Eigenvalues of saturated hydrocarbons

Klein, Douglas J.; Larson, Craig E.

doi:10.1007/s10910-013-0168-1

Cited by 8 publications

(18 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Klein and Larson themselves pointed out that alkenes are stable with half their (Huckel-type MO) eigenvalues positive and half negative. 17 This is further made evident from the Figure 3 eigenvalue summary in ref 18; note that these eigenvalues are not ± paired. 3.2.…”

Section: Xmentioning

confidence: 90%

“…1,2 As stressed repeatedly by Dewar, 1,2,16 resonance integrals between hybrid AOs of each carbon atom never vanish; a single nonzero parameter in the Klein-Larson model has to do with these resonance integrals. 17 One electron was then assigned to every carbon hybrid orbital and to every hydrogen 1s orbital. Dias showed that such Huckel-type calculations nicely correlate with the experimental enthalpy of formation and also with the ionization energy for saturated hydrocarbons.…”

Section: ■ Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bond Resonance Energy Verification of σ-Aromaticity in Cycloalkanes

2020

View full text Add to dashboard Cite

The Klein-Larson bonding model is best suited for describing σ-conjugation and σ-aromaticity of cycloalkanes. Methylene groups (−CH2−) in cycloalkanes are isoconjugates with ethylene groups (−CHCH−) in annulenes, both contributing two electrons to cyclic conjugation and aromaticity. As in the case of π-aromatic stabilization, σ-aromatic stabilization must be associated with ring-current diamagnetism. Both nucleus-independent chemical shift (NICS) and bond resonance energy (BRE) values support this interpretation. Bond resonance energy has been used to determine local ring aromaticity in nonalternant hydrocarbons, alternant hydrocarbons, heterocyclic conjugated molecules, fullerenes, pure boron clusters, and porphyrins. This contribution represents the first application of bond resonance energy toward the evaluation of σ-aromaticity/σ-antiaromaticity of polycyclic alkanes.

show abstract

Section: Xmentioning

confidence: 90%

Section: ■ Introductionmentioning

confidence: 99%

Bond Resonance Energy Verification of σ-Aromaticity in Cycloalkanes

2020

View full text Add to dashboard Cite

show abstract

“…In the following, we consider two important families of graphs, one is called stellated graphs [13,26] and the other is called corona graphs [19]. Let G be a graph.…”

Section: Signed Graphs With a Unique Sachs Subgraphmentioning

confidence: 99%

“…A graph G is called a stellated graph if G = st(H) for some graph H. The spectrum of stellated graphs (or para-line graphs) have been studied in [24]. For chemical applications of the stellated graphs of trees, refer to [13].…”

Section: Corollary 32 ([25] Cf[18]mentioning

confidence: 99%

See 1 more Smart Citation

Graph invertibility and median eigenvalues

Yang

Mandal

et al. 2017

Linear Algebra and its Applications

View full text Add to dashboard Cite

Let (G, w) be a weighted graph with a weight-function w : E(G) → R\{0}. A weighted graph (G, w) is invertible to a new weighted graph if its adjacency matrix is invertible. A graph inverse has combinatorial interest and can be applied to bound median eigenvalues of a graph such as have physical meanings in Quatumn Chemistry. In this paper, we characterize the inverse of a weighted graph based on its Sachs subgraphs that are spanning subgraphs with only K2 or cycles (or loops) as components. The characterization can be used to find the inverse of a weighted graph based on its structures instead of its adjacency matrix. If a graph has its spectra split about the origin, i.e., half of eigenvalues are positive and half of them are negative, then its median eigenvalues can be bounded by estimating the largest and smallest eigenvalues of its inverse. We characterize graphs with a unique Sachs subgraph and prove that these graphs has their spectra split about the origin if they have a perfect matching. As applications, we show that the median eigenvalues of stellated graphs of trees and corona graphs belong to different halves of the interval [−1, 1].

show abstract

The spectrum of the vertex quadrangulation of a 4-regular toroidal graph and beyond

Rosenfeld

2021

J Math Chem

View full text Add to dashboard Cite

Eigenvalues of saturated hydrocarbons

Cited by 8 publications

References 17 publications

Bond Resonance Energy Verification of σ-Aromaticity in Cycloalkanes

Bond Resonance Energy Verification of σ-Aromaticity in Cycloalkanes

Graph invertibility and median eigenvalues

The spectrum of the vertex quadrangulation of a 4-regular toroidal graph and beyond

Contact Info

Product

Resources

About