ANOMALOUS ROTATIONAL LINE INTENSITIES IN ELECTRONIC TRANSITIONS OF POLYATOMIC MOLECULES: AXIS-SWITCHING

Abstract

It is convenient when performing calculations on a vibrating and rotating molecule to define an axis system which is somehow fixed to the molecule. The orientation of the usual molecule-fixed axis system, however, depends not only upon the instantaneous positions of the nuclei, but also upon the equilibrium positions from which the nuclei are regarded as being displaced. Thus, when a molecule of low enough symmetry undergoes an electronic transition accompanied by a change in geometry, it will, in general, be necessary to consider two molecule-fixed axis systems, corresponding to the two different electronic states. This change in axis system from one electronic state to another will be called axis-switching. The two axis systems can be related to each other by the 3 × 3 rotation matrix which brings them into coincidence. The elements of this matrix are functions of the equilibrium geometries of the two electronic states as well as of the instantaneous positions of the atoms in the molecule. Axis-switching leads to departures from the usual expressions for the intensities of rotational lines, the effects of which are most noticeable in near-symmetric tops. The forbidden subbands occurring in the 2 400 Å system of acetylene can be satisfactorily explained by axis-switching. Axis-switching effects may also be present in the spectra of HCN, HSiCl, and HSiBr.