S U (2s+1) ×ζr and spin statistical weights for tetrahedral XY4, trigonal bipyramidal XY5, and octahedral XY6

Using Schur’s theorem we obtain explicit expressions for the spin degeneracies of the three molecular types; XY4 of Td symmetry, XY5 of D3h symmetry, and XY6 of Oh symmetry. Tables of spin statistical weights for all spins up to 11/2 are given.