Koopmans' Theorem in the ROHF Method: Canonical Form for the Hartree-Fock Hamiltonian Full article
| Journal |
Journal of Chemical Physics
ISSN: 0021-9606 , E-ISSN: 1089-7690 |
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| Output data | Year: 2006, Volume: 125, Number: 20, Pages: 204110 Pages count : 10 DOI: 10.1063/1.2393223 | ||||||
| Tags | Computation theory; Electrons; Hamiltonians; Ionization; Theorem proving | ||||||
| Authors |
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| Affiliations |
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Funding (5)
| 1 | Russian Foundation for Basic Research | 06-03-32587 |
| 2 | Президиум РАН | |
| 3 | Russian Science Support Foundation | |
| 4 | Council for Grants of the President of the Russian Federation | МК-4362.2006.3 |
| 5 | Council for Grants of the President of the Russian Federation | НШ-4821.2006.3 |
Abstract:
Since the classic work of Roothaan [Rev. Mod. Phys.32, 179 (1960)], the one-electron energies of a ROHF method are known as ambiguous quantities having no physical meaning. Together with this, it is often assumed in present-day computational studies that Koopmans’ theorem is valid in a ROHF method. In this work we analyze the specific dependence of orbital energies on the choice of the basic equations in a ROHF method which are the Euler equations and different forms of the generalized Hartree-Fock equation. We first prove that the one-electron open-shell energies εm derived by the Euler equations can be related to the respective ionization potentials Im via the modified Koopmans’ formula Im=−εm∕fmIm=−εm∕fm where fm is an occupation number. As compared to this, neither the closed-shell orbital energies nor the virtual ones derived by the Euler equations can be related to the respective ionization potentials and electron affinities via Koopmans’ theorem. Based on this analysis, we derive the new (canonical) form for the Hamiltonian of the Hartree-Fock equation, the eigenvalues of which obey Koopmans’ theorem for the whole energy spectrum. A discussion of new orbital energies is presented on the examples of a free N atom and an endohedral N@C60N@C60 (Ih)(Ih). The vertical ionization potentials and electron affinities estimated via Koopmans’ theorem are compared with the respective observed data and, for completeness, with the respective estimates derived via a ΔSCFΔSCF method. The agreement between observed data and their estimates via Koopmans’ theorem is qualitative and, in general, appears to possess the same accuracy level as in the closed-shell SCF.
Cite:
Plakhutin B.N.
, Gorelik E.V.
, Breslavskaya N.N.
Koopmans' Theorem in the ROHF Method: Canonical Form for the Hartree-Fock Hamiltonian
Journal of Chemical Physics. 2006. V.125. N20. P.204110. DOI: 10.1063/1.2393223 WOS Scopus РИНЦ ANCAN PMID OpenAlex
Koopmans' Theorem in the ROHF Method: Canonical Form for the Hartree-Fock Hamiltonian
Journal of Chemical Physics. 2006. V.125. N20. P.204110. DOI: 10.1063/1.2393223 WOS Scopus РИНЦ ANCAN PMID OpenAlex
Dates:
| Submitted: | May 5, 2006 |
| Accepted: | Oct 17, 2006 |
| Published print: | Nov 28, 2006 |
| Published online: | Nov 30, 2006 |
Identifiers:
| Web of science: | WOS:000242408100014 |
| Scopus: | 2-s2.0-33751563553 |
| Elibrary: | 13510772 |
| Chemical Abstracts: | 2006:1306548 |
| Chemical Abstracts (print): | 146:69022 |
| PMID: | 17144693 |
| OpenAlex: | W2089831956 |