Permutationally Invariant Fitting of Many-Body, Non-covalent Interactions with Application to Three-Body Methane–Water–Water

A modified, computationally efficient method to provide permutationally invariant polynomial bases for molecular energy surface fitting via monomial symmetrization (Xie Z.; Bowman J. M. J. Chem. Theory Comput. 2010, 6, 26-34) is reported for applications to complex systems, characterized by many-body, non-covalent interactions. Two approaches, each able to ensure the asymptotic zero-interaction limit of intrinsic potentials, are presented. They are both based on the tailored selection of a subset of the polynomials of the original basis. A computationally efficient approach exploits reduced permutational invariance and provides a compact fitting basis dependent only on intermolecular distances. We apply the original and new techniques to obtain a number of full-dimensional potentials for the intrinsic three-body methane-water-water interaction by fitting a database made of 22,592 ab initio energies calculated at the MP2-F12 level of theory with haTZ (aug-cc-pVTZ for C and O, cc-pVTZ for H) basis set. An investigation of the effects of permutational symmetry on fitting accuracy and computational costs is reported. Several of the fitted potentials are then employed to evaluate with high accuracy the three-body contribution to the CH4-H2O-H2O binding energy and the three-body energy of three conformers of the CH4@(H2O)20 cluster.