Identification and Resolution of Unphysical Multielectron Excitations in the Real-Time Time-Dependent Kohn-Sham Formulation

TL;DR

This paper identifies a fundamental flaw in the conventional real-time time-dependent Kohn-Sham method, where fixed orbitals lead to unphysical excitations, and proposes a new adaptive formulation to correct this issue, improving the accuracy of electron density predictions.

Contribution

A novel formulation that dynamically updates the number of Kohn-Sham orbitals and their occupations to eliminate unphysical multielectron excitations in real-time TDDFT.

Findings

Correct electron density obtained with the new method.

Accurate Rabi oscillation simulations for noninteracting electrons.

Demonstrated removal of unphysical excitations in simulations.

Abstract

We resolve a fundamental issue associated with the conventional Kohn-Sham formulation of real-time time-dependent density functional theory. We show that unphysical multielectron excitations, generated during time propagation of the Kohn-Sham equations due to fixation of the total number of Kohn-Sham orbitals and their occupations, result in incorrect electron density and, therefore, wrong predictions of physical properties. A new formulation is proposed in that the number of Kohn-Sham orbitals and their occupations are updated on the fly, the unphysical multielectron excitations are removed, and the correct electron density is determined. The correctness of the new formulation is demonstrated by simulations of Rabi oscillation, as analytical results are available for comparison in the case of noninteracting electrons.