Using Gradients in Permutationally Invariant Polynomial Potential Fitting: A Demonstration for CH4 Using as Few as 100 Configurations

We describe software to incorporate electronic energies and gradients to develop high-dimensional potential energy surfaces, using a permutationally invariant polynomial basis. The energies and gradients are obtained using direct dynamics, using the efficient B3LYP/6-31+G(d) level of theory. The new software is described along with extensive testing and assessment of the benefits of using gradients as well as energies for CH4. Starting with a data set of 9000 configurations, we examine training and testing on data sets of energies only and energies plus gradients with data sets as small as 50. In addition to standard root-mean-square fitting errors of energies and gradients, normal-mode analyses and diffusion Monte Carlo calculations are performed to examine the fidelity of the fits using gradients. We show that a precisely fitted potential surface can be obtained using energies and gradients with only 100 or even just 50 widely scattered configurations. Finally, several fits are done using all the data from direct-dynamics trajectories with 1000 steps. These are more demanding fits compared to the one based on pruning data sets. The results of these fits are encouraging.