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

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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.

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Acknowledgments

We acknowledge Dr. Lukáš Bučinský for drawing our attention to the problem of the derivation of GCHF spin contamination, and to the fact that S 2 does not commutes with the “spin-same-orbit” coupling term, usually used in quantum chemistry. The referees and the editor are acknowledged for suggesting many improvements to the manuscript. This article is a tribute to Prof. P. Surjàn and is also dedicated to the memory of the late Prof. Gaston Berthier, who introduced to the author in the course of vivid discussions, many of the references listed below.

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Authors and Affiliations

  1. CNRS, LJAD, UMR 7351, University of Nice Sophia Antipolis, 06100, Nice, France

    Patrick Cassam-Chenaï

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  1. Patrick Cassam-Chenaï
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Correspondence to Patrick Cassam-Chenaï.

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

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Cassam-Chenaï, P. Spin contamination and noncollinearity in general complex Hartree–Fock wave functions. Theor Chem Acc 134, 125 (2015). https://doi.org/10.1007/s00214-015-1731-6

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