Topological Properties of Circumcoronenes

1998 ◽  
Vol 53 (8) ◽  
pp. 699-703 ◽  
Author(s):  
Ivan Gutman ◽  
Sven J. Cyvina ◽  
Vesna Ivanov-Petrović
Keyword(s):  
Regular Hexagon ◽  
Topological Properties ◽  
Benzenoid Hydrocarbons ◽  
Spectral Moments ◽  
Energy Effect ◽  
Cyclic Conjugation ◽  
Clar Structures ◽  
First Time ◽  
Structural Invariants

Abstract The regular-hexagon-shaped benzenoid hydrocarbons: B1 = benzene (C6H6), B2 = coronene (C24H12), B3 = circumcoronene (C54H18), B4 = circumcircumcoronene (C150H30), etc. possess unique topological properties. General expressions for the most important of such properties (number of fun-damental structural invariants, number of Kekule and Clar structures, number of aromatic sextets, Wiener and Szeged indices, spectral moments) are given, including a number of results that are communicated here for the first time. Cyclic conjugation in circumcoronenes is analyzed by means of its energy-effect, and found to agree with the predictions of Clar's aromatic sextet theory only in the case of B1 and B2.

scholarly journals Annelated perylenes: Benzenoid molecules violating the Kekulé-structure-based cyclic conjugation models

2005 ◽  
Vol 70 (8-9) ◽  
pp. 1023-1032 ◽  
Author(s):  
Ivan Gutman ◽  
Boris Furtula ◽  
Jelena Djurdjevic ◽  
Rradmila Kovacevic ◽  
Sonja Stankovic
Keyword(s):  
Anomalous Behavior ◽  
Kekulé Structure ◽  
Benzenoid Hydrocarbons ◽  
Energy Effect ◽  
Structural Formulas ◽  
Cyclic Conjugation

Several currently used models for assessing the extent of cyclic conjugation in benzenoid hydrocarbons, all based on Kekul?-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 Kekul?- structure-based models fail. The cause for such an "anomalous" behavior of annelated perylenes is discussed.

scholarly journals Topological properties of altan-benzenoid hydrocarbons

2014 ◽  
Vol 79 (12) ◽  
pp. 1515-1521 ◽  
Author(s):  
Ivan Gutman
Keyword(s):  
Topological Properties ◽  
Benzenoid Hydrocarbons ◽  
Energy Effect ◽  
Topological Characteristics

The main topological characteristics of altan-benzenoids are established. In particular, it is shown that the perimeter of Kekul?an altan-benzenoids is of size 4k , having a destablizing (antiaromatic) energy effect, similar to (4k)-annulenes.

scholarly journals Cyclic conjugation in benzo-annelated triphenylenes

2010 ◽  
Vol 75 (7) ◽  
pp. 943-950 ◽  
Author(s):  
Svetlana Jeremic ◽  
Slavko Radenkovic ◽  
Ivan Gutman
Keyword(s):  
Membered Ring ◽  
Electron Content ◽  
Strongly Correlated ◽  
Energy Effect ◽  
Cyclic Conjugation ◽  
Non Linear ◽  
Linear Manner

Cyclic conjugation in benzo-annelated triphenylenes was studied by means of the energy effect (ef) and the ?-electron content (EC) of the six-membered rings. A regularity that was earlier discovered in the case of acenaphthylene and fluoranthene congeners is now shown to hold also for benzo-annelated triphenylenes: Benzenoid rings that are annelated angularly with regard to the central six-membered ring Z0 of triphenylene increase the intensity of the cyclic conjugation in Z0, whereas linearly annelated benzenoid rings decrease the cyclic conjugation in Z0. The efand EC-values are strongly correlated, yet in a non-linear manner.

scholarly journals Verifying the PCP-rule by five-center bond indices

2009 ◽  
Vol 74 (5) ◽  
pp. 549-554 ◽  
Author(s):  
Jelena Djurdjevic ◽  
Ivan Gutman ◽  
Robert Ponec
Keyword(s):  
Membered Ring ◽  
Energy Effect ◽  
Conjugated Hydrocarbons ◽  
Cyclic Conjugation ◽  
Bond Indices ◽  
Polycyclic Conjugated Hydrocarbons

According to the recently discovered PCP-rule, the (stabilizing) energy- effect of the cyclic conjugation in the 5-membered ring of acenaphthyleneand fluoranthene-type polycyclic conjugated hydrocarbons increases with the number of phenyl-cyclopentadienyl (PCP) fragments present in the molecule. It is now shown that the validity of the PCP-rule is also supported by the 5-center bond indices, an independent quantitative theoretical measure of cyclic conjugation in 5-membered rings.

Cyclic Conjugation in Total Resonant Sextet Benzenoid Hydrocarbons

2000 ◽  
Vol 18 (2) ◽  
pp. 221-229 ◽  
Author(s):  
Ivan Gutman ◽  
Vesna Ivanov-Petrović ◽  
Jerry R. Dias
Keyword(s):  
Benzenoid Hydrocarbons ◽  
Cyclic Conjugation

scholarly journals On molecular topological properties of diamond-like networks

2017 ◽  
Vol 95 (7) ◽  
pp. 758-770 ◽  
Author(s):  
Muhammad Imran ◽  
Abdul Qudair Baig ◽  
Hafiz Muhammad Afzal Siddiqui ◽  
Rabia Sarwar
Keyword(s):  
Molecular Graph ◽  
Topological Indices ◽  
Connectivity Index ◽  
Topological Properties ◽  
Benzenoid Hydrocarbons ◽  
Connectivity Indices

The Randić (product) connectivity index and its derivative called the sum-connectivity index are well-known topological indices and both of these descriptors correlate well among themselves and with the π-electronic energies of benzenoid hydrocarbons. The general n connectivity of a molecular graph G is defined as [Formula: see text] and the n sum connectivity of a molecular graph G is defined as [Formula: see text], where the paths of length n in G are denoted by [Formula: see text] and the degree of each vertex vi is denoted by di. In this paper, we discuss third connectivity and third sum-connectivity indices of diamond-like networks and compute analytical closed results of these indices for diamond-like networks.

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