We calculate 1542 ab initio points for the HF2+ ground state at the QCISD(T)/6-311 ++G(2df,2pd) level for a wide range of geometries. We fit the ab initio points to a multiparameter analytic function to obtain a multidimensional potential energy surface (PES) valid far large amplitude hydrogen motion. We then calculate and assign vibrational levels for this PES,There is intramolecular proton transfer when the hydrogen atom tunnels through a triangular transition state separating the two equivalent equilibrium geometries. The barrier to proton transfer is 9547 cm(-1) (8340 cm(-1) with zero-point correction). Below the barrier to proton transfer, the energy levels are split and measurable splittings are predicted for relatively low-lying vibrational levels that may be experimentally accessible. The first three levels with splitting greater than 0.01 cm(-1) are, in order of increasing energy, (0,3,1), (0,4,0), and (0,3,2), while the first three levels with splitting greater than 0.1 cm(-1) are, in : order of increasing energy, (0,4,1), (0,5,0), and (0,4,2), where nu(2) is the H-F-F bend quantum number and nu(3) is the F-F stretch quantum number. We conclude that H-F-F bend excitation is essential far proton transfer, and that F-F stretch excitation facilitates proton transfer. Ln addition, there is a 3:1 Fermi resonance between the HF stretch (harmonic frequency 3334 cm(-1)) and the H-F-F bend (harmonic frequency 1141 cm(-1)), and levels with HF stretch excitation can have significant splittings. For example, the splitting is greater than 0.01 cm-l for the (1,1,1) level, which is Fermi resonant with (0,4,1) and greater than 0.1 cm(-1) for the (1,2,1) level, which is Fermi resonant with (0,5,1). This is relevant for the experimental observation of the vibrational splittings since the IR intensity of the HF stretch is four times that of the H-F-F bend.