Some comments on topological approaches to the π-electron currents in conjugated systems

Journal of Chemical Theory and Computation

Volumn 7, Issue 11, 2011, Pages 3661-3674

  Dickens, Timothy K ^a   Gomes, José A N F ^b   Mallion, Roger B ^c  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF PORTO   (Portugal)

^c UNIVERSITY OF KENT   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80755150251     PISSN: 15499618     EISSN: 15499626     Source Type: Journal    
DOI: 10.1021/ct2002539     Document Type: Review

References (70)

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41. In view of the theoretical formulation of the method proposed by Gomes, (17-19) this rule-printed in the text in italics -is here given a wording that is more general than that adopted for the corresponding rule (iii) in ref 16. (The original wording in ref 16 was "(iii) If at least one bond of a particular ring forms a part of a given "conjugation circuit", this ring shall be said to "participate" in that "conjugation circuit."'). Professor P. W. Fowler (36b, 36c) has recently proposed an equivalent version of rule (iii) that is couched entirely in terms of bond currents, rather than ring currents
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69. This observation is re-enforced by Figure 3 of ref 61b, in which the bond currents in the 60 bonds of kekulene are expressed in terms of just three independent parameters, A, B, and δ. These are not actually the ring currents in the three symmetrically non-equivalent rings of kekulene, but they are related to them in the following way: the ring current in the six-membered ring that Steiner et al. (61b) label "I" is equal to (A + δ); the ring current in ring II is (A - δ), and that in the internal, 18-membered, ring III is (A - B). Once again, therefore, in this example, a bond-current description is entirely equivalent to a ring-current one, with as many independent variables being needed to specify the several bond currents as there are symmetrically non-equivalent rings (and, hence, distinct ring currents) in the structure under consideration
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