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11976 Phys. Chem. Chem. Phys., 2011, 13, 11976–11984 This journal is c the Owner Societies 2011
Cite this: Phys. Chem. Chem. Phys., 2011, 13, 11976–11984
Does the concept of Clar’s aromatic sextet work for dicationic forms of
polycyclic aromatic hydrocarbons?—testing the model against charged
systems in singlet and triplet statesw
Justyna Dominikowska and Marcin Palusiak*
Received 27th February 2011, Accepted 5th May 2011
DOI: 10.1039/c1cp20530g
The concept of Clar’s p-electron aromatic sextet was tested against a set of polycyclic aromatic
hydrocarbons in neutral and doubly charged forms. Systems containing different types of rings
(in the context of Clar’s concept) were chosen, including benzene, naphthalene, anthracene,
phenanthrene and triphenylene. In the case of dicationic structures both singlet and triplet states
were considered. It was found that for singlet state dicationic structures the concept of aromatic
sextet could be applied and the local aromaticity could be discussed in the context of that model,
whereas in the case of triplet state dicationic structures Clar’s model rather failed. Different
aromaticity indices based on various properties of molecular systems were applied for the purpose
of the studies. The discussion about the interdependence between the values of different
aromaticity indices applied to neutral and charged systems in singlet and triplet states is also
included.
Introduction
In 1972 Erich Clar published his book entitled ‘‘The aromatic
sextet’’1 where he introduced an original concept that makes it
possible to explain several physical and chemical properties of
polycyclic aromatic hydrocarbons (PAHs). According to that
concept p-electrons forming delocalized double bonds, e.g. in
the benzene ring (with the p-electron structure often considered
as a superposition of localized Kekule structures),2 belong to
an aromatic sextet localized within that ring. Additionally,
according to Clar’s concept, if more than one canonical
structure can be considered for a given system, then those of
them which have the highest number of localized sextets are
the most stable structures. Such structures are called Clar
structures. In the case of a benzene molecule consisting of a
single benzenoid ring it rather is not justified to consider the
difference between Kekule-type resonance structures and
Clar’s localized sextet. However, if we take into consideration
the PAHs, the difference between these two concepts appears
to be crucial. Let us explain the case of phenanthrene, i.e. PAH
consisting of three fused benzene rings. Scheme 1 shows two
(out of five possible) Kekule structures of phenanthrene and
corresponding to them two structures with localized sextets
denoted as the circles within the rings. Obviously, according to
Clar’s concept, structure 2 is more stable, as it contains the
greatest possible number of localized sextets. Therefore, this
structure can be called the Clar structure. In fact, the lateral
rings in phenanthrene are significantly more aromatic than
their inner counterpart. This was shown using several indicators
of aromaticity.3–10 Thus, it can be concluded that structure 2
(in meaning of Clar’s structure or its Kekule equivalents)
contributes more to the superposition of all resonance structures
that are possible for phenanthrene. In the case of the topological
analogue of phenanthrene, i.e. the anthracene, the situation is
significantly different. There are three structures, equivalent
from the point of view of Clar’s concept, in which there is
always only one Clar’s sextet localized in one of the three
Scheme 1
Department of Theoretical and Structural Chemistry,University of Łodz, Tamka 12, 91-403 Łodz, Poland.E-mail: marcinp@uni.lodz.plw Electronic supplementary information (ESI) available. See DOI:10.1039/c1cp20530g
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fused rings. This situation is presented in Scheme 2. As a
result, all three rings in anthracene should exhibit a compar-
able degree of aromatic character, which in fact is observed if
one considers local aromaticity of anthracene.3–10
Following Clar’s concept it is possible to define four types of
benzenoid rings present in PAHs:
– The ring with the localized sextet, usually exhibiting
strongly aromatic character. As an example of this type of
ring we can mention a lateral ring in phenanthrene.
– The ring with the migrating sextet, usually exhibiting less
aromatic character than the ring with the localized sextet. As
an example of such a ring we can mention any of the rings in
anthracene, but also in naphthalene and larger acenes.
