A new challenge for time-dependent density-functional theory

TL;DR

This paper investigates the limitations of time-dependent density functional theory (TDDFT) in accurately predicting Rydberg states of Be and He atoms, revealing specific failures in current functionals and highlighting new challenges for development.

Contribution

The study identifies a significant failure of the ALDA functional in describing d-quantum defects in Rydberg states, exposing a new challenge for TDDFT functional development.

Findings

ALDA accurately describes s- and p-quantum defects

ALDA fails to accurately predict d-quantum defects

Failure observed in both Be and He atoms

Abstract

Time-dependent density functional theory is thought to work well for the test cases of He and Be atoms. We perform a quantum defect analysis of the s, p, and d Rydberg states of Be with accurate ground state Kohn-Sham potentials. The s- and p-quantum defects are well described by the ALDA, but fails badly for the d-quantum defect. The same failure is observed in case of He. This provides a new challenge for functional development in time-dependent density functional theory.