Existence and uniqueness of solutions to the time-dependent Kohn-Sham equations coupled with classical nuclear dynamics

TL;DR

This paper establishes the mathematical conditions under which solutions to coupled time-dependent Kohn-Sham and nuclear dynamics equations exist and are unique, advancing the theoretical foundation of quantum molecular simulations.

Contribution

It proves existence and uniqueness of solutions for a class of coupled Kohn-Sham and nuclear equations with a generalized exchange term.

Findings

Existence and uniqueness of $H^2$ solutions identified

Range of exponents for solution existence determined

Mathematical framework for coupled quantum-classical dynamics provided

Abstract

We prove existence and uniqueness of solutions to the initial-value problem associated with a class of time-dependent Kohn-Sham equations coupled with Newtonian nuclear dynamics. We consider a pure power exchange term within a generalisation of the Local Density Approximation (LDA), identifying a range of exponents for the existence and uniqueness of $H^2$ solutions to the Kohn-Sham equations.