– The ring with the localized double bond, usually exhibiting
significantly reduced aromatic character. As an example of
such a ring we can mention the inner ring in phenanthrene.
– The empty ring, which formally does not possess
p-electrons. An example of this type of ring can be the inner
ring in triphenylene.
The original idea developed by Clar in 1972 was later
revisited and assessed in many articles and it was shown that
various methods developed for the estimation of local and
global aromaticity are in excellent agreement with Clar’s
concept.3,6,8,11–15 In particular, it is worth mentioning that
the application of different aromaticity indices based on the
properties being typical of aromatic compounds proves
numerically the correctness of Clar’s concept.3
Although unsubstituted PAHs and their various derivatives
are very common in chemistry,16,17 their isolated cationic
and dicationic counterparts are practically unavailable in
experimental conditions due to extreme reactivity of such
chemical species. However, increasing attention has recently
been paid to positively charged PAHs due to the fact that such
compounds are supposed to be widespread in the interstellar
space. In 1979 Cohen et al.18 discovered the extended red
emission (ERE) which is a broad emission band that begins
near 540 nm and extends into the near infrared (IR) emitted by
an object known as Red Rectangle nebula. Later ERE
was detected in spectral analysis of such objects as some
carbon-rich planetary nebulae19–21 and in the interstellar
medium of the Galaxy.22 However, the exact source of ERE
is unknown yet, and among several explanations proposed the
most probable one is that PAHs and their positively charged
analogues are responsible for this phenomenon.23–30 Recently
it was also suggested that cationic PAHs, being an open-
shell systems, may tend to form more stable closed-shell
complexes.31 Yet it can be supposed that doubly charged
PAHs, although they may form complexes, in appropriate
conditions can also exist as the separate closed-shell molecular
systems.
In this paper we analyze local aromaticity of doubly charged
PAHs, focusing our attention on the possibility of using Clar’s
concept for doubly charged structures in singlet and triplet
states. For this purpose we make use of several aromaticity
indices which are based on different properties of the considered
systems, including their geometry, electron density distribution
and magnetic properties.
Methodology
The following systems were studied: dications of benzene,
naphthalene, anthracene, phenanthrene and triphenylene both
in singlet and triplet states. As the reference structures neutral
hydrocarbons mentioned above (in the singlet state) were
taken into account. Geometries of all the systems were
optimized without any symmetry constraints using DFT32,33
methods implemented in Gaussian0934 program. The B3LYP35–38
functional was used together with the 6-311++G(d,p)39 basis
set. The frequency analysis on the same level of theory was
performed in order to verify if the optimized geometries
correspond to stationary points. No imaginary frequencies
were found. In the first approach we found several discrepancies
as concerns numerical results. In particular we observed
unusual values of NICS indices (see below for the defini-
tion of NICS) for some of the cationic systems (mostly
for benzene dications, e.g. NICS around �90 for benzene
dications in the singlet state). For this reason we repeated
the optimization procedures using very tight optimization
criteria (Opt = VeryTight in Gaussian09) together with a
larger DFT integration grid (Int = Ultrafine in Gaussian09).
For such calculations the values seem to be much more reliable,
thus we maintained that level of calculations for all the cases
examined.
For the aromaticity description several indices based on
different physical properties of the systems under consideration
were applied. The HOMA index40,41 was used as a geometry-
based indicator of aromaticity. According to its definition
HOMA40,41 can be expressed by the following equation:
HOMA ¼ 1� 1
n
Xnj¼1
ai Ropt;i � Rj
� �2;
where n represents the number of bonds forming the ring, ai isthe normalization constant chosen to give HOMA = 0 for
the Kekule benzene structure (with the CC bond length as in
Scheme 2
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1,3-butadiene) and 1 for all the systems with all the bonds
equal to the optimal value Ropt.
