Reflection symmetries of linear-molecular rovibronic levels

Abstract

Coriolis forces break the infinite-fold axis of symmetry of a linear molecule, but leave a residual plane of symmetry normal to the axis of rotation. This plane is subject to quantum uncertainties at low rotation, but becomes semiclassically well defined at high rotation. The spin-rovibronic wavefunctions can be classified according to their behavior under reflection of the spin-vibronic variables in this plane, whose orientation depends on the coupling case. In Hund's case (a) or (c) the plane is through the molecular axis normal to the perpendicular component of the angular momentum J, while in Hund's case (b) it is normal to the perpendicular component of N. The former gives a symmetry classification that is exact in the absence of hyperfine mixing, and is equivalent to the e f classification of J. M. Brown et al. [ J. Mol. Spectrosc. 55, 500–503 (1975)], while the latter gives the A′ A″ approximate symmetry classification proposed by M. H. Alexander et al. [ J. Chem. Phys. 89, 1749–1753 (1989)]. This latter classification is equivalent to a generalization to nonsinglet states of the c d classification of G. Herzberg [“Spectra of Diatomic Molecules”, 2nd ed., Van Nostrand, Princeton, NJ (1950)], in which c and d levels are defined to have parities +(−1) N and −(−1) N , respectively. Usually N is not a perfect quantum number, but this notation provides a useful characterization whenever N is well defined. The classification of case (d) rovibronic levels in terms of the symmetries of the levels of the core is considered briefly.