Post-pulse dipole instability in adiabatic TDDFT: fact or artifact?

TL;DR

This paper investigates a reported dipole instability in real-time TDDFT calculations, revealing it as an artifact caused by the adiabatic approximation and boundary conditions, not a physical phenomenon.

Contribution

The study demonstrates that the observed instability is an artifact of the adiabatic approximation in TDDFT, contrasting with response-reformulated methods where the instability is absent.

Findings

The instability is linked to the adiabatic exchange-correlation approximation.

Using response-reformulated RR-TDDFT removes the instability.

Absorbing boundary conditions are crucial in the analysis.

Abstract

Recent real-time TDDFT calculations have reported an unexpected delayed growth of molecular dipole oscillations some time after an extreme-ultraviolet (XUV) pulse is applied. We show that numerical and analytical arguments suggest that this instability is an artifact of an incorrect non-linearity introduced by the computational approach: Propagation with an adiabatic exchange-correlation approximation within the time-dependent Kohn-Sham equations of time-dependent density functional theory (TDDFT) tends to amplify initially small and pure sinusoidal oscillations in a system. On the other hand, when this same adiabatic approximation is used within the recent response-reformulated RR-TDDFT,the instability is absent. The absorbing boundary condition plays a crucial role consistent with our argument. We demonstrate this explicitly on the N2 molecule subject to an XUV pulse, with a range of adiabatic functionals.