Electron-Spin Electron-Spin, Electron-Spin Rotation Interactions, and Quartic Centrifugal Distortion Terms for an Open-Shell Diatomic Molecule van der Waals Bonded to a Closed-Shell Partner

Abstract

Effective Hamiltonians H sr, H ss, H λd, H cd, and their matrix elements are derived for calculating electron-spin rotation, electron-spin electron-spin splittings, and centrifugal distortion correction terms to electron-spin electron-spin interaction and rotational energy levels, respectively. This formalism is valid for a near rigid, nonlinear planar open-shell complex consisting of an open-shell diatomic unit in an electronic state described by 2 S+1 Λ, where Λ = Σ, Π, Δ, Φ, etc,; S ≥ 1 2 , and a closed-shell partner (a rare gas atom or a closed shell diatomic molecule). Electron-spin electron-spin interaction and its centrifugal distortion correction terms (described by H ss and H λd, respectively) are needed only for complexes containing an open-shell diatomic unit with S > 1 2 , whereas electron-spin rotation and centrifugal distortion correction terms to rotational energy levels (described by H sr and H cd respectively) are required for complexes containing an open-shell diatomic unit with S ≥ 1 2 . For calculating effects of H sr, H ss, H λd, and H cd on rotational energy levels in the mentioned types of complexes, the total Hamiltonian is written as H = H rot + H so + H q + H sr + H ss + Hλ d + H cd. Rotational energy levels are then obtained by numerically diagonalizing this Hamiltonian matrix for each given J. Matrix elements of H rot, H so, H q, and calculations of relative intensities in spin and orbitally allowed transitions in the open-shell diatomic fragment and in rotationally or vibrationally allowed transitions in the closed-shell partner (when the closed-shell partner is a dipolar diatom) are the same as described in our previous work (W. M. Fawzy and J. T. Hougen, J. Mol. Spectrosc. 137, 154-165 (1989)). A brief discussion of the matrix elements of H sr, H ss, H Λd, H cd, and their inclusion in our previous computer program for calculating rotational energy levels and relative intensities of allowed transitions is given.