Adapting approximate memory potentials for time-dependent density functional theory

TL;DR

This paper proposes methods to correct approximate exchange-correlation potentials in time-dependent density functional theory, ensuring they satisfy essential symmetry conditions for stable and accurate applications, demonstrated on a sodium cluster.

Contribution

The paper introduces pragmatic correction methods for frequency-dependent XC potentials to enforce translational covariance and zero-force conditions in TDDFT.

Findings

Corrected potentials are more stable in simulations.

Violations of symmetries cause instabilities and spurious modes.

Numerical tests on sodium cluster validate the corrections.

Abstract

Frequency dependent exchange correlation kernels for time-dependent density functional theory can be used to construct approximate exchange-correlation potentials. The resulting potentials are usually not translationally covariant nor do they obey the so-called zero-force condition. These two basic symme-try requirements are essential for using the potentials in actual applications (even within the linear re-sponse regime). We provide two pragmatic methods for imposing these conditions. As an example we take the Gross and Kohn (GK) frequency dependent XC functional (Phys. Rev.Lett. 55, 2850 (1985)), correct it, and numerically test it on a sodium metal cluster. Violation of the basic symme-tries causes instabilities or spurious low frequency modes.