Simulation Methods for the Calculation of Surface Properties

I present two new methods for the calculation of surface properties. Firstly, a method of thermodynamic integration to calculate surface free energies. A strain is applied to a unit cell of the bulk material, that opens up a vacuum gap and creates two surfaces. A parameter s describes this process, from 5 = 0 (the bulk material) to s = si (large vacuum gap). The difference in free energy between these two systems is then calculated by the integration of the stress on the unit cell over s. I use this general theory to find the surface free energy of the titanium dioxide (110) surface using density functional theory. The second part of the thesis gives a general transition state theory method for the calculation of the desorption rate of a molecule from a surface, at any coverage and temperature. This approach depends on the density of molecules as a function of the distance from the surface, and I show that this can be found from the potential of mean force. This is especially useful a t low temperatures, where experiments are conducted but brute force simulation is computationally unfeasible. I use this theory to calculate the desorption rate of water from the (0 0 1 ) surface of magnesium oxide at 100 — 1200K and 0 — 2/3 coverage, with classical potentials. An important outcome of these calculations is that the frequency prefactor (from the Polanyi-Wigner equation) is dependent on temperature.