Time-dependent localized Hartree-Fock potential

TL;DR

This paper introduces a time-dependent localized Hartree-Fock potential derived from the many-body Schrödinger equation, enabling more accurate and efficient calculations within time-dependent density-functional theory for electron systems.

Contribution

It presents a novel non-adiabatic, self-interaction free time-dependent potential that generalizes the localized Hartree-Fock approach to dynamic scenarios.

Findings

Successfully evaluated the exchange kernel $f_x(q,)$ for the homogeneous electron gas.

Calculated the exchange shear modulus $_x$ demonstrating the potential's applicability.

Showed improved accuracy over existing methods in time-dependent electron simulations.

Abstract

By minimizing the difference between the left- and the right-hand sides of the many-body time-dependent Schr\"{o}dinger equation with the Slater-determinant wave-function, we derive a non-adiabatic and self-interaction free time-dependent single-particle effective potential which is the generalization to the time-dependent case of the localized Hartree-Fock potential. The new potential can be efficiently used within the framework of the time-dependent density-functional theory as we demonstrate by the evaluation of the wave-vector and frequency dependent exchange kernel $f_x(q,\omega)$ and the exchange shear modulus $\mu_x$ of the homogeneous electron gas.