Rotational energy levels and line intensities for 2S+1Λ-2S+1Λ and 2S+1(Λ ± 1)-2S+1Λ transitions in a diatomic molecule van der Waals bonded to a closed shell partner

Abstract

Abstract Hamiltonian matrix elements needed for calculating rotational energy levels are derived for a planar complex consisting of an open-shell diatomic molecule and a closed-shell partner. These matrix elements take account of spin-orbit interaction and a Renner-Teller-like splitting term, but not of the effects of large-amplitude internal rotation of the diatomic fragment within the complex. Rotational levels obtained by numerically diagonalizing this Hamiltonian matrix for given J are, as expected, strongly influenced by the degree of quantization of projections of the electron orbital, electron spin, and total angular momentum along the two natural axes in the problem, i.e., by the degree of quantization along the internuclear axis of the open-shell diatomic fragment, or along the inertial a axis of the near-symmetric-top planar complex. The degree of quantization of these varioss projections is in turn determined by the relative sizes of the spinorbit interaction, the Renner-Teller interaction, and products of the rotational constants and quantum numbers of the form BJ , CJ , and AK , as well as by the angle between the diatomic internuclear axis and the inertial a axis of the complex. Transition-moment matrix elements needed for calculating intensities in spin and orbitally allowed transitions in the open-shell diatomic fragment are also derived. Such transitions have the form 2 S +1 Λ- 2 S +1 Λ and 2 S +1 (Λ ± 1)- 2 S +1 Λ, where Λ = Σ, Π, Δ, Φ, etc. A brief discussion of how to use the Hamiltonian and transition-moment matrix elements in a computer program is given.