Excited states of f electron systems

In Section 11.3 a ground term for the P configuration was obtained by feeding electrons with spins parallel into rotating orbitals characterized by angular momenta of 3 and 2. Had we been prepared to pair these electrons they could both have been placed in the orbital with angular momentum 3 

Russell-Saunders term Spin-orbit states 

Now add the only two possible spin labels, 1 and 3, alternately, in such a way as to include and 7. We obtain  

This is a complete list of the terms that arise from the f configuration. A check on the correctness of the result can be obtained by counting wavefunctions. For the f configuration the first electron can be inserted in any one of 14 ways (we have seven orbitals, the spin can be either up or down) the second electron can be fed in in any one of 13 ways (it cannot be in the same orbital as the first and also have the same spin). Because the electrons are indistinguishable we have counted every possibility twice—so, ti and it have been counted as different. It follows that the total number of wavefunctions is 14 x 13/2 = 91. This number, 91, is the same as the number of functions contained in the terms that we generated above  

This completes our discussion of the excited states of f electron systems. For completeness, however, Table 11.8 gives a more complete list of the Russell-Saunders terms arising from all f configurations. It does not include the effects of spin-orbit coupling, which have to be worked out for each case individually. The reader may find it a helpful exercise to select a configuration from Table 11.8 and use it to construct a table similar to Table 11.7. 

---