Modeling of Coupled Proton Transfers by Analytic Functions

Potential energy surfaces are generated by ab initio calculations for the transfer of two protons in the pentameric chains (H2O ·· H2O ·· H2OH+ ·· OH2 ·· OH2) and (H3N ·· H3N ·· H3NH+ NH3 ·· NH3). These surfaces are then fit by the sum of (a) two functions, each of which reproduces the transfer potential of a single proton plus (b) a function that models the coupling between the two protons. Several candidates are tested for the latter coupling function. A simple linear dependence upon the motion of the two protons reproduces the full two–dimensional surface to an accuracy of some 1 kcal/mol. The popular quadratic function provides a poorer approximation as also do exponential and Coulombic-type functions