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    Proper and improper zero energy modes in Hartree-Fock theory and their relevance for symmetry breaking and restoration

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    Author
    Cui, Yao; Bulik, Ireneusz W.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Scuseria, Gustavo E.
    Date
    2013
    Abstract
    We study the spectra of the molecular orbital Hessian (stability matrix) and random-phase approximation (RPA) Hamiltonian of broken-symmetry Hartree-Fock solutions, focusing on zero eigenvalue modes. After all negative eigenvalues are removed from the Hessian by following their eigenvectors downhill, one is left with only positive and zero eigenvalues. Zero modes correspond to orbital rotations with no restoring force. These rotations determine states in the Goldstone manifold, which originates from a spontaneously broken continuous symmetry in the wave function. Zero modes can be classified as improper or proper according to their different mathematical and physical properties. Improper modes arise from symmetry breaking and their restoration always lowers the energy. Proper modes, on the other hand, correspond to degeneracies of the wave function, and their symmetry restoration does not necessarily lower the energy. We discuss how the RPA Hamiltonian distinguishes between proper and improper modes by doubling the number of zero eigenvalues associated with the latter. Proper modes in the Hessian always appear in pairs which do not double in RPA. We present several pedagogical cases exemplifying the above statements. The relevance of these results for projected Hartree-Fock methods is also addressed.
    Citation
    Cui, Yao, Bulik, Ireneusz W., Jiménez-Hoyos, Carlos A., et al.. "Proper and improper zero energy modes in Hartree-Fock theory and their relevance for symmetry breaking and restoration." The Journal of Chemical Physics, 139, no. 15 (2013) American Institute of Physics: https://doi.org/10.1063/1.4824905.
    Published Version
    https://doi.org/10.1063/1.4824905
    Type
    Journal article
    Publisher
    American Institute of Physics
    Citable link to this page
    https://hdl.handle.net/1911/94176
    Rights
    Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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    • Chemistry Publications [636]
    • Faculty Publications [4988]
    • Physics and Astronomy Publications [1771]

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    Home | FAQ | Contact Us | Privacy Notice | Accessibility Statement
    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892
    Site Map