From special unitary groups SU(2 I+1) to nuclear spin statistical weights

Abstract

Following a suggestion of S.R. Polo, Galbraith [J. Chem. Phys. 68 (1978) 1677] was the first to obtain nuclear spin statistical weights for molecules of the type XY 4 (T d) , XY 5 (D 3h) , and XY 6 (O h ) starting from special unitary groups. In the present contribution, an analogous but simpler method is presented allowing the calculation of nuclear spin statistical weights of rigid molecules belonging to all important molecular point groups. The molecules under consideration may contain more than one set of identical nuclei with spins up to 3. The method proposed can easily be extended to nonrigid molecules.