Spin Contamination - Elimination

Elimination

Although the ROHF approach does not suffer from spin contamination, it is far less commonly available in quantum chemistry computer programs. Given this, several approaches to remove or minimize spin contamination from UHF wave functions have been proposed.

The annihilated UHF (AUHF) approach involves the annihilation of first spin contaminant of the density matrix at each step in the self-consistent solution of the Hartree–Fock equations using a state-specific Löwdin annihilator. The resulting wave function, while not completely free of contamination, dramatically improves upon the UHF approach especially in the absence of high order contamination.

Projected UHF (PUHF) annihilates all spin contaminants from the self-consistent UHF wave function. The projected energy is evaluated as the expectation of the projected wave function.

The spin-constrained UHF (SUHF) introduces a constraint into the Hartree–Fock equations of the form λ(Ŝ2 − S(S + 1)), which as λ tends to infinity reproduces the ROHF solution.

All of these approaches are readily applicable to unrestricted Møller–Plesset perturbation theory.