A modified Ehrenfest method that achieves Boltzmann quantum state populations

A modification of the hybrid quantum/classical mean-field or Ehrenfest method is proposed which allows us to reproduce the Boltzmann quantum state populations when simulating the vibrational energy transfer between quantum systems and classical thermal baths. The modified Ehrenfest results are shown to be able to simulate the energy fluxes between the solute vibration and the classical solvent in the proper directions, depending on their relative temperatures.