Se. Wonchoba et Dg. Truhlar, EFFECT OF PHONON COUPLING ON HYDROGEN TUNNELING RATES AT GAS-SURFACE INTERFACES, The Journal of chemical physics, 99(12), 1993, pp. 9637-9651
The centrifugal-dominant small-curvature semiclassical adiabatic tunne
ling approximation is used with variational transition state theory to
calculate diffusion coefficients for hydrogen, deuterium, and tritium
atoms on the (100) face of copper for temperatures in the range 80-10
00 K. The system is modeled by the embedded cluster method, and the co
pper lattice is constructed with a lattice constant optimized for the
assumed potential energy function. Calculations are presented with up
to 171 nonfixed degrees of freedom. The results are well converged wit
h respect to the number of lattice atoms whose motion is allowed to co
uple to the adatom. The difference between the diffusion coefficients
calculated with rigid and nonrigid lattices at 300 K are 3.7, 3.3, and
3.1 for H, D, and T, respectively, increasing to factors of 24.1, 19.
4, and 17.2 at 120 K. The effect levels off for lower temperatures, e.
g., the ratio for H is 27.3 at 100 K and 24.4 at 80 K. The convergence
with respect to the number of moving copper atoms is nonmonotonic; de
tailed examination of the intermediate results shows that such nonmono
tonicities result from the nonsmooth cancellation of a large number of
competing effects attributable to many surface phonon modes. We compa
re the present results to those predicted by path integral transition
state theory and to those predicted by transition state theory with qu
antum effective potentials, and we find them to be in reasonably good
agreement. This is very encouraging since tests of multidimensional se
miclassical tunneling approximations have been limited to systems with
only a few degrees of freedom in the past.