Unrestricted Hartree-Fock Method

The unrestricted Hartree-Fock method is based upon the use of a single-determinant total wave function in which orbitals of the same $n$, $l$, and $m_l$ values but different $m_s$ values are regarded as being independent. The differences which arise between such orbitals are discussed. It is shown, using the Li atom as an example, that these differences are not merely a result of using a single determinant which has improper symmetry, but arise when the full spin-degeneracy problem is carried through. Conclusions for Li are generalized to more complicated systems. The influence of the unrestricted Hartree-Fock method on the calculation of magnetic form factors, its influence on hyperfine interactions, and its bearing on antiferromagnetism is pointed out.