The interaction potential energy surface (PES) of He-H-2 is of great importance for quantum chemistry, as the simplest test case for interactions between a molecule and a closed-shell atom. It is also required for a detailed understanding of certain astrophysical processes-namely, collisional excitation and dissociation of H-2 in molecular clouds-at densities too low to be accessible experimentally. A new set of 23 703 ab initio energies was computed for He-H-2 geometries where the interaction energy was expected to be non-negligible. These have an estimated rms "random" error of similar to0.2 mhartree and a systematic error of similar to0.6 mhartree (0.4 kcal/mol). A new analytic He-H-2 PES, with 112 parameters, was fitted to 20 203 of these new ab initio energies (and to an additional 4862 points generated at large separations). This yielded an improvement by better than an order of magnitude in the fit to the interaction region, relative to the best previous surfaces (which were accurate only for near-equilibrium H-2 molecule sizes). This new PES has an rms error of 0.95 mhartree (0.60 kcal/mol) relative to the 14 585 ab initio energies that lie below twice the H-2 dissociation energy and 2.97 mhartree (1.87 kcal/mol) relative to the full set of 20 203 ab initio energies (the fitting procedure used a reduced weight for high energies, yielding a weighted rms error of 1.42 mhartree-i.e., 0.89 kcal/mol). These rms errors are comparable to the estimated error in the ab initio energies themselves; the conical intersection between the ground state and the first excited state is the largest source of error in the PES. (C) 2003 American Institute of Physics.