Exact-exchange kernel of time-dependent density functional theory: Frequency dependence and photoabsorption spectra of atoms

TL;DR

This paper investigates the frequency dependence of the exact-exchange kernel in TDDFT for atoms, revealing its importance for certain excitations and identifying limitations at higher energies, with implications for photoabsorption spectra.

Contribution

It provides a detailed analysis of the frequency dependence of the EXX kernel in TDDFT and proposes a new method for deriving Fano parameters of autoionizing resonances.

Findings

Frequency dependence is crucial for some discrete excitations.

EXX approximation fails at high energies, missing inner-shell excitations.

Identified vanishing eigenvalues as the cause of breakdown.

Abstract

In this work we have calculated excitation energies and photoionization cross sections of Be and Ne in the exact-exchange (EXX) approximation of time-dependent density functional theory (TDDFT). The main focus has been on the frequency dependence of the EXX kernel and on how it affects the spectrum as compared to the corresponding adiabatic approximation. We show that for some discrete excitation energies the frequency dependence is essential to reproduce the results of time-dependent Hartree-Fock theory. Unfortunately, we have found that the EXX approximation breaks down completely at higher energies, producing a response function with the wrong analytic structure and making inner-shell excitations disappear from the calculated spectra. We have traced this failure to the existence of vanishing eigenvalues of the Kohn-Sham non-interacting response function. Based on the adiabatic TDDFT formalism we propose a new way of deriving the Fano parameters of autoionizing resonances.