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

摘要

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