An approach to the anomalous commutation relations of rotational angular momenta in molecules

In molecular quantum mechanics, angular momentum operators occur which obey anomalous commutation relations. A direct method of evaluating the matrix elements of such operators is presented. The method is particularly well suited to calculations which use spherical tensor techniques; it also avoids some confusing aspects of Van Vleck's reversed angular momentum method [2]. The relationship between results derived in space- and molecule-fixed axis systems is made explicit and a consistent phase convention is established. The transformation matrix relating coupled and decoupled basis sets for problems with molecular quantization is also derived.