Connection between Hybrid Functionals and Importance of the Local Density Approximation

Martín A. Mosquera, Carlos H. Borca, Mark A Ratner, George C Schatz

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The exchange-correlation (XC) local density approximation (LDA) is the original density functional used to investigate the electronic structure of molecules and solids within the formulation of Kohn and Sham. The LDA is fundamental for the development of density-functional approximations. In this work we consider the generalized Kohn-Sham (GKS) theory of hybrid functionals. The GKS formalism is an extension of the Kohn-Sham theory for electronic ground states and leads to a vast set of alternative density functionals, which can be estimated by the LDA and related methods. Herein we study auxiliary electronic systems with parametrized interactions and derive (i) a set of exact equations relating the GKS XC energies in the parameter space and (ii) a formal relation between the parameters and the standard XC derivative discontinuity. In view of the new results and previously reported findings, we discuss why the inclusion of Fock exchange, and its long-range-corrected form (in the ground-state calculations and in linear-response Kohn-Sham equations), dominate over the generalized gradient corrections to enhance the quality of the fundamental gap and to enhance excitation-energy estimations. As an example, we show that the adiabatic CAM-LDA0 (a functional with 1/4 global and 1/2 long-range Hartree-Fock interaction, respectively, a range separation factor of 1/3, and pure LDA exchange and correlation) works for electronic excitations as well as the adiabatic CAM-B3LYP functional.

Original languageEnglish
Pages (from-to)1605-1612
Number of pages8
JournalJournal of Physical Chemistry A
Volume120
Issue number9
DOIs
Publication statusPublished - Mar 10 2016

Fingerprint

Local density approximation
functionals
Computer aided manufacturing
approximation
Ground state
computer aided manufacturing
Excitation energy
Electronic structure
electronics
Ion exchange
ground state
Derivatives
Molecules
excitation
discontinuity
interactions
inclusions
formalism
electronic structure
formulations

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry

Cite this

Connection between Hybrid Functionals and Importance of the Local Density Approximation. / Mosquera, Martín A.; Borca, Carlos H.; Ratner, Mark A; Schatz, George C.

In: Journal of Physical Chemistry A, Vol. 120, No. 9, 10.03.2016, p. 1605-1612.

Research output: Contribution to journalArticle

@article{c5c8b323ce9f4d68b98bd826a7055d23,
title = "Connection between Hybrid Functionals and Importance of the Local Density Approximation",
abstract = "The exchange-correlation (XC) local density approximation (LDA) is the original density functional used to investigate the electronic structure of molecules and solids within the formulation of Kohn and Sham. The LDA is fundamental for the development of density-functional approximations. In this work we consider the generalized Kohn-Sham (GKS) theory of hybrid functionals. The GKS formalism is an extension of the Kohn-Sham theory for electronic ground states and leads to a vast set of alternative density functionals, which can be estimated by the LDA and related methods. Herein we study auxiliary electronic systems with parametrized interactions and derive (i) a set of exact equations relating the GKS XC energies in the parameter space and (ii) a formal relation between the parameters and the standard XC derivative discontinuity. In view of the new results and previously reported findings, we discuss why the inclusion of Fock exchange, and its long-range-corrected form (in the ground-state calculations and in linear-response Kohn-Sham equations), dominate over the generalized gradient corrections to enhance the quality of the fundamental gap and to enhance excitation-energy estimations. As an example, we show that the adiabatic CAM-LDA0 (a functional with 1/4 global and 1/2 long-range Hartree-Fock interaction, respectively, a range separation factor of 1/3, and pure LDA exchange and correlation) works for electronic excitations as well as the adiabatic CAM-B3LYP functional.",
author = "Mosquera, {Mart{\'i}n A.} and Borca, {Carlos H.} and Ratner, {Mark A} and Schatz, {George C}",
year = "2016",
month = "3",
day = "10",
doi = "10.1021/acs.jpca.5b10864",
language = "English",
volume = "120",
pages = "1605--1612",
journal = "Journal of Physical Chemistry A",
issn = "1089-5639",
publisher = "American Chemical Society",
number = "9",

}

TY - JOUR

T1 - Connection between Hybrid Functionals and Importance of the Local Density Approximation

AU - Mosquera, Martín A.

AU - Borca, Carlos H.

AU - Ratner, Mark A

AU - Schatz, George C

PY - 2016/3/10

Y1 - 2016/3/10

N2 - The exchange-correlation (XC) local density approximation (LDA) is the original density functional used to investigate the electronic structure of molecules and solids within the formulation of Kohn and Sham. The LDA is fundamental for the development of density-functional approximations. In this work we consider the generalized Kohn-Sham (GKS) theory of hybrid functionals. The GKS formalism is an extension of the Kohn-Sham theory for electronic ground states and leads to a vast set of alternative density functionals, which can be estimated by the LDA and related methods. Herein we study auxiliary electronic systems with parametrized interactions and derive (i) a set of exact equations relating the GKS XC energies in the parameter space and (ii) a formal relation between the parameters and the standard XC derivative discontinuity. In view of the new results and previously reported findings, we discuss why the inclusion of Fock exchange, and its long-range-corrected form (in the ground-state calculations and in linear-response Kohn-Sham equations), dominate over the generalized gradient corrections to enhance the quality of the fundamental gap and to enhance excitation-energy estimations. As an example, we show that the adiabatic CAM-LDA0 (a functional with 1/4 global and 1/2 long-range Hartree-Fock interaction, respectively, a range separation factor of 1/3, and pure LDA exchange and correlation) works for electronic excitations as well as the adiabatic CAM-B3LYP functional.

AB - The exchange-correlation (XC) local density approximation (LDA) is the original density functional used to investigate the electronic structure of molecules and solids within the formulation of Kohn and Sham. The LDA is fundamental for the development of density-functional approximations. In this work we consider the generalized Kohn-Sham (GKS) theory of hybrid functionals. The GKS formalism is an extension of the Kohn-Sham theory for electronic ground states and leads to a vast set of alternative density functionals, which can be estimated by the LDA and related methods. Herein we study auxiliary electronic systems with parametrized interactions and derive (i) a set of exact equations relating the GKS XC energies in the parameter space and (ii) a formal relation between the parameters and the standard XC derivative discontinuity. In view of the new results and previously reported findings, we discuss why the inclusion of Fock exchange, and its long-range-corrected form (in the ground-state calculations and in linear-response Kohn-Sham equations), dominate over the generalized gradient corrections to enhance the quality of the fundamental gap and to enhance excitation-energy estimations. As an example, we show that the adiabatic CAM-LDA0 (a functional with 1/4 global and 1/2 long-range Hartree-Fock interaction, respectively, a range separation factor of 1/3, and pure LDA exchange and correlation) works for electronic excitations as well as the adiabatic CAM-B3LYP functional.

UR - http://www.scopus.com/inward/record.url?scp=84960372242&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84960372242&partnerID=8YFLogxK

U2 - 10.1021/acs.jpca.5b10864

DO - 10.1021/acs.jpca.5b10864

M3 - Article

VL - 120

SP - 1605

EP - 1612

JO - Journal of Physical Chemistry A

JF - Journal of Physical Chemistry A

SN - 1089-5639

IS - 9

ER -