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dc.contributor.authorCui, Yao
Bulik, Ireneusz W.
Jiménez-Hoyos, Carlos A.
Henderson, Thomas M.
Scuseria, Gustavo E.
dc.date.accessioned 2017-05-04T19:43:54Z
dc.date.available 2017-05-04T19:43:54Z
dc.date.issued 2013
dc.identifier.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.
dc.identifier.urihttps://hdl.handle.net/1911/94176
dc.description.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.
dc.language.iso eng
dc.publisher American Institute of Physics
dc.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.
dc.title Proper and improper zero energy modes in Hartree-Fock theory and their relevance for symmetry breaking and restoration
dc.type Journal article
dc.citation.journalTitle The Journal of Chemical Physics
dc.citation.volumeNumber 139
dc.citation.issueNumber 15
dc.type.dcmi Text
dc.identifier.doihttps://doi.org/10.1063/1.4824905
dc.identifier.pmid 24160500
dc.type.publication publisher version
dc.citation.articleNumber 154107


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