Unlike a single atom, the Hamiltonian of a diatomic molecule doesn't commute with L 2 . So the quantum number l is no longer a good quantum number. The internuclear axis chooses a specific direction in space and the potential is no longer spherically symmetric. Instead, L z and J z commutes with the Hamiltonian H (taking the arbitrary internuclear axis as the Z axis). But L x , L y do not commute with H due to the fact that the electronic Hamiltonian of a diatomic molecule is invariant under rotations about the internuclear line (the Z axis), but not under rotations about the X or Y axes. Again, S 2 and S z act on a different Hilbert space, so they commute with H in this case also. The electronic Hamiltonian for a diatomic molecule is also invariant under reflections in all planes containing the internuclear line. The (X-Z) plane is such a plane, and reflection of the coordinates of the electrons in this plane corresponds to the operation y i → → − − y i . If A y is the operator that performs this reflection, then [ A y , H ] = 0 . So the Complete Set of Commuting Operators (CSCO) for a general heteronuclear diatomic molecule is { H , J z , L z , S 2 , S z , A } ; where A is an operator that inverts only one of the two spatial co-ordinates (x or y).