Electric-Quadrupole and Magnetic-Dipole Radiation in Linear Molecules. Applications to 1Π—3Π Transitions

Abstract

The electric-quadrupole and magnetic-dipole operators of a rotating, linear molecule interacting with a radiation field are formulated, in the space-fixed and in the molecular-coordinate systems, as contractions of irreducible spherical tensors. Radiative transition probabilities are obtained for the initial and final rotation-electronic states that are in Hund's Coupling Case a or b, using the normalized rotation matrix as the separated rotational wavefunction in the Born—Oppenheimer approximation. Line-strength formulas are derived for (1) transitions between singlet Case b states, in the case of an electric quadrupole, the 1Σ—1Σ, 1Π—1Σ, 1Δ—1Σ, 1Π—1Π, 1Δ—1Π, 1Φ—1Π, 1Δ—1Δ, 1Φ—1Δ, and 1Γ—1Δ transitions; in the case of a magnetic dipole, the 1Π—1Σ, 1Π—1Π, 1Δ—1Π, 1Δ—1Δ, and 1Φ—1Δ transitions; (2) the 1Π—3Π(a) transitions; (3) the 1Π—3Π(b) transitions. The master line-strength formula as well as intensity distribution for different branches are given. In (2) and (3), some of the transitions are found to be dependent on the absolute Kronig reflection symmetry, giving, for molecules of unequal nuclei, an intensity alternation for the two Λ-doubling components. A discussion of this reflection symmetry and the inversion symmetry is given and a consistent set of molecular wavefunctions of a given symmetry is constructed for (1) singlet Case b states and triplet Case a states (2) triplet Case b states expressed as a linear combination of Case a state wavefunctions through angular momentum coupling. The rotation—vibration spectra due to these higher multipole radiations are briefly discussed. A new point of view for the possibility of ΔΛ=0 (for Λ≠0) magnetic-dipole pure rotation spectra is advanced.