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The dependence of the enthalpy change of formation of saturated acyclic ketones on molecular structure (the number of carbon atoms, the position of the carbonyl group, and the branching of the molecules) was investigated. For this purpose, a simple computational model, the parameterization of which is based on spectral graph theory, was developed. It was found that the major part of the enthalpy change of formation is determined by molecular size, whereas the fine structure of the enthalpy change of formation is determined by the branching of the molecule and the position of the carbonyl group. The developed model proved itself very useful for such investigations. The model is simple and practical, and the agreement between the experimental and calculated enthalpy changes of formation is very good, with an average relative error of 0.7%.

A novel geometric method is proposed for constructing vertex‐degree‐based molecular structure descriptors (topological indices). The model is based on an ellipse whose focal points represent the degrees of a pair of adjacent vertices. This approach enables a geometric interpretation of several previously known topological indices, and lead to design of a few new. The area of the ellipse induces a vertex‐degree‐based topological index of remarkable simplicity, which we call elliptic Sombor index(ESO$$ ESO $$). The main mathematical properties of ESO$$ ESO $$ are established, especially its relations to other, earlier known, indices. Then the applicative potential of ESO$$ ESO $$ is analyzed. [ABSTRACT FROM AUTHOR]

The atom-bond connectivity index (ABC) is a degree-based molecular structure descriptor with well-documented chemical applications. In 2010 a distance-based new variant of this index (ABCGG) has been proposed. Until now, the relation between ABC and ABCGG has not been analyzed. In this paper, we establish the basic characteristics of this relation. In particular, ABC and ABCGG are not correlated and both cases ABC > ABCGG and ABC < ABCGG may occur in the case of (structurally similar) molecules. However, in the case of benzenoid hydrocarbons, ABC always exceeds ABCGG. [Projekat Ministarstva nauke Republike Srbije, br. 174033]

Abstract: The extended energy ([ζ.sub.ex]) is a vertex degree based and spectrum-based molecular structure descriptor, shown to be well correlated with a variety of physicochemical molecular properties. We investigate the [...]

The Wiener index W can be viewed as a molecular structure descriptor composed of increments representing interactions between pairs of atoms. A generalization of the W are the Steiner-Wiener indices kW, k=3,4,.... In the quantity Wk, interactions between k-tuples of atoms play role, based on the concept of Steiner distance. It is shown that the term W+λWk provides an approximation for the boiling points of alkanes better than W itself. The best such approximation is obtained for k=7.

The quality and correlating ability of some recently deduced bounds and approximate formulas for total π-electron energy are tested on a sample of 106 Kekuléan benzenoid hydrocarbons. It was found that not a single new approximate formula and not a single new bound is better than those from the 1970s.

A simple graph-theory-based model is put forward, by means of which it is possible to express the energy difference between geometrically non-equivalent forms of a conjugated polyene. This is achieved by modifying the adjacency matrix of the molecular graph, and including into it information on cis/trans constellations. The total π-electron energy thus calculated is in excellent agreement with the enthalpies of the underlying isomers and conformers. [Projekat Ministarstva nauke Republike Srbije, br. 174033]

Several recently published papers report expressions for various vertex-degree-based molecular structure descriptors of benzenoid systems and phenylenes. We deduce here the general expression for these descriptors, and show that a simple and generally valid relation exists between such structure descriptors of phenylenes and their hexagonal squeezes.

A recently proposed method for calculating the π-electron contents (EC) of rings of heteroatom-containing polycyclic conjugated molecules was applied to the aza-derivatives of naphthalene. The main finding was that a nitrogen atom in position α (resp.β) diminishes (resp. increases) the EC-value of the respective ring. Such a regularity in the displacement of π-electrons can be (qualitatively) rationalized by means of resonance-theoretical reasoning. .