For the CC bond ai and Ropt values are equal to 257.7 and
1.388 A, respectively. HOMA can also be expressed by the
equation:42,43
HOMA = 1 � EN � GEO,
where EN42,43 can be expressed as:
EN = fa(Ropt � Rav)2,
where f= sgn(Rav � Ropt). The term EN is connected with the
elongation or shortening of the CC bond in comparison with
Ropt. The term GEO42,43 is connected with the bond length
alternation and can be expressed as follows:
GEO ¼ 1
n
Xni¼1
aiðRav � RiÞ2:
For another description of aromaticity two indices (PDI44 and
FLU)45 based on electron delocalization indices were applied.
The delocalization index of atoms A and B can be defined by
the following expression:46,47
dðA;BÞ ¼ 4XN=2i;j
SijðAÞSijðBÞ
The sums in the above equation run over N/2 occupied
molecular orbitals. Sij(A) is the overlap between orbitals i
and j within the basin of atom A. The physical meaning of the
delocalization index can be explained as the number of
electron pairs shared by atoms A and B. The definition
of the delocalization index comes from Bader’s Atoms in
Molecules (AIM) theory48,49 according to which it is possible
to compute Sij values on the basis of the zero-flux gradient
condition on one-electron density. Delocalization indices in
this work were computed using AIMAll program.50
Aromaticity indices mentioned above are the measure of
cyclic electron delocalization of mobile electrons in the ring.
The first one, para-delocalization index, PDI,44 is a mean value
of all delocalization indices estimated for para-related carbon
atoms in a six-membered ring. The other one, the aromatic
fluctuation index (FLU)45 can be defined by the equation:
FLU ¼ 1
n
XRING
A�B
VðBÞVðAÞ
� �a dðA;BÞ � drefðA;BÞdrefðA;BÞ
� �� �2:
The sum in the equation runs over all adjacent pairs of
atoms—members of a given ring, n is their number, dref (C, C)is the delocalization index for two adjacent carbon atoms in
benzene computed on the same level of theory as the system
under consideration. V(A) is a global delocalization of an
atom A, given by the expression:
VðAÞ ¼XBaA
dðA;BÞ:
Finally, a is a function defined as:
a ¼ 1 VðBÞ4VðAÞ�1 VðBÞ � VðAÞ
�;
which makes the valueVðBÞVðAÞ equal to or greater than 1. FLU is
close to zero for aromatic systems and is different from zero
for non-aromatic ones.
Recently it was demonstrated that the density of total
electron energy measured in ring critical points (RCP, according
to QTAIM48 the local extrema of electron density being
characteristic of ring systems) may in some cases serve as an
additional measure of the degree of delocalization, although it
should not be considered as the aromaticity index, but rather
as a physical property which in some cases reflects the degree
of delocalization.7 We estimated the values of HRCP and
confronted them with the values of aromaticity indices used
in these studies.
Finally, nucleus-independent chemical shifts (NICS)51 were
applied as an indicator of aromaticity. NICS(0)51 is defined as
a negative value of absolute shielding computed at the ring
centre determined as an arithmetic mean of coordinates of the
atoms forming the ring. The more negative the NICS value,
the more aromatic the ring is. Also NICS(1)52 estimated 1 A
above the ring centre and NICS(1)zz,53 the NICS(1) component
corresponding to the principal axis perpendicular to the ring
plane, were computed. Since NICS indications generally differ
from those derived from the rest of aromaticity indices, we will
discuss NICS values separately at the end of the discussion.
Results and discussion
The aim of this study was to check whether the concept of
Clar’s p-aromatic sextet can be applied to dicationic forms of
PAHs. For this purpose we selected a set of the most basic
PAHs consisting of different (from the point of view of Clar’s
concept) types, that is, rings with localized p-electron sextet
(benzene, phenanthrene and triphenylene), rings with migrating
sextets (naphthalene and anthracene), rings with localized
double bonds (phenanthrene) and with empty rings (triphenylene).
