The transfer of atoms, ions and molecular groups in solution. Part 2.—Tunnelling between harmonic wells

Abstract

We consider the use of a harmonic-oscillator model to investigate the tunnelling of atoms, ions and molecular groups between positions of equilibrium for systems in condensed phases. The use of the oscillator model is warranted in many instances for which one has reasonably accurate information about the vibrational frequencies of atoms or molecular groups together with information about the distance over which the species transfers. Thus, the harmonic-oscillator model can be used in the absence of more complete information to make estimates of the rates of various kinds of heavy-centre transfers in solution. In this paper we present a general treatment for the determination of the tunnel factors which are involved in the transfer. The work constitutes an extension of the analysis of Wall and Glockler, who used a symmetric double potential well in order to investigate the resonance doubling of the vibrational spectrum of ammonia. We consider the general problem of the tunnelling between any two vibrational states of the separate potential wells. As an example, we apply the analysis to the consideration of a simple ion transfer between two centres of solvation.