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Issue 44, 2012
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Local spins: improved Hilbert-space analysis

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The decomposition of 〈Ŝ2〉 for a general wave function has been carried out in the framework of the Hilbert-space analysis. The one and two-center components fulfill all physical requirements imposed to date. An inherent ambiguity of the Hilbert-space decomposition of a two-electron quantity, in particular using a Mulliken-type scheme, is also discussed in detail. The formalism of effective atomic densities has allowed us to derive in a simple manner appropriate expressions for the decomposition of 〈Ŝ2〉 in the framework of Hilbert space analysis that are consistent with Mulliken population analysis and related quantities. Using a particular mapping we have derived the Hilbert-space expressions also in the framework of Löwdin population analysis in a straightforward manner. The numerical results obtained with the latter formalism have proved to be more robust and reliable.

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The article was received on 29 May 2012, accepted on 17 Sep 2012 and first published on 17 Sep 2012

Article type: Paper
DOI: 10.1039/C2CP42513K
Citation: Phys. Chem. Chem. Phys., 2012,14, 15291-15298
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    Local spins: improved Hilbert-space analysis

    E. Ramos-Cordoba, E. Matito, P. Salvador and I. Mayer, Phys. Chem. Chem. Phys., 2012, 14, 15291
    DOI: 10.1039/C2CP42513K

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