Some effects of spin-orbit interaction on rotational levels and rotational line intensities in vibrationally unexcited 2A, 2E, and 2F electronic states of open-shell XY 4 molecules

Abstract

Rotational energy levels in vibronic ground states of 2 A, 2 E, and 2 F electronic states of open-shell XY 4 molecules, as well as rotational line intensities for allowed transitions between such states, are discussed, including the effects of spin-orbit interaction and tetrahedral splittings. Jahn-Teller effects are assumed to be small, and are only taken into account implicitly, through their contributions to various parameters in the effective Hamiltonian. Qualitative information is obtained by considering several limiting-case coupling schemes among the electron spin angular momentum S, the electron orbital angular momentum L, and the pure rotational angular momentum R. These limiting cases are similar in spirit to Hund's coupling cases in diatomic molecules, but differ sufficiently from the latter to make detailed correspondences unhelpful. Quantitative information on rotational energy levels and line intensities is obtained numerically by diagonalizing a Hamiltonian matrix set up in a basis set characterized by uncoupled moleculefixed projections of S, L, and the total angular momentum J, and symmetrized so that all basis set functions belong to a definite species in the subgroup D 2 d of the true point group T d . Hamiltonian matrix elements are determined by ladder operator techniques. Three sample calculated spectra, corresponding to p( 2F 2)-s( 2A 1) , d( 2E)-p( 2F 2) , and d( 2F 2)-p( 2F 2) are presented. As one might expect, when the spin-orbit constant A is set equal to zero, then both qualitative and quantitative aspects of the rotational-electronic problem in open-shell XY 4 molecules can be mapped easily onto discussions of the rotation-vibration problem from the CH 4 literature.