A series of ab initio Hartree-Fock calculations have been performed for the systems Ne2, Ne+2 and Ne++2 for different values of the interatomic distance R. Satisfactory convergence was reached for R>=1 a. u. For R<1 a. u. molecular-orbital energies were determined from a united-atom approximation. From the total energies and from energies of occupied and nonoccupied orbitals approximated-diabatic-potential curves were obtained for a large number of excited states of the Ne+2 system. The approximations used were checked by comparison with the results of open-shell Hartree-Fock calculations on Ne+2. The potential-energy curves obtained show that there are energetical possibilities for new assignments of the inelastic energy losses observed in nonviolent Ne-Ne+ collisions. These assignments are able to explain observations that cannot be described by the models proposed earlier.