On nuclear spin statistics in rotational transition intensities in tetrahedral AB4 molecules

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Abstract
A general expression is derived for the integrated intensity of rotational transitions in the vibronic ground state of tetrahedral molecules, taking into account the nuclear spin statistics. It is shown that the ratio of this expression to previously published spin-free integrated intensities depends only on the tensor character N of the operator driving the transition, the appropriate rotational quantum numbers J and J′, and the nuclear spin IB of the identical nuclei. Tables are given for N = 3, 4 and J ≤ 50 which enable the calculation of integrated intensities for octopole and hexadecapole collision induced dipole moment transitions, centrifugal distortion induced dipole moment transitions, and centrifugal distortion induced anisotropic polarizability tensor Raman transitions. It is shown that the relative error of the spin-free integrated intensity calculation is proportional to (2IB + 1)−2.

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