The genealogical coupling scheme

We give in this section an introduction to the construction of CSFs and more generally to the construction of spin tensor operators. We shall employ the genealogical coupling scheme, where the final CSF for N electrons is arrived at in a sequence of N steps [2]. At each step, a new electron is introduced and coupled to those already present. We thus arrive at the final CSF through a sequence of N —I intermediate CSFs, each of which represents a spin eigenfunction. 

The first spin orbital corresponds to a doublet spin eigenfunction. When the second spin orbital is introduced, it may be coupled to the first one to yield either a singlet or a triplet spin eigenfunction. These two intermediate CSFs for two electrons may then be coupled to a third spin orbital, giving rise to two three-electron doublet CSFs and one quartet. This process is continued until all N electrons have been coupled to yield a final CSF of the desired spin symmetry. 

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