Quadratic Herman-Wallis factors for symmetric- and asymmetric-top molecules

Abstract

As a result of vibration-rotation interactions, the effective dipole moment operator of a molecule depends on the total angular momentum as well as the vibrational operators. This leads to a rotational dependence of transition moments additional to that implied by the direction-cosine matrix elements. For allowed rotational transitions in the ν i fundamental band of a symmetrictop molecule, the linestrengths S are given by S = S 0 F HW, where S 0 is given by the rotation-independent part of the effective dipole moment and the Herman-Wallis rotational correction factor F HW is F HW ={1+A i im J+A K i m K+A JJ(Q) i[ J(J + 1)−m 2 J]+A JJ(PR) i m 2 J+A KK i K 2 +A JK im Jm K} 2 , where m J = [J′(J′ + 1) − J″(J″ + 1)] 2 , m K = [k′ 2 − k″ 2] 2 , J(J + 1) = [J′(J′ + 1) + J″(J″ + 1)] 2 , and K 2 = [K′ 2 + K″ 2] 2 . The terms in m K are absent for a parallel band. If different ( J, k) transitions are mixed together, as in l-resonance, the factor in braces can be applied to the individual matrix elements. Relations are given between the A i coefficients and the θ i β, α and θ i βγ, α coefficients in the expansion of the effective dipole moment operator for both parallel and perpendicular fundamentals, and the theory is illustrated by comparing variational and perturbation calculations for ν 2 of H 3 +. Results are also given for asymmetric-top molecules, where a formula analogous to the above but with k 2 replaced by the rotational energy F( J K a K c ) is derived.