Finite group theory for large systems. 3. Symmetry‐generation of reduced matrix elements for icosahedral C20 and C60 molecules

Ellzey, M. L.

doi:10.1002/jcc.20593

Cited by 8 publications

(6 citation statements)

References 8 publications

(6 reference statements)

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“…A C 20 fullerene consists of 12 pentagons and 30 bonds. It is the only fullerene smaller than C 60 with the icosahedral ( I h ) symmetry . As shown in Fig.…”

Section: Resultsmentioning

confidence: 92%

First‐Principles Study of NO₂ Adsorption on C₂₀ Fullerene

Baei

2013

Heteroatom Chemistry

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Using different density functional theory methods, covalent functionalization of C20 fullerene with the NO2 molecule in terms of energy, geometry, and electronic properties was investigated. It was found that the molecule has strongly chemisorbed on the fullerene surface with Gibbs free energies in the range of −25.23 to −33.07 kcal/mol at the PBE level and −21.03 to −37.95 kcal/mol at the B3LYP level. The HOMO–LUMO gap of the fullerene has changed significantly upon the NO2 adsorption. The Fermi‐level energy and work function of the fullerene are decreased, which may facilitate the field electron emission from the fullerene surface. The present results are expected to provide a useful guidance for the adsorption of NO2, generation of the new hybrid compounds, and other applications.

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“…A C 20 fullerene consists of 12 pentagons and 30 bonds. It is the only fullerene smaller than C 60 with the icosahedral ( I h ) symmetry . As shown in Fig.…”

Section: Resultsmentioning

confidence: 92%

First‐Principles Study of NO₂ Adsorption on C₂₀ Fullerene

Baei

2013

Heteroatom Chemistry

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“…The partitioning of matrix (17) into scalar blocks illustrates the invariances that give rise to the symmetry-generation theorem [6]. If H sym is obtained by symmetry-averaging of H, as in equation (10) That is, the reduced matrix elements of the symmetry-averaged operator are simple averages of particular matrix elements of the original operator over the symmetry-adapted basis.…”

Section: If the Operator Is Defined As A Matrix [H]mentioning

confidence: 99%

Using Group Theory to Obtain Eigenvalues of Nonsymmetric Systems by Symmetry Averaging

Ellzey

2009

Symmetry

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If the Hamiltonian in the time independent Schrödinger equation, H E    , isinvariant under a group of symmetry transformations, the theory of group representations can help obtain the eigenvalues and eigenvectors of H. A finite group that is not a symmetry group of H is nevertheless a symmetry group of an operator H sym projected from H by the process of symmetry averaging. In this case H = H sym + H R where H R is the nonsymmetric remainder. Depending on the nature of the remainder, the solutions for the full operator may be obtained by perturbation theory. It is shown here that when H is represented as a matrix [H] over a basis symmetry adapted to the group, the reduced matrix elements of [H sym ] are simple averages of certain elements of [H], providing a substantial enhancement in computational efficiency. A series of examples are given for the smallest molecular graphs. The first is a two vertex graph corresponding to a heteronuclear diatomic molecule. The symmetrized component then corresponds to a homonuclear system. A three vertex system is symmetry averaged in the first case to C s and in the second case to the nonabelian C 3v . These examples illustrate key aspects of the symmetry-averaging process.

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“…In abstract algebra and mathematics group theory studies the algebraic structures known as groups [10,11,12,13]. The idea of a group is central to abstract algebra: other well-known algebraic structures, for example rings, fields, and vector spaces, are all able to be viewed as groups supplied with extra axioms and operations.…”

Section: Introductionmentioning

confidence: 99%

Words for maximal Subgroups of Fi24‘

2019

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Group Theory is the mathematical application of symmetry to an object to obtain knowledge of its physical properties. The symmetry of a molecule provides us with the various information, such as - orbitals energy levels, orbitals symmetries, type of transitions than can occur between energy levels, even bond order, all that without rigorous calculations. The fact that so many important physical aspects can be derived from symmetry is a very profound statement and this is what makes group theory so powerful. In group theory, a finite group is a mathematical group with a finite number of elements. A group is a set of elements together with an operation which associates, to each ordered pair of elements, an element of the set. In the case of a finite group, the set is finite. The Fischer groups Fi22, Fi23 and Fi24‘ are introduced by Bernd Fischer and there are 25 maximal subgroups of Fi24‘. It is an open problem to find the generators of maximal subgroups of Fi24‘. In this paper we provide the generators of 10 maximal subgroups of Fi24‘.

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Finite group theory for large systems. 3. Symmetry‐generation of reduced matrix elements for icosahedral C₂₀ and C₆₀ molecules

Cited by 8 publications

References 8 publications

First‐Principles Study of NO₂ Adsorption on C₂₀ Fullerene

First‐Principles Study of NO₂ Adsorption on C₂₀ Fullerene

Using Group Theory to Obtain Eigenvalues of Nonsymmetric Systems by Symmetry Averaging

Words for maximal Subgroups of Fi24‘

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Finite group theory for large systems. 3. Symmetry‐generation of reduced matrix elements for icosahedral C20 and C60 molecules

Cited by 8 publications

References 8 publications

First‐Principles Study of NO2 Adsorption on C20 Fullerene

First‐Principles Study of NO2 Adsorption on C20 Fullerene

Using Group Theory to Obtain Eigenvalues of Nonsymmetric Systems by Symmetry Averaging

Words for maximal Subgroups of Fi24‘

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Finite group theory for large systems. 3. Symmetry‐generation of reduced matrix elements for icosahedral C₂₀ and C₆₀ molecules

First‐Principles Study of NO₂ Adsorption on C₂₀ Fullerene

First‐Principles Study of NO₂ Adsorption on C₂₀ Fullerene