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

  • Patrick Cassam-ChenaïEmail author
Part of the Highlights in Theoretical Chemistry book series (HITC, volume 12)


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.


Spin contamination Collinearity General complex Hartree–Fock 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.CNRS, LJAD, UMR 7351University of Nice Sophia AntipolisNiceFrance

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