The Estrada index EE is a recently proposed molecular structure-descriptor, used in the modeling of certain features of the 3D structure of organic molecules, in particular of the degree of folding of proteins and other long-chain biopolymers. The Estrada index is computed from the spectrum of the molecular graph. Therefore, finding its relation with the spectral radius r (= the greatest graph eigenvalue) is of interest, especially because the structure-dependency of r is relatively well understood. In this work, the basic characteristics of the relation between EE and r, which turned out to be much more complicated than initially anticipated, was determined.

The graph of atomic orbitals (GAO) is a novel type of molecular graph recently proposed by one of the authors. Various molecular structure-descriptors computed for GAO are compared with their analogs computed for ordinary molecular graphs. The quality of these structure-descriptors was tested for correlation with the normal boiling points of alkanes and cycloalkanes. In all the studied cases, the results based on GAO are similar to, and usually slightly better than, those obtained by means of ordinary molecular graps.

Several currently used models for assessing the extent of cyclic conjugation in benzenoid hydrocarbons, all based on Kekulé-type structural formulas predict that there is no cyclic conjugation in the central, "empty", ring of perylene and its annelated derivatives. In this paper it is shown that in some annelated perylenes the cyclic conjugation in the "empty" ring (measured by its energy-effect) may be unexpectedly high. Therefore, in the case of these annelated perylenes, the Kekulé- structure-based models fail. The cause for such an "anomalous" behavior of annelated perylenes is discussed.

The distribution of -electrons in rings of fully benzenoid hydrocarbons was investigated. It was found that the electron content EC of "full" rings varies significantly (between 5.5 and 2.5 electrons), and depends on the annelation mode, mainly on the number of adjacent rings. "Full" rings belonging to the same annelation class have nearly equal EC-values. The EC-values of all "empty" rings are also nearly equal (around 2 electrons).

A relatively complicated relation was found to exist between the quantity U recently introduced by Zenkevich (providing a measure of internal molecular energy), and the Wiener index W (measuring molecular surface area and intermolecular forces). We now report a detailed analysis of this relation and show that, in the case of alkanes, its main features are reproduced by the formula U = –αW + β + γν1; where ν1 is the number of methyl groups, and α, β and γ are constants, depending only on the number of carbon atoms. Thus for isomeric alkanes with the same number of methyl groups, U and W are linearly correlated.

In earlier studies it was established that internal molecular energies (Eint) of alkanes can be reproduced, in an approximate yet reliable manner by means of a molecular-graph-based structure-descriptor U. It was also established that U is linearly correlated with the Wiener index W. We now show that the correlation between U and W is more complicated than earlier expected, and that it cannot be represented by a single line. We also show that a very good linear correlation exists between U and a modified version Wm(λ) of the Wiener index, which is thus more suitable for modeling Eint than the ordinary Wiener index. .

Let n1(e|T) and n2(e|T) denote the number of vertices of a tree T, lying on the two sides of the edge e. Let T1 and T2 be two trees with equal number of vertices, let e be an edge of T1 and f an edge of T2. Then e and f are said to be equiseparable if either n1(e|T1) = n1(f|T2) or n1(e|T1) = n2(f|T2). If all edges of T1 and T2 can be chosen so as to form equiseparable pairs, then T1 and T2 are equiseparable trees. A number of molecular structure-descriptors of equiseparable chemical trees coincide, implying that the corresponding alkane isomers must have similar physico-chemical properties. It is shown how equiseparable chemical trees can be constructed in a systematic manner. .

The hyper-Wiener index WW of a chemical tree T is defined as the sum of the products n1n2, over all pairs υ,ν of vertices of T, where n1 and n2 are the number of vertices of T, lying on the two sides of the path which connects υ and ν. We examine a slight modification WWW of the hyper-Wiener index defined as the sum of the products n1n2n3, over all pairs υ,ν of vertices of T, where n3 is the number of vertices of T, lying between υ and ν. It is found that WWW correlates significantly better with various physico-chemical properties of alkanes than WW. Lower and upper bounds for WWW, and an approximate relation between WWW and WW are obtained.