Optimal control theory for quantum-classical systems: Ehrenfest Molecular Dynamics based on time-dependent density-functional theory

TL;DR

This paper develops an optimal control framework for quantum-classical systems using Ehrenfest dynamics and time-dependent density-functional theory, enabling precise manipulation of molecular systems with classical ions and quantum electrons.

Contribution

It introduces a novel optimal control approach tailored for quantum-classical systems modeled with Ehrenfest dynamics and adapts it for density-functional theory.

Findings

Derived fundamental equations for quantum-classical optimal control.

Modified control equations for density-functional theory.

Illustrated approach with H2+ molecule in a laser field.

Abstract

We derive the fundamental equations of an optimal control theory for systems containing both quantum electrons and classical ions. The system is modeled with Ehrenfest dynamics, a non-adiabatic variant of molecular dynamics. The general formulation, that needs the fully correlated many-electron wave function, can be simplified by making use of time-dependent density-functional theory. In this case, the optimal control equations require some modifications that we will provide. The abstract general formulation is complemented with the simple example of the H$_2^+$ molecule in the presence of a laser field.