The Sextic Centrifugal Distortion Terms for an Open-Shell Complex Consisting of a Diatomic Molecule in a Σ Electronic State and a Closed-Shell Partner

An effective Hamiltonian for calculating rotational energy levels of an open-shell diatomic molecule, in a ^2S+1Σ electronic state, weakly bonded to a closed-shell partner was presented (W. M. Fawzy, J. Mol. Spectrosc. 191, 68–80 (1998)). The Hamiltonian was given as H = H_ev + H_rot + H_sr + H_ss + H_cd + H_srcd + H_sscd, where all the quartic centrifugal distortion correction terms were included in the Hamiltonian term H_cd but the sextic centrifugal distortion terms were ignored. This Hamiltonian is useful in cases where the complex has a well-defined equilibrium geometry and if the barrier to large-amplitude motion is large compared to the rotational constant of both the closed-shell molecule and its paramagnetic partner; if the barrier to large-amplitude motion is small compared to the rotational constant of one or both of the fragments, then a different treatment is required. In this paper, we introduce the new Hamiltonian terms H^sex(A)_cd and H^sex(S)_cd, which represent the sextic centrifugal distortion correction terms for an asymmetric rotor. We also introduce all the nonvanishing matrix elements of each of the H^sex(A)_cd and H^sex(S)_cd operators. These operators and their matrix elements are required for calculating the rotational energy levels of relatively high J values in the described type of weakly bonded open-shell complexes. The terms H^sex(A)_cd and H^sex(S)_cd and their matrix elements are also valid for any stable asymmetric rotor in a nondegenerate electronic state. A brief discussion of the new Hamiltonian terms and their matrix elements is given.