Here S denotes the spin value and M denotes spin projection, which goes from -S, -S + 1, . . . , S -1, S. Any set of operators satisfying these relations are called irreducible spintensor operators. For example, the S = 0 case corresponds to singlet operators, which commute with S z , S + , and S -. Any spin-independent operator, such as a dipole moment operator, is a singlet operator. Spin-orbit operator depends on spin, and as shown below, it is composed from triplet spin-tensor operators. In particular, McWeeny writes down both angular momentum and spin in irreducible tensor form for spin-orbit operator in Eqs. (2.1) and (2.2) in Ref. (see also exercise 2.10 in ).