Partitioning Hückel–London Currents into Cycle Contributions

Ring-current maps give a direct pictorial representation of molecular aromaticity. They can be computed at levels ranging from empirical to full ab initio and DFT. For benzenoid hydrocarbons, Hückel–London (HL) theory gives a remarkably good qualitative picture of overall current patterns, and a useful basis for their interpretation. This paper describes an implemention of Aihara’s algorithm for computing HL currents for a benzenoid (for example) by partitioning total current into its constituent cycle currents. The Aihara approach can be used as an alternative way of calculating Hückel–London current maps, but more significantly as a tool for analysing other empirical models of induced current based on conjugated circuits. We outline an application where examination of cycle contributions to HL total current led to a simple graph-theoretical approach for cycle currents, which gives a better approximation to the HL currents for Kekulean benzenoids than any of the existing conjugated-circuit models, and unlike these models it also gives predictions of the HL currents in non-Kekulean benzenoids that are of similar quality.

Energetic and geometric characteristics of the substituents. Part 1. The case of NO2 and NH2 groups in their mono-substituted derivatives of simple benzenoid hydrocarbons

Simple polycyclic aromatic hydrocarbons, substituted by strongly electron-donating (NH2) and withdrawing (NO2) groups, are studied employing density functional theory (DFT) calculations. A new approach to a description of the substituent effect, the energy of substituent, E(X), is proposed and evaluated. It is defined as E(X) = E(R-X)−E(R), where R is the unsubstituted system; X = NH2, NO2. Changes in the energy of the substituents, estimated for the benzene analog, Erel(X), allow the energy of the various substituents to be compared. The obtained values are interpreted through correlations with the geometry of the substituent and the substituted system. We show that Erel(X) is strongly dependent on the proximity of the substitution. Values of Erel(X) are also compared with a substituent descriptor based on atomic charge distribution–charge of the substituent active region, cSAR(X). It has been shown that these two descriptors correlate very well (R2 > 0.99); however, only for linear acenes with similar, “benzene-like” proximity. Moreover, relations between Erel(X) and cSAR(X), the geometry of the substituents, and angle at the ipso carbon atom can be explained by the well-established Bent–Walsh rule.

Hosoya Polynomial for Subdivided Caterpillar Graphs

Background: Computing Hosoya polynomial for the graph associated with the chemical compound plays a vital role in the field of chemistry. From Hosoya polynomial, it is easy to compute Weiner index(Weiner number) and Hyper Weiner index of the underlying molecular structure. The Wiener number enables the identifying of three basic features of molecular topology: branching, cyclicity, and centricity (or centrality) and their specific patterns, which are well reflected by the physicochemical properties of chemical compounds. Caterpillar trees have been used in chemical graph theory to represent the structure of benzenoid hydrocarbons molecules. In this representation, one forms a caterpillar in which each edge corresponds to a 6-carbon ring in the molecular structure, and two edges are incident at a vertex whenever the corresponding rings belong to a sequence of rings connected end-to-end in the structure. Due to the importance of Caterpillar trees, it is interesting to compute the Hosoya polynomial and the related indices. Method: The Hosoya polynomial of a graph G is defined as H(G;x)=∑_(k=0)d(G) d(G,k) x^k . In order to compute the Hosoya polynomial, we need to find its coefficients d(G,k) which is the number of pair of vertices of G which are at distance k. We classify the ordered pair of vertices which are at distance m,2≤m≤(n+1)k in the form of sets. Then finding the cardinality of these sets and adding up will give us the value of coefficient d(G,m). Finally using the values of coefficients in the definition we get the Hosoya polynomial of Uniform subdivision of caterpillar graph. Result: In this work we compute the closed formula of Hosoya polynomial for subdivided caterpillar trees. This helps us to compute the Weiner index and hyper-Weiner index of uniform subdivision of caterpillar graph. Conclusion: Caterpillar trees are among one of the important and general classes of trees. Thorn rods and thorn stars are the important subclasses of caterpillar trees. The ideas of the present research article is to give a road map to those researchers who are interesting to study the Hosoya polynomial for different trees.