In unrestricted
Hartree–Fock method, the wavefunctions obtained are eigenfunctions of the Hamiltonian and
the
spin projection
operators, but not eigenfunctions of the

operator. As a result, the wavefunctions of the doublet systems are spin-contaminated
to some extent by admixtures of quartet, sextet, and higher spin states. The eigenvalues
of the

operator are given as a measure of the spin
contamination.
Source: