Ring currents in silicon tetramer (Si4, Si42+) and planar tetracoordinate carbon doped cluster Si4C2+: σ versus π aromaticity

Chemical Physics Letters 608 (2014) 255–263

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Chemical Physics Letters

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Ring currents in silicon tetramer (Si4, Si42+) and planar tetracoordinate

carbon doped cluster Si4C2+: r versus p aromaticity

http://dx.doi.org/10.1016/j.cplett.2014.05.0980009-2614/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Fax: +32 16 32 79 92.E-mail address: [email protected] (M.T. Nguyen).

Nguyen Minh Tam a,b, Hung Tan Pham a, Minh Tho Nguyen b,⇑a Institute for Computational Science and Technology (ICST), Quang Trung Software City, Ho Chi Minh City, Viet Namb Department of Chemistry, University of Leuven, B-3001 Leuven, Belgium

a r t i c l e i n f o a b s t r a c t

Article history:Received 7 April 2014In final form 26 May 2014Available online 6 June 2014

We revisited the aromaticity of silicon tetramer Si4, Si42+ and isoelectronic four-membered rings without

and with a planar tetracoordinate carbon dopant (Si4C2+). Electron localizability indicators and magneticring currents were used to probe bonding patterns. Comparison with Al4

2�, Si2Al2, Al4C2� and Si2Al2C wasperformed. The 14 (Si4

2+), 16 (Si4) and 18 (Si4C2+) valence electrons systems exhibit diatropic ring current,but this is determined by r electrons. Electrons in p orbitals do not significantly take part in the diatropicmagnetic response which determines aromaticity. These clusters can thus be regarded as r-aromaticspecies and do not follow the classical Hückel rule.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

There has been continuing interest in small silicon clusters,mainly due to the intensive searches for building blocks to be usedas assemblies forming new types of optoelectronic nanomaterialsand semiconductor devices [1–4]. A deep understanding of theirgeometrical and electronic properties is a necessary prerequisitefor the design of desired compounds. In addition, the simplest sil-icon clusters are also of astrophysical interest as Si3 was detectedin the absorption and emission spectra of carbon stars and comets[5].

It is well established that the chemical bonding phenomena inthe compounds containing carbon and silicon, both lighter ele-ments of the group IV, are basically different from each other.The simplest clusters, namely the trimers X3 and tetramers X4

(X = C, Si), form a set of representative examples illustrating asharp difference between the elements across the Periodic Table.Of the pair of trimers C3/Si3, C3 exhibits a singlet linear structure(X1R+

g) which is located at 1.91 eV (16930 cm�1) below the tripletlinear a3Pu state [6], whereas Si3 is strongly bent in two quasi degen-erate low-spin 1A1 (C2v) and high-spin 3A2

0 (D3h) states [7–10].An opposite situation holds for the pair of tetramers. The singlet

state of the rhombic C4 cycle (D4h, 1Ag) was found to be nearlyisoenergetic with the corresponding triplet linear state (D1h,3R�g ) [6]. On the contrary, both lowest-lying singlet and triplet statesof Si4 have a rhombic shape, but the low spin state is calculated to

be �0.9 eV lower in energy than the triplet counterpart, making itbeyond any doubt the ground state of Si4 [11].

Regarding the electronic structure, the singlet Si3 ring has beenshown to be non-aromatic, whereas interaction with a proton or aLi+ cation (Si3Li+) renders it anti-aromatic [10]. The chemical bond-ing of the silicon tetramer in different charge states has also beenthe subject of a previous theoretical study [12]. Using molecularorbitals (MO), the authors [12] argued that the neutral rhombicSi4, which has 16 valence electrons, is a r-anti-aromatic and p-aro-matic system. The Si4

2+ dication, which possesses 14 valence elec-trons and is thus isoelectronic with the Al4

2� dianion, wasaccordingly assigned to have multiple aromaticity with a p-aroma-ticity and a double r-aromaticity. For its part, the 18 valence elec-trons Si4

2� dianion was found to exist in either an anti-aromaticparallelogram or an aromatic butterfly structure, both having com-parable energy content [12].

