Response Potential in the Strong-Interaction Limit of Density Functional Theory: Analysis and Comparison with the Coupling-Constant Average

Overview

Journal J Chem Theory Comput

Publisher American Chemical Society

Specialties Biochemistry
Chemistry

Date 2018 Jun 16

PMID 29906106

Citations 2

Authors

Sara Giarrusso

Stefan Vuckovic

Paola Gori-Giorgi

Affiliations

Soon will be listed here.

Abstract

Using the formalism of the conditional amplitude, we study the response part of the exchange-correlation potential in the strong-coupling limit of density functional theory, analyzing its peculiar features and comparing it with the response potential averaged over the coupling constant for small atoms and for the hydrogen molecule. We also use a simple one-dimensional model of a stretched heteronuclear molecule to derive exact properties of the response potential in the strong-coupling limit. The simplicity of the model allows us to unveil relevant features also of the exact Kohn-Sham potential and its different components, namely the appearance of a second peak in the correlation kinetic potential on the side of the most electronegative atom.

Citing Articles

Exchange-Correlation Energy Densities and Response Potentials: Connection between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond.

Giarrusso S, Gori-Giorgi P J Phys Chem A. 2020; 124(12):2473-2482.

PMID: 32118422 PMC: 7104238. DOI: 10.1021/acs.jpca.9b10538.

Kinetic Correlation Functionals from the Entropic Regularization of the Strictly Correlated Electrons Problem.

Gerolin A, Grossi J, Gori-Giorgi P J Chem Theory Comput. 2019; 16(1):488-498.

PMID: 31855421 PMC: 6964418. DOI: 10.1021/acs.jctc.9b01133.

References

Gori-Giorgi P, Vignale G, Seidl M . Electronic Zero-Point Oscillations in the Strong-Interaction Limit of Density Functional Theory. J Chem Theory Comput. 2015; 5(4):743-53. DOI: 10.1021/ct8005248. View

Vuckovic S, Levy M, Gori-Giorgi P . Augmented potential, energy densities, and virial relations in the weak- and strong-interaction limits of DFT. J Chem Phys. 2017; 147(21):214107. DOI: 10.1063/1.4997311. 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

Kohut S, Polgar A, Staroverov V . Origin of the step structure of molecular exchange-correlation potentials. Phys Chem Chem Phys. 2016; 18(31):20938-44. DOI: 10.1039/c6cp00878j. View

Mirtschink A, Seidl M, Gori-Giorgi P . Energy Densities in the Strong-Interaction Limit of Density Functional Theory. J Chem Theory Comput. 2015; 8(9):3097-107. DOI: 10.1021/ct3003892. View

Vuckovic S, Irons T, Savin A, Teale A, Gori-Giorgi P . Exchange-Correlation Functionals via Local Interpolation along the Adiabatic Connection. J Chem Theory Comput. 2016; 12(6):2598-610. PMC: 4910137. DOI: 10.1021/acs.jctc.6b00177. View

Lani G, Di Marino S, Gerolin A, van Leeuwen R, Gori-Giorgi P . The adiabatic strictly-correlated-electrons functional: kernel and exact properties. Phys Chem Chem Phys. 2016; 18(31):21092-101. DOI: 10.1039/c6cp00339g. View

Vuckovic S, Wagner L, Mirtschink A, Gori-Giorgi P . Hydrogen Molecule Dissociation Curve with Functionals Based on the Strictly Correlated Regime. J Chem Theory Comput. 2015; 11(7):3153-62. DOI: 10.1021/acs.jctc.5b00387. View

Almbladh , von Barth U . Exact results for the charge and spin densities, exchange-correlation potentials, and density-functional eigenvalues. Phys Rev B Condens Matter. 1985; 31(6):3231-3244. DOI: 10.1103/physrevb.31.3231. View

10.

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

11.

Teale A, Coriani S, Helgaker T . Accurate calculation and modeling of the adiabatic connection in density functional theory. J Chem Phys. 2010; 132(16):164115. DOI: 10.1063/1.3380834. 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.

Hodgson M, Kraisler E, Schild A, Gross E . How Interatomic Steps in the Exact Kohn-Sham Potential Relate to Derivative Discontinuities of the Energy. J Phys Chem Lett. 2017; 8(24):5974-5980. DOI: 10.1021/acs.jpclett.7b02615. View

14.

Levy , Perdew . Hellmann-Feynman, virial, and scaling requisites for the exact universal density functionals. Shape of the correlation potential and diamagnetic susceptibility for atoms. Phys Rev A Gen Phys. 1985; 32(4):2010-2021. DOI: 10.1103/physreva.32.2010. View

15.

Gritsenko , van Leeuwen R , van Lenthe E , Baerends . Self-consistent approximation to the Kohn-Sham exchange potential. Phys Rev A. 1995; 51(3):1944-1954. DOI: 10.1103/physreva.51.1944. View

16.

Gritsenko O, Mentel L, Baerends E . On the errors of local density (LDA) and generalized gradient (GGA) approximations to the Kohn-Sham potential and orbital energies. J Chem Phys. 2016; 144(20):204114. DOI: 10.1063/1.4950877. View

17.

Umrigar , Gonze . Accurate exchange-correlation potentials and total-energy components for the helium isoelectronic series. Phys Rev A. 1994; 50(5):3827-3837. DOI: 10.1103/physreva.50.3827. View

18.

Mirtschink A, Seidl M, Gori-Giorgi P . Derivative discontinuity in the strong-interaction limit of density-functional theory. Phys Rev Lett. 2013; 111(12):126402. DOI: 10.1103/PhysRevLett.111.126402. View

19.

Buijse , Baerends , Snijders . Analysis of correlation in terms of exact local potentials: Applications to two-electron systems. Phys Rev A Gen Phys. 1989; 40(8):4190-4202. DOI: 10.1103/physreva.40.4190. View

20.

Levy , Perdew . Tight bound and convexity constraint on the exchange-correlation-energy functional in the low-density limit, and other formal tests of generalized-gradient approximations. Phys Rev B Condens Matter. 1993; 48(16):11638-11645. DOI: 10.1103/physrevb.48.11638. View