Path integral Monte Carlo simulations of molecular hydrogen on graphite

We have used the Path-Integral Monte Carlo simulation method in order to study molecular hydrogen films physically adsorbed on the basal plane surface of graphite. We have investigated the first and second layers in detail using realistic hydrogen-hydrogen and hydrogen-graphite interactions. We have chosen the semiempirical Crowell-Brown potential as an interaction between a hydrogen molecule and a carbon atom on the graphite surface and combined this potential with the method developed by Steele to determine the full interaction potential for a hydrogen molecule on the graphite surface. We have used the Silvera-Goldman model for the interaction between hydrogen molecules. First, we have simulated the first layer with the molecule-graphite interaction that includes only the laterally averaged potential and neglects the substrate corrugations. In this case the phase diagram of the first layer consists of a solid-vapor coexistence phase and a triangular solid phase. The phase diagram is similar to the one of the actual second layer. We have determined the equilibrium density, the boundary of the coexistence phase, and the second layer promotion density. When we use the full molecule-graphite interaction with the substrate corrugation amplitude, we can reproduce all the phases determined from several experimental measurements: a commensurate-vapor coexistence phase, a $3\times 3$ commensurate solid phase, a striped domain-wall solid phase, and an incommensurate solid phase. We found that the substrate corrugation has a major effect on the phase diagram of the first layer. We have computed the total energy, the static structure factor, the probability distribution of the H₂ molecules, and the specific heat of each phase in order to study the structure and the melting of the monolayer solids. For the second layer we approximated the effect of the first layer by placing the first layer hydrogen molecules on the sites of a triangular lattice at a fixed height above the substrate graphite. We found that the second layer consists of a solid-vapor coexistence phase and a solid phase and the second layer forms an incommensurate solid phase just before promotion. We have determined the completion density of the second layer, the melting temperatures, and the solid-vapor coexistence region.