The chemical bonding of Al42� and similar compounds has been

in the last decade the subject of continuing debate. This dianion,which is unstable with respect to electron detachment, is consid-ered as a prototype for all-metal aromatic clusters [13,14].Although there is now a large consensus on this property, twomain different points of view emerged on its characteristics. Thefirst view is that Al4

2� has a threefold (p and double r) aromaticity[13,15–17], whereas in the second view, such an aromatic charac-ter should solely be attributed to the r electrons [18–22]. Themain argument for the former view is that when evaluating thearomaticity of a molecule, the contributions of all delocalized elec-tron systems should be considered. More than one independentdelocalized electron type can simultaneously satisfy the electroncounting rule, and thereby lead to multiple-fold aromaticity [16].

(a) Si42+ (D4h,

1A1g) (b) Si4 (D2h,1Ag)

V(Si)=2.3

V(Si)=2.3V(Si,Si)=1.5

V(Si)=1.8

V(Si,Si)=1.7

Figure 1. The ELI-D plots (at isosurface = 1.5) of both (a) Si42+ (D4h, 1A1g) and (b) Si4

(D2h, 1Ag). Electron populations are computed using B3LYP/6-311+G(d) densities.

256 N.M. Tam et al. / Chemical Physics Letters 608 (2014) 255–263

In the second point of view, consideration of all delocalized p andr electrons is also put forward, but their presence, as indicated bycanonical MOs, should only be regarded as a necessary conditionand not a sufficient condition for aromaticity [22]. Accordingly,the sufficient condition is an effective contribution of the relevantdelocalized MOs to the molecular ring current, which is a magneticresponse of the molecule considered. The delocalized electronsshould thus be able to contribute to the diamagnetic ring current

Figure 2. Current density maps of Si

[22–24]. In the case of Al42�, the two p electrons in the orbital

1a2u (D4h) were found to make no, or very small, contribution tothis defining magnetic property. The delocalized r electrons(paired in the orbitals 2a1g, 1b2g and 1b1g) sustain a great dealthe molecular diatropic ring current [18,22,25–27]. It has beendemonstrated that 85% fraction of the diatropic ring current ofAl4

2� is transported by r electrons and 15% by p electrons [25].On the basis of such low magnetic activity of its p electrons, Al4

2�

has been considered as a r-aromatic species [18,22,25].In view of the fact that the silicon dication Si4

2+ is not only iso-electronic with Al4

2� but also has the same squared geometry, alegitimate question arises as to whether they also exhibit a similarbonding pattern. We recently found that Si4 constitutes an inter-esting framework which can be further stabilized upon doping.The Si4C2+ dication, which is formed by doping a carbon atom atthe centre of the squared Si ring, was found to be a stable structurecontaining a planar tetracoordinate carbon (ptC) atom [28]. Thelatter dication, which is isovalent with the dianion Si4

2�, has 18valence electrons with the following electron shell configurationof [1S21P4

x,y2S21D21P2z2P2

x,y1D2]. Its HOMO, being the 1D orbital ofthe electron shell model, is a bonding orbital arising from ligand–ligand interaction and plays a key role in maintaining the planarityof the doped pentatomic dication Si4C2+. The ptC entity can subse-quently be extended by adding two Si2 molecules making the cube

4, Si42+ and Al4

2� (B3LYP/cc-pVTZ).

N.M. Tam et al. / Chemical Physics Letters 608 (2014) 255–263 257

Si8C2+, which turns out the be a global minimum with peculiar fea-ture of a cubic bonding [29]. Perhaps a more practical way of stabi-lizing the ptC is to combine the cation Si4C2+ with the Zintl ion Si5

2�

yielding a stable Si9C cage in the neutral form [28]. In order to obtaina deeper understanding of this chemical bonding phenomenon, weset out in the present theoretical work to reinvestigate the silicontetramer Si4 and its doubly charged derivatives Si4

2+ and Si42�. We

perform a comparative analysis of the isoelectronic systems Si42+,

Al42� and Si2Al2 and Si2Ga2 that all have 14 valence electrons. The

doped pentatomic 18 valence electrons systems including Si4C2+

and Al4C2� are also examined. We thus pay a particular attentionto the identity of the aromaticity in these systems.

