For polyatomic molecules, these operators include point-group symmetry operators (which act on all N electrons) and the spin angular momentum ($$S^2 \text{ and } S_z$$) of all of the electrons taken as a whole (this is true in the absence of spin-orbit coupling which is treated later as a perturbation). For linear molecules, the point group symmetry operations involve rotations $$R_z$$ of all N electrons about the principal axis, as a result of which the total angular momentum $$L_z$$ of the N electrons (taken as a whole) about this axis commutes with the Hamiltonian, H. Rotation of all N electrons about the x and y axes does not leave the total coulombic potential energy unchanged, so $$L_x \text{ and } L_y$$ do not commute with H. Hence for a linear molecule, $$L_z , S^2, \text{ and } S_z$$ are the operators that commute with H. For atoms, the corresponding operators are $$L^2, L_z, S^2, \text{ and } S_z$$ (again, in the absence of spin-orbit coupling) where each operator pertains to the total orbital or spin angular momentum of the N electrons.