The contribution of tunnelling to the diffusion of protons and deuterons in rare gas solids

The stability and diffusion of protons and deuterons in rare gas matrices are reexamined. These are known to be stabilized in rare gas matrices in the form of linear, centrosymmetric Rg₂H⁺ cations. The elementary step in their diffusion, displacement from one Rg-Rg bond to a neighboring one, can be modelled as an isomerization of the triangular Rg ₃H⁺ cation. Using an analytic approximation for thermally averaged transmission coefficients for tunnelling through and reflection by a truncated parabolic potential barrier (R.T. Skodje and D.G. Truhlar, J. Phys. Chem. 85, 624 (1981)) we calculate the rate constants for this elementary diffusion step. The calculated rate constants are consistent with all experimental observations, and confirm that tunnelling makes the dominant contribution to the diffusion of protons and deuterons in rare gas solids. Deuteration reduces the tunnelling rates by 5 to 8 orders of magnitude, which agrees with the observation that D⁺ in rare gas solids is signficantly more stable than H⁺.