Centroid Molecular Dynamics Can Be Greatly Accelerated through Neural Network Learned Centroid Forces Derived from Path Integral Molecular Dynamics

Abstract

For nearly the past 30 years, Centroid Molecular Dynamics (CMD) has proven to be a viable classical-like phase space formulation for the calculation of quantum dynamical properties.However, calculation of the centroid effective force remains a significant computational cost and limits the ability of CMD to be an efficient approach to study condensed phase quantum dynamics.In this paper we introduce a neural network-based methodology for first learning the centroid effective force from path integral molecular dynamics data, which is subsequently used as an effective force field to evolve the centroids directly with the CMD algorithm. This method, called Machine-Learned Centroid Molecular Dynamics (ML-CMD) is faster and far less costly than both standard "on the fly" CMD and ring polymer molecular dynamics (RPMD). The training aspect of ML-CMD is also straightforwardly implemented utilizing the DeepMD software kit. ML-CMD is then applied to two model systems to illustrate the approach: liquid para-hydrogen and water. The results show comparable accuracy to both CMD and RPMD in the estimation of quantum dynamical properties, including the self-diffusion constant and velocity time correlation function, but for significantly reduced overall computational cost. e.g., to better treat heterogenous systems, rare events, etc, will also provide clear benefit to the ML-CMD approach developed in this work.

Neural Network Corrections to Intermolecular Interaction Terms of a Molecular Force Field Capture Nuclear Quantum Effects in Calculations of Liquid Thermodynamic Properties

“…The method we have discussed shares several similarities with the techniques presented in refs ,− , which employed the atom-centered descriptors and different types of neural network models to fit effective forces acting on centroids in CMD and RPMD calculations. It was shown that effective NN potentials reproduced NQE effects for properties such as RDF, diffusion constants, pressure, and vibrational spectra.…”

“…Coarsegraining theory of PIMD simulations has been recently reported in refs 38,39. Derivations of effective centroid potentials for chemical systems using analytical functions and neural network based on atom-centered descriptors have been reported previously in 8,9,24,39,40 Here, we focus on an accurate description of intermolecular interactions that play a dominant role in determining properties of interest in biochemistry such as ligand binding free energies and solvation free energies. We expect the PIMD intermolecular interactions to be numerically close to intermolecular energies evaluated in centroid coordinates, with corrections rapidly decaying with increasing atom−atom distances.…”

“…While the ARROW FF is polarizable and a multipolar force field, we note that it may not capture small effects related to electronic degrees of freedom. 42−44 ■ METHODS An encapsulation of PIMD corrections in a neural network has been discussed recently, 39 and so it is worthwhile to explain why we choose to do this in an alternative manner. First and foremost, we recently published 11 a hybrid NN-analytical model of intermolecular interactions, parametrized from firstprinciples, which achieves chemical accuracy for prediction of properties of diverse molecular systems.…”

“…A derivation of an effective centroid energy functional can also be considered as a coarse-graining of ring-polymer PIMD simulations. Coarse-graining theory of PIMD simulations has been recently reported in refs , . Derivations of effective centroid potentials for chemical systems using analytical functions and neural network based on atom-centered descriptors have been reported previously in ,,,, …”

“…Coarse-graining theory of PIMD simulations has been recently reported in refs , . Derivations of effective centroid potentials for chemical systems using analytical functions and neural network based on atom-centered descriptors have been reported previously in ,,,, …”