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Meta-generalized gradient approximation made in the Hartree gauge

Yan Oueis, Akilan Ramasamy, James W. Furness, Jamin Kidd, Timo Lebeda, Jianwei Sun

Abstract

In density functional theory (DFT), exact constraints, fundamental mathematical properties of the exchange-correlation (XC) energy and its underlying XC hole, along with paradigm systems such as the uniform electron gas and the hydrogen atom have been instrumental in developing exchange- correlation (XC) density functional approximations (DFAs). However, since the spatial XC energy density is not uniquely defined, its exact constraints can only be formulated within a chosen gauge and are therefore seldom utilized in DFA construction. Here, we propose a meta-generalized gradient approximation for the exchange energy, explicitly constructed within the Hartree gauge, using the hydrogen atom's exchange energy density for gauge alignment in core and asymptotic regions. By formulating DFAs at the XC energy density level, this approach expands reference datasets for machine learning and establishes a foundation for more accurate nonlocal density functionals requiring gauge alignment.

Meta-generalized gradient approximation made in the Hartree gauge

Abstract

In density functional theory (DFT), exact constraints, fundamental mathematical properties of the exchange-correlation (XC) energy and its underlying XC hole, along with paradigm systems such as the uniform electron gas and the hydrogen atom have been instrumental in developing exchange- correlation (XC) density functional approximations (DFAs). However, since the spatial XC energy density is not uniquely defined, its exact constraints can only be formulated within a chosen gauge and are therefore seldom utilized in DFA construction. Here, we propose a meta-generalized gradient approximation for the exchange energy, explicitly constructed within the Hartree gauge, using the hydrogen atom's exchange energy density for gauge alignment in core and asymptotic regions. By formulating DFAs at the XC energy density level, this approach expands reference datasets for machine learning and establishes a foundation for more accurate nonlocal density functionals requiring gauge alignment.
Paper Structure (2 sections, 11 equations, 3 figures, 1 table)

This paper contains 2 sections, 11 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Acknowledgments

Figures (3)

  • Figure 1: Exchange enhancement factor of the hydrogen atom for different density functionals including LSDA, PBE, B88, SCAN, and SORFKL, and the exact exchange. The analytical electron density of the hydrogen atom is used. The corresponding exchange energies in Hartree are $-0.2680$ (LSDA), $-0.3059$ (PBE), $-0.3098$ (B88), $-0.3125$ (SCAN), $-0.3125$ (SORFKL), and $-0.3125$ (Exact).
  • Figure 2: Exchange enhancement factors of B88, SORFKL, and HG exact exchange, as well as $s$ and $\beta$ against $(Z^{1/3}r)$ for the xenon atom. Z is the nuclear charge.
  • Figure 3: Exchange enhancement factors $F_\mathrm{x}$ of selected DFAs and HG exact exchange along the bond axis of molecules representative of different chemical bond types. For Na$_2$ and Ar$_2$, the bond center is at $r=0$.