About the computation of finite temperature ensemble averages of hybrid quantum-classical systems with molecular dynamics

Abstract Molecular or condensed matter systems are often well approximated by hybrid quantum-classical models: the electrons retain their quantum character, whereas ions considered to be classical particles. We discuss various alternative approaches for computation of equilibrium (canonical) ensemble averages observables these through use molecular dynamics (MD)-i.e. performing in presence a thermostat and computing time-averages over trajectories. Often, ab initio MD, temperature is ignored they assumed remain at instantaneous ground state given each ionic configuration during evolution. Here, however, we general case that considers both subsystems finite canonical equilibrium. Inspired recent formal derivation hybrids, previous found literature, provide some new formulas.