A Hessian-Free Method to Prevent Zero-Point Energy Leakage in Classical Trajectories

The problem associated with the zero-point energy (ZPE) leak in classical trajectory calculations is well known. Since ZPE is a manifestation of the quantum uncertainty principle, there are no restrictions on energy during the classical propagation of nuclei. This phenomenon can lead to unphysical results, such as forming products without the ZPE in the internal vibrational degrees of freedom (DOFs). The ZPE leakage also permits reactions below the quantum threshold for the reaction. We have developed a new Hessian-free method, inspired by the Lowe-Andersen thermostat model, to prevent energy dipping below a threshold in the local-pair (LP) vibrational DOFs. The idea is to pump the leaked energy to the corresponding local vibrational mode taken from the other vibrational DOFs. We have applied the new correction protocol on the ab-initio ground-state molecular dynamics simulation of the water dimer (H₂O)₂, which dissociates due to unphysical ZPE spilling from high-frequency OH modes. The LP-ZPE method has been able to prevent the ZPE spilling of the OH stretching modes by pumping back the leaked energy into the corresponding modes, while this energy is taken from the other modes of the dimer itself, keeping the system as a microcanonical ensemble.