Data for Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression

The standard approach, motivated by computational tractability for direct dynamics, is to approx- imate the PES with a second order Taylor expansion, for example centred at each GWP.

In this Article, we propose an alternative method for approximating PES ma- trix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited num- ber of configurations in each time-step; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5- and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of- magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices.