Roadmap to CCSD(T)-Quality Machine-Learned Potentials for Condensed Phase Simulations

Accurate, yet computationally efficient energy functions are essential for state-of-the-art molecular dynamics (MD) studies of condensed phase systems. Here, a generic workflow based on a combination of machine-learning-based and empirical representations of intra- and intermolecular interactions is presented. The total energy is decomposed into internal contributions and electrostatic and van der Waals interactions between monomers. The monomer potential energy surface is described using a neural network, whereas for the electrostatics the flexible minimally distributed charge model is employed. Remaining contributions between reference energies from electronic structure calculations and the model are fitted to standard Lennard-Jones (12-6) terms. For water as a topical example, reference energies for the monomers are determined from CCSD(T)-F12 calculations, whereas for an ensemble of cluster structures containing [2, 60] and [2, 4] monomers DFT and CCSD(T) energies, respectively, were used to adjust the van der Waals contributions. Based on the bulk liquid density and heat of vaporization, the best-performing set of LJ(12-6) parameters was selected and a wide range of condensed phase properties were determined and compared with experiment. MD simulations on the multiple-nanosecond time scale were carried out for water boxes containing 2000 to 8000 monomers, depending on the property considered. The performance of such a generic ML-inspired parametrization scheme is very promising and future improvements and extensions are discussed, also in view of recent advances for water in particular in the literature.