Electronic structure of the N4+ molecular ion

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Abstract
The N4+ ion is an important species in the chemistry of the atmosphere. Here N4+ has been studied theoretically using the methods of ab initio molecular quantum mechanics. There is considerable complexity involved in the theoretical study of N4+ due to (a) the fact that N2+ has two low‐lying electronic states, X 2Σg+ and A 2Πu and the order of these is reversed within the Hartree–Fock approximation and (b) there are six low‐lying electronic states of N4+. Results are first presented at the self‐consistent‐field (SCF) level of theory using a double zeta (DZ) basis set N(9s 5p/4s 2p). Both Koopmans’ theorem and direct positive ion calculations in both D2h (rectangle) and C2v (regular trapezoid) symmetry suggest only a single (out of six) substantially bound electronic state, the 2B2u(D2h) or 2A1(C2v) state. Because the D2h SCF wave function necessitates a compromise description of the N2+N2+ asymptote, the predicted dissociation energy is artificially large, although in reasonable agreement with experiment. Polarization functions were added to the basis set and all three geometrical parameters examined to locate the C2v equilibrium structure, which lies 19.9 kcal below the dissociation limit N2+N2+(2Σg+). Similar theoretical methods were applied to the T‐shape geometry, with the constrained equilibrium structure bound by 24.2 kcal. The linear conformation represents the absolute minimum on the N4+ potential energy surface, lying 30.4 kcal below N2+N2+. The latter dissociation energy agrees well with the experimental value of ∼26 kcal. In studying the linear 2Σ+ state, the surprising result was found that the 2Σg+ restricted Hartree–Fock wave function is unstable with respect to the removal of the g/u element of symmetry. The 2Π state is stable in this respect, and as a result, the 2Σg+ state of N2+ falls closer to the 2Πu state in this mildly unrestricted form of Hartree–Fock theory.