Since it is not clear whether the singlet or triplet state
structures are more stable for each of charged systems, both
states were investigated. Additionally, neutral parent PAHs
were also taken into account as reference systems. The values
of aromaticity indices are collected in Table 1. The ESIw file
contains data with all optimized geometries. The notation of
individual rings is given in Scheme 3.
The case of benzene and its dicationic forms
The benzene molecule consists of a single aromatic ring, and
so the application of Clar’s concept to the benzene molecule
does not lead to any specific conclusions related to that
concept. However, benzene is an archetype of aromatic species
and as such it reflects all properties characteristic of aromatic
compounds. For this reason we shortly comment on the results
of calculations performed for this molecular system and in
particular to its dicationic counterparts.
As expected, the ionization of benzene by reduction of the
number of its electrons leads to a significant lowering of its
aromatic character. As it can be concluded from HOMA
values (being distinct from the rest of aromaticity indices the
HOMA index is normalized within the range of 0 and 1 for
fully aromatic and fully nonaromatic systems, respectively),
due to double ionization the aromatic character of benzene
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was reduced by about 50%, both in the case of singlet and
triplet states. The geometry of both cationic forms is clearly
nonplanar with deformation towards chair conformation.
Similar observations had been made already earlier for the
benzene dication in the singlet state.54 The torsion angle
describing this deformation equals 12.251 and 10.511 for
singlet and triplet, respectively. It should be mentioned that
optimization with Cs symmetry led to imaginary frequency
corresponding to out-of-plane vibrations, although the neutral
benzene ring converges to a fully planar structure, as expected.
It should be mentioned that the benzene dication was recently
investigated at the B3LYP/6-31G(d) level of calculations55 and
that the reported HOMA and NICS values were different from
those found by us. This might result from too low accuracy in
calculations which we also experienced at the first stage of
our analysis, as was described in the Methodology section.
Unfortunately, we could not compare geometries since no
such data were associated with the mentioned paper.
From the comparison of singlet and triplet state energies of
dicationic benzene it results that the triplet state is slightly
more stable. Thus it is worth noting that all aromaticity indices
point to the triplet state as being relatively more delocalized.
What is interesting, the PDI value is even larger than in the
case of neutral benzene, which may be surprising, since it
could be expected that the dicationic form of benzene should
not be more aromatic than its parent molecule. According to
its definition PDI is a mean of dicentre delocalization indices
estimated for para-related carbon atoms in the benzene (or
benzene-like) ring.44 Thus, it can be concluded that although
the cyclic delocalization in benzene is significantly disturbed
when two electrons have been removed from its pi-electron
structure, the through-the-space delocalization between para-
related carbon atoms is still very efficient in the triplet state,
but clearly reduced in the singlet state. Also the bond lengths
are fully equalized in the triplet state, as shown by the GEO
parameter, but relatively longer with respect to the neutral
parent system.
