Ensemble Time-Dependent Density Functional Theory

TL;DR

This paper introduces ensemble time-dependent density functional theory (ETDDFT), combining ensemble DFT and TDDFT to improve calculations of optical excitations in molecules and solids.

Contribution

It generalizes the Gross-Kohn equation and exchange-correlation kernel, providing a new framework for approximations in time-dependent ensemble DFT.

Findings

Illustrated on the 2-site Hubbard model

Relates coordinate scaling to the adiabatic connection

Connects to non-perturbative time dependence

Abstract

Time-dependent density functional theory (TDDFT) is a standard approach for calculating optical excitations of molecules and solids, while ensemble DFT (EDFT) is a promising alternative under development. We introduce ensemble TDDFT (ETDDFT), a practical theory that combines the two, generalizing both; we ensemble-generalize the Gross-Kohn equation and the exchange-correlation kernel of TDDFT, and generalize EDFT to time-dependent problems. We relate coordinate scaling to the adiabatic connection. The new theory provides multiple avenues for constructing and using approximations. We illustrate these on the 2-site Hubbard model. We connect our results to the more general case of non-perturbative time-dependence.