# Excited-State Densities from Time-Dependent Density Functional Response Theory

## TL;DR

This paper introduces a new method to calculate excited-state densities using time-dependent density functional theory, focusing on double-excitation states.

## Contribution

The paper derives a real-space expression for excited-state densities that includes nonadiabatic kernels, enabling accurate double-excitation density calculations.

## Key findings

- The derived method successfully yields densities for states with double-excitation character.
- The local-density and exact-exchange approximations show distinct performance on local and charge-transfer excitations.
- The dressed TDDFT approach provides good results for double-excitation densities under certain simplifications.

## 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 or how nonadiabatic
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, which includes
the case of nonadiabatic 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 the opposite extremes of the fundamental functional
approximations, on local and charge-transfer excitations in one-dimensional
model systems and show that the dressed Time-Dependent Density Functional
Theory (TDDFT) approach gives good densities of double excitations.