We have calculated ground state interaction energies for an antihydrogen atom and a hydrogen molecule within the Born-Oppenheimer approximation. Leptonic energies were calculated using a large basis set of explicitly correlated Gaussian functions. Energies were calculated at over 2800 geometries including different proton-proton distances. The energies have been fit to functional forms using a neural network for the short-range interaction which is combined with asymptotic formulas at long

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... . A two-dimensional rigid rotor and a three-dimensional atommolecule potential energy surface (PES) have been determined. Rigid-rotor scattering calculations on these surfaces have been carried out using the S-matrix Kohn variational method with a two-dimensional Gaussian basis set. We have calculated cross sections for elastic, rotationally inelastic and annihilation collisions on the two-dimensional PES. This includes the first calculation of leptonic annihilation for this system. Supplementary material for this article is available online