Journal of Molecular Structure: THEOCHEM 943 (2010) 23–31

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Journal of Molecular Structure: THEOCHEM

journal homepage: www.elsevier .com/locate / theochem

In search of aromatic seven-membered rings q

Ling Lin a,c, Peter Lievens b,c, Minh Tho Nguyen a,c,*

a Department of Chemistry, Katholieke Universiteit Leuven, B-3001 Leuven, Belgiumb Laboratory of Solid State Physics and Magnetism, Katholieke Universiteit Leuven, B-3001 Leuven, Belgiumc Institute for Nanoscale Physics and Chemistry (INPAC), Katholieke Universiteit Leuven, B-3001 Leuven, Belgium

a r t i c l e i n f o

Article history:Received 20 June 2009Received in revised form 2 September 2009Accepted 2 September 2009Available online 6 September 2009

Keywords:Seven-membered ringsSigma aromaticityElectron localization functionGold clusterSilver cluster

0166-1280/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.theochem.2009.09.004

q Paper submitted for the Journal of Molecular StrIssue on ‘‘Conceptual Insights from Density Functiona

* Corresponding author. Address: Institute for Nano(INPAC), Katholieke Universiteit Leuven, B-3001 Leuv

E-mail address: minh.nguyen@chem.kuleuven.be (

a b s t r a c t

A theoretical search for aromatic seven-membered rings has been carried out using density functionaltheory calculations with the B3LYP functional. The rings considered include the C7H7

+ cation and its het-ero-derivatives by replacing C, CH or CC units by B, Al, Ga, Si, Ge, N, P, As and BN group, the B8

2� dianion,the CB7

� anion, the neutral S3N4 ring and its derivatives by substituting one or two N atoms by CH group,the S4N3

+ cation and the all-metallic cycles M73� and M7T with M = Cu, Ag, Au and T = Y, Sc. Most mole-

cules studied have planar structure in their electronic ground state. Vibrational spectra of some deriva-tives are plotted. Nucleus independent chemical shift (NICS) indices show that the parent molecule C7H7

+

has a higher degree of aromaticity than its derivatives. Substitution of N in S3N4 by CH marginally influ-ences the aromaticity in such a way that S3N4, S3N3(CH) and S3N2(CH)2 are similarly aromatic. The B8

2�

dianion and both D7h and C2v isomers of CB7� possess comparable aromatic character. As for the all-metal

clusters Cu73�, Ag7

3�, Au73�, Cu7Sc, Cu7Y, Ag7Y and Au7Y, the binary clusters become more aromatic than

the pure metal anions, and are thus characterized by r-aromaticity.� 2009 Elsevier B.V. All rights reserved.

1. Introduction

Aromaticity, which is beyond any doubt one of the most funda-mental and popular concepts in chemistry, is widely employed andsuccessfully applied in many areas to interpret and predict themolecular structure, electronic and thermodynamic properties, aswell as chemical reactivities of cyclic compounds [1]. The higherthermodynamic stability of planar aromatic rings is usually ratio-nalized in terms of the number of delocalized electrons which sat-isfy the classical (4n + 2) Hückel rule. Although this was originallyderived for organic p-delocalized rings, its applicability was laterextended to r- and also multiply r-, p-aromatic systems [1b,2].More recently, the concept of aromaticity was applied to planar cy-cles formed by metallic elements [3] but its origin and characterremain a matter of discussion [1a,4] as these cycles could be con-sidered as either p- or r-aromatic or both. This concept can also beapplied to three-dimensional cage-shaped atomic clusters [5]. Sim-ilar to the planar rings, a closed electronic shell (or subshell) oftenmakes a cage aromatic according to the large negative NICS valueat the center of the cage [5]. In the case of icosahedral cage-shaped

ll rights reserved.

ucture – THEOCHEM Speciall Theory”.scale Physics and Chemistry

en, Belgium.M.T. Nguyen).

clusters, a closed electronic shell and aromaticity can be reached ifthe number of the delocalized electrons satisfies the 2(n + 1)2

Hirsch rule [5].As originally discovered by Kekulé from benzene, aromaticity

usually implies a stabilizing effect in organic or inorganic com-pounds that commonly involve planar six-membered rings asbuilding blocks. Aromaticity of five-membered cycles such as pyr-ole derivatives is also well established. In contrast, aromatic seven-membered rings are rather scarce. The most well known represen-tative for this class is the tropylium cation C7H7

+ 1 (cf. Chart 1)which exhibits D7h point group symmetry [6]. Replacement of aCH+ group in 1 by a BH and AlH leads to neutral C6H6BH 2 andC6H6AlH 3, respectively. Earlier molecular orbital calculations [7]showed, however, that the parent borepin 2 is planar but onlyweakly aromatic. Spectroscopic data of the substituted borepinspointed out that steric hindrance and attenuated aromatic charac-ter induce significant non-planarity of the seven-membered skele-ton [7]. More recently, the gallepin C6H6GaH 4, which is thegallium analogue of 1, has been prepared and quantum chemicalcalculations have shown that although gallepin 4 contains the ex-pected 6p-electron structure, it is even less aromatic than borepin2 [8].

