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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.

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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

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