Spin contamination analogy, Kramers pairs symmetry and spin density representations at the 2-component unrestricted Hartree-Fock level of theory

Handle URI:
http://hdl.handle.net/10754/553011
Title:
Spin contamination analogy, Kramers pairs symmetry and spin density representations at the 2-component unrestricted Hartree-Fock level of theory
Authors:
Bučinský, Lukáš; Malček, Michal; Biskupič, Stanislav; Jayatilaka, Dylan; Büchel, Gabriel E. ( 0000-0002-5055-7099 ) ; Arion, Vladimir B.
Abstract:
"Kramers pairs symmetry breaking" is evaluated at the 2-component (2c) Kramers unrestricted and/or general complex Hartree-Fock (GCHF) level of theory, and its analogy with "spin contamination" at the 1-component (1c) unrestricted Hartree-Fock (UHF) level of theory is emphasized. The GCHF "Kramers pairs symmetry breaking" evaluation is using the square of overlaps between the set of occupied spinorbitals with the projected set of Kramers pairs. In the same fashion, overlaps between α and β orbitals are used in the evaluation of "spin contamination" at the UHF level of theory. In this manner, UHF Š2 expectation value is made formally extended to the GCHF case. The directly evaluated GCHF expectation value of the Š2 operator is considered for completeness. It is found that the 2c GCHF Kramers pairs symmetry breaking has a very similar extent in comparison to the 1c UHF spin contamination. Thus higher excited states contributions to the 1c and 2c unrestricted wave functions of open shell systems have almost the same extent and physical consequences. Moreover, it is formally shown that a single determinant wave function in the restricted open shell Kramers case has the expectation value of K2 operator equal to the negative number of open shell electrons, while the eigenvalue of K2 for the series of simple systems (H, He, He*-triplet, Li and Li*-quartet) are found to be equal to minus the square of the number of open shell electrons. The concept of unpaired electron density is extended to the GCHF regime and compared to UHF and restricted open shell Hartree-Fock spin density. The "collinear" and "noncollinear" analogs of spin density at the GCHF level of theory are considered as well. Spin contamination and/or Kramers pairs symmetry breaking, spin populations and spin densities are considered for H<inf>2</inf>O+, Cl, HCl+, phenoxyl radical (C<inf>6</inf>H<inf>5</inf>O) as well as for Cu, Cu2+, Fe and the [OsCl<inf>5</inf>(1H-pyrazole)]- anion. The 1c and 2c unpaired electron density representation is found useful for visualization and/or representation of spin density. © 2015 Elsevier B.V.
KAUST Department:
Physical Sciences and Engineering (PSE) Division; KAUST Catalysis Center (KCC)
Citation:
Spin contamination analogy, Kramers pairs symmetry and spin density representations at the 2-component unrestricted Hartree-Fock level of theory 2015 Computational and Theoretical Chemistry
Publisher:
Elsevier BV
Journal:
Computational and Theoretical Chemistry
Issue Date:
11-May-2015
DOI:
10.1016/j.comptc.2015.04.019
Type:
Article
ISSN:
2210271X
Additional Links:
http://linkinghub.elsevier.com/retrieve/pii/S2210271X15001760
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division; KAUST Catalysis Center (KCC)

Full metadata record

DC FieldValue Language
dc.contributor.authorBučinský, Lukášen
dc.contributor.authorMalček, Michalen
dc.contributor.authorBiskupič, Stanislaven
dc.contributor.authorJayatilaka, Dylanen
dc.contributor.authorBüchel, Gabriel E.en
dc.contributor.authorArion, Vladimir B.en
dc.date.accessioned2015-05-17T20:28:35Zen
dc.date.available2015-05-17T20:28:35Zen
dc.date.issued2015-05-11en
dc.identifier.citationSpin contamination analogy, Kramers pairs symmetry and spin density representations at the 2-component unrestricted Hartree-Fock level of theory 2015 Computational and Theoretical Chemistryen
dc.identifier.issn2210271Xen
dc.identifier.doi10.1016/j.comptc.2015.04.019en
dc.identifier.urihttp://hdl.handle.net/10754/553011en
dc.description.abstract"Kramers pairs symmetry breaking" is evaluated at the 2-component (2c) Kramers unrestricted and/or general complex Hartree-Fock (GCHF) level of theory, and its analogy with "spin contamination" at the 1-component (1c) unrestricted Hartree-Fock (UHF) level of theory is emphasized. The GCHF "Kramers pairs symmetry breaking" evaluation is using the square of overlaps between the set of occupied spinorbitals with the projected set of Kramers pairs. In the same fashion, overlaps between α and β orbitals are used in the evaluation of "spin contamination" at the UHF level of theory. In this manner, UHF Š2 expectation value is made formally extended to the GCHF case. The directly evaluated GCHF expectation value of the Š2 operator is considered for completeness. It is found that the 2c GCHF Kramers pairs symmetry breaking has a very similar extent in comparison to the 1c UHF spin contamination. Thus higher excited states contributions to the 1c and 2c unrestricted wave functions of open shell systems have almost the same extent and physical consequences. Moreover, it is formally shown that a single determinant wave function in the restricted open shell Kramers case has the expectation value of K2 operator equal to the negative number of open shell electrons, while the eigenvalue of K2 for the series of simple systems (H, He, He*-triplet, Li and Li*-quartet) are found to be equal to minus the square of the number of open shell electrons. The concept of unpaired electron density is extended to the GCHF regime and compared to UHF and restricted open shell Hartree-Fock spin density. The "collinear" and "noncollinear" analogs of spin density at the GCHF level of theory are considered as well. Spin contamination and/or Kramers pairs symmetry breaking, spin populations and spin densities are considered for H<inf>2</inf>O+, Cl, HCl+, phenoxyl radical (C<inf>6</inf>H<inf>5</inf>O) as well as for Cu, Cu2+, Fe and the [OsCl<inf>5</inf>(1H-pyrazole)]- anion. The 1c and 2c unpaired electron density representation is found useful for visualization and/or representation of spin density. © 2015 Elsevier B.V.en
dc.publisherElsevier BVen
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S2210271X15001760en
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Computational and Theoretical Chemistry. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computational and Theoretical Chemistry, 11 May 2015. DOI: 10.1016/j.comptc.2015.04.019en
dc.subjectSpin contaminationen
dc.subjectKramers pairen
dc.subjectSpin densityen
dc.subjectKramers unrestricteden
dc.subject2-componenten
dc.subjectUnpaired electronen
dc.subjectGeneral complexen
dc.titleSpin contamination analogy, Kramers pairs symmetry and spin density representations at the 2-component unrestricted Hartree-Fock level of theoryen
dc.typeArticleen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentKAUST Catalysis Center (KCC)en
dc.identifier.journalComputational and Theoretical Chemistryen
dc.eprint.versionPost-printen
dc.contributor.institutionInstitute of Physical Chemistry and Chemical Physics FCHPT, Slovak University of Technology, Radlinskeho 9, Bratislava, SK-812 37, Slovakiaen
dc.contributor.institutionDepartment of Chemistry, University of Western Australia, 35 Stirling Hwy, Crawley WA 6009, Australiaen
dc.contributor.institutionUniversity of Vienna, Institute of Inorganic Chemistry, Währinger Str. 42, A-1090 Vienna, Austriaen
kaust.authorBüchel, Gabriel E.en
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