Spin contamination in single-determinant wavefunctions

Andrews, Jamie Stuart; Jayatilaka, Dylan; Bone, Richard G. A.; Handy, Nicholas C.; Amos, Roger D.

doi:10.1016/0009-2614(91)90405-x

Cited by 102 publications

(67 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Several properties of the 1c unpaired electron density have been already highlighted and its usage within the DFT framework has been tested [44,46]. Herein, the possible lowering of the extent of "spin contamination"/"Kramers pairs symmetry breaking" in 1c/2c KU spin densities is presented, without having to employ spin annihilation or spin projection [47,48,49,50,51,52,53,54,55,56] The paper is subdivided as follows: In the first part of Methods section the properties of the Kramers pairs are considered, the analog of the spin contamination (Kramers pairs symmetry breaking) at the 2c level of theory is introduced, with presenting the formal analog for <Ŝ 2 > evaluation at the GCHF level of theory. Afterwards, the evaluation of the expectation value ofK 2 for a single determinant wave function is highlighted and compared to its eigenvalues and their eigenfunctions (including Appendix which is devoted to H, He, He*-triplet, Li and Li*-quartet cases).…”

Section: -Kramers Pairs) Regime Anmentioning

confidence: 99%

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

Bučinský

Malček

Biskupič

et al. 2015

Computational and Theoretical Chemistry

Self Cite

View full text Add to dashboard Cite

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, UHFŜ 2 expectation value is made formally extended to the GCHF case. The directly evaluated GCHF expectation value of theŜ 2 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 so 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 ofK 2 operator equal to the negative number of open shell electrons, while the eigenvalue ofK 2 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

show abstract

Section: -Kramers Pairs) Regime Anmentioning

confidence: 99%

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

Bučinský

Malček

Biskupič

et al. 2015

Computational and Theoretical Chemistry

Self Cite

View full text Add to dashboard Cite

show abstract

“…The latter are generally considered to be inadequate because of spin contamination inherent in the UHF reference. [92][93][94][95][96][97][98][99][100] However, in the case of p-benzyne, we show correlation-corrected UHF methods provide highly reliable results that can be used for the analysis of the experimental data. Accordingly, the third objective of this work is to critically reanalyze the measured infrared ͑IR͒ spectrum.…”

Section: Introductionmentioning

confidence: 99%

Problematic p-benzyne: Orbital instabilities, biradical character, and broken symmetry

Crawford

Kraka

Stanton³

2001

The Journal of Chemical Physics

162

129

View full text Add to dashboard Cite

Articles you may be interested inTheoretical prediction of nuclear magnetic shieldings and indirect spin-spin coupling constants in 1,1-, cis-, and trans-1,2-difluoroethylenes A benchmark theoretical study of the electronic ground state and of the singlet-triplet split of benzene and linear acenes J. Chem. Phys. 131, 224321 (2009); 10.1063/1.3270190 CCSD(T) study of the far-infrared spectrum of ethyl methyl etherThe equilibrium geometry, harmonic vibrational frequencies, and infrared transition intensities of p-benzyne were calculated at the MBPT͑2͒, SDQ-MBPT͑4͒, CCSD, and CCSD͑T͒ levels of theory using different reference wave functions obtained from restricted and unrestricted Hartree-Fock ͑RHF and UHF͒, restricted Brueckner ͑RB͒ orbital, and Generalized Valence Bond ͑GVB͒ theory. RHF erroneously describes p-benzyne as a closed-shell singlet rather than a singlet biradical, which leads to orbital near-instabilities in connection with the mixing of orbital pairs b 1u -a g ͑HOMO-LUMO͒, b 2g -a g ͑HOMO-1-LUMO͒, and b 1g -a g ͑HOMO-2-LUMO͒. Vibrational modes of the corresponding symmetries cause method-dependent anomalous increases ͑unreasonable force constants and infrared intensities͒ or decreases in the energy ͑breaking of the D 2h symmetry of the molecular framework of p-benzyne͒. This basic failure of the RHF starting function is reduced by adding dynamic electron correlation. However RHF-MBPT͑2͒, RHF-SDQ-MBPT͑4͒, RHF-CCSD, RB-CCD, and RHF-CCSD͑T͒ descriptions of p-benzyne are still unreliable as best documented by the properties of the b 1u -, b 2g -, and b 1g -symmetrical vibrational modes. The first reliable spin-restricted description is provided when using Brueckner orbitals at the RB-CCD͑T͒ level. GVB leads to exaggerated biradical character that is reduced at the GVB-MP2 level of theory. The best results are obtained with a UHF reference wave function, provided a sufficient account of dynamic electron correlation is included. At the UHF-CCSD level, the triplet contaminant is completely annihilated. UHF-CCSD͑T͒ gives a reliable account of the infrared spectrum apart from a CCH bending vibrational mode, which is still in disagreement with experiment.

show abstract

“…Unrestricted Hartree‐Fock (UHF) theory is a convenient starting point for single‐determinant MP theory or CC methods for the description of open‐shell molecules . However, one of the major shortcomings of the UHF method is that the wave function is not an eigenfunction of the spin operator

\overset{S^{2}}{true}

. Contaminations from higher spin states are mixed into the wave function and may lead to erroneous energies that affect the shape of a potential energy surface determined at the UHF or post‐UHF levels of theory.…”

Section: Post‐scf Methodsmentioning

confidence: 99%

Dieter Cremer's contribution to the field of theoretical chemistry

Kraka

Cremer²

2019

Int J of Quantum Chemistry

View full text Add to dashboard Cite

This legacy article reviews the contributions of Dieter Cremer (1944‐2017) to the field of theoretical chemistry, highlighting his major accomplishments in method development and applied quantum chemistry, which has led to many advances in the field. His work reflects an extraordinary breadth and deep understanding of theory, which is needed to solve complex chemical problems. His passion for science has inspired many colleagues in the past and will do so in the future.

show abstract

Spin contamination in single-determinant wavefunctions

Cited by 102 publications

References 26 publications

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

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

Problematic p-benzyne: Orbital instabilities, biradical character, and broken symmetry

Dieter Cremer's contribution to the field of theoretical chemistry

Contact Info

Product

Resources

About