen, Aron J.; Handy, Nicholas C. The Journal of Chemical Physics, Vol. 117, Issue 4 https://doi.org/10.1063/1.1485073	journal	July 2002
Why Not Use Slater Orbitals of Nonintegral Principal Quantum Number? Parr, Robert G.; Joy, Hubert W. The Journal of Chemical Physics, Vol. 26, Issue 2 https://doi.org/10.1063/1.1743314	journal	February 1957
Describing static correlation in bond dissociation by Kohn–Sham density functional theory Fuchs, M.; Niquet, Y. -M.; Gonze, X. The Journal of Chemical Physics, Vol. 122, Issue 9 https://doi.org/10.1063/1.1858371	journal	March 2005
Spurious fractional charge on dissociated atoms: Pervasive and resilient self-interaction error of common density functionals Ruzsinszky, Adrienn; Perdew, John P.; Csonka, Gábor I. The Journal of Chemical Physics, Vol. 125, Issue 19 https://doi.org/10.1063/1.2387954	journal	November 2006
Many-electron self-interaction error in approximate density functionals Mori-Sánchez, Paula; Cohen, Aron J.; Yang, Weitao The Journal of Chemical Physics, Vol. 125, Issue 20 https://doi.org/10.1063/1.2403848	journal	November 2006
Density functionals that are one- and two- are not always many-electron self-interaction-free, as shown for H2+, He2+, LiH+, and Ne2+ Ruzsinszky, Adrienn; Perdew, John P.; Csonka, Gábor I. The Journal of Chemical Physics, Vol. 126, Issue 10 https://doi.org/10.1063/1.2566637	journal	March 2007
Derivative discontinuity, bandgap and lowest unoccupied molecular orbital in density functional theory Yang, Weitao; Cohen, Aron J.; Mori-Sánchez, Paula The Journal of Chemical Physics, Vol. 136, Issue 20 https://doi.org/10.1063/1.3702391	journal	May 2012
The density matrix, density, and Fermi hole in Hartree–Fock theory Dawson, K. A.; March, N. H. The Journal of Chemical Physics, Vol. 81, Issue 12 https://doi.org/10.1063/1.447639	journal	December 1984
A multicenter numerical integration scheme for polyatomic molecules Becke, A. D. The Journal of Chemical Physics, Vol. 88, Issue 4 https://doi.org/10.1063/1.454033	journal	February 1988
Density‐functional thermochemistry. III. The role of exact exchange Becke, Axel D. The Journal of Chemical Physics, Vol. 98, Issue 7, p. 5648-5652 https://doi.org/10.1063/1.464913	journal	April 1993
Linear dependencies among basis set products and near locality of some nonlocal operators Hoch, Douglas E.; Harriman, John E. The Journal of Chemical Physics, Vol. 102, Issue 24 https://doi.org/10.1063/1.468775	journal	June 1995
Molecular exchange‐correlation Kohn–Sham potential and energy density from ab initio first‐ and second‐order density matrices: Examples for XH (X=Li, B, F) Gritsenko, Oleg V.; Leeuwen, Robert van; Baerends, Evert Jan The Journal of Chemical Physics, Vol. 104, Issue 21 https://doi.org/10.1063/1.471602	journal	June 1996
Exchange‐correlation potentials Tozer, David J.; Ingamells, Victoria E.; Handy, Nicholas C. The Journal of Chemical Physics, Vol. 105, Issue 20 https://doi.org/10.1063/1.472753	journal	November 1996
Perspective: Fifty years of density-functional theory in chemical physics Becke, Axel D. The Journal of Chemical Physics, Vol. 140, Issue 18 https://doi.org/10.1063/1.4869598	journal	May 2014
On extending Kohn-Sham density functionals to systems with fractional number of electrons Li, Chen; Lu, Jianfeng; Yang, Weitao The Journal of Chemical Physics, Vol. 146, Issue 21 https://doi.org/10.1063/1.4982951	journal	June 2017
Multiplicative potentials for kinetic energy and exact exchange Oueis, Yan; Staroverov, Viktor N. The Journal of Chemical Physics, Vol. 157, Issue 20 https://doi.org/10.1063/5.0128508	journal	November 2022
Density-functional theory vs density-functional fits: The best of both Becke, Axel D. The Journal of Chemical Physics, Vol. 157, Issue 23 https://doi.org/10.1063/5.0128996	journal	December 2022
Toward routine Kohn–Sham inversion using the “Lieb-response” approach Gould, Tim The Journal of Chemical Physics, Vol. 158, Issue 6 https://doi.org/10.1063/5.0134330	journal	February 2023
