Potential Energy Surfaces for Chemical Reactions: An Analytical Representation from Coarse Grianed Data with an Application to Proton Transfer in Water

In this paper we address the issue of how to represent the potential energy surfaces that arise in chemical reactions from coarse grained electronic structure calculations. Using a reductionistic method based on the reaction surface model, we develop a computational protocol which combines tensor product spline fitting with bivariate interpolation. This approach is particularly useful when one wishes to retain a high degree of accuracy for a few special degrees of freedom. An application of the procedure has been developed for the transfer of a proton between two water molecules. Starting from MP2/6-311G** calculations on H5O2+ dimer, we construct the global potential energy surface governing the proton transfer as well as the pattern of charge distributions. In order to study large reactive systems embedded in an external medium, we show how a less demanding procedure can be implemented. It rests on a minimum coupling approach of second-order Taylor expansions of the potential about quasi-stationary points. The resulting potential energy surface is termed a “minimum coupling potential”