Local Potentials Reconstructed Within Linearly Independent Product Basis Sets of Increasing Size

Overview

Journal J Phys Chem A

Publisher American Chemical Society

Specialty Chemistry

Date 2023 Mar 10

PMID 36898043

Authors

Yan Oueis

Georgii N Sizov

Viktor N Staroverov

Affiliations

Soon will be listed here.

Abstract

Given a matrix representation of a local potential () within a one-electron basis set of functions that form linearly independent products (LIP), it is possible to construct a well-defined local potential that is equivalent to () within that basis set and has the form of an expansion in basis function products. Recently, we showed that for exchange-correlation potentials () defined on the infinite-dimensional Hilbert space, the potentials reconstructed from matrices of () within minimal LIP basis sets of occupied Kohn-Sham orbitals bear only qualitative resemblance to the originals. Here, we show that if the LIP basis set is enlarged by including low-lying virtual Kohn-Sham orbitals, the agreement between and () improves to the extent that the basis function products are appropriate as a basis for (). These findings validate the LIP technology as a rigorous potential reconstruction method.

Citing Articles

Analytic Construction of One-Electron Reduced Density Matrices from Electron Densities within Finite Basis Sets.

Sizov G, Staroverov V J Chem Theory Comput. 2024; 20(12):5157-5163.

PMID: 38836443 PMC: 11210478. DOI: 10.1021/acs.jctc.4c00398.

References

Kollmar C, Neese F . The static response function in Kohn-Sham theory: an appropriate basis for its matrix representation in case of finite AO basis sets. J Chem Phys. 2014; 141(13):134106. DOI: 10.1063/1.4896897. View

Rybkin V . Formulation and Implementation of Density Functional Embedding Theory Using Products of Basis Functions. J Chem Theory Comput. 2021; 17(7):3995-4005. DOI: 10.1021/acs.jctc.1c00175. View

Ryabinkin I, Kohut S, Staroverov V . Reduction of Electronic Wave Functions to Kohn-Sham Effective Potentials. Phys Rev Lett. 2015; 115(8):083001. DOI: 10.1103/PhysRevLett.115.083001. View

Harriman . Densities, operators, and basis sets. Phys Rev A Gen Phys. 1986; 34(1):29-39. DOI: 10.1103/physreva.34.29. View

Gritsenko , Baerends . Effect of molecular dissociation on the exchange-correlation Kohn-Sham potential. Phys Rev A. 1996; 54(3):1957-1972. DOI: 10.1103/physreva.54.1957. View

Zhang X, Carter E . Kohn-Sham potentials from electron densities using a matrix representation within finite atomic orbital basis sets. J Chem Phys. 2018; 148(3):034105. DOI: 10.1063/1.5005839. View

Hesselmann A, Gotz A, Della Sala F, Gorling A . Numerically stable optimized effective potential method with balanced Gaussian basis sets. J Chem Phys. 2007; 127(5):054102. DOI: 10.1063/1.2751159. View

Gorling A, Hesselmann A, Jones M, Levy M . Relation between exchange-only optimized potential and Kohn-Sham methods with finite basis sets, and effect of linearly dependent products of orbital basis functions. J Chem Phys. 2008; 128(10):104104. DOI: 10.1063/1.2826366. View

Oueis Y, Staroverov V . Multiplicative potentials for kinetic energy and exact exchange. J Chem Phys. 2022; 157(20):204107. DOI: 10.1063/5.0128508. View

10.

Oueis Y, Staroverov V . Reconstruction of Exchange-Correlation Potentials from Their Matrix Representations. J Chem Theory Comput. 2022; 18(10):6092-6098. DOI: 10.1021/acs.jctc.2c00655. View

11.

Smith D, Burns L, Sirianni D, Nascimento D, Kumar A, James A . Psi4NumPy: An Interactive Quantum Chemistry Programming Environment for Reference Implementations and Rapid Development. J Chem Theory Comput. 2018; 14(7):3504-3511. DOI: 10.1021/acs.jctc.8b00286. View

12.

Helbig N, Tokatly I, Rubio A . Exact Kohn-Sham potential of strongly correlated finite systems. J Chem Phys. 2009; 131(22):224105. DOI: 10.1063/1.3271392. View

13.

El-Samman A, Staroverov V . Asymptotic behavior of the average local ionization energy in finite basis sets. J Chem Phys. 2020; 153(13):134109. DOI: 10.1063/5.0023459. View

14.

El-Samman A, Ospadov E, Staroverov V . First Ionization Energy as the Asymptotic Limit of the Average Local Electron Energy. J Chem Theory Comput. 2020; 16(11):6886-6893. DOI: 10.1021/acs.jctc.0c00806. View

15.

Kollmar C, Filatov M . Optimized effective potential method: is it possible to obtain an accurate representation of the response function for finite orbital basis sets?. J Chem Phys. 2007; 127(11):114104. DOI: 10.1063/1.2777144. View

16.

Kollmar C, Filatov M . The role of orbital products in the optimized effective potential method. J Chem Phys. 2008; 128(6):064101. DOI: 10.1063/1.2834214. View

17.

Shi Y, Wasserman A . Inverse Kohn-Sham Density Functional Theory: Progress and Challenges. J Phys Chem Lett. 2021; 12(22):5308-5318. DOI: 10.1021/acs.jpclett.1c00752. View

18.

Perdew , Wang . Accurate and simple analytic representation of the electron-gas correlation energy. Phys Rev B Condens Matter. 1992; 45(23):13244-13249. DOI: 10.1103/physrevb.45.13244. View

19.

Ospadov E, Ryabinkin I, Staroverov V . Improved method for generating exchange-correlation potentials from electronic wave functions. J Chem Phys. 2017; 146(8):084103. DOI: 10.1063/1.4975990. View

20.

Staroverov V, Scuseria G, Davidson E . Optimized effective potentials yielding Hartree-Fock energies and densities. J Chem Phys. 2006; 124(14):141103. DOI: 10.1063/1.2194546. View