# Direct extraction of excitation energies from ensemble density-functional theory

## TL;DR

This paper introduces a new ensemble density-functional theory approach that directly computes excitation energies as simple corrections, avoiding complex calculations required by traditional TDDFT, and captures double excitations.

## Contribution

It presents an exact formula for excitation energies from a specific ensemble, enabling direct extraction without extensive unoccupied state calculations or multiple ensemble iterations.

## Key findings

- SEHX approximation yields results comparable to TDDFT for atoms.
- The method captures double-excitations missed by adiabatic TDDFT.
- Avoids the need for many unoccupied orbitals or self-consistent ensemble calculations.

## Abstract

A very specific ensemble of ground and excited states is shown to yield an exact formula for any excitation energy as a simple correction to the energy difference between orbitals of the Kohn-Sham ground state. This alternative scheme avoids either the need to calculate many unoccupied levels as in time-dependent density functional theory (TDDFT) or the need for many self-consistent ensemble calculations. The symmetry-eigenstate Hartree-exchange (SEHX) approximation yields results comparable to standard TDDFT for atoms. With this formalism, SEHX yields approximate double-excitations, which are missed by adiabatic TDDFT.