Excited State Densities from Time-Dependent Density Functional Response Theory

TL;DR

This paper develops a real-space expression for excited-state densities in time-dependent density functional theory, enabling analysis of different functional approximations and their performance for complex excitations.

Contribution

It introduces a new real-space formulation for excited-state densities, including double excitations, and compares the performance of LDA and exact exchange approximations.

Findings

Dressed TDDFT provides accurate densities for double excitations.

LDA and exact exchange approximations show contrasting performance.

New formulation allows analysis of non-adiabatic effects on densities.

Abstract

While the variational principle for excited-state energies leads to a route to obtaining excited-state densities from time-dependent density functional theory, relatively little attention has been paid to the quality of the resulting densities in real space obtained with different exchange-correlation functional approximations, nor how non-adiabatic approximations developed for energies of states of double excitation character perform for their densities. Here we derive an expression directly in real space for the excited-state density, that includes the case of non-adiabatic kernels, and consequently is able, for the first time, to yield densities of states of double-excitation character. Under some well-defined simplifications, we compare the performance of the local-density approximation and exact-exchange approximation, which are in a sense at opposite extremes of the fundamental functional approximations, on local and charge-transfer excitations in one-dimensional model systems, and show that the dressed TDDFT approach gives good densities of double-excitations.