Correcting ZPE leakage in dynamics

A hessian-free method to avoid ZPE leakage in quasi-classical dynamics is available.

Zero-point energy (ZPE) leakage in classical trajectories is a well-known problem. Because ZPE is a quantum feature, there are no zero-point restrictions on energy during the classical propagation of nuclei. Thus, in Born-Oppenheimer (BO) dynamics, the energy that should be trapped in the zero-point of the hot modes (like C-H stretching) artificially flows to low-frequency modes.

This phenomenon can lead to unphysical results, such as forming products without the ZPE in the internal vibrational degrees of freedom. The ZPE leakage also allows reactions below its quantum threshold. For example, ground-state BO dynamics simulations of a water dimer predict the dimer dissociation, while quantum simulations don’t.

ZPE leakage has been a source of worry for decades. All pioneers of the field have dealt with it. Miller, Hase, Bowman, Varandas, Kim, and others proposed ways to constrain the leakage. However, their methods require knowing the Hessian matrix during the dynamics. We can do that if we have pre-computed potential energy surfaces, but keeping track of Hessians in on-the-fly dynamics is absolutely unaffordable.

Saikat Mukherjee and I have developed a Hessian-free method to correct ZPE leakage. Named local-pair (LP)  ZPE correction, it monitors the moving average kinetic energy stored in local pair of atoms with hot vibrations, such as C-H or N-H pairs. Whenever this mean kinetic energy drops below some threshold, LP-ZPE tops up the energy in the deficient pair, pumping it from all other atom pairs.

We built LP-ZPE to have minimum interference on the dynamics. It conserves total energy, of course. Moreover, the energy transfer is analogous to that of central forces. Thus, the total linear momentum of the molecule and the total angular momentum of the pair are conserved, too.

The method has only four adjustable parameters (to define the transfer thresholds and moving average), can be applied to any system size, can be used with on-the-fly dynamics, does not require Hessian matrices, and is compatible with ground- and excited-state propagations.

We have applied the LP-ZPE correction on the ab initio ground-state BO dynamics of the water dimer. Without correction, the dimer dissociates after a couple of picoseconds (top graph).

LP-ZPE (bottom graph) prevents the ZPE spilling of the OH stretching modes by pumping back the leaked energy into the corresponding modes, taking it from the other modes of the dimer, keeping the system as a microcanonical ensemble.

LP-ZPE is implemented into Newton-X. Its code is open-source (a stand-alone version is available) and can be easily integrated into any other dynamics program.

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Reference

[1] S. Mukherjee and M. Barbatti, A Hessian free method to prevent zero-point energy leakage in classical trajectories, J. Chem. Theory Comp. (2022). DOI: 10.1021/acs.jctc.2c00216