A valence bond view of fullerenes

Schmalz, Thomas

doi:10.1016/s1380-7323(02)80018-8

Cited by 10 publications

(14 citation statements)

References 64 publications

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“…This is in contrast to the delocalized, non-interacting electron-gas picture offered by Hückel theory. We agree with Hachmann et al [35] and Schmalz [34] on the fact that the bonding is most simply expressed in terms of a valence bond framework. Ionic contributions (zero and double occupations) in the π-orbitals are diminished in favor of a resonating valence bond structure between the localized electrons in each carbon center.…”

Section: Density-matrix Renormalization Group (Dmrg) Calculations Of supporting

confidence: 92%

“…Our results support a different interpretation, one where the system is strongly correlated in the sense that short-range spin-spin interactions drive long-range magnetic ordering. This is more consistent with the nature of valence bond solutions to the Heisenberg Hamiltonian [34] and with accurate Monte-Carlo results to the Hubbard Hamiltonian (see, e.g., Ref. [22]).…”

Section: Spin-spin Correlationssupporting

confidence: 84%

“…We shall also mention the work of a few quantum chemists in trying to understand the nature of the chemical bonding in fullerene molecules from a valence bond treatment of the Heisenberg Hamiltonian (see Ref. [34] and references therein). These studies have helped to rationalize the preference of π-electron density in C 60 to lie on 6-6 bonds, which explains the observed reactivity patterns.…”

Section: Introductionmentioning

confidence: 99%

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Polyradical Character and Spin Frustration in Fullerene Molecules: An Ab Initio Non-Collinear Hartree–Fock Study

2014

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Most ab initio calculations on fullerene molecules have been carried out on the basis of the paradigm of the Hückel model. This is consistent with the restricted nature of the independent-particle model underlying such calculations, even in single-reference-based correlated approaches. Notwithstanding, previous works on some of these molecules using model Hamiltonians have clearly indicated the importance of short-range interatomic spin-spin correlations. In this work, we consider ab initio non-collinear Hartree-Fock (HF) solutions for representative fullerene systems: the bowl, cage, ring, and pentagon isomers of C20, and the larger C30, C36, C60, C70, and C84 fullerene cages. In all cases but the ring we find that the HF minimum corresponds to a truly non-collinear solution with a torsional spin density wave. Optimized geometries at the generalized HF (GHF) level lead to fully symmetric structures, even in those cases where Jahn-Teller distortions have been previously considered. The nature of the GHF solutions is consistent with the π-electron space becoming polyradical in nature: each p-orbital remains effectively singly occupied. The spin frustration, induced by the presence of pentagon rings on an otherwise antiferromagnetic background, is minimized at the HF level by aligning the spins with non-collinear arrangements. The long-range magnetic ordering observed is reminiscent of the character of broken symmetry HF solutions in polyacene systems.

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Section: Density-matrix Renormalization Group (Dmrg) Calculations Of supporting

confidence: 92%

Section: Spin-spin Correlationssupporting

confidence: 84%

Section: Introductionmentioning

confidence: 99%

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Polyradical Character and Spin Frustration in Fullerene Molecules: An Ab Initio Non-Collinear Hartree–Fock Study

2014

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“…, the electrons are viewed to interact so strongly that there is negligible probability of finding two electrons in the same orbital. The wave function is thus considered to be dominated by purely covalent contributions in which each electron is spin paired to another electron [ 29 ]. Another consequence is: The non-orthogonality of VB CSFs poses difficulties for the interpretation of wave functions that are more severe than the numerical problems of the VB method frequently mentioned.…”

Section: The Differences Between Conventional Vb and Ovbmentioning

confidence: 99%

Chemical Bonding: The Orthogonal Valence-Bond View

Sax

2015

IJMS

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Chemical bonding is the stabilization of a molecular system by charge- and spin-reorganization processes in chemical reactions. These processes are said to be local, because the number of atoms involved is very small. With multi-configurational self-consistent field (MCSCF) wave functions, these processes can be calculated, but the local information is hidden by the delocalized molecular orbitals (MO) used to construct the wave functions. The transformation of such wave functions into valence bond (VB) wave functions, which are based on localized orbitals, reveals the hidden information; this transformation is called a VB reading of MCSCF wave functions. The two-electron VB wave functions describing the Lewis electron pair that connects two atoms are frequently called covalent or neutral, suggesting that these wave functions describe an electronic situation where two electrons are never located at the same atom; such electronic situations and the wave functions describing them are called ionic. When the distance between two atoms decreases, however, every covalent VB wave function composed of non-orthogonal atomic orbitals changes its character from neutral to ionic. However, this change in the character of conventional VB wave functions is hidden by its mathematical form. Orthogonal VB wave functions composed of orthonormalized orbitals never change their character. When localized fragment orbitals are used instead of atomic orbitals, one can decide which local information is revealed and which remains hidden. In this paper, we analyze four chemical reactions by transforming the MCSCF wave functions into orthogonal VB wave functions; we show how the reactions are influenced by changing the atoms involved or by changing their local symmetry. Using orthogonal instead of non-orthogonal orbitals is not just a technical issue; it also changes the interpretation, revealing the properties of wave functions that remain otherwise undetected.

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“…The PPP model was developed in the 1950's to describe excited states of conjugated hydrocarbons, and its use for this purpose continues unabated [9][10][11] since it can be applied to larger molecules beyond the reach of modern ab initio methods. More recently it has played a critical role in understanding dimerization in onedimensional conjugated polymers, [12][13][14][15] and has been applied to the electronic structure of fullerenes, 16 and to a variety of other problems including organic chargetransfer salts. 17 In the next section the model Hamiltonians will be presented in detail and the evaluation of the long-range electron repulsion terms from standard interpolation formulas discussed.…”

Section: Introductionmentioning

confidence: 99%

From the Hubbard to the PPP Model

Schmalz¹

2013

Croat. Chem. Acta

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Abstract. This paper presents an extension of the Hubbard Model to Pariser-Parr-Pople form. Although the Hubbard model contains most of the essentials of chemical bonding, it is unable to describe excited states with separated charges, such as the lowest 1 B u states of linear polyenes. The PPP model adds longrange electron-electron repulsions to the Hubbard model to remedy this defect. If the long range repulsion integrals are assumed to follow a standard form, all parameters in the model can be evaluated exactly from high accuracy ab initio computations on stretched ethlyene. This yields a model based on the MatagaNishimoto form for the long-range integrals which gives excellent agreement with both excitation energies and ground-state bond lengths, but with a significantly smaller value of the one center electron repulsion U than is usually assumed. A major conclusion of this work is that the exact form of the long-range integrals is not so important, but that the value of the one center integral U must be chosen smaller than traditional values. The PPP-MN model is recommended for applications because it contains no adjustable parameters, with all parameter values determined directly from ab initio results.

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A valence bond view of fullerenes

Cited by 10 publications

References 64 publications

Polyradical Character and Spin Frustration in Fullerene Molecules: An Ab Initio Non-Collinear Hartree–Fock Study

Polyradical Character and Spin Frustration in Fullerene Molecules: An Ab Initio Non-Collinear Hartree–Fock Study

Chemical Bonding: The Orthogonal Valence-Bond View

From the Hubbard to the PPP Model

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