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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This journal is c the Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 11976–11984 11977

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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11978 Phys. Chem. Chem. Phys., 2011, 13, 11976–11984 This journal is c the Owner Societies 2011

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 5 Correlation matrix for aromaticity indices—the case of triplet state charged PAHs

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