2. Computational methods

All electronic structure calculations are carried out using theGAUSSIAN 09 [30] suite of programs. Geometry optimizations andharmonic vibrational calculations are performed using densityfunctional theory with the hybrid B3LYP functional which has beenshown to behave well for silicon clusters [31] in conjunction withthe 6-311+G(d) basis set. For an analysis of the electronic distribu-tion, we make use of canonical MOs, and electron localizability

Figure 3. Current density maps from all valence o

indicator (ELI-D) [32] maps, as well as the ring current approach[33,34] along with the ipsocentric model [35–37]. The magneticresponses are computed using the Gamess-UK program [38]. Cal-culations of the ring current are carried out using the CTOCD-DZmethod [34] implemented in the SYSMO program [39] which isconnected to Gamess-UK. Previous study [36] demonstrated thatfor second-row atoms such as Si, reduced size basis sets tend tooveremphasize diamagnetism. Therefore, we use the correlationconsistent cc-pVTZ basis set which contains 4f Gaussian functionsin order to get more accurate ipsocentric current densities. We plotthe ring current maps using the 6-31G(d), 6-311+G(d) and cc-pVTZbasis sets. The results obtained using these basis sets emphasizesome small variations in the intensities of the currents, but themain conclusions about the magnetic properties, in particular thedirection of the density currents remain valid when using thesmaller basis set. We use both HF wavefunctions and DFT (B3LYPfunctional) densities to compute the ring currents [18]. The useof HF or DFT densities does not change the current patterns. Unlessotherwise stated, the maps reported in this Letter are constructedusing B3LYP/cc-pVTZ densities. We plot the ring current maps inthe molecular plane of each system considered because the aro-matic character of a molecule is mainly determined in this plane.

ccupied orbitals of Si42+ (D4h, B3LYP/cc-pVTZ).

258 N.M. Tam et al. / Chemical Physics Letters 608 (2014) 255–263

3. Results and discussion

3.1. Structure of the tetramer Si4 and its dication Si42+

Preparation and spectroscopic characterization of Si4 were car-ried out in a number of experimental studies. Infrared [40], Raman[41,42] and electronic absorption [42] spectra of the neutral tetra-mer were recorded and well interpreted. Thermochemical param-eters including the total atomization energy and heat of formationof Si4 were also determined [9,11,43]. Si4 was also produced on aninert surface [44].

Geometries and vibrational parameters of silicon tetramer werewell determined and abundantly discussed in the literature[9,11,12]. As stated above, the main geometrical characteristic ofSi4 is that it has a rhombic shape (D2h) in both singlet and tripletstates, which basically differs from the linear homologue C4. Forthe purpose of comprehension, let us briefly consider its geometricfeatures.

Si4 could a priori has a squared form. However, a squared Si4

with optimized Si–Si bond distances is not a stationary point inthe singlet energy surface. In the triplet state [3A1g�...(6eu)2] thesquared form becomes a first-order saddle point with one imagi-nary vibrational frequency (b2u mode). The squared singlet state1A1g is obviously unstable due to the fact that the degenerate fron-tier orbital is occupied only by two electrons (6eu)2, and thereforeits structure is subjected to a Jahn–Teller effect. This effect is

Figure 4. Current density maps from all valence o

operative in splitting the D4h eu orbital to give rise to an energeti-cally more stable rhombic form. The resulting D2h structure has Si–Si bond distances of 2.33 Å. The D2h HOMO (b1u)2, whose shape issimilar to that of the D4h eu orbital, is now stabilized by �1.7 eVupon geometry relaxation. The Jahn–Teller splitting of the relevantMOs in going from D4h to D2h structure is illustrated in Figure S1 ofthe Supplementary Information (ESI) file.

The rhombic D2h form remains the lowest-lying in the Si4 tripletstate 3B3u: [....(b1u)1(b2g)1]. The Si-Si distances are slightly short-ened upon excitation (being now 2.29 Å). The singlet–triplet sepa-ration gap of Si4 is calculated at �20 kcal/mol (B3LYP/6-311+G(d)+ZPE). Such a gap is quite large as compared to the degen-eracy of both states of Si3 (see above).

Removal of one electron from, or addition of one electron to Si4,is expected to keep the rhombic structure, yielding the groundstate 2B1u for Si4

+ and 2B2g for Si4� [9]. Removal of two electrons from

the D4h Si4 yields the dication Si42+ in which the degenerate 6eu

orbital becomes empty. As a consequence, the squared planarstructure is no longer affected by a Jahn–Teller distortion, andthe 1A1g (D4h) is now the lowest-lying structure of the dication,having comparable Si–Si bond lengths of 2.31 Å. Due to the factthat the 6eu orbital becomes now the LUMO of Si4

2+, excitation tothe triplet manifold induces a Jahn–Teller stabilization to a rhom-bic form. The resulting 3B2g [....(b3u)1(b1u)1] state of the dication haslonger Si-Si distances of 2.45 Å. The singlet–triplet energy gap ofSi4

2+ amounts now to �16 kcal/mol (B3LYP/6-311+G(d)+ZPE).

ccupied orbitals of Si4 (D2h, B3LYP/cc-pVTZ).

