How Semilocal Are Semilocal Density Functional Approximations? -Tackling Self-Interaction Error in One-Electron Systems

TL;DR

This paper introduces a new meta-GGA density functional that significantly reduces self-interaction error in one-electron systems, improving accuracy over existing semilocal functionals while maintaining computational efficiency.

Contribution

A non-empirical meta-GGA functional incorporating the Laplacian of the density that mitigates self-interaction error within semilocal approximations.

Findings

Reduces self-interaction error in $H_2^+$

Matches exact binding energy at equilibrium

Outperforms PBE and SCAN across bond lengths

Abstract

Self-interaction error (SIE), arising from the imperfect cancellation of the spurious classical Coulomb interaction between an electron and itself, is a persistent challenge in modern density functional approximations. This issue is illustrated using the prototypical one-electron system $H_2^+$. While significant efforts have been made to eliminate SIE through the development of computationally expensive nonlocal density functionals, it is equally important to explore whether SIE can be mitigated within the framework of more efficient semilocal density functionals. In this study, we present a non-empirical meta-generalized gradient approximation (meta-GGA) that incorporates the Laplacian of the electron density. Our results demonstrate that the meta-GGA significantly reduces SIE, yielding a binding energy curve for $H_2^+$ that matches the exact solution at equilibrium and improves across a broad range of bond lengths over those of the Perdew-Burke-Ernzerhof (PBE) and strongly-constrained and appropriately-normed (SCAN) semilocal density functionals. This advancement paves the way for further development within the realm of semilocal approximations.