Replacement of a carbon atom in the typical hydrocarbon cation1 by the heavier congeners Si and Ge leads to the silatropylium 5(C6H6SiH+) and germatropylium 6 (C6H6GeH+) cations, respec-tively. It was predicted that they are higher in energy than the

H

H

H

H

H

H

H

B

H

H

H

H

H

H

H

Al

H

H

H

H

H

H

H

Ga

H

H

H

H

H

H

H

Si

H

H

H

H

H

H

H

Ge

H

H

H

H

H

H

H

B

B

B B

B

BB

2

B

B

B

B B

B

BB

C

B

B

B B

B

BC

B

Cu

Cu

Cu Cu

Cu

CuCu

Sc

1 2 3 4 5

6 7 8 9 10

Chart 1.

24 L. Lin et al. / Journal of Molecular Structure: THEOCHEM 943 (2010) 23–31

silabenzyl and germabenzyl cations by �9 and �16 kcal/mol,respectively [9]. While D7h C7H7

+ is the global minimum on thepotential energy surface, and the nonclassical isomers have rela-tively higher energies, the nonclassical bridged isomers ofC6H6GeH+ have been found to be more stable than the seven-mem-bered counterpart. The situation of C6H6SiH+ is intermediated be-tween C7H7

+ and C6H6GeH+ in that both classical and nonclassicalisomers of C6H6SiH+ tend to have comparable energy content [9c].

The B82� anion 7 is a planar molecular wheel with D7h point

group [10], and it can be stabilized by a Li+ cation, forming a C7v

symmetric LiB8� complex [11]. Substitution of the central B� unit

of B82� by one C results in the CB7

� anion 8, which maintains theD7h symmetry [12]. Based on electron counts and analysis of thecanonical molecular orbitals, it was indicated that both of themhave a double r- and p-aromaticity, even thought that the r-aro-maticity is less pronounced for CB7

� [13]. The D7h aromatic CB7�

anion bears a heptacoordinated carbon atom [12–14] but it wassubsequently demonstrated that such a form is extremely unfavor-able, and the lowest energy isomer 9 has a C2v shape with a hepta-coordinate boron atom at the ring center and the carbon atom inthe outside ring [15].

Recently, using quantum chemical calculations, we have shownthat the bimetallic cluster Cu7Sc 10 turns out to be a planar systembearing D7h point group symmetry [16]. More importantly, Cu7Screpresents a prototype of a class of metallic clusters featuring ahigh r-aromaticity. The Cu7

3� cluster is isoelectronic with Cu7Scwith respect to the number of delocalized valence s-electrons,and it has been predicted to be similarly r-aromatic with Cu7Sc[16]. Although multiply charged anions are not electronically sta-ble, the calculations of such species do make sense due to therepulsive Coulomb barrier, which prevents the autodetachmentof electrons, as has been discussed in the case of Al4

2� [17].In view of the scarcity of this type of potentially interesting

compounds, we set out to search for the seven-membered cyclescontaining different elements that possess a relative thermody-namic stability and a certain degree of aromaticity. In addition,we attempt to probe such aromaticity using the approaches de-rived from density functional theory.

2. Computational methods

Quantum chemical calculations were carried out making useof the density functional theory with the popular hybrid B3LYP

functional [18] in conjunction with the all electron augmentedcorrelation consistent basis set aug-cc-pVTZ [19] for the non-metallic systems and aug-cc-pVDZ-PP [20] for all-metal systemsM7

