Time-Dependent Density Functional Theory Beyond Kohn-Sham Slater Determinants

TL;DR

This paper investigates how the choice of initial Kohn-Sham state affects the accuracy of TDDFT simulations, proposing a new decomposition of the exchange-correlation potential to improve approximations beyond the traditional adiabatic approach.

Contribution

It introduces a novel decomposition of the exchange-correlation potential into a single-particle part and a remainder, and explores initial state choices to minimize errors in TDDFT.

Findings

Matching the Kohn-Sham state to the dominant interacting configuration can reduce errors temporarily.

The traditional exchange-correlation split has limited usefulness when the initial state is not a Slater determinant.

A new orbital-functional for the single-particle contribution offers an alternative to adiabatic approximations.

Abstract

When running time-dependent density functional theory (TDDFT) calculations for real-time simulations of non-equilibrium dynamics, the user has a choice of initial Kohn-Sham state, and typically a Slater determinant is used. We explore the impact of this choice on the exchange-correlation potential when the physical system begins in a 50:50 superposition of the ground and first-excited state of the system. We investigate the possibility of judiciously choosing a Kohn-Sham initial state that minimizes errors when adiabatic functionals are used. We find that if the Kohn-Sham state is chosen to have a configuration matching the one that dominates the interacting state, this can be achieved for a finite time duration for some but not all such choices. When the Kohn-Sham system does not begin in a Slater determinant, we further argue that the conventional splitting of the exchange-correlation potential into exchange and correlation parts has limited value, and instead propose a decomposition into a "single-particle" contribution that we denote $v_{xc}^s$, and a remainder. The single-particle contribution can be readily computed as an explicit orbital-functional, reduces to exchange in the Slater determinant case, and offers an alternative to the adiabatic approximation as a starting point for TDDFT approximations.