Ab initio statistical mechanics of surface adsorption and desorption. I. H2O on MgO (001) at low coverage

We present a general computational scheme based on molecular dynamics (MD) simulation for calculating the chemical potential of adsorbed molecules in thermal equilibrium on the surface of a material. The scheme is based on the calculation of the mean force in MD simulations in which the height of a chosen molecule above the surface is constrained and subsequent integration of the mean force to obtain the potential of mean force and hence the chemical potential. The scheme is valid at any coverage and temperature, so that in principle it allows the calculation of the chemical potential as a function of coverage and temperature. It avoids all statistical mechanical approximations, except for the use of classical statistical mechanics for the nuclei, and assumes nothing in advance about the adsorption sites. From the chemical potential, the absolute desorption rate of the molecules can be computed, provided that the equilibration rate on the surface is faster than the desorption rate. We apply the theory by ab initio MD simulation to the case of H2O on MgO (001) in the low-coverage limit, using the Perdew-Burke-Ernzerhof (PBE) form of exchange correlation. The calculations yield an ab initio value of the Polanyi-Wigner frequency prefactor, which is more than two orders of magnitude greater than the value of 10(13) s(-1) often assumed in the past. Provisional comparison with experiment suggests that the PBE adsorption energy may be too low, but the extension of the calculations to higher coverages is needed before firm conclusions can be drawn. The possibility of including quantum nuclear effects by using path-integral simulations is noted.