Permutationally Invariant Polynomial Basis for Molecular Energy Surface Fitting via Monomial Symmetrization

We describe a procedure to develop a fitting basis for molecular potential energy surfaces (PESs) that is invariant with respect to permutation of like atoms. The method is based on a straightforward symmetrization of a primitive monomial basis and illustrated for several classes of molecules. A numerically efficient method to evaluate the resulting expression for the PES is also described. The fitting basis is used to obtain a new PIES for H3O+ based on roughly 62 000 ab initio energies.