Magnetic indices point to significantly antiaromatic singlet
state dications and partially or fully aromatic triplet state
dications. It can be noticed that in the case of triplet state
the NICS(1) value, and even more so the NICS(1)zz value, is
similar to that in neutral benzene. The NICS values estimated
for the dicationic triplet state are much closer to zero in
comparison with the value estimated for neutral benzene. On
the other hand, it was reported that NICS might contain
important spurious contributions from the in-plane tensor
Table 1 The values of aromaticity indices estimated for individual rings of all investigated systems. M values correspond to multiplicity (s standsfor singlet and t for triplet). HRCP � 105 values are given in atomic units. Ring notation corresponds to that in Scheme 3
M Ring HOMA EN GEO PDI FLU HRCP � 103 NICS NICS(1) NICS(1)zz
Benzene s A 0.989 0.011 0.000 0.103 0.000 7.766 �8.060 �10.228 �29.247Benzene2+ s A 0.531 0.189 0.280 0.059 0.015 7.295 10.628 7.334 27.222Benzene2+ t A 0.601 0.399 0.000 0.109 0.009 7.519 �1.436 �8.831 �21.088Naphthalene s A 0.783 0.082 0.134 0.075 0.009 7.357 �8.392 �10.477 �29.091
B 0.783 0.082 0.134 0.075 0.009 7.357 �8.392 �10.466 �29.032Naphthalene2+ s A 0.666 0.198 0.135 0.044 0.014 7.325 30.150 20.133 65.069
B 0.666 0.198 0.135 0.044 0.014 7.325 30.150 20.123 64.987Naphthalene2+ t A 0.517 0.305 0.178 0.050 0.013 7.200 �4.653 �9.939 �24.996
B 0.517 0.305 0.178 0.050 0.013 7.200 �4.653 �9.926 �24.938Anthracene s A 0.629 0.127 0.244 0.065 0.015 7.259 �7.281 �9.444 �25.996
B 0.720 0.168 0.112 0.065 0.009 7.166 �11.053 �12.682 �34.889C 0.629 0.127 0.244 0.065 0.015 7.259 �7.281 �9.438 �25.972
Anthracene2+ s A 0.812 0.125 0.063 0.050 0.008 7.376 11.101 4.695 18.245B 0.672 0.291 0.037 0.026 0.016 7.115 16.729 9.802 34.346C 0.812 0.125 0.063 0.050 0.008 7.376 11.101 4.696 18.236
Anthracene2+ t A 0.593 0.234 0.173 0.050 0.014 7.220 2.304 �3.274 �5.491B 0.621 0.270 0.109 0.043 0.014 7.129 �1.826 �6.039 �13.461C 0.593 0.234 0.173 0.050 0.014 7.220 2.304 �3.268 �5.473
Phenanthrene s A 0.868 0.056 0.076 0.081 0.005 7.364 �8.512 �10.714 �28.851B 0.459 0.296 0.245 0.047 0.019 7.027 �5.461 �8.209 �20.609C 0.868 0.056 0.076 0.081 0.005 7.364 �8.512 �10.705 �28.812
Phenantherene2+ s A 0.602 0.164 0.235 0.046 0.015 7.252 26.872 18.000 58.714B 0.196 0.428 0.376 0.033 0.025 6.989 23.872 16.130 53.699C 0.602 0.164 0.235 0.046 0.015 7.252 26.873 17.992 58.649
Phenantherene2+ t A 0.723 0.164 0.084 0.053 0.010 7.249 �1.944 �6.970 �15.987B 0.602 0.428 0.088 0.037 0.013 7.105 1.860 �3.087 �4.301C 0.723 0.164 0.084 0.053 0.010 7.249 �1.944 �6.955 �15.949
Triphenylene s A 0.901 0.041 0.058 0.085 0.003 7.372 �7.433 �9.595 �25.684B 0.097 0.758 0.145 0.028 0.023 6.626 �1.928 �5.301 �10.378C 0.901 0.041 0.058 0.085 0.003 7.371 �7.510 �9.866 �25.795D 0.901 0.041 0.058 0.085 0.003 7.373 �7.593 �9.895 �25.945
Triphenylene2+ s A 0.134 0.269 0.597 0.043 0.023 7.108 67.531 53.440 164.764B �0.185 0.908 0.278 0.026 0.029 6.585 57.460 47.577 148.718C 0.723 0.113 0.164 0.052 0.011 7.303 66.647 53.493 165.347D 0.723 0.113 0.164 0.052 0.011 7.303 66.565 52.354 161.931
Triphenylene2+ t A 0.714 0.137 0.149 0.055 0.009 7.276 �6.504 �6.515 �26.765B 0.714 0.137 0.149 0.022 0.025 6.569 �0.947 �5.439 �10.364C 0.714 0.137 0.149 0.055 0.009 7.276 �6.634 �10.648 �26.934D 0.714 0.137 0.149 0.055 0.008 7.276 �6.703 �10.697 �27.090
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11980 Phys. Chem. Chem. Phys., 2011, 13, 11976–11984 This journal is c the Owner Societies 2011
components that are not related to aromaticity.56–58 Perhaps
this is in connection with the relatively lowered value of NICS
in the case of dicationic structures.
