Violation of the `Zero-Force Theorem' in the time-dependent Krieger-Li-Iafrate approximation

TL;DR

This paper reveals that the time-dependent Krieger-Li-Iafrate approximation with exchange-only functional violates the Zero-Force Theorem, causing unphysical self-excitation in certain systems, which challenges its physical reliability.

Contribution

It identifies a fundamental violation of the Zero-Force Theorem in a widely used approximation, analyzing its implications and connection to invariance principles.

Findings

Violation of the Zero-Force Theorem demonstrated

Unphysical self-excitation observed in Na5 and Na9+

Analytical link between the theorem and potential invariance

Abstract

We demonstrate that the time-dependent Krieger-Li-Iafrate approximation in combination with the exchange-only functional violates the `Zero-Force Theorem'. By analyzing the time-dependent dipole moment of Na5 and Na9+, we furthermore show that this can lead to an unphysical self-excitation of the system depending on the system properties and the excitation strength. Analytical aspects, especially the connection between the `Zero-Force Theorem' and the `Generalized-Translation Invariance' of the potential, are discussed.