Isomeric Benzenoid Hydrocarbons Research Articles

Comparative study on structural sensitivity of eigenvalue–based molecular descriptors

Structural sensitivity is one of the most important and the least investigated property of the topological molecular descriptors. This paper reports results on the structural sensitivity of graph energy, Estrada index, and resolvent energy on several series of catacondensed and pericondensed isomeric benzenoid hydrocarbons. Recently, a novel method for assessing the structural sensitivity of topological molecular descriptors was put forward, which is applied here. This algorithm consists of several different steps and it is based on Tanimoto index and Morgan circular fingerprints. It was found that graph energy, Estrada index, and resolvent energy exert similar structural sensitivity on catacondensed isomers. The graph energy showed the best performance on pericondensed molecules. Additionally, the sensitivities of these descriptors were tested on the catacondensed isomers with the increasing number of bays, coves, and fjords. It was revealed that these descriptors gradually change with the increasing number of these structural features. The Estrada index and resolvent energy perform similarly and in some cases with the same structural sensitivity. This may be attributed to the high correlation between them. The graph energy showed superiority over the Estrada index and resolvent energy on pericondensed isomers.

RESOLVENT ENERGY AND ESTRADA INDEX OF BENZENOID HYDROCARBONS

The relationship between the resolvent and Estrada indices for the alkanes has been recently demonstrated. That relationship involved the first Zagreb index besides these two eigenvalue-based molecular descriptors. In this paper, the quality of the correlation is tested in the case of isomeric benzenoid hydrocarbons, where the first Zagreb index is constant. Extraordinary linear correlations are identified for all studied groups of isomeric benzenoid hydrocarbons. Additionally, the relationship of these indices with the boiling points of a set of benzenoid hydrocarbons is presented.

Stability order of isomeric benzenoid hydrocarbons and Kekulé structure count

The commonly accepted opinion that the thermodynamic stability of isomeric benzenoid hydrocarbons (assessed by their total ?-electron energy and various resonance energies) increases with increasing number of Kekul? structures is shown to be violated in numerous cases. The smallest examples of such anomalous behavior are two hexacyclic pericondensed benzenoids of formula C24H14 and several pairs of heptacyclic catacondensed benzenoids of formula C30H18.

Comparing the stability of tribenzo[b,n,pqr]perylene and tribenzo[b,k,pqr]perylene

Two isomeric benzenoid hydrocarbons – tribenzo[b,n,pqr]perylene and tribenzo[b,k,pqr]perylene played a crucial role in the formulation of the Clar aromatic sextet theory. The basic assumption of this theory is that tribenzo[b,n,pqr]perylene is more stable than tribenzo[b,k,pqr]perylene because the former has five, whereas the latter only four aromatic sextets. We now approach this stability problem from a different direction. By means of a recently developed molecular-orbital-based method it is possible to estimate the energy effects of individual cycles, as well as pairs, triplets, etc. of cycles in polycyclic conjugated molecules. From these energy-effects one can better understand which structural details are responsible for the thermodynamic stability of the underlying molecule. In particular, it is possible to rationalize (in a quantitative manner) the causes of differences in the thermodynamic stability of isomers. Our analysis corroborates the conclusion of Clar theory, but points out a number of hitherto overlooked structure-stability connections.

Why is phenanthrene more stable than anthracene

By means of a recently developed molecular-orbital-based method it is possible to estimate the energy effects of individual cycles, as well as pairs, triplets, etc. of cycles in polycyclic conjugated molecules. From these energyeffects one can better understand which structural details are responsible for the thermodynamic stability of the underlying molecule. In particular, it is possible to rationalize (in a quantitative manner) the causes of differences in the thermodynamic stability of isomers. Such an analysis is here performed on the two isomeric benzenoid hydrocarbons with three hexagons – anthracene and phenanthrene.

