The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.
Perturbation Theory for the Fock-Dirac Density Matrix
Abstract
In Hartree-Fock theory and its various generalizations, it is customary to solve an eigenvalue problem involving an effective one-body Hamiltonian. The eigenvectors determine the Fock-Dirac density matrix, which also appears in the effective Hamiltonian, and solution proceeds iteratively until self-consistency is achieved.An alternative (necessary and sufficient) condition for a solution is that the density matrix ($\ensuremath{\rho}$) is idempotent and commutes with the Hamiltonian (h). The change in $\ensuremath{\rho}$, accompanying a change $\ensuremath{\Delta}$ in h, can then be expressed as a perturbation series. Formulas for the perturbation, to all orders, are obtained in terms of the unperturbed Hamiltonian and density matrix. It is also shown that the whole perturbation may be obtained directly, without separating the orders, and that the approach is related to earlier steepest-descent methods.
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Cites
New Developments in Molecular Orbital Theory
Roothaan, C. C. J. (1951) · Reviews of Modern Physics · doi:10.1103/revmodphys.23.69 · Cited by 5,519
Some Recent Advances in Density Matrix Theory
McWeeny, R. (1960) · Reviews of Modern Physics · doi:10.1103/revmodphys.32.335 · Cited by 1,460
Self-citationLöwdin, P.-O. (1955) · Physical Review · doi:10.1103/physrev.97.1509 · Cited by 1,140
The density matrix in self-consistent field theory I. Iterative construction of the density matrix
McWeeny, R. (1956) · Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences · doi:10.1098/rspa.1956.0100 · Cited by 203
Self-citationNote on the Interpretation of the Density Matrix in the Many-Electron Problem
Dirac, P. A. M. (1931) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004100010343 · Cited by 131
Wave Functions of Many-Electron Atoms
Lennard-Jones, J. E. (1931) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004100010057 · Cited by 63
Cited by
Werner, H.-J., & Meyer, W. (1976) · Molecular Physics · doi:10.1080/00268977600100651 · Cited by 640
Orbital magnetoelectric coupling in band insulators
Essin, A. M., Turner, A. M., Moore, J. E., & Vanderbilt, D. (2010) · Physical Review B · doi:10.1103/physrevb.81.205104 · Cited by 193
Multireference Electron Correlation Methods: Journeys along Potential Energy Surfaces
Park, J. W., Al-Saadon, R., MacLeod, M. K., Shiozaki, T., & Vlaisavljevich, B. (2020) · Chemical Reviews · doi:10.1021/acs.chemrev.9b00496 · Cited by 155
Platzer, G., Ptaszek, A. L., Böttcher, J., Fuchs, J. E., Geist, L., Braun, D., McConnell, D. B., Konrat, R., Sánchez‐Murcia, P. A., & Mayer, M. (2024) · ChemPhysChem · doi:10.1002/cphc.202300636 · Cited by 8
Metadata
- Authors
- McWeeny, R.
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1962-05-01
- Volume
- 126
- Issue
- 3
- Pages
- 1028-1034
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W2148080533
- Cited by
- 833
- References
- 6
- FWCI
- 1.14
- Type
- journal article
- Language
- en
- Open access
- closed
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