Analytic Functions Fit to Proton Transfer Potentials

Proton transfer potentials are traced out in (H2OH2OH+OH2OH2) and (H3NH3NH+NH3NH3) by ab initio computations for a series of different H-bond lengths. Attempts are then made to fit these quantum mechanical results by various forms of analytic functions. Best results are achieved by a pair of Morse functions with correlation coefficients in excess of 0.997. The numerical values of the Morse parameters are fairly insensitive to H-bond length, allowing their use in more general situations. The Φ4 function and its related fourth-order polynomial also fit well, but the parameters are much more sensitive to H-bond length. Gaussian-type functions or a Lippincott—Schroeder potential do not fit as well and a sinusoidal function gives rather poor agreement with the quantum mechanical results