Interpolation of intermolecular potentials using Gaussian processes

A procedure is proposed to produce intermolecular potential energy surfaces from limited data. The procedure involves generation of geometrical configurations using a Latin hypercube design, with a maximin criterion, based on inverse internuclear distances. Gaussian processes are used to interpolate the data, using over-specified inverse molecular distances as covariates, greatly improving the interpolation. Symmetric covariance functions are specified so that the interpolation surface obeys all relevant symmetries, reducing prediction errors. The interpolation scheme can be applied to many important molecular interactions with trivial modifications. Results are presented for three systems involving CO₂, a system with a deep energy minimum (HF-HF), and a system with 48 symmetries (CH₄-N₂). In each case, the procedure accurately predicts an independent test set. Training this method with high-precision ab initio evaluations of the CO₂-CO interaction enables a parameter-free, first-principles prediction of the CO₂-CO cross virial coefficient that agrees very well with experiments.