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The vibrational energy levels of ammonia

1999; Taylor & Francis; Volume: 96; Issue: 4 Linguagem: Inglês

10.1080/00268979909482985

1362-3028

Nicholas C. Handy, Stuart Carter, Susan M. Colwell,

Atomic and Molecular Physics

A variational 6-dimensional method is used to determine the low lying vibrational energy levels of ammonia. The six internal coordinates were chosen to be appropriate for the symmetry and inversion motion of the molecule; they were the three NH bond lengths, r1, r2, r3, the unique angle β which each bond makes with the trisector of them, and two (of the three) angles, θ2 and θ3, between the bonds when projected on to a plane perpendicular to the trisector. The Wilson G matrix was determined for these internal coordinates both by computer algebra and by hand. An appropriate Jacobian for the motion was determined and the full Hermitian kinetic energy operator was obtained using the Podolsky transformation. Expansion functions were in the usual product form. Special attention was given to the θ2, θ3 expansion functions so that appropriate A1, A2 and E symmetry vibrational modes were obtained explicitly. Matrix elements of the kinetic energy operator were expressed in terms of one-dimensional integrals.Variational calculations have been performed with two six-dimensional surfaces: (i) that due to Martin, Lee and Taylor; and (ii) that due to Spirko and Kraemer. Although some of the vibrational levels for both surfaces are accurate, both have inadequacies: (a) because it is a Taylor expansion about an equilibrium, based on ab initio calculations, with no attention paid to planarity; and (b) because the non-inversion part of the surface was treated perturbatively in its derivation, and in fact some of the quartic displacement powers have negative coefficients. Therefore, neither surface gave good results overall, and there is a need for a refined 6 dimensional NH3 surface.