Evaluation of moments and their application in H�ckel molecular orbital theory

Jiang, Yue; Tang, An‐Na; Hoffmann, Roald

doi:10.1007/bf00549668

Cited by 95 publications

(56 citation statements)

References 8 publications

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“…(2), the resonance energy per electron (REPE) of a molecule is defined as: where n electron is the number of π electrons and E ref is the π electron energy of an acyclic reference structure. A number of proposals for defining the reference structure appear in the literature 8–11. In the current work, we adopt the form suggested by Jiang, Tang, and Hoffmann (JTH) for extracting resonance energies from Hückel calculations 9.…”

Section: Resonance Energy Per Electronmentioning

confidence: 99%

“…A number of proposals for defining the reference structure appear in the literature 8–11. In the current work, we adopt the form suggested by Jiang, Tang, and Hoffmann (JTH) for extracting resonance energies from Hückel calculations 9. The JTH scheme gives the energy of the acyclic reference as the sum of contributions from five bond energies: where E ij belongs to bond [ i , j ] with atoms of degrees i and j , respectively, and n ij is the number of such bonds in the molecule.…”

Section: Resonance Energy Per Electronmentioning

confidence: 99%

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Environmental sustainability and climate change mitigation—CCS technology, better having it than not having it at all!

Butt

Giddings

Jones

2012

Env Prog and Sustain Energy

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Objective Six recent genome scans of different systemic lupus erythematosus (SLE) multiplex family cohorts showed multiple putative susceptibility loci. In the present study, we examined 4 previously identified loci to replicate findings of significant linkage to 1q23 and 16q12, and to support findings of suggestive linkage to 14q21‐23 and 20p12 in a cohort of 115 multiethnic nuclear families containing 145 SLE‐affected sibpairs. Methods Model‐free, multipoint linkage analyses (SIBPAL2, SAGE version 4.0) and exclusion mapping (GeneHunter) were performed. Results Linkages to 1q23 (peak at D1S2675, mean allele sharing [MAS] 0.56; P = 0.003) and to 16q12 (peaks between D16S753 and D16S757, MAS 0.57; P = 0.003) were confirmed, but linkage evidence at 20p12 was weak and inconsistent (MAS 0.52–0.56; from P = 0.005 to P not significant). Evidence for linkage to 1q23 and 16q12 was stronger in 68 non‐Caucasian affected sibpairs than in 77 Caucasian affected sibpairs. Exclusion mapping ruled out linkage at 14q21‐23 (λs [sib recurrence risk or genotypic risk ratio] = 1.8). Because the pericentromeric region of chromosome 16 has been identified by genome scans in several autoimmune diseases, we postulated that it might harbor an autoimmune modifier gene. To explore this possibility, we tested for an interaction between 16q12 and 1q23, and between 16q12 and 20p12. Haplotype sharing at 1q23 increased concomitantly with increased haplotype sharing at 16q12 (P = 0.008 by nonparametric Jonckheere‐Terpstra exact statistical test). No evidence supporting an interaction between 16q12 and 20p12 was observed. Analysis of sibpairs sharing 2 alleles at 16q12 also showed increased allele sharing at 1q23 (MAS from 0.56 to 0.65). Conclusion These data support the presence of SLE susceptibility genes at 1q23 and 16q12, particularly in non‐Caucasians. The skewed distribution of haplotypes suggests that genetic interaction of these two loci may affect SLE susceptibility.

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Section: Resonance Energy Per Electronmentioning

confidence: 99%

Section: Resonance Energy Per Electronmentioning

confidence: 99%

Environmental sustainability and climate change mitigation—CCS technology, better having it than not having it at all!

Butt

Giddings

Jones

2012

Env Prog and Sustain Energy

View full text Add to dashboard Cite

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“…The blocked off portions of the table are filled with Os, as is implied by simple inequalities obtained by demanding nonnegativity of the numbers v (5',6) and v (5,6') counting the vertices of types 52,6 and 5,62, respectively. That is, utilizing the "Euleric" formulas for these numbers from reference 10 one obtains a constraint on p and q, 15 + 3q/4 5 p 5 3912 (1) Here the left and right inequalities respectively give the upper and lower bounds in the table. Often many of the 0 entries near to, but within this boundary, may be easily understood.…”

Section: Enumerationmentioning

confidence: 99%

Sixty‐atom carbon cages

et al. 1991

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The enumeration of all 60-atom carbon cages associated to trivalent polyhedra with five-and six-sided faces is addressed. This isomer problem is computationally solved to give 1790 cages, with a further resolution into subclasses of cages with differing numbers p of abutting pairs of pentagonal faces. The individual cages are generated, and then there are computed various graph-theoretic invariants, including Huckel MO energies, HOMO-LUMO gaps, Kekule structure counts, and coqjugated-circuit counts. Associated properties as a function of p are reported and found to be in concert with earlier qualitative arguments. It is found that the most stable of these cages is the unqiue p = 0 Buckminsterfullerene structure.

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“…Formulas of moments that have been tabulated [16] are quite needed in the present discussion. Here, we present a few of the simplest members in order to facilitate later illustrations: …”

Section: Some Preliminariesmentioning

confidence: 99%

A graphical evaluation of characteristic polynomials of huckel trees

Kiang

Tang

1986

Int J of Quantum Chemistry

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Characteristic polynomials of acyclic carbon chains (Huckel trees) are treated in a systematic way. Formulas of coefficients (ar) of the polynomial are obtained in terms of connectivities that were introduced for dealing with moments in a previous paper. Based on the meaning of at, a graph-theoretical analysis is given such that ah can be expressed as a linear combination of binomial factors specified by a set of graphs containing fk edges. The numerical relationship is disclosed between each binomial factor and its specified graph. This stimulates the proposal of a novel approach for evaluating at by simply collecting the graph set of definite edges. The approach is equally applicable for the evaluation of matching polynomals of cyclic systems and extendable to the investigation of general trees.

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Evaluation of moments and their application in H�ckel molecular orbital theory

Cited by 95 publications

References 8 publications

Environmental sustainability and climate change mitigation—CCS technology, better having it than not having it at all!

Environmental sustainability and climate change mitigation—CCS technology, better having it than not having it at all!

Sixty‐atom carbon cages

A graphical evaluation of characteristic polynomials of huckel trees

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