Learning the Quantum Centroid Force Correction in Molecular Systems: A Localized Approach

Abstract

Molecular mechanics (MM) is a powerful tool to study the properties of molecular systems in the fields of biology and materials science. With the development of ab initio force field and the application of ab initio potential energy surface, the nuclear quantum effect (NQE) is becoming increasingly important for the robustness of the simulation. However, the state-of-the-art path-integral molecular dynamics simulation, which incorporates NQE in MM, is still too expensive to conduct for most biological and material systems. In this work, we analyze the locality of NQE, using both analytical and numerical approaches, and conclude that NQE is an extremely localized phenomenon in nonreactive molecular systems. Therefore, we can use localized machine learning (ML) models to predict quantum force corrections both accurately and efficiently. Using liquid water as example, we show that the ML facilitated centroid MD can reproduce the NQEs in both the thermodynamical and the dynamical properties, with a minimal increase in computational time compared to classical molecular dynamics. This simple approach thus largely decreases the computational cost of quantum simulations, making it really accessible to the studies of large-scale molecular systems.

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.…”

“…It was shown that effective NN potentials reproduced NQE effects for properties such as RDF, diffusion constants, pressure, and vibrational spectra. The authors of ref emphasized the local nature of NQE corrections that allowed them to reduce the size of water clusters used in NN training to 7 water molecules, while ∼30 water molecule clusters were used in ref . In contrast to the cited works, we fitted NN corrections only to intermolecular energies and forces of molecular dimers, resulting in a more localized description of NQE effects.…”

“…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 ,,,, …”

“…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.…”

“…Because of the localized nature of NQE, we hypothesize that corrections to intermolecular energies and forces, trained on PIMD simulations of molecular dimers, can accurately model NQE. Atom-centered machine learning methods achieved a good transferability of quantum corrections to centroid forces across phases or learning them using very short distance cutoffs . Intermolecular interactions are relatively small perturbations of total energies of molecular systems; therefore, we expect that NQE in intermolecular interactions can be adequately described with even more local descriptors than those used for total potential energies and forces.…”