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 PES for H3O(+) based on roughly 62 000 ab initio energies.

An accurate global potential-energy surface (PES) is reported for H5+ based on more than 100 000 CCSD(T)/aug-cc-pVTZ ab initio energies. This PES has full permutational symmetry with respect to interchange of H atoms and dissociates to H3+ and H2. Ten known stationary points of H5+ are characterized and compared to previous ab initio calculations. Quantum diffusion Monte Carlo calculations are performed on the PES to obtain the zero-point energy of H5+ and the anharmonic dissociation energy (D0) of H5+→H3++H2. The rigorous zero-point state of H4D+ is also calculated and discussed within the context of a strictly classical approach to obtain the branching ratio of the reaction H4D+→H3++HD and H2D++H2. Such an approach is taken using the PES and critiqued based on the properties of the quantum zero-point state. Finally, a simple procedure for adding the long range-interaction energy is described.