Concluding, according to our calculations the benzene
dication is more stable as a triplet state structure, which may
be due to the relatively more delocalized character of the
triplet state with respect to its singlet counterpart. In particular
the through-the-space delocalization may be efficient in this
case, as shown by PDI values.
The case of PAHs and their dicationic forms
According to Clar’s concept both in naphthalene and anthracene
all rings can be classified as those with migrating Clar’s sextets.
This is very well reflected by the values of aromaticity indices
collected in Table 1. The removal of two electrons from such a
polycyclic system may lead to two situations. Namely, it may
lead to full localization of the six electrons within some of
the rings, which will result in the asymmetry in p-electrondistribution within the molecule, or else it may lead to equalized
reduction in p-electron distribution in the molecule, which in
turn should appear as a uniform reduction of the delocalized
character of all rings. The latter situation takes place in the
case of naphthalene dications. Clearly both rings reflect
uniformly lower aromatic character with respect to the neutral
parent molecule. Thus, the possible structure with one ring
containing a p-electron sextet and the other ring formally
possessing only two p-type electrons is less favoured with
respect to the structure with the deficit of p-type electrons
distributed equally on two rings. These observations are more
or less the same for both singlet and triplet states. It is also
worth mentioning that both singlet and triplet states are fully
planar and that the singlet state is energetically more stable
than the triplet state by about 11 kcal mol�1. The latter
observation cannot be explained solely on the basis of
delocalization degree since although HOMA points to the
singlet as being more delocalized, electron density based
indices show an opposite result.
Interestingly, a significantly different situation can be
noticed in the case of anthracene and its dicationic forms. In
the singlet state structure the removal of two electrons results
in an increase of delocalization within both lateral rings.
Simultaneously the aromatic character of the inner ring
becomes significantly reduced. (The only exception is the
PDI index, which, as distinct from the rest of indices, shows
slightly lower aromatic character of lateral rings with respect
to neutral anthracene, but still much more delocalized than the
inner ring.) Remarkably, in singlet state doubly charged
anthracene the degree of delocalization in lateral rings is close
to that observed for lateral rings in neutral phenanthrene.
Therefore, it can be stated that in doubly charged anthracene
in the singlet state we have two Clar’s sextets localized within
two lateral rings separated by the inner ring which has the
deficit of p-electrons. Scheme 4 illustrates this situation.
Therefore, as shown in Scheme 4, although anthracene
partially loses stability due to its double ionization, it gains
two localized Clar’s sextets, which may result in its relatively
greater energetic stability with respect to its doubly charged
triplet state counterparts. When forcing the triplet state
structure, the loss in energy by around 23 kcal mol�1 can be
observed.
As it was mentioned earlier, in neutral phenanthrene there
are two Clar’s sextets localized in lateral rings separated by the
ring possessing a localized double bond. In such a case the
double ionization may proceed via removal of two electrons
from the rings with localized Clar’s sextets or from the ring
with the localized double bond. The more stable dicationic
form is that of the singlet state. Since all aromaticity indices
reveal that in this structure the lateral rings are more aromatic,
it can be concluded that double ionization proceeds via
removal of two electrons from the inner phenanthrene ring.
This is accompanied by the elongation of the C9–C10 bond
from 1.357 A in neutral phenanthrene to 1.445 A in its singlet
state dication. The double ionization of phenanthrene is
illustrated in Scheme 5.
Scheme 4
Scheme 3
Scheme 5
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Therefore, both in neutral phenanthrene and its singlet state
dication there are two Clar’s sextets localized in lateral rings.
When this topologically favourable situation is disturbed and
the triplet state structure in dicationic form is forced, the loss
of energy by about 2.13 kcal mol�1 is observed.
