Permanent Dipole Moments of Methane-Type Molecules: Calculation of the ΔJ = 0 Matrix Elements in the l = 1 Vibrational State

We examined permanent dipole moments (PDMs) of methane-type molecules induced by molecular internal motions which are expanded in terms of the vibrational coordinate operator q, total angular momentum operator J, and vibrational angular momentum operator l. The qq-, JJ-, Jl-, and ll-type quadratic terms of these operators contribute to the production of PDMs. The ΔJ = 0 matrix elements of the four PDMs are calculated for the first excited state of the triply degenerate vibrational mode; a portion are numerically given in a table for the J ≤ 6 levels. We have also compared them with the PDM represented by the rotational angular momentum operator R = J - l and discussed an application of the present calculations to the υ₃ = 2 state of methane.