Calculation of vibration-rotation line intensities of polyatomic molecules based on the formalism of irreducible tensorial sets

Abstract

Irreducible tensorial sets of the point-symmetry groups are used to determine the general formulae for calculating the matrix elements of the reduced dipole moment operator of a polyatomic molecule. These general expressions allow different types of intramolecular interactions and accidental resonances to be considered. Transitions from one type of molecule to another are accounted for by substitution of isoscalar factors and 9 Gamma symbols of the point-symmetry group in the formulae. As an illustration the general expressions obtained are used to analyse the dependences of matrix elements of the reduced dipole moment on the rotational quantum numbers for some vibrational absorption bands of molecules with D3h, C3v and Td symmetries. For allowed transitions contributions to the reduced dipole moment operator which are linear and quadratic in Jalpha are taken into account. for forbidden transitions the main contributions are taken into account. It is shown that the general formulae obtained describe the generalised Herman-Wallis effect (1955) for polyatomic molecules.