On a class of approximate formulas for total ח-electron energy of benzenoid hydrocarbons

Gutman, Ivan; Soldatović, Tanja

doi:10.2298/jsc0102101g

Cited by 18 publications

(13 citation statements)

References 5 publications

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“…Thus, among others, not included into our statistics are the papers concerned with: a) the countless approximate formulas for total π-electron energy (in terms of n, m, and other graph parameters), in particular such formulas for π E of benzenoid hydrocarbons; [6,7] b) empirical correlations between π E and various structural parameters, in particular the Kekulè structure count; [24] c) various resonance energies; [25,26] d) studies of the energy effect of individual cycles in polycyclic conjugated molecules. [27,28] …”

Section: Statisticsmentioning

confidence: 99%

“…The method that eventually became known as the Hückel molecular orbital (HMO) theory enabled a reasonably accurate quantitative prediction of thermodynamic properties, resonance stabilization, and aromaticity of conjugated polycyclic π-electron systems and gained much popularity in the next 50 years. [2−4] A bibliography of the early researches of total π-electron energy [5] and details of its chemical applications can be found in the surveys [6,7] and books. [8,9] The connection between HMO theory and spectral graph theory is nowadays a well established and fully elaborated part of chemical graph theory.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Total π-Electron Energy Saga

Gutman¹,

Furtula²

2017

Croat. Chem. Acta

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Abstract:The total π-electron energy, as calculated within the Hückel tight-binding molecular orbital approximation, is a quantum-theoretical characteristic of conjugated molecules that has been conceived as early as in the 1930s. In 1978, a minor modification of the definition of total π-electron energy was put forward, that made this quantity interesting and attractive to mathematical investigations. The concept of graph energy, introduced in 1978, became an extensively studied graph-theoretical topic, with many hundreds of published papers. A great variety of graph energies is being considered in the current mathematical-chemistry and mathematical literature. Recently, some unexpected applications of these graph energies were discovered, in biology, medicine, and image processing.We provide historic, bibliographic, and statistical data on the research on total π-electron energy and graph energies, and outline its present state of art. The goal of this survey is to provide, for the first time, an as-complete-as-possible list of various existing variants of graph energy, and thus help the readers to avoid getting lost in the jungle of references on this topic.

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Section: Statisticsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Total π-Electron Energy Saga

Gutman¹,

Furtula²

2017

Croat. Chem. Acta

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“…In fact, in the case of benzenoid hydrocarbons, this formula with a 1 = 0.898 and a 2 = 0.45 happens to be the best (n, m)-type approximation for E [20,21]. In view of this, we examined how well an expression of the form a 1 EE * + a 2 would approximate the Estrada index.…”

Section: An (N M N M N M)-type Approximation For the Estrada Indexmentioning

confidence: 99%

“…Least-squares fitting, using the standard data set of 106 Kekuléan benzenoid hydrocarbons from [22] (same as employed in [20,21] and elsewhere [23,24]), yields the regression line…”

Section: An (N M N M N M)-type Approximation For the Estrada Indexmentioning

confidence: 99%

Estrada Index of Benzenoid Hydrocarbons

Gutman

Radenković

2007

Zeitschrift Für Naturforschung A

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A structure-descriptor EE, recently proposed by Estrada, is examined. If λ 1 , λ 2 ,...,λ n are the eigenvalues of the molecular graph, then EE = n ∑ i=1 e λ i . In the case of benzenoid hydrocarbons with n carbon atoms and m carbon-carbon bonds, EE is found to be accurately approximated by means of the formula a 1 n cosh 2m/n + a 2 , where a 1 ≈ 1.098 and a 2 = −0.64 are empirically determined fitting constants. Within classes of benzenoid isomers (which all have equal n and m), the Estrada index is linearly proportional to the number of bay regions.

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“…These approximations are of the form E ≈ a E * + b, where E * is some upper or lower bound for E. The coefficients a and b are determined by least squares fitting, and are adjusted for a particular class of molecular graphs (usually benzenoid hydrocarbons). A large number of such approximate formulas was investigated, and their comparative studies can be found in our earlier works [6,9,11]. In particular, in [9], 10 (n, m)-type approximate formulas for E were tested.…”

Section: Introductionmentioning

confidence: 99%