Canonical quantum correlation observables can be approximated by classical molecular dynamics. In the case of low temperature the ab intio molecular dynamics potential energy is based on the ground state electron eigenvalue problem and the accuracy has been proven to be O(1/M), provided the first electron eigenvalue gap is sufficiently large compared to the given temperature and M is the ratio of nuclei and electron masses.
For higher temperature several eigenvalues and paths corresponding to excited electron states are required to obtain O(1/M) accuracy and the derivations assume that all electron eigenvalues are separated, which e.g. excludes conical intersections. In the talk I will present a mean-field molecular dynamics that approximates canonical quantum correlation observables, including coinciding electron eigenvalues and a path integral alternative to the well known electron eigenvalue computational bottleneck.