Abstract The fitting of highly accurate potential energy points and of the diagonal adiabatic coupling for H 3 + using different functional forms is presented. A recently derived analytical potential based on 69 points has been extended to give a highly reliable form of the topology of the surface far beyond the barrier to linearity. Rovibrational frequencies have been derived and are compared with experiment. Detailed information about the experimentally observed rovibrational transitions near 1.25 μm will be given. The computed transition frequencies reproduce experimental transitions within a tenth up to a few hundredths of a wavenumber, if a simulation of non-adiabatic effects is taken into account.