Oscillator strengths and excited-state couplings for double excitations in time-dependent density functional theory

TL;DR

This paper develops a modified non-adiabatic kernel in time-dependent density functional theory that accurately predicts both excitation energies and oscillator strengths for double-excitation states, improving spectral and dynamic simulations.

Contribution

The authors introduce a new non-adiabatic kernel that simultaneously improves excitation energies and oscillator strengths for double excitations in TDDFT.

Findings

Significant improvement in excitation energy predictions.

Accurate oscillator strengths for double excitations.

Enhanced modeling of excited-state properties.

Abstract

Although useful to extract excitation energies of states of double-excitation character in time-dependent density functional theory that are missing in the adiabatic approximation, the frequency-dependent kernel derived earlier [J. Chem. Phys. {\bf 120}, 5932 (2004)] was not designed to yield oscillator strengths. These are required to fully determine linear absorption spectra and they also impact excited-to-excited-state couplings that appear in dynamics simulations and other quadratic response properties. Here we derive a modified non-adiabatic kernel that yields both accurate excitation energies and oscillator strengths for these states. We demonstrate its performance on a model two-electron system, the Be atom, and on excited-state transition dipoles in the LiH molecule at stretched bond-lengths, in all cases producing significant improvements over the traditional approximations.