Machine Learning Approaches for Developing Potential Surfaces: Applications to OH^-(H$_2$O)$_n$ ($n=1-3$) Complexes

An approach for obtaining high-level ab initio potential surfaces is described. The approach takes advantage of machine learning strategies in a two-step process. In the first, the molecular-orbital based machine learning (MOB-ML) model uses Gaussian process regression to learn the correlation energy at the CCSD(T) level using the molecular orbitals obtained from Hartree-Fock calculations. In this work, the MOB-ML approach is expanded to use orbitals obtained using a smaller basis set, aug-cc-pVDZ, as features for learning the correlation energies at the complete basis set (CBS) limit. This approach is combined with the development of a neural-network potential, where the sampled geometries and energies that provide the training data for the potential are obtained using a diffusion Monte Carlo (DMC) calculation, which was run using the MOB-ML model. Protocols are developed to make full use of the structures that are obtained from the DMC calculation in the training process. These approaches are used to develop potentials for OH-(H2O) and H3O+(H2O), which are used for subsequent DMC calculations. The results of these calculations are compared to those performed using previously reported potentials. Overall, the results of the two sets of DMC calculations are in good agreement for these very floppy molecules. Potentials are also developed for OH-(H2O)2 and OH-(H2O)3, for which there are not available potential surfaces. The results of DMC calculations for these ions are compared to those for the correspondingOH-(H2O)2 and OH-(H2O)3 ions. It is found that the level of delocalization of the shared proton is similar for a hydroxide or hydronium ion bound to the same number of water molecules. This finding is consistent with the experimental observation that these sets of ions have similar spectra.