Electron-Affinity Time-Dependent Density Functional Theory: Formalism and Applications to Core-Excited States

TL;DR

This paper introduces a new formalism in time-dependent density functional theory that significantly improves the accuracy of core-excited state predictions in X-ray absorption spectra by addressing particle-hole interaction errors.

Contribution

The authors develop an orbital-optimized linear-response formalism that generalizes the static-exchange approximation within TDDFT, reducing errors in core-excitation calculations.

Findings

Achieves 0.5 eV root-mean-square error in XAS predictions.

Reduces particle-hole interaction errors by orders of magnitude.

Maintains computational efficiency comparable to standard TDDFT.

Abstract

The particle-hole interaction problem is longstanding within time-dependent density functional theory (TDDFT) and leads to extreme errors in the prediction of K-edge X-ray absorption spectra (XAS). We derive a linear-response formalism that uses optimized orbitals of the n-1-electron system as reference, building orbital relaxation and a proper hole into the initial density. Our approach is an exact generalization of the static-exchange approximation that ameliorates particle-hole interaction error associated with the adiabatic approximation and reduces errors in TDDFT XAS by orders of magnitude. With a statistical performance of just 0.5 eV root-mean-square error and the same computational scaling as TDDFT under the core-valence separation approximation, we anticipate that this approach will be of great utility in XAS calculations of large systems.