Table 1The values of jmax (a.u.) related to the ring currents of some structures considered (HF/cc-pVTZ).

Structure jmax Total jmax r-Electrons jmax p-Electrons

Si4 0.12 0.11 0.01Si4

2+ 0.08 0.07 0.01Al4

2� 0.05 0.05 0.00Si4C2+ 0.05 0.17 0.02Al4C2� 0.05 0.06 0.02

N.M. Tam et al. / Chemical Physics Letters 608 (2014) 255–263 259

Let us now analyze in some detail the electron distribution inboth Si4 and Si4

2+. Figure 1 displays the ELI-D plots for both species.The ELI-D is a simple measure of the electron localization in amolecular system and thus gives information about the molecularspaces, called basins, where electrons are likely to occupy. It is use-ful to address localization domains which correspond to bonds orlone pairs. The ELI-D description of the bonding is quite compara-ble to the picture given by the electron localization function (ELF).Both localization approaches of the electron density basicallyassign a lone pair at each Si centre. Integration of the electron den-sities over the basins leads to the corresponding populations (V).Populations of the bonds V(Si,Si) are rather comparable in bothspecies, being around 1.5–1.7 electrons. It is clear that in order togenerate the dication, populations are mainly removed from Silone pairs, V(Si), by up to �0.5 electron by centre. Let us note thatin Si4 there is a population of �0.8 electron for the shorter diagonalSi–Si bond.

As both the geometry and electronic structure of Si42+ are similar

to those of Al42� [12], let us now compare their ring currents. Fig-

ure 2 displays the current density maps of the neutral Si4, dicationSi4

2+ and dianion Al42� in their molecular planes The ring current of

Figure 5. Excitation responsible for the ring current of Si42+ and Si4. Black arrows: tran

forming paratropic current.

the dianion has extensively been examined in previous reports[18–22,25]. We just reproduce it here for purpose of comparison.The ipsocentric model is usually used to evaluate the aromaticcharacter of planar compounds [36]. In the framework of thismodel, an excitation from an occupied MO to an unoccupied MOcan result in a contribution to the ring current which can be eitherdiatropic, paratropic or null. A diatropic current occurs when theproduct of symmetries of occupied and unoccupied orbitals con-tains the in-plane translational symmetry. On the contrary, a para-tropic current is produced when the product of symmetries ofoccupied and unoccupied MOs contains the in-plane rotationalsymmetry.

The electron density can be decomposed in terms of r and pelectron contributions. Figure 2 points out that the magneticresponse of Si4

2+ is basically similar to that of Al42�, in terms of elec-

tron contributions. The main difference between the ring current inboth charged species resides in the intensities of the displacement.In both squared molecules, p electrons do not (Al4

2�), or only mar-ginally (Si4

2+), contribute to the ring current, even though they aredelocalized over the whole molecule. As a matter of fact, the ringcurrent due to p electrons is equal to zero in the molecular planeof Al4

2�, but there is a small contribution from them in Si42+. The

total current density turns out to be diatropic and essentially arisesfrom contributions of delocalized r electrons.

The individual contributions of MOs can clearly be seen ininspecting Figure 3, which shows the magnetic responses arisingfrom all 14 valence electrons of Si4

2+. The p-MO a2u has no contribu-tion to total current density (as already shown in Figure 2). The rMOs eu and a1g (lower) also do not take part in the current. Onlythe three r-MOs b1g, b2g and a1g have characteristic contributionsto diatropic current density. Contributions of the a1g MO aremainly located in the central position. For purpose of comparison,

slational transitions forming diatropic current, white arrow: rotational transition

260 N.M. Tam et al. / Chemical Physics Letters 608 (2014) 255–263

orbital contributions to the current densities of Al42� are displayed

in Figure S2 of the ESI file. Again a similar pattern emerges as in thecases of Si4

2+ and Al42�.

For its part, orbital contributions shown in Figure 4 point outthat the diatropic magnetic response in the 16 valence electronSi4 comes from contributions of r electrons, again without signif-icant contributions from p electrons.

