The Sextic Centrifugal Distortion Terms for an Open-Shell Complex Consisting of a Diatomic Molecule in a 2S+1Σ Electronic State and a Closed-Shell Partner

Abstract

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 = Hev + Hrot + Hsr + Hss + Hcd + Hsrcd + Hsscd, where all the quartic centrifugal distortion correction terms were included in the Hamiltonian term Hcd 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 Hsex(A)cd and Hsex(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 Hsex(A)cd and Hsex(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 Hsex(A)cd and Hsex(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.