Time-dependent potential through an Ansatz for the Kohn-Sham orbitals

TL;DR

This paper introduces a new approach to modeling the time-dependent Kohn-Sham potential in TDDFT by decomposing it into instantaneous and dynamic parts using an Ansatz for the orbitals, validated on simple two-particle systems.

Contribution

The authors propose a novel Ansatz for TD-KS orbitals that satisfies key constraints and relates time-dependent and ground-state V-representability, providing a new way to approximate TDDFT potentials.

Findings

The proposed potential approximates exact TD-KS potentials for test systems.

The Ansatz satisfies orthonormality, N- and J-representability constraints.

Numerical results demonstrate the approach's validity on simple two-particle models.

Abstract

Given the time-evolution of an electron charge density, the local potential in Kohn-Sham time-dependent density functional theory (KS-TDDFT) can be modeled as a sum of instantaneous and dynamic contributions by assuming a certain form of the time-dependent Kohn-Sham (TD-KS) orbitals. The instantaneous part is obtained numerically using methods from ground-state density functional theory (DFT) and the dynamic part is expressed in terms of a velocity potential that depends on the electron current density. The suggested form of the TD-KS orbitals satisfies several known constraints (orthonormality, N-representability, J-representability), and the domain of validity is shown to depend on the evolution of the instantaneous quantities. Through this decomposition, we can relate time-dependent and ground -state V-representability. The resulting potentials are shown numerically to approximate the exact time-dependent Kohn-Sham potentials for a set of 3 non-singlet two-particle systems (a Kohn-mode, a Coulomb explosion, and a double quantum well) where the exact solutions and reference densities are known or obtained through configuration interaction (CI) approaches.