It was well proven, both experimentally and theoretically,
that phenanthrene is relatively more stable than anthracene
and that this energy relation is connected with the more
favourable p-electron structure in the former (see e.g. ref. 11
and references therein). In accordance with Clar’s concept this
energy relation can be explained by the presence of two
localized sextets in phenanthrene and only one migrating
sextet in anthracene. Our calculations reveal that neutral
phenanthrene is by 5.11 kcal mol�1 more stable than its
straight counterpart, which is very close to the values reported
by other authors (see ref. 11 and references therein). However,
in the case of singlet state dicationic structures the situation is
reverse with the anthracene dication being more stable by
around 16.42 kcal mol�1 in comparison with the phenanthrene
dication. However, as distinct from neutral anthracene and
phenanthrene, in both dicationic systems there are two Clar’s
sextets localized in lateral rings separated by the ring formally
possessing the deficit of p electrons (see Schemes 4 and 5). It
seems that as concerns the lateral rings, those in anthracene
dication are slightly more aromatic. This would explain why
this analogue is relatively more stable. Also, in anthracene
there are no H� � �H steric (repulsive) interactions, which in the
case of phenanthrene dications may partly destabilize the
molecular system (e.g. ref. 11 and references therein). (It is
worth to mention that some authors considered the above-
mentioned H� � �H interactions as the stabilizing ones. See
ref. 59 for more information.) Note that in the case of triplet
state structures again the phenanthrene analogue is more
stable. The energy difference is close to that in neutral species,
being equal to 4.27 kcal mol�1.
According to Clar’s concept in neutral triphenylene the
inner ring is empty whereas all three lateral rings contain
localized Clar’s sextets. All aromaticity indices illustrate this
situation very well (see Table 1). Therefore, it could be
expected that the ionization will proceed via the removal of
p-electrons from lateral rings. In fact, both in singlet and
triplet state dications the reduction of the aromatic character
(in comparison with the neutral parent molecule) can be
observed. However, in the singlet state structure there is clear
asymmetry in distribution of local aromaticity, which suggests
that in this case one of lateral rings is no more the one with the
localized sextet, but the one with four p-electrons (two
localized double bonds) while the two remaining lateral rings
can still be considered as those possessing Clar’s sextets.
This (as it seems, unfavourable) situation is reflected by the
significantly lower aromatic character of one of lateral rings
and the nonaromatic or even antiaromatic inner ring (see
Scheme 6 and data in Table 1).
It is worth noting that according to HOMA and its two
components the antiaromatic character of the inner ring
results in this case mostly from the bond elongation, but not
necessarily from the differences in bond lengths. More uniform
distribution of aromatic properties can be found in the triplet
state dication. Interestingly, in this case even the inner ring
gains relatively high aromatic character. This could be
connected with the delocalization along the peripheral sequence
of bonds predominating over the localization of Clar’s sextets.
The HOMA value estimated for all 18 peripheral bonds is
0.809, which is even larger than the values estimated for
individual rings. In consequence, the more stable dicationic
structure is that of the triplet state, since generally more
aromatic character of four rings can be noticed in this case.
Summarizing this part of the discussion it can be said that
Clar’s concept of the aromatic p-electron sextet can success-
fully be applied to all singlet state structures dications.
However, this concept cannot be directly applied to triplet
state counterparts, at least not to the systems investigated
here. This observation will also be true for other dicationic
forms of PAHs, since all types of rings (in accordance with
Clar’s concept) were taken into account and all topological
situations in larger PAHs will just be a combination of the
situations present in the systems investigated here.
Furthermore, the dependences between the values of
aromaticity indices used in the present studies are worth
considering. In Fig. 1 there are diagrams showing graphical
relations between the discussed values. More detailed graphical
representations can be found in the ESIw associated with this
article (Fig. S1–S3). Additionally, the correlation coefficient
matrices are given in Tables 2–5. It can be said that for neutral
PAHs the dependences are very clear and such as expected,
which is not surprising in this case. However, if we take into
account the complete set of data, including doubly charged
singlets and triplets, the interrelation is much worse. Still some
general trends can be seen, however, it cannot be said that
linear regressions were found. If we exclude the values estimated
for triplet state structures, and thus maintain neutral and
the singlet state dications, the interrelations are much more
systematic. For instance, the relation between HOMA and
FLU is practically linear with R = 0.95. This would suggest
that in the case of triplet state structures the character of
delocalization differs from that in closed shell systems.
