We report an analytic potential energy surface (PES) based on several hundred DFT energies for H interacting with a Au(111) surface. Effective medium theory is used to fit the DFT data, which were obtained for the Au atoms held at their equilibrium positions. This procedure also provides an adequate treatment of the PES for displacements of Au atoms that occur during scattering of H atoms. The fitted PES is compared to DFT energies obtained from ab initio molecular dynamics trajectories. We present molecular dynamics simulations of energy and angle resolved scattering probabilities at five incidence angles at an incidence energy, E i = 5 eV, and at a surface temperature, T S = 10 K. Simple single bounce trajectories are important at all incidence conditions explored here. Double bounce events also make up a significant fraction of the scattering. A qualitative analysis of the double-bounce events reveals that most occur as collisions of an H-atom with two neighboring surface gold atoms. The energy losses observed are consistent with a simple binary collision model, transferring typically less than 150 meV to the solid per bounce.