3� and M7T with M = Cu, Ag, Au, T = Sc, Y, where PP standsfor an effective core potential. Harmonic vibrational frequencieswere subsequently calculated to characterize the stationarypoints located as equilibrium structures having all real vibrationalfrequencies. A scale factor of 0.9614 was used to scale the fre-quencies [21]. To facilitate comparison and to obtain a certainspectroscopic signature of the rings considered, calculated vibra-tional spectra were folded with a Gaussian line width functionof 20 cm�1 full width at half maximum. All geometry optimiza-tions were performed using the Gaussian 03 package [22]. Wehave considered a localization of the electron density in orderto identify the chemical bonds and their origin. For this purpose,we have applied the electron localization function (ELF) [23], theelectron localizability indicator (ELI-D) [24–26] and its canonicalMO decomposition (partial p-ELI-D) [27], which have been provedto be valuable tools to study the structure and bonding in mole-cules. To ensure the accuracy of basin integrations, a thresholdvalue of 10�7 has been adopted for ELF. Both the ELI-D and p-ELI-D approaches were computed using the DGrid-4.2 programsuite [28]. The isosurfaces were plotted with the graphical pro-gram gOpenMol [29]. To investigate further the electronic struc-ture of the all-metal clusters, the total and the partial densityof states (DOS, computed using the Pymolyze program [30]) werealso plotted using the densities computed at the B3LYP/aug-cc-pVDZ-PP level of theory.

To evaluate the possible aromaticity of these systems, the nu-cleus independent chemical shift (NICS) indices [1b,31], which isdefined as the negative value of the absolute shielding computedat certain point of the ring, were calculated. There has been muchdiscussion about the validity of NICS as an index for aromaticity.Recent study [16] showed that it can be used to describe this prop-erty of planar seven-membered cycles. Accordingly, a ring withlarge negative NICS value in its center is considered aromatic,and usually the more negative the NICS value the ring has, themore aromatic the ring is. Since the NICS(0) value (the referenceghost atom being put at the center of the ring) is largely influencedby the central atom of the ring, and it is also influenced by theframework, the NICS(1), NICS(2) in which the reference dummyatom is placed at 1 and 2 Å above the ring center, respectively, in-stead of NICS(0), were evaluated for some molecules. The corre-

L. Lin et al. / Journal of Molecular Structure: THEOCHEM 943 (2010) 23–31 25

sponding zz tensor gives NICS(1)zz value which has been pointedout to be a better measure of the aromaticity of a system amongthe different NICS indices [32]. The GIAO [33] method at theB3LYP level of theory was employed to evaluate all NICS values.

3. Results and discussion

3.1. Tropylium cation (C7H7+), borepin (C6H6BH), aluminepin

(C6H6AlH) and gallepin (C6H6GaH)

C7H7+ 1 (D7h) has been well characterized [6,9,34]. Its analogous

compounds such as borepin, aluminepin and gallepin are neutralderivatives in which a BH, AlH and GaH group substituting a CH+ unitwithin the cyclic framework, respectively. B3LYP/aug-cc-pVTZ cal-culations show that for all of them, the singlet state is energeticallypreferred over the triplet state. Their equilibrium structures, alongwith selected bond lengths and corresponding vibrational spectraare displayed in Fig. 1. The NICS indices and HOMO–LUMO gapsare listed in Table 1. For C7H7

+, the C–C and C–H bond distances arepredicted to be 1.392 and 1.083 Å, respectively, which are slightlydifferent from those of benzene (1.399 and 1.093 Å obtained at thesame level). The NICS(1)zz of�27.0 ppm of 1 is also similar to the cor-responding value of benzene (�29.6 ppm), implying that they aresimilarly aromatic. The HOMO–LUMO gap of 5.66 eV in 1 is smallerthan the corresponding value for benzene by �0.87 eV.

Among the isoelectronic analogues of 1, the borepin 2 has alsobeen investigated, especially about its aromaticity [7,35] whereasthe other two analogues C6H6AlH 3 and C6H6GaH 4 have receivedmuch less attention [8]. At the B3LYP/aug-cc-pVTZ level, the bond

Fig. 1. IR spectra of C7H7+, C6H6BH, C6H6AlH and C6H6GaH and their geometries with sele

light grey: H). (For interpretation of the references to colour in this figure legend, the re

lengths of C–B, C–Al and C–Ga are predicted to be 1.522, 1.926 and1.938 Å, respectively, and the C–C bonds are only marginally chan-ged upon the substitution. The NICS(1)zz for C6H6BH 2, C6H6AlH 3and C6H6GaH 4 amount to �20.5, �8.4 and �9.5 ppm, respectively(Table 1), which implies that a CH+ substitution induces a sharp de-crease of the molecular aromaticity. The NICS(0) values are onlyslightly negative, being �0.3 ppm (C6H6AlH) and �0.8 ppm(C6H6GaH), suggesting that they are rather non-aromatic. Thisarises from a difficult overlap between the 2p(C) and 3p(Al) or4p(Ga) orbitals. Such a weak orbital overlap invariably leads to aweak electronic delocalization and weak multiple bonds.

