Density functional theory: excited states and spin annihilation

Cramer, Christopher J.; Dulles, Frederic J.; Giesen, David J.; Almlöf, Jan

doi:10.1016/0009-2614(95)01008-w

Cited by 88 publications

(57 citation statements)

References 31 publications

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“…As these multi-reference based methods are beyond our computational capability, a specially designed method within the single-reference based DFT frame was utilized here to calculate the S-T gap [31]. Briefly, a 50:50 mixture of the singlet and the triplet states was generated by flipping the spin of the highest energy SOMO of the triplet state, and the S-T gap was estimated to be twice the splitting between the triplet and the 50:50 mixing states.…”

Section: Resultsmentioning

confidence: 99%

Mechanistic Study on Electronic Excitation Dissociation of the Cellobiose-Na⁺ Complex

Huang

et al. 2015

J. Am. Soc. Mass Spectrom.

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The recent development of electron activated dissociation (ExD) techniques has opened the door for high-throughput, detailed glycan structural elucidation. Among them, ExD methods employing higher-energy electrons offer several advantages over low-energy electron capture dissociation (ECD), owing to their applicability towards chromophore-labeled glycans and singly charged ions, and ability to provide more extensive structural information. However, a lack of understanding of these processes has hindered rational optimization of the experimental conditions for more efficient fragmentation, as well as the development of informatics tools for interpretation of the complex glycan ExD spectra. Here, cellobiose-Na+ was used as the model system to investigate the fragmentation behavior of metal-adducted glycans under irradiation of electrons with energy exceeding their ionization potential, and served as the basis on which a novel electronic excitation dissociation (EED) mechanism was proposed. It was found that ionization of the glycan produces a mixture of radical cations and ring-opened distonic ions. These distonic ions then capture a low-energy electron to produce diradicals with trivial singlet-triplet splitting, and subsequently undergo radical-induced dissociation to produce a variety of fragment ions, whose abundances are influenced by the stability of the distonic ions from which they originate.

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Section: Resultsmentioning

confidence: 99%

Mechanistic Study on Electronic Excitation Dissociation of the Cellobiose-Na⁺ Complex

Huang

et al. 2015

J. Am. Soc. Mass Spectrom.

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“…A more detailed presentation of this approach can be found elsewhere. 35,36,38 Early applications of DFT spin-annihilation techniques 35 to TMM were problematic, and were not further explored. Finally, for the closed-shell singlet, energies were calculated either with enforced double occupation of a single frontier Kohn-Sham orbital or with two electrons worth of paired spin density "smeared" equally over both frontier orbitals.…”

Section: Methodsmentioning

confidence: 99%

Trimethylenemethane. Comparison of Multiconfiguration Self-Consistent Field and Density Functional Methods for a Non-Kekulé Hydrocarbon

1996

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Relative energies for different multiplets of trimethylenemethane and methylenecyclopropane are calculated at MCSCF, CASPT2N, and DFT levels of theory. Comparison to the experimentally measured heat of formation for the 3 A 2 ′ state and to the experimentally measured 3 A 2 ′-1 A 1 gap permits analysis of the relative importance of active space and basis set selection in the multiconfigurational methods. Such comparison also reveals that while DFT accurately treats triplet trimethylenemethane, there is a limitation in present DFT functionals with respect to accurately treating nondynamic correlation effects for closed-shell singlets in a molecule characterized by degenerate frontier molecular orbitals. Implications for calculations on larger systems are discussed.

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“…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

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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

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Density functional theory: excited states and spin annihilation

Cited by 88 publications

References 31 publications

Mechanistic Study on Electronic Excitation Dissociation of the Cellobiose-Na⁺ Complex

Mechanistic Study on Electronic Excitation Dissociation of the Cellobiose-Na⁺ Complex

Trimethylenemethane. Comparison of Multiconfiguration Self-Consistent Field and Density Functional Methods for a Non-Kekulé Hydrocarbon

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

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Density functional theory: excited states and spin annihilation

Cited by 88 publications

References 31 publications

Mechanistic Study on Electronic Excitation Dissociation of the Cellobiose-Na+ Complex

Mechanistic Study on Electronic Excitation Dissociation of the Cellobiose-Na+ Complex

Trimethylenemethane. Comparison of Multiconfiguration Self-Consistent Field and Density Functional Methods for a Non-Kekulé Hydrocarbon

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

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Mechanistic Study on Electronic Excitation Dissociation of the Cellobiose-Na⁺ Complex

Mechanistic Study on Electronic Excitation Dissociation of the Cellobiose-Na⁺ Complex