cf. Eq. (11.5). These rings do not contain, and are not embraced by any, conjugated
circuit. Their π-electron contents are small (but non-zero), never exceeding 2.00.
For both Herndon resonance energy, Eq. (11.3), Swinborne–Sheldarke resonance
energy, Eq. (11.4), and conjugated–circuits resonance energy, Eq. (11.6),
REðPÞ ¼ REðXÞ þ REðYÞ:
In addition, it can be easily verified [116] that KðPÞ ¼ KðXÞ Á KðYÞ.
Randić’s model of induced π-electron currents predicts zero current through the
“vertical” bonds of the rings E 1 ; E 2 ; . . .; E n .
Of course, a sober chemist would never consider the above stated “predictions”
of properties of the benzenoid systems P as something absolutely true, but rather as
a more-or-less plausible approximation. Thus, the above Kekulé–structure–based
claims should be understood as follows:
(1) The local aromaticity of the rings E 1 ; E 2 ; . . .; E n is small, significantly smaller
than that of other rings of P.
(2) The extent of cyclic conjugation in these rings is small, significantly smaller
than that in other rings of P.
(3) The π-electron contents of these rings is small, significantly smaller than that
of other rings of P.
(4) The difference of resonance energies
REðPÞ À ½REðXÞ þ REðYÞ
is small, but non-zero.
(5) The induced π-electron current through the fixed single bonds of P is small but
non-zero.
The statements (1)–(5) can be checked by other, Kekulé–structure–independent,
theoretical methods. By this, the Kekulé–structure–based models can be tested, and
their general applicability either verified or refuted.
We begin with a good news.
The extent of cyclic conjugation can be estimated by a molecular–orbital–based
method, whose details are described elsewhere (see the survey [124], the recent
papers [125–128], and the references cited therein). This method renders the πelectron energy–effect ef (BH,R) of the rings R of a polycyclic conjugated hydrocarbon BH. The greater the (positive) ef-value, the greater is the thermodynamic
stabilization caused by cyclic conjugation in the underlying ring R. The ef-values
may be viewed as a measure of local aromaticity [129–132].
Now, the ef-method gives the following results for perylene (with rings labeled
as in Fig. 11.8): ef ð8; AÞ ¼ ef ð8; BÞ ¼ ef ð8; CÞ ¼ ef ð8; DÞ ¼ 0:1093 and
ef ð8; EÞ ¼ 0:0218 [133]. These are in a fairly good agreement with the Kekulé–
structure–based predictions: the extent of cyclic conjugation in the central ring of
perylene is found to be ca. five times weaker than in its four peripheral rings.
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I. Gutman and S. Radenković
circuit. Their π-electron contents are small (but non-zero), never exceeding 2.00.
For both Herndon resonance energy, Eq. (11.3), Swinborne–Sheldarke resonance
energy, Eq. (11.4), and conjugated–circuits resonance energy, Eq. (11.6),
REðPÞ ¼ REðXÞ þ REðYÞ:
In addition, it can be easily verified [116] that KðPÞ ¼ KðXÞ Á KðYÞ.
Randić’s model of induced π-electron currents predicts zero current through the
“vertical” bonds of the rings E 1 ; E 2 ; . . .; E n .
Of course, a sober chemist would never consider the above stated “predictions”
of properties of the benzenoid systems P as something absolutely true, but rather as
a more-or-less plausible approximation. Thus, the above Kekulé–structure–based
claims should be understood as follows:
(1) The local aromaticity of the rings E 1 ; E 2 ; . . .; E n is small, significantly smaller
than that of other rings of P.
(2) The extent of cyclic conjugation in these rings is small, significantly smaller
than that in other rings of P.
(3) The π-electron contents of these rings is small, significantly smaller than that
of other rings of P.
(4) The difference of resonance energies
REðPÞ À ½REðXÞ þ REðYÞ
is small, but non-zero.
(5) The induced π-electron current through the fixed single bonds of P is small but
non-zero.
The statements (1)–(5) can be checked by other, Kekulé–structure–independent,
theoretical methods. By this, the Kekulé–structure–based models can be tested, and
their general applicability either verified or refuted.
We begin with a good news.
The extent of cyclic conjugation can be estimated by a molecular–orbital–based
method, whose details are described elsewhere (see the survey [124], the recent
papers [125–128], and the references cited therein). This method renders the πelectron energy–effect ef (BH,R) of the rings R of a polycyclic conjugated hydrocarbon BH. The greater the (positive) ef-value, the greater is the thermodynamic
stabilization caused by cyclic conjugation in the underlying ring R. The ef-values
may be viewed as a measure of local aromaticity [129–132].
Now, the ef-method gives the following results for perylene (with rings labeled
as in Fig. 11.8): ef ð8; AÞ ¼ ef ð8; BÞ ¼ ef ð8; CÞ ¼ ef ð8; DÞ ¼ 0:1093 and
ef ð8; EÞ ¼ 0:0218 [133]. These are in a fairly good agreement with the Kekulé–
structure–based predictions: the extent of cyclic conjugation in the central ring of
perylene is found to be ca. five times weaker than in its four peripheral rings.
308
I. Gutman and S. Radenković