Spin contamination and noncollinearity in general complex Hartree–Fock wave functions

Abstract

An expression for the square of the spin operator expectation value, $\langle{S^{2}}\rangle$, is obtained for a general complex Hartree–Fock wave function and decomposed into four contributions: the main one whose expression is formally identical to the restricted (open-shell) Hartree–Fock expression. A spin contamination one formally analogous to that found for spin unrestricted Hartree–Fock wave functions. A noncollinearity contribution related to the fact that the wave function is not an eigenfunction of the spin-S _z operator. A perpendicularity contribution related to the fact that the spin density is not constrained to be zero in the xy - plane. All these contributions are evaluated and compared for the H₂O⁺ system. The optimization of the collinearity axis is also considered.

Published as part of the special collection of articles “Festschrift in honour of P. R. Surjan.”