Inversion-vibration and inversion-rotation interactions in the ammonia molecule

Abstract

An attempt has been made to extend the theory of ammonia inversion in order to account for the dependence of the inversion splitting on the full set of vibrational and rotational quantum numbers. The potential energy of ammonia is approximated by a double minimum potential V([zeta]) plus the potential of a system of harmonic oscillators in the remaining five vibrational coordinates. V([zeta]) has been chosen to have the form V([zeta]) = -2F cos ([zeta]/L) + 2G cos (2[zeta]/L) in which [zeta] is an inversion coordinate and L a constant, ([zeta] | [less, double equals] [pi]L). The double minimum wave functions are computed numerically. Inversion-vibration interactions are obtained by developing the parameters F and G, which are regarded as mild functions of the five vibrational coordinates, in a Taylor expansion in the vibrational coordinates. With the exception of the state this potential accounts for the dependence of the inversion splittings on the vibrational quantum numbers of the two doubly degenerate modes [nu]2 and [nu]4 (eleven experimental data are fitted with four empirical interaction constants). However, the potential fails to describe completely the interaction between the inversion coordinate and the remaining nondegenerate vibrational coordinate associated with [nu]1. Since the task of diagonalizing the complete rotation-inversion Hamiltonian is complicated by the presence of several resonances, the rotation-inversion constants B- - B+ and C- - C+ are calculated only from the lowest order vibration-rotation-inversion Hamiltonian. The calculated constants for the pure inversion states n2 = 0, 1, 2, and 3 and the states n2 = 1 in combination with the remaining vibrational modes agree surprisingly well with the experimentally observed values.