Exact time-dependent density functional theory for non-perturbative dynamics of helium atom

TL;DR

This paper demonstrates that key features of the exact correlation potential in time-dependent density functional theory (TDDFT) persist in real three-dimensional helium atoms, highlighting the importance of non-adiabatic effects.

Contribution

It provides the first exact inversion of the time-dependent Kohn-Sham equation for a 3D atom, revealing persistent dynamical features and differences between Kohn-Sham and true currents.

Findings

Dynamical step and peak features persist in 3D systems.

Kohn-Sham and true current densities differ by a rotational component.

Results emphasize the need to go beyond the adiabatic approximation in TDDFT.

Abstract

By inverting the time-dependent Kohn-Sham equation for a numerically exact dynamics of the helium atom, we show that the dynamical step and peak features of the exact correlation potential found previously in one-dimensional models persist for real three-dimensional systems. We demonstrate that the Kohn-Sham and true current-densities differ by a rotational component. The results have direct implications for approximate TDDFT calculations of atoms and molecules in strong fields, emphasizing the need to go beyond the adiabatic approximation, and highlighting caution in quantitative use of the Kohn-Sham current.