On the challenge to improve the density response with unusual gradient approximations

TL;DR

This paper investigates the response properties of unusual GGA-type functionals with divergences on orbital nodal surfaces, revealing their potential and limitations for improving long-range charge transfer excitation descriptions in TDDFT.

Contribution

It analyzes the response behavior of AK13 and B88 functionals with divergences, highlighting their qualitative differences and instabilities in TDDFT applications.

Findings

AK13 response differs from semi-local functionals

AK13 causes instabilities in the asymptotic region

Sternheimer formalism effectively analyzes TDDFT responses

Abstract

Certain excitations, especially ones of long-range charge transfer character, are poorly described by time-dependent density functional theory (TDDFT) when typical (semi-)local functionals are used. A proper description of these excitations would require an exchange-correlation response differing substantially from the usual (semi-)local one. It has recently been shown that functionals of the generalized gradient approximation (GGA) type can yield unusual potentials, mimicking features of the exact exchange derivative discontinuity and showing divergences on orbital nodal surfaces. We here investigate whether these unusual potential properties translate into beneficial response properties. Using the Sternheimer formalism we closely investigate the response obtained with the 2013 exchange approximation by Armiento and K\"ummel (AK13) and the 1988 exchange approximation by Becke (B88), both of which show divergences on orbital nodal planes. Numerical calculations for Na2 as well as analytical and numerical calculations for the hydrogen atom show that the response of AK13 behaves qualitatively different from usual semi local functionals. However, the AK13 functional leads to fundamental instabilities in the asymptotic region that prevent its practical application in TDDFT. Our findings may help the development of future improved functionals, and corroborate that the frequency-dependent Sternheimer formalism is excellently suited for running and analyzing TDDFT calculations.