Toward Gaussian Process Regression Modeling of a Urea Force Field

FFLUX is a next-generation, machine-learnt force field built on three cornerstones: quantum chemical topology, Gaussian process regression, and (high-rank) multipolar electrostatics. It is capable of performing molecular dynamics with near-quantum accuracy at a lower computational cost than standard <i>ab initio</i> molecular dynamics. Previous work with FFLUX was concerned with water and formamide. In this study, we go one step further and challenge FFLUX to model urea, a larger and more flexible system. In result, we have trained urea models at the B3LYP/aug-cc-pVTZ level of theory, with a mean absolute error of 0.4 kJ mol^-1 and a maximum prediction error below 7.0 kJ mol^-1. To test their performance in molecular dynamics simulations, two sets of FFLUX geometry optimizations were carried out: 5 dimers corresponding to energy minima and 75 random dimers. The 5 dimers were recovered with a root-mean-square deviation below 0.1 Å with respect to their <i>ab initio</i> references. Out of the 75 random dimers, 68% converged to the qualitatively same dimer as those obtained at the <i>ab initio</i> level. Furthermore, we have ranked the 5 FFLUX-optimized dimers in the order of their relative FFLUX single-point energies and compared them with the <i>ab initio</i> method. The energy ranking fully agreed but for one crossover between two successive minima. Finally, we have demonstrated the importance of geometry-dependent (<i>i</i>.<i>e</i>., flexible) multipole moments, showing that the lack of multipole moment flexibility can lead to average errors in the total intermolecular electrostatic energy of more than 2 orders of magnitude.