Relating Total π-Electron Energy and Resonance Energy of Benzenoid Molecules with Kekulé- and Clar-Structure-Based Parameters

Within classes of isomeric benzenoid hydrocarbons various Kekule- and Clar-structure-based parameters (Kekule structure count, Clar cover count, Herndon number, Zhang–Zhang polynomial) are all mutually correlated. This explains why both the total π-electron energy (E), the Dewar resonance energy (DRE), and the topological resonance energy (TRE) are well correlated with all these parameters. Nevertheless, there exists an optimal value of the variable of the Zhang–Zhang polynomial for which it yields the best results. This optimal value is negative-valued for E, around zero for TRE, and positive-valued for DRE. A somewhat surprising result is that TRE and DRE considerably differ in their dependence on Kekule- and Clar-structure-based parameters.

On the Relationship between π-Electron Energy and Topological Resonance Energy

Within series of isomeric benzenoid hydrocarbons there is a very good linear correlation between the topological resonance energy (TRE) and the total π-electron energy (Eπ ). Furthermore, the slope of the TRE vs. Eπ regression line is almost independent of the benzenoid isomers considered, and (for all sets of isomers) is nearly equal to 0.5. This implies that comparison of benzenoid isomers with regard to their aromaticity can be made, with equal success, by using both TRE and Eπ . However, Eπ is computed significantly simpler than TRE, and thus advantage should be given to the former. Correlations between TRE and Eπ exist also in the case of non-benzenoid isomers (both alternant and non-alternant), but are of much inferior quality.

Extending and modifying the Hall rule

The Hall rule claims that the HMO total π-electron energy ( E) of isomeric benzenoid hydrocarbons is a linear function of the number of Kekulé structures ( K). We now show that already in the case of benzenoid isomers with a small number of hexagons (4 ⩽ h ⩽ 9), E is better reproduced by a linear function of K λ , where the exponent λ is significantly smaller than unity. This exponent is found to be a decreasing function of h and its limit value (for h → ∞) seems to be equal to, or near to, 1/3. A simple model of such a K-dependence of E is constructed.

Correlations between the benzene character of acenes or helicenes and simple molecular descriptors

Aromatic stabilities of acenes and helicenes, which are responsible for their biological, environmental and cancerous behavior have been modeled using a newly introduced Sadhana (Sd) and A indices. The results are compared with those obtained from PI (Padmakar-Ivan) index. The regression analysis has shown that excellent results are obtained by considering acenes and helicenes as separate classes of isomeric benzenoid hydrocarbons and that A index is better index than both PI and Sd indices.

On the Hall rule in the theory of benzenoid hydrocarbons

In 1973, Hall noticed that the total π-electron energy (E) of isomeric benzenoid hydrocarbons is a linear function of the number of Kekule structures (K). Since then, this remarkable rule has been confirmed on a plethora of examples. Twenty years later, it was discovered that for large benzenoids (with nine or more hexagons) the E–K dependence is slightly curvilinear. We now elaborate a novel approach, describing and, to some extent, rationalizing these peculiar features of the E–K dependence. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 627–632, 1999

Revisiting a simple regularity for benzenoid hydrocarbons. Total π-electron energy versus the number of Kekulé structures

The linear dependence, previously claimed, of the total π-electron energy ( E π ) of isomeric benzenoid hydrocarbons on the number of Kekulé structures ( K) is found to be a satisfactory approximation only for benzenoids having eight or fewer six-membered rings ( h ⩽ 8), and is violated if h ⩾ 9. For sets of isomeric ubranched catocondensed benzenoids (having fixed values of h, h ⩾ 9), E π is well reproduced by the expression a + bK − cK − 1 2 , where a, b and c are constant.

Comparability graphs and electronic spectra of condensed benzenoid hydrocarbons

A systematic topological approach to the search for regularities in molecular properties has been proposed on the basis of the so-called comparability graphs of isomeric classes of molecules. It is shown that the ordering of the isomeric benzenoid hydrocarbons in the comparability graphs coincides with that of the longest wavelenght in the p band of their electronic spectra.