Effectively Unpaired Electrons for Singlet States: From Diatomics to Graphene Nanoclusters

Luzanov, A. V.

doi:10.1007/978-1-4899-7699-4_6

Cited by 16 publications

(25 citation statements)

References 118 publications

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“…В данной форме, но в несколько иной технике проектор ] [  был получен Местечкиным в [18], и это выражение согласуется с результатом Ребане, найденным ранее в [17]. Недавно полезность матрицы (8) обнаружилась при решении в [23,24] совсем иной задачи -оценки эффективно распаренных электронов в рамках простой модели π-корреляций в АУ (см. разделы 3 и 6).…”

Section: J -симметрия в моделях сильной связи (метод хюккеля)unclassified

“…В неэмпирическом подходе [83] для зигзаг-трубки как раз и было найдено синглетное состояние с открытой оболочкой («open-shell singlet»). Ниже мы коснемся этой темы; детали можно найти в обзоре [24], посвященном теории так называемых эффективно распаренных электронов (effectively unpaired electrons, сокращенно EUE).…”

Section: особенности сопряженных радикалов и полирадикаловunclassified

“…Как показало развитие теории МО, блочная структура (9) и свойство (10) сохраняют силу для всех корректно сформулированных π-моделей нейтральных АУ -от хартри-фоковской схемы вплоть до полного конфигурационного взаимодействия (FCI) π-электронов (см. далее обсуждение после формулы (24)). По сути (9) есть отражение симметрии парности в терминах матрицы плотности.…”

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“…а следовательно, она наделена J-симметрией того же типа, что и TB h . Далее следует перейти к обобщенным π-моделям TB-типа, относительно недавно развитым в работах [23,24]. Предшественник этих моделей появился ранее в одной фактически забытой статье [36], которая не сразу была обнаружена и нами.…”

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Parity symmetry in a number of problems of quantum and structural chemistry

Luzanov

2019

Chemical Series

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A synthetic review and new results are given of the alternant symmetry theory and its applications within a unified approach. It is based on J–symmetry (parity) operators. Unlike usual commutation rules, these symmetry operators anticommute with Hamiltonians or other relevant quantities. In the J–symmetry terms we treat a variety of problems and topics, mainly related to π-shells of conjugated molecules. In particular, various orbital theories are outlined with a systematic use of block-matrix technique (density matrices, operator functions etc.). Noval π‑models and their J–symmetry are studied within the current context of single-molecule conductance and the relevant problems concerning Green’s function and electron transmission evaluation. We stress on the key importance of account for π-electron correlation for describing correctly transmission π-spectra. We discuss electron-structure peculiarities of alternant radical states and the validity of the Lieb-Ovchinnikov spin rule resulting from the J–symmetry and electron correlation effects. It is shown how the simplified (based on Hückel’s MOs) spin-polarized theory provides a correct number of effectively unpaired electrons in polyradicaloid alternant molecules. Another type of problems is concerned with chirality (generllly, structural asymmetry) problems. By spectral analysys of the previously defined chirality operator we could reinterpret the problem in terms of J–symmetry. It allowed us to construct here the noval chirality operator which is nonnegative definite and vanishes on achiral structures. Its simplest invariant, the matrix trace, surves us as a quantitative measure of the structural (electronic) chirality. Preliminary calculations tell us that the new chirality index behaves reasonably even for the difficult (high-symmetry) chiral systems.

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Section: J -симметрия в моделях сильной связи (метод хюккеля)unclassified

Section: особенности сопряженных радикалов и полирадикаловunclassified

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Parity symmetry in a number of problems of quantum and structural chemistry

Luzanov

2019

Chemical Series

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“…One of the areas in which the HMO density matrix has found new grounds of interesting applications is in the diagnostic of radicaloid states in formally closed-shell molecules. In particular, the quasi-correlated tight-binding (QCTB) model quantifies the number of unpaired electrons and the distribution of effectively unpaired electrons (EUE) over the molecule [24][25][26]. The theory has been successfully applied to polycyclic aromatic hydrocarbons and graphene-like molecules.…”

Section: Quasi-correlated Tight-binding Modelmentioning

confidence: 99%

The electron density function of the Hückel (tight-binding) model

Estrada

2018

Proc. R. Soc. A.

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The Hückel (tight-binding) molecular orbital (HMO) method has found many applications in the chemistry of alternant conjugated molecules, such as polycyclic aromatic hydrocarbons (PAHs), fullerenes and graphene-like molecules, as well as in solid-state physics. In this paper, we found analytical expressions for the electron density matrix of the HMO method in terms of odd-powers of its Hamiltonian. We prove that the HMO density matrix induces an embedding of a molecule into a high-dimensional Euclidean space in which the separation between the atoms scales very well with the bond lengths of PAHs. We extend our approach to describe a quasi-correlated tight-binding model, which quantifies the number of unpaired electrons and the distribution of effectively unpaired electrons. In this case, we found that the corresponding density matrices induce embedding of the molecules into high-dimensional Euclidean spheres where the separation between the atoms contains information about the spin–spin repulsion between them. Using our approach, we found an analytic expression which explains the bond length alternation in polyenes inside the HMO framework. We also found that spin–spin interaction explains the alternation of distances between pairs of atoms separated by two bonds in conjugated molecules.

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Magnetic exchange interactions in binuclear and tetranuclear iron(III) complexes described by spin‐flip DFT and Heisenberg effective Hamiltonians

et al. 2022

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Low‐energy spectra of single‐molecule magnets (SMMs) are often described by Heisenberg Hamiltonians. Within this formalism, exchange interactions between magnetic centers determine the ground‐state multiplicity and energy separation between the ground and excited states. In this contribution, we extract exchange coupling constants (J) for a set of iron (III) binuclear and tetranuclear complexes from all‐electron calculations using non‐collinear spin‐flip time‐dependent density functional theory (NC‐SF‐TDDFT). For 12 binuclear complexes with J‐values ranging from −6 to −132 cm−1, our benchmark calculations using the short‐range hybrid ωPBEh functional and 6‐31G(d,p) basis set agree well with the experimentally derived values (mean absolute error of 4.7 cm−1). For the tetranuclear SMMs, the computed J constants are within 6 cm−1 from the experimentally derived values. We explore the range of applicability of the Heisenberg model by analyzing bonding patterns in these Fe(III) complexes using natural orbitals (NO), their occupations, and the number of effectively unpaired electrons. The results illustrate the efficiency of the spin‐flip protocol for computing the exchange couplings and the utility of the NO analysis in assessing the validity of effective spin Hamiltonians.

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Effectively Unpaired Electrons for Singlet States: From Diatomics to Graphene Nanoclusters

Cited by 16 publications

References 118 publications

Parity symmetry in a number of problems of quantum and structural chemistry

Parity symmetry in a number of problems of quantum and structural chemistry

The electron density function of the Hückel (tight-binding) model

Magnetic exchange interactions in binuclear and tetranuclear iron(III) complexes described by spin‐flip DFT and Heisenberg effective Hamiltonians

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