Table 1 summarizes the jmax values [45] of the ring currents indifferent systems. This quantity is a measure of the maximumstrength of the current per unit inducing field. For example, a valueof jmax = 0.077 was determined for the total p-electrons of benzene[45]. By definition, the larger the jmax value, the more delocalizedthe electrons, and thereby the stronger the current, irrespectiveof the direction of the current. Accordingly, we could only comparethe jmax values for the same magnetic current, either diatropic orparatropic.

Two main results emerge from Table 1. In each molecule, thestrength of the r-electrons is consistently much larger than that

Figure 6. The current density maps of Si4C2+, Al4C2� and Si42� having 18 valence

of the p-electrons. When considering the total jmax(total) valuesfor the diatropic current, it appears that the Si4 molecule turnsout to be an aromatic species, whose strength is even larger thanthat of Si4

2+ and Al42�.

Figure 5 schematically illustrates the electron excitationsresponsible for the ring currents in Si4 and Si4

2+. The model basedon orbital contributions gives a plausible explanation for magneticresponses in both situations. In Si4, three excitations are allowedby a translational transition T(x,y) (see also Figure 3). There is alsoone rotational transition. The ion Si4

2+ has three allowed transla-tional transitions from the HOMOs to the LUMO. In both casesthe translational excitations lead to a total diamagnetic currentdensity (Figure 3).

In the CTOCD-DZ method [34], the energy gap between bothMOs involved in the allowed transition appears in the denominatorof the main wavefunctions. Therefore, the smaller this energy gap,the stronger the current intensity. The energy separation betweenboth a1g (occupied) and eu (unoccupied) of Si4

2+ (Figure 5) is calcu-

electrons (B3LYP/cc-pVTZ). Si42� has a hypothetical D4h geometry (see text).

Figure 7. Excitations from occupied to vacant MOs of Si4C2+ (18 valence electrons).Black arrows: translational transitions; white narrow: rotational transition.

N.M. Tam et al. / Chemical Physics Letters 608 (2014) 255–263 261

lated to be �7 eV (HF/cc-pVTZ). The gap for the translationallyallowed transition between the ag (occupied) and b2u (unoccupied)orbitals of Si4 (Figure 5) amounts to �4 eV at the same level. This isconsistent with the jmax values listed in Table 1, that also show astronger current of the neutral Si4.

Let us note that the current density maps mainly convey qual-itative information about aromaticity, whereas the jmax valuesare a more quantitative criterion. Of the latter, the current suscep-tibility [26] could also be used to quantitatively measure thedegree of aromaticity.

3.2. Structure of Si42� and the doped dication Si4C 2+and dianion Al4C2�

The electronic and molecular properties of silicon clusters areknown to basically be modified following doping [46]. We recentlyfound that the dication Si4C2+ also exhibits in its most stable con-figuration a squared planar form in which the carbon dopant issimply inserted at the centre of the Si4 square [28]. This gives riseto a typical structure for a planar tetracoordinate carbon atom(ptC). It is therefore of interest to compare the bonding in somedoped systems generated from the tetratomic framework. In addi-tion to Si4C2+, we also consider the dianion Al4C2�. Both species areisoelectronic with the dianion Si4

2�.The electron distribution of Si4C2+ has been analyzed in detail in

our recent Letter [28]. Here we supplement the information by per-forming the magnetic response. The ELF plots [28] pointed out thatelectrons in Si4C2+ are largely delocalized over the entire skeleton.It is also characterized by localized C–Si bonds (up to 1.8 electrons)and lone pairs centered at Si atoms. A large accumulation of elec-tron densities on lone pair regions (up to 2.6 electrons at each Silone pair). This suggests that both ligand–ligand (Si–Si) and cen-ter-ligand (C–Si) interactions are important to maintain the planar-ity of Si4C2+ and thereby a ptC atom. The dianion Al4C2� also has aD4h shape enclosing a ptC. For the sake of comparison, Si4

2� is con-sidered here in a hypothetical D4h geometry.

