Coriolis interaction between νt and 2 νn for axially symmetric molecules of the group C3 v: Application to the Stark effect of NH 3 in v 4 = 1 state

Abstract

The accidental Coriolis resonance interaction between a fundamental vibration ν i ( E) and an overtone 2 ν n ( A 1) is considered theoretically for axially symmetric molecules of the group C 3 v . General expressions for the matrix elements connecting the resonating states are derived up to second order of approximation. The coefficient of the matrix elements is given in terms of the molecular constants for two cases: (A) in the absence of other accidental resonances, (B) in the presence of Coriolis resonance between ν t and ν n . The theory developed for case (B) is then applied to the analysis of the Stark shifts of 28 inversion transitions in the ν 4 = 1 vibrational state of NH 3 obtained by microwave techniques. In order to fit the observed Stark effect as a function of J, k, and l 4, it is necessary to obtain sufficiently accurate wavefunctions for ν 4 which included the contributions from the nearby vibrational states ν 2 and 2 ν 2. This is done by reanalyzing Garing, Nielsen, and Rao's infrared data, taking into account the Coriolis resonance interaction of ν 4 with both ν 2 and 2 ν 2 as well as the l-type doubling. Refined molecular constants for the states for ν 4, ν 2, and 2 ν 2 are obtained from the analysis and the Coriolis coupling coefficient between ν 4 and 2 ν 2 is determined to be 1.27 cm −1. A subsequent analysis of the Stark effect data using the corrected wavefunctions and including the effect of higher-order Stark perturbation terms in the Hamiltonian is carried out and values for some dipole moment parameters of NH 3 are obtained from the analysis.