The conservation of quantum zero-point energies in classical trajectory simulations

Abstract

We propose a computational technique to constrain the vibrational modes of a classical molecule to have energy greater than the quantum zero-point energy (ZPE). The trajectory of any mode with energy less than ZPE is projected to a neighboring point in phase space where the energy is equal to the ZPE and the phase angle of the mode is unchanged. All other modes are then perturbed in such a way as to conserve the total energy of the system. This technique is similar in principle to the method of holonomic constraints. We apply this ‘‘semiholonomic’’ TRAPZ (trajectory projection onto ZPE orbit) scheme to the two mode Hénon–Heiles system and find that it results in a decrease of ergodicity. Periodic limit cycle internal vibrational energy redistribution is observed. Implications of this method for the conservation of ZPE in quasiclassical trajectory simulations are discussed.