Configuration interaction matrix elements. III. Spin functions relating the unitary and symmetric group approaches

Spin functions that are compatible with orbital ordering and geminal antisymmetry conditions are investigated. It is shown that two widely used classes of spin functions, namely, the spin-bonded functions and Yamanouchi–Kotani (or, equivalently, Gelfand–Tsetlin) functions possess these properties. The relationship of the latter with Young–Yamanouchi spin functions is also outlined using graphical techniques of spin algebras. These techniques are also used to rederive the Hamiltonian matrix elements between spin-bonded functions and to show the relationship among the various schemes used in this case.