Figure 6 displays the ring current maps of three 18-electronsspecies considered. The squared Si4

2� results in a paratropic ringcurrent in both r electrons and total current densities (computedusing HF/cc-pVTZ). Its electrons occupying the p MOs do not takepart in the magnetic response. Addition of a C atom at the centerof a D4h Si4

2+ or Al42� ring induces a clear-cut diatropic ring current

in both resulting pentatomic clusters Si4C2+ and Al4C2�. Again, onlyr electrons are magnetically active, and no significant current den-sity is detected from delocalized p MOs. The excitations responsi-ble for the magnetic response is illustrated in Figure 7. The twoallowed translational transitions from b1g and b2g to eu and a rota-tional transition from eu to eu lead to diatropic and paratropic cur-rent densities, respectively. Accordingly, the total current densitycould be either diatropic or paratropic. In this case, the diatropiccurrent becomes dominant. Both pentatomic ions have thus an raromatic character.

Concerning jmax values of both ptC species listed in Table 1, thejmax(total) turns out to be smaller than the corresponding jmax(r)value. This indicates that there is in both Si4C2+ and Al4C2� a para-tropic contribution from p electrons to the total current (jmax(p)having a different sign) which thereby induces a partial cancella-tion of the jmax(total) value.

3.3. Structure of the mixed neutral Si2Al2 and doped Si2Al2C clusters

Let us now consider some additional four-membered ringsbased on a neutral Si2Al2 framework which is isoelectronic withSi4

2+. As for additional cases, they are mainly based on qualitativeaspects of the ring current maps. Both isomers t-Si2Al2 (Al-Si-Al-Si ring) and c-Si2Al2 (Si-Si-Al-Al ring) are considered (Figure 8).Doping of carbon atom at the center of each neutral ring again

leads to a planar pentatomic Si2Al2C cluster. The aromatic charac-ter of the mixed Si2Al2 cluster has been probed in previous studies[47,48]. Figure 8 displays the ring current maps computed for Si2-

Al2 and Si2Al2C. The main characteristic is again marked by theabsence of meaningful magnetic response arising from electronspaired in p orbitals, even though all the rings exhibit a diatropiccurrent. This again makes them r-aromatic species.

Figure S3 of the ESI file displays the ring current maps of somefour-membered systems without and with a doped C atom, includ-ing the pairs Si2Ga2 and Si2Ga2C; Al2Ge2 and Al2Ge2C. On the basisof their magnetic responses, they can all be classified as raromatic.

4. Concluding remarks

In this theoretical study we revisited the chemical bonding andin particular the aromatic features of the silicon tetramer Si4 andSi4

2+, along with some isoelectronic four-membered rings withoutand with the presence of a carbon atom. We used the electronlocalizability indicator (ELI-D) and the magnetic ring currents toprobe the bonding patterns. A comparison between the dicationSi4

2+ and the prototypical Al42� (14 valence electron species), as well

as between the carbon doped Si4C2+ and Al4C2� (18 valence elec-tron systems) was performed. The Si4 (16 valence electrons) andthe mixed Si2Al2 and Si2Al2C clusters were also examined.

A consistent picture which emerges from our results is that the14, 16 and 18 electrons systems exhibit an aromatic character, butthis is essentially determined by contribution of r electrons. Theelectrons located in p orbitals do not significantly take part inthe magnetic response. Accordingly, the four-membered squaredSi4

2+ and the doped Si4C2+ cluster can best be regarded r aromaticspecies. Our analysis has not detected a multiple-fold aromaticity

Figure 8. The current density maps of Si2Al2 (14 valence electrons) and Si2Al2C (18 valence electrons) (B3LYP/cc-pVTZ). Black square indicates a Si atom and black circlestands for Al. A carbon atom is always located at the center of each ring.

262 N.M. Tam et al. / Chemical Physics Letters 608 (2014) 255–263

in these species. For its part, the singlet tetramer Si4, having 16valence electrons, is equally shown to be a r-aromatic four-mem-bered ring and this does not follow the classical Hückel countingrule.

Overall, the present study provides a further support for thepoint of view that the existence of delocalized occupied molecularorbitals in a planar molecule is a necessary but not sufficient con-dition to assign a certain aromatic character (aromatic, non-aro-matic or anti-aromatic) to that specific type of electrons.Different criteria need to be considered for a more consistent eval-uation of this popular but intriguing molecular property.

Acknowledgments

The authors are grateful to the Department of Science and Tech-nology of Ho Chi Minh City, Viet Nam, for granting major researchprojects at ICST. MTN is indebted to the KU Leuven Research Coun-cil for continuing support (GOA and IDO programs). We greatly

appreciate the help of Dr. Remco Havenith for allowing us plottingthe ring current maps using his computers at the University ofGroningen, The Netherlands.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.cplett.2014.05.098.

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