ABSTRACT
This chapter considers the connection between the symmetry properties of the spin and spatial functions. It explores how to construct spin eigenfunctions and the representations of the symmetric group generated by the spin eigenfunctions. The expectation values of physical observables, like the energy depend on the spatial function. The importance of the spin eigenfunctions arises from the fact that they play an important role in the symmetry specification of the spatial functions. The spin eigenfunctions are linearly independent and they form an orthonormal system. In the description of the electronic structure of atoms and molecules the notion of the electron pair plays an important role. Pairs of electrons associated with inner shells, lone pairs or chemical bonds occur as basic building blocks in the formation of the many-electron wavefunction. It is therefore important to construct a many-electron spin eigenfunction in such a way that pairs of electrons occur in a natural way.
