Investigations on the Unrestricted Hartree–Fock Method as a Tool for Computing Potential Surfaces

The possible uses of the ab initio spin-unrestricted Hartree–Fock (UHF) method for computing potential energy surfaces have been investigated, expanding the molecular orbitals from a basis set of Gaussian functions. In order to approximate spin-pure states, an exact spin projection operator, as well as an operator annihilating only the state of next higher multiplicity, has been used. Preliminary studies undertaken on the H2 and LiH molecules indicate that among the various methods employed, the unprojected UHF approach gives the most satisfactory shape for potential curves. The HNO molecule was then investigated, and five electronic states of the system were considered, namely A1,A″3,A″1 symmetry. The ground state is A′1. Its UHF energy was minimized by varying the three geometrical parameters independently. A value of 〈Ŝ2〉 of 0.32 was obtained at the experimental geometry. This system with an even number of electrons thus has the unexpected property of being unstable with respect to a splitting of the α and β orbitals. Application of the spin projection operator lowers the energy by 0.0265 a.u. The UHF wavefunctions give an excitation energy A″1←A′1 of 3860 cm−1. When pure spin states are produced, it becomes 11 660 cm−1 (experimental value 13 150 cm−1). The A″3 state practically coincides with the ground state in the UHF approximation, but after projection an excitation energy of 5850 cm−1 is obtained. A slight maximum is observed in the UHF potential energy curve of the A″ states as a function of the N–H distance, which we associate with the predissociation observed in the spectrum of the compound. Based upon projection at the experimental minimum for the ground state, and at infinite N–H separation, a set of adjusted curves has been generated for the system H + NO. The features of these curves are discussed in relation with the mechanism of the recombination reaction between hydrogen atoms and nitric oxide.