The intramolecular tunnelling of hydrogen†

Abstract

This paper reports an approach to the analysis of the local anharmonic states of motion and tunnelling of hydrogen illustrated with the molecule malonaldehyde. A potential energy function is used accurately to fit the local potential energy surface. The basis fitting functions in the potential resemble the Morse basis function, , but are intrinsically Gaussian: . After rearrangement to isolate the Gaussian operators, the new form of the potential allows the direct use of mathematically friendly (Gaussian) manipulations that are needed to carry out the quantum mechanical analysis of the anharmonic features, namely tunnelling. The quantal analysis uses Cartesian harmonic oscillator basis functions together with the Talmi–Moshinsky–Smirnov methods to evaluate matrix elements of the potential energy operator. The longer term objective of this kind of work is to develop practical methods of hybrid analysis with which to treat the local atom dynamics associated with a reactive species while the rest of the dynamics are modelled as simple harmonic oscillators. The goal is eventually to have a computational theory of proton/hydrogen or small molecular group transfer reactions in condensed-phase systems. This paper addresses only the detailed local dynamical analysis. †Dedicated to Pavel Rosmus on the occasion of the celebration of his scienti.c achievements, in Prague.