Fourth-order series expansion of the exchange hole

Fourth-order series expansion of the exchange hole Approximate functionals for the exchange-correlation energy of electrons often draw on explicit or implicit models for the exchange-correlation hole. Here we focus on the spherically averaged exchange hole ρX(r,u), which depends on the reference point r and on the electron-electron distance u. We extend the well-known [A. D. Becke and M. R. Roussel, Phys. Rev. A 39, 3761 (1989)0556-279110.1103/PhysRevA.39.3761] second-order Taylor-series expansion in u to fourth order and we show that the fourth-order term can add important additional information that is particularly relevant for molecules compared to atoms. Drawing on these findings, we explore exchange functionals that depend on the fourth-order term of the expansion of ρX(r,u). We also find that Gaussian basis set expansions, frequently used in electronic structure codes, result in unsatisfactory representations of the fourth-order term. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review A American Physical Society (APS)

Fourth-order series expansion of the exchange hole

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Fourth-order series expansion of the exchange hole

Abstract

Approximate functionals for the exchange-correlation energy of electrons often draw on explicit or implicit models for the exchange-correlation hole. Here we focus on the spherically averaged exchange hole ρX(r,u), which depends on the reference point r and on the electron-electron distance u. We extend the well-known [A. D. Becke and M. R. Roussel, Phys. Rev. A 39, 3761 (1989)0556-279110.1103/PhysRevA.39.3761] second-order Taylor-series expansion in u to fourth order and we show that the fourth-order term can add important additional information that is particularly relevant for molecules compared to atoms. Drawing on these findings, we explore exchange functionals that depend on the fourth-order term of the expansion of ρX(r,u). We also find that Gaussian basis set expansions, frequently used in electronic structure codes, result in unsatisfactory representations of the fourth-order term.
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Publisher
American Physical Society (APS)
Copyright
Copyright © ©2017 American Physical Society
ISSN
1050-2947
eISSN
1094-1622
D.O.I.
10.1103/PhysRevA.96.022502
Publisher site
See Article on Publisher Site

Abstract

Approximate functionals for the exchange-correlation energy of electrons often draw on explicit or implicit models for the exchange-correlation hole. Here we focus on the spherically averaged exchange hole ρX(r,u), which depends on the reference point r and on the electron-electron distance u. We extend the well-known [A. D. Becke and M. R. Roussel, Phys. Rev. A 39, 3761 (1989)0556-279110.1103/PhysRevA.39.3761] second-order Taylor-series expansion in u to fourth order and we show that the fourth-order term can add important additional information that is particularly relevant for molecules compared to atoms. Drawing on these findings, we explore exchange functionals that depend on the fourth-order term of the expansion of ρX(r,u). We also find that Gaussian basis set expansions, frequently used in electronic structure codes, result in unsatisfactory representations of the fourth-order term.

Journal

Physical Review AAmerican Physical Society (APS)

Published: Aug 1, 2017

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