Knowledge Bank

The m-fold extended group , corresponding to the permutation-inversion group $C18$ derived by Bunker for molecules like $H3C-SiH3$, has been obtained. In this treatment, m is the smallest integer for which mo is also an ``integer,” where p is the usual ratio of the moment of inertia of the top about the rotational A axis to the moment of inertia of the molecule about the A axis. The extended group has 18m elements, divided into (9m+3)/2 or (9m+6)/2 classes, for odd and even values of m, respectively. Using the extended group it is possible to assign definite symmetry species in an internal-axis-method treatment to top-fixed projections, frame-fixed projections, molecule-fixed projections, and laboratory-fixed projections of vector operators like the rotational angular momentum and the nuclear spin angular moments. Thus, it is possible to express the spin-rotation and spin-spin contributions to the hyperfine interaction operator in terms of rotational angular momentum components, nuclear spin angular momentum components, and functions of the torsional angle of known symmetry species and selection rules in the internal-axis-method basis set. Such operators may be useful in treating the selection rule anomalies uncovered in the ingenious molecular beam avoided crossing studies of Meerts and Ozier on molecules like $H3C-SiH3$.""