There is several things I don't quite understand about crystal-field splitting. Q1: Why is crystal-field effect is not explained for f-orbitals like in d-orbitals in terms of real-orbitals? Correct me if I am wrong, but typically for d-orbitals, crystal-field splitting is explained classically in terms of alignment of d-orbitals in real-orbitals form (xy, yz, zx, z2, x2-y2) to the surrounding electric field potential (such as oxygen). Why is the same type of explanation not done for f-orbitals? Crystal-field splitting for f-orbitals (Stark-splitting) is explained instead through use of complex-orbitals (so magnetic quantum number is a good quantum number) and their use in eventual derivation of term symbols. Q2: I don't quite understand the lack of degeneracy of 4f-orbitals for 8S-state Gadolinium(III) ion. I read that because L = 0 (hence the 8S-state), the crystal-field splitting (to the first order) is nonexistent. That much I can understand since L = 0, which means the magnitude of orbital angular momentum is 0. But it also explain that this is because the orbitals are nondegenerate. That sounds contradicting. There are seven 4f-orbitals and term 8S means that this state has one electron in each of those orbitals which should be degenerate.