# Ground state term symbol for Cerium (Ce)

I need to calculate the term symbol of the ground state configuration of Cerium.
The electron configuration is: $$[Xe] 4f^1 5d^1 6s^2$$
Since the d and f electrons are in different subshelles, they are non-equivalent electrons and Pauli exclusion principle doesn't apply, so:
$$l_1=2$$;$$l_2=3$$
using addition of angular momentum:
$$L=5,4,3,2,1$$ and $$S=1,0$$
Using Hund's rules, the ground state term symbol should be the one with $$S=1$$ and $$L=5$$, this is $$^3H$$. However, NIST lists $$^1G$$ as the ground state.
Any help would be really apreciated.

Iván, you are right on your determination using Hund's rules. However, for heavy elements, with strong spin-orbit coupling, the LS coupling assumed by Hund's rules may not apply. In this case, the j-j coupling may give better agreement with experiment.

There are extensions of Hund's rules for j-j coupling [1].

If you check NIST Atomic Spectra Database Levels Data, you will see that the wavefunction for the ground state of the Ce atom is 55% $$^1\text{G}^\circ$$ and 29% $$^3\text{H}^\circ$$. This mixture between singlet and triplet is due to the spin-orbit coupling.

[1] T. E. H. Walker, J. T. Waber, Modified Hund’s Rule for jj Coupling. Physical Review A. 7, 1218–1224 (1973). https://dx.doi.org/10.1103/PhysRevA.7.1218