Exchange correlation potentials from full configuration interaction in a Slater orbital basis Tribedi, Soumi; Dang, Duy-Khoi; Kanungo, Bikash The Journal of Chemical Physics, Vol. 159, Issue 5 https://doi.org/10.1063/5.0157942	journal	August 2023
Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals Mardirossian, Narbe; Head-Gordon, Martin Molecular Physics, Vol. 115, Issue 19 https://doi.org/10.1080/00268976.2017.1333644	journal	April 2017
Exact expressions for the height of the interatomic step in the exchange-correlation potential from the derivative discontinuity of the energy Hodgson, M. J. P. Physical Review A, Vol. 104, Issue 3 https://doi.org/10.1103/PhysRevA.104.032803	journal	September 2021
Orthonormal orbitals for the representation of an arbitrary density Harriman, John E. Physical Review A, Vol. 24, Issue 2 https://doi.org/10.1103/PhysRevA.24.680	journal	August 1981
Hellmann-Feynman, virial, and scaling requisites for the exact universal density functionals. Shape of the correlation potential and diamagnetic susceptibility for atoms Levy, Mel; Perdew, John P. Physical Review A, Vol. 32, Issue 4 https://doi.org/10.1103/PhysRevA.32.2010	journal	October 1985
Exact density-potential relation for the ground state of the Be atom March, N. H.; Nalewajski, R. F. Physical Review A, Vol. 35, Issue 2 https://doi.org/10.1103/PhysRevA.35.525	journal	January 1987
One-body potential theory in terms of the phase of wave functions for the ground state of the Be atom Nagy, A.; March, N. H. Physical Review A, Vol. 39, Issue 11 https://doi.org/10.1103/PhysRevA.39.5512	journal	June 1989
Toward understanding the exchange-correlation energy and total-energy density functionals Parr, Robert G.; Ghosh, Swapan K. Physical Review A, Vol. 51, Issue 5 https://doi.org/10.1103/PhysRevA.51.3564	journal	May 1995
Molecular Kohn-Sham exchange-correlation potential from the correlated ab initio electron density Gritsenko, Oleg V.; van Leeuwen, Robert; Baerends, Evert Jan Physical Review A, Vol. 52, Issue 3 https://doi.org/10.1103/PhysRevA.52.1870	journal	September 1995
Kinetic-energy systems, density scaling, and homogeneity relations in density-functional theory Chan, Garnet Kin-Lic; Handy, Nicholas C. Physical Review A, Vol. 59, Issue 4 https://doi.org/10.1103/PhysRevA.59.2670	journal	April 1999
Kohn-Sham potentials in exact density-functional theory at noninteger electron numbers Gould, Tim; Toulouse, Julien Physical Review A, Vol. 90, Issue 5 https://doi.org/10.1103/PhysRevA.90.050502	journal	November 2014
Reply to “Comment on ‘Significance of the highest occupied Kohn-Sham eigenvalue’ ” Kleinman, Leonard Physical Review B, Vol. 56, Issue 24 https://doi.org/10.1103/PhysRevB.56.16029	journal	December 1997
Degenerate Ground States and a Fractional Number of Electrons in Density and Reduced Density Matrix Functional Theory Yang, Weitao; Zhang, Yingkai; Ayers, Paul W. Physical Review Letters, Vol. 84, Issue 22 https://doi.org/10.1103/PhysRevLett.84.5172	journal	May 2000

Similar Records

The static response function in Kohn-Sham theory: An appropriate basis for its matrix representation in case of finite AO basis sets

Journal Article · 2014 · Journal of Chemical Physics · OSTI ID:22436536

Kollmar, Christian; Neese, Frank

On the physical nature and chemical utility of Kohn-Sham orbitals

Conference · 1996 · OSTI ID:447588

Baerends, E J

Hierarchy of model Kohn–Sham potentials for orbital-dependent functionals: A practical alternative to the optimized effective potential method

Journal Article · 2014 · Journal of Chemical Physics · OSTI ID:22253027

Kohut, Sviataslau V.; Ryabinkin, Ilya G.

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS

Title: Kohn–Sham Density in a Slater Orbital Basis Set

Citation Formats

References (61)

Similar Records

Related Subjects