π‐electron currents in polycyclic conjugated hydrocarbons: Coronene and its isomers having five and seven member rings

Abstract

ABSTRACT:We have outlined novel graph theoretical model for computing p-electron currents in p-electron polycyclic conjugated hydrocarbons. We start with Kekulé valence structures of a polycyclic conjugated hydrocarbon and their conjugated circuits. To each 4nþ2 conjugated circuits we assign counter clockwise current i and to each 4n conjugated circuit we assign clockwise current i. By adding the contributions from all conjugated circuits in a single Kekulé valence structure one obtains p-electron current pattern for the particular Kekulé valence structure. By adding the conjugated circuit currents in all Kekulé valence structure one obtains the pattern of p-electron currents for considered molecule. We report here p-electron current patters for coronene and 17 its isomers, which have been recently considered by Balaban et al., obtained by replacing one or more pairs of peripheral benzene rings with five and seven member rings. Our results are compared with their reported p-electron current density patters computed by ab initio molecular orbital (MO) computations and satisfactory parallelism is found between two so disparate approaches. V C 2011 Wiley Periodicals, Inc. Int J Quantum Chem 112: [972][973][974][975][976][977][978][979][980][981][982][983][984][985] 2012

An Analysis of Topological Ring-Currents and their Use in Assessing the Annulene-Within-an-Annulene Model for Super-Ring Conjugated Systems

“…Statement (a), above, is verified by our calculations on the Aihara 27 Structures 1-7, studied here, as well as by all the calculations reported in Refs. 22 We must, however, caution that exceptions have been noted to both of the above; they are especially to be found amongst the eighteen isomers of coronene, initially studied by Balaban, Bean and Fowler 21 by their ab-initio, 'pseudo-π' approach, 34 and later tested by the present authors using the topological 9-13 HLPM 1-4 process described in this paper; the same structures have also since been studied by Randić et al 82 by application of their method involving circuits of conjugation. 83 annulenes'.…”

“…21 (b) One structure that is decoupled but, nevertheless, does not appear to respect the provisions of the AWA 'rule' when tested by the HLPM topological approach -or, indeed, by the abinitio 'pseudo-π' formalism 21,34 (though this is contradicted 82 when the Randić 'conjugationcircuit' 83,84 approach is applied): structure 18 (with 4 Kekulé structures). 21 The overall statistics concerning this sample of eighteen isomers of coronene 21,23,82 when treated by the HLPM approach may thus be summarised as follows: (i) of 15 coupled structures (1-15 of Refs. 21 and 23), five (listed above) obey the AWA rule (with a ratio, therefore, of 1 : 2, for structures in this set that respect the rule), and (ii) of three decoupled structures (16-18 of Refs.…”

Ring-Current Assessment of the Annulene-Within-an-Annulene Model for some Large Coupled Super-Ring Conjugated-Systems

“…Furthermore, similar overall conclusions have largely been drawn when the AWA rule has been tested against the predictions of much more sophisticated 'ipso-centric' ab-initio calculations [20][21][22][23]35 -please see Ref. 36 for a detailed history of this approach -and of those 34,37,38 based on the 'pseudo-π' approximation, 37 as well as on predictions obtained via more-rudimentary methods (not considered in this paper), which make appeal to the idea 12,[39][40][41][42][43][44][45][46] of what Randić 47 called 'conjugated circuits' (defined in Ref. 47).…”

Conjugated circuits currents in hexabenzocoronene and its derivatives formed by joining proximal carbons

“…For example, recently calculated ring currents for rings in different coronene isomers having five‐ and seven‐membered rings on their periphery have shown considerable variations in magnitudes and directions. [15–18] We decided therefore to investigate CC bond currents in hexabenzocoronene and its derivatives formed by joining proximal carbons, to see if we can find some regularity for ring currents in these compounds. Our analysis of magnetic properties of polycyclic‐conjugated hydrocarbons is graph‐theoretical in nature, and considers contributions to bond currents coming from currents in conjugated circuits of a compound.…”