An interesting general observation can be made on the basis
of NICS values. Namely, it can be observed that for all singlet
state dications the values are systematically significantly
positive, thus showing strong antiaromatic character of the
species under consideration. However, when coming from
singlet state dications to triplet state dications, the values
become systematically negative, which suggests rather aromatic
character of triplet state structures. This observation is in
agreement with earlier observations performed for 4n p-electronannulenes60 for which it was found that the partially aromatic
character can be observed for triplet state structures, despite
the fact that as 4n p-electron systems they are antiaromatic in
Scheme 6
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11982 Phys. Chem. Chem. Phys., 2011, 13, 11976–11984 This journal is c the Owner Societies 2011
the closed shell ground state. According to NICS measure of
aromaticity the 4n p-electron singlet states are antiaromatic
and 4n p-electron triplet states seem to be partially aromatic. It
should be noted that this conclusion cannot be transferred to
the results obtained with the use of the rest of aromaticity
indices. Additionally, the overestimated values of NICS found
for an inner anthracene ring should be noted (this fact was
already reported and explained in the literature),7,9,61,62 since
corresponding values seem to be overestimated also for
anthracene dicationic counterparts.
Fig. 1 Diagrams with interrelations between selected aromaticity indices. Circles correspond to neutral PAHs, rhombuses to singlet state
dications, empty triangles to triplet state dications. For more detailed graphical representations produced for all aromaticity indices see ESIw,Fig. S1–S3.
Table 2 Correlation matrix for aromaticity indices—the case of neutral PAHs
HOMA EN GEO PDI FLU HRCP � 103 NICS NICS(1) NICS(1)zz
HOMA 1.000EN �0.951 1.000GEO �0.641 0.371 1.000PDI 0.975 �0.898 �0.695 1.000FLU �0.960 0.827 0.828 �0.960 1.000HRCP � 103 0.934 �0.912 �0.538 0.967 �0.871 1.000NICS �0.770 0.808 0.305 �0.664 0.664 �0.678 1.000NICS(1) �0.772 0.801 0.328 �0.663 0.674 �0.672 0.998 1.000NICS(1)zz �0.790 0.835 0.300 �0.701 0.677 �0.735 0.994 0.990 1.000
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This journal is c the Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 11976–11984 11983
Conclusions
It has been demonstrated that the concept of aromatic
p-electron sextet proposed by Erich Clar can successfully be
applied to dicationic forms of polycyclic aromatic hydro-
carbons, but only in the case of singlet state structures. In
the case of triplet state structures Clar’s concept fails, which
shows a different character of delocalization from that in
neutral PAHs. On that basis the properties connected with
local aromaticity of such charged species can be explored with
the use of Clar’s concept. Such a conclusion was drawn based
on several aromaticity indices applied to neutral and charged
species. The different character of triplet state aromaticity is
additionally confirmed by the fact that there is no clear
relation between the values of aromaticity indices when all
systems are considered. However, if the data corresponding to
triplet state structures are excluded, the interdependence
between aromaticity indices becomes such as expected.
Acknowledgements
Calculations using the Gaussian09 set of codes were carried
out in Wroc"aw Centre for Networking and Supercomputing
(http://www.wcss.wroc.pl) and Academic Computer Centre
CYFRONET in Cracow (www.cyf-kr.edu.pl). Access to
HPC machines and licensed software is gratefully acknowledged.
References
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Table 3 Correlation matrix for aromaticity indices—the case of all systems investigated
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HOMA EN GEO PDI FLU HRCP � 103 NICS NICS(1) NICS(1)zz
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