An application of the Pariser-Parr approximation to the nitrogen molecule

Abstract

The semi-empirical method due to Pariser and Parr [1] is extended to make it applicable to an axially symmetrical molecule. Wave functions are expressed in terms of atomic orbitals before deriving expressions for the matrix elements of the effective Hamiltonian, instead of the more usual method of first expressing the matrix elements in terms of integrals involving molecular orbitals; this is found to facilitate the treatment, in that it enables us to make more direct use of atomic valence-state energies. An empirical formula is derived for a one-centre integral which does not occur in the more usual applications of the Pariser-Parr method. The method is used to calculate, for fixed nuclei, the energies, relative to the 1σg + ground term, of those six spectroscopic terms which can be obtained from the ground term by exciting one of the π u2p electrons to a π g2p orbital. Agreement with experiment is satisfactory, especially for those excited states which are not strongly affected by a neglected electronic configuration. Formulae are given for certain valence-state energies, additional to those earlier published.