Modelling potential energy surfaces for small clusters using Shepard interpolation with Gaussian-form nodal functions

Abstract

The potential energy surface (PES) of a chemical system is an analytical function that outputs the potential energy of the system when a nuclear configuration is given as input. The PESs of small atmospheric clusters have theoretical as well as environmental significance. A common method used to generate analytical PESs is the Shepard interpolation, where the PES is a weighed sum of Taylor series expansions (nodal functions) at ab initio sample points. Based on this, in this study we present a new method based on the Shepard interpolation, where the nodal functions are composed of a symmetric Gaussian term and an asymmetric exponential term in each dimension. Corresponding sampling methods were also developed. We tested the method on several atmospheric bimolecular clusters and achieved root mean square errors (RMSE) below 0.13 kJ mol⁻¹ in 150 samples for Ar-rigid H₂O and Ne-rigid CO₂, and below 0.39 kJ mol⁻¹ in 1800 samples for rigid N₂-rigid CO₂.