Canonical mean-field molecular dynamics derived from quantum mechanics

Canonical quantum correlation observables can be approximated by classical molecular dynamics. In the case of low temperature ab initio dynamics potential energy is based on ground state electron eigenvalue problem and accuracy has been proven to O ( M -1 ), provided first gap sufficiently large compared given ratio nuclei masses. For higher eigenvalues corresponding excited states are required obtain ) derivations assume that all separated, which for instance excludes conical intersections. This work studies a mean-field approximation where Hamiltonian partial trace h := Tr He − βH )/ (e with respect degrees freedom H Weyl symbol many body ̂ . It proved approximates canonical + tϵ 2 time t ϵ related variance mean value Furthermore, proof derives precise asymptotic representation Gibbs density operator using path integral formulation. Numerical experiments model one two show similar or better than standard eigenvalue.