11.2.5 Induced π-Electron Currents
As a relatively recent Kekulé–structure–based application, a method for calculating
induced currents of π-electrons in a polycyclic conjugated molecule placed in a
magnetic field was proposed by Randić [92]. Such “ring currents” [93] are traditionally related with aromaticity of the underlying π-electron system [94–99]. For
benzenoid hydrocarbons, the procedure proposed by Randić proceeds as follows:
(1) All Kekulé structures have to be constructed.
(2) All conjugated circuits in all Kekulé structures have to be recognized.
(3) The edges in each conjugated circuit have to be directed in an anti-clockwise
manner, representing a “current”.
(4) The “currents” thus obtained have to be superimposed over all conjugated
circuits of all Kekulé structures.
Randić and his coworkers have offered a number of examples [92, 100–104] in
which their results appear to be in a reasonably good agreement with π-electron
current densities obtained by ab initio quantum chemical computations.
11.2.6 Comments
The Kekulé–structure–based models briefly outlined in the previous parts of this
section, have been corroborated by numerous examples (mainly benzenoid
hydrocarbons) and—statistically speaking—give chemically satisfactory results. In
the subsequent section we will show that there exist cases in which these models
fail, sometimes completely disagreeing with experimental findings.
At this point we call the reader’s attention to a detail that sometimes is overlooked. All models described above give equal importance to each Kekulé structure. This is explicitly visible from Eqs. (11.2), (11.3), and (11.6), and implicitly
from any approach in which the simple count of Kekulé structures (i.e., K) or
averaging over all Kekulé structures is encountered.
On the other hand, it was recognized quite early [105] that some Kekulé
structures give a better description of the actual molecule than others. Attempts to
incorporate this feature into resonance theoretical models [106–108] did not gain
much popularity. It may be that such distinguishing between Kekulé structures is
not at all justified. When the Pauling bond order concept was modified, by giving
different weights to different Kekulé structures (in line with the “Fries rule”), the
accuracy of the calculated bond lengths did not significantly improve [108].
Here must be mentioned the “aromatic sextet theory” developed by Erich Clar
[109], within which some Kekulé structures are represented via “Clar formulas”
whereas some are fully ignored. Details of Clar’s theory can be found in [38,
pp. 93–116] and [109, 110], but cannot be further elaborated in this survey.
11 Paradise Lost—π-Electron Conjugation in Homologs …
305
As a relatively recent Kekulé–structure–based application, a method for calculating
induced currents of π-electrons in a polycyclic conjugated molecule placed in a
magnetic field was proposed by Randić [92]. Such “ring currents” [93] are traditionally related with aromaticity of the underlying π-electron system [94–99]. For
benzenoid hydrocarbons, the procedure proposed by Randić proceeds as follows:
(1) All Kekulé structures have to be constructed.
(2) All conjugated circuits in all Kekulé structures have to be recognized.
(3) The edges in each conjugated circuit have to be directed in an anti-clockwise
manner, representing a “current”.
(4) The “currents” thus obtained have to be superimposed over all conjugated
circuits of all Kekulé structures.
Randić and his coworkers have offered a number of examples [92, 100–104] in
which their results appear to be in a reasonably good agreement with π-electron
current densities obtained by ab initio quantum chemical computations.
11.2.6 Comments
The Kekulé–structure–based models briefly outlined in the previous parts of this
section, have been corroborated by numerous examples (mainly benzenoid
hydrocarbons) and—statistically speaking—give chemically satisfactory results. In
the subsequent section we will show that there exist cases in which these models
fail, sometimes completely disagreeing with experimental findings.
At this point we call the reader’s attention to a detail that sometimes is overlooked. All models described above give equal importance to each Kekulé structure. This is explicitly visible from Eqs. (11.2), (11.3), and (11.6), and implicitly
from any approach in which the simple count of Kekulé structures (i.e., K) or
averaging over all Kekulé structures is encountered.
On the other hand, it was recognized quite early [105] that some Kekulé
structures give a better description of the actual molecule than others. Attempts to
incorporate this feature into resonance theoretical models [106–108] did not gain
much popularity. It may be that such distinguishing between Kekulé structures is
not at all justified. When the Pauling bond order concept was modified, by giving
different weights to different Kekulé structures (in line with the “Fries rule”), the
accuracy of the calculated bond lengths did not significantly improve [108].
Here must be mentioned the “aromatic sextet theory” developed by Erich Clar
[109], within which some Kekulé structures are represented via “Clar formulas”
whereas some are fully ignored. Details of Clar’s theory can be found in [38,
pp. 93–116] and [109, 110], but cannot be further elaborated in this survey.
11 Paradise Lost—π-Electron Conjugation in Homologs …
305