Elements of irreducible tensorial matrices generated by finite groups with applications to ligand field Hamiltonians

Ellzey, M. L.

doi:10.1007/bf01165126

Cited by 4 publications

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“…The next article in this series treats the Symmetry-Generation Theorem for large systems. 16 Using this theorem the reduced matrix elements of the Hamiltonian are determined from a simple generating matrix instead of the complete Hamiltonian matrix, thereby providing computational savings that increase with the size of the basis and corresponding matrix.…”

Section: Discussionmentioning

confidence: 99%

Finite Group Theory for Large Systems. 2. Generating Relations and Irreducible Representations for the Icosahedral Point Group, _h

Ellzey

Villagrán

2003

J. Chem. Inf. Comput. Sci.

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Generating relations and irreducible representations are given for the icosahedral point group, I(h), that are suited to computerized projection of symmetry-adapted bases of arbitrary spaces invariant to the group. With 120 elements I(h ) is a good prototype for symmetry-adaptation to a large finite nonabelian group. The four- and five-dimensional irreducible representations are obtained by coupling direct products of the three-dimensional irreducible representations using the symmetry-adaptation algorithm. The method is applied to the Hückel treatment of icosahedral C(20) fullerene.

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Section: Discussionmentioning

confidence: 99%

Finite Group Theory for Large Systems. 2. Generating Relations and Irreducible Representations for the Icosahedral Point Group, _h

Ellzey

Villagrán

2003

J. Chem. Inf. Comput. Sci.

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“…This paper focuses on the evaluation of reduced Hamiltonian matrix elements using symmetry-generation. 3,4 Specifically, reduced Hückel matrices for icosahedral C 20 and C 60 fullerenes are symmetry-generated with single atom reference structures. Since each irreducible representation of the icosahedral point group occurs no more than once for C 20 , its Hückel states are symmetry determined.…”

Section: Introductionmentioning

confidence: 99%

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

Ellzey

2007

J Comput Chem

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This paper uses symmetry-generation to simplify the determination of Hamiltonian reduced matrix elements. It is part of a series on using computers to apply finite group theory to quantum mechanical calculations on large systems. Symmetry-generation is an expression of the whole molecule as a sum of symmetry transformations on a smaller reference structure. Then on a suitably-conditioned symmetry-adapted basis, the reduced matrix elements of the Hamiltonian are averages of certain elements of the simpler reference structure matrix. The smaller the reference structure, the greater is the computational savings. Single atom reference structures are used here for the Hückel treatment of icosahedral C(20) and C(60) fullerenes. The analytical power of this approach is illustrated by determining the two bond lengths of C(60) from spectral data.

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Symmetry-generated valence orbital effective Hamiltonian treatment of photoelectron spectra of hydrogen fluoride, water, ammonia and methane

Ellzey

2000

Journal of Molecular Structure: THEOCHEM

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Elements of irreducible tensorial matrices generated by finite groups with applications to ligand field Hamiltonians

Cited by 4 publications

References 10 publications

Finite Group Theory for Large Systems. 2. Generating Relations and Irreducible Representations for the Icosahedral Point Group, _h

Finite Group Theory for Large Systems. 2. Generating Relations and Irreducible Representations for the Icosahedral Point Group, _h

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

Symmetry-generated valence orbital effective Hamiltonian treatment of photoelectron spectra of hydrogen fluoride, water, ammonia and methane

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Elements of irreducible tensorial matrices generated by finite groups with applications to ligand field Hamiltonians

Cited by 4 publications

References 10 publications

Finite Group Theory for Large Systems. 2. Generating Relations and Irreducible Representations for the Icosahedral Point Group, h

Finite Group Theory for Large Systems. 2. Generating Relations and Irreducible Representations for the Icosahedral Point Group, h

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

Symmetry-generated valence orbital effective Hamiltonian treatment of photoelectron spectra of hydrogen fluoride, water, ammonia and methane

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Finite Group Theory for Large Systems. 2. Generating Relations and Irreducible Representations for the Icosahedral Point Group, _h

Finite Group Theory for Large Systems. 2. Generating Relations and Irreducible Representations for the Icosahedral Point Group, _h

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