To obtain a spectroscopic signature of the rings, their infraredspectra were simulated. The vibrational spectrum of 1 has gainedmuch attention [6b–e] of both experimental and theoretical chem-ists. The four bands calculated at 639, 971, 1459 and 3059 cm�1

using the B3LYP/aug-cc-pVTZ method, can be assigned to be theC–H wagging, C–C stretching, C–H in-plane bending, and C–Hstretching, respectively. These agree well with the correspondingexperimental peaks [6c] centered at 633, 992, 1477 and3020 cm�1, and also agree with the numerous previous theoreticalstudies [6d,e]. The C–H wagging and C–H in-plane bending peaksare very intensive in C7H7

+, while they are relatively weak inC6H6BH, C6H6AlH and C6H6GaH, in which the most intensive peakscorrespond to those centered at 2471, 1857 and 1898 cm�1 ab-sorbed by B–H, Al–H and Ga–H stretching modes, respectively. Acorrespondence between the shift of these bands and the changeof the bond length (B–H: 1.196, Al–H: 1.583, and Ga–H: 1.563 Å)can be established. The C–H stretching mode is reflected in a peakat 3059 cm�1 for C7H7

+ 1. At similar positions, several peaks are

cted bond lengths (Å) calculated at the B3LYP/aug-cc-pVTZ level (heavy grey: C, andader is referred to the web version of this article.)

Table 1The NICS values (in ppm) and HOMO–LUMO gaps (in eV) of the different seven-member rings and two six member rings obtained with B3LYP method and aug-cc-pVTZ basis set(aug-cc-pVDZ-PP for the metal clusters).

Symm. NICS(0) NICS(1) NICS(2) NICS(0)zz NICS(1)zz NICS(2)zz H-L gap

C7H7+ D7h �6.0 �9.2 �5.4 �17.2 �27.0 �17.6 5.66

C6H6BH C2v �3.4 �6.8 �4.4 �10.7 �20.5 �15.0 4.76C6H6AlH C2v �0.3 �2.9 �2.5 0.7 �8.4 �9.2 4.25C6H6GaH C2v �0.8 �3.4 �2.8 1.2 �9.5 �10.6 4.33C6H6SiH+ C2v �4.6 �7.0 �4.4 �10.6 �19.5 �14.8 4.52C6H6GeH+ C2v �4.5 �6.9 �4.5 �8.8 �18.9 �15.3 4.41C6H6Si C2v �1.8 �5.5 �4.1 �6.5 �16.0 �13.2 3.21C6H6Ge C2v �1.2 �5.0 �4.0 �4.4 �14.6 �13.0 3.54C6H6N+ C2v �5.1 �9.2 �5.3 �15.8 �26.0 �16.7 4.11C6H6P+ C2v �4.8 �8.4 �5.4 �14.7 �24.3 �17.2 4.46C6H6As+ C2v �4.4 �8.0 �5.3 �12.9 �22.9 �17.2 4.25S4N3

+ C2v �9.8 �9.3 �5.4 �16.2 �24.9 �18.2 4.25S3N4 C2v �10.6 �10.0 �5.5 �21.6 �28.7 �19.2 4.35S3N3CH Cs �10.6 �9.4 �5.2 �20.0 �27.4 �19.0 4.35S3N2C2H2 C2v �10.6 �9.1 �5.1 �18.6 �26.4 �18.9 4.35C5H5BNH2

+ Cs �2.4 �5.8 �3.8 �5.5 �16.6 �12.9 4.46C3H3(BNH2)2

+ Cs 0.8 �2.5 �2.3 4.9 �7.0 �8.3 4.65CH (BNH2)3

+ Cs 0.7 �1.9 �1.6 9.0 �2.9 �6.5 5.01B8

2� D7h �24.8 �8.0 �60.1 �26.3 1.25CB7

� D7h �27.3 �7.6 �61.3 �24.1 3.59CB7

� C2v �24.6 �7.7 �58.8 �24.7 3.54Cu7

3� D7h �14.1 �12.2 �8.6 �35.7 �34.2 �28.0 0.98Cu7Sc D7h �24.3 �14.3 �46.0 �28.7 2.72Cu7Y D7h �22.6 �14.4 �64.3 �34.6 2.97Ag7

3� D7h �12.7 �11.4 �8.6 �29.6 �29.4 �26.4 0.95Ag7Y D7h �21.0 �12.6 �69.6 �33.2 2.39Au7

3� D7h �15.1 �13.2 �9.5 �32.4 �32.3 �29.0 1.28Au7Y D7h �19.9 �11.0 �55.8 �31.3 3.0C6H6 D6h �8.0 �9.8 �5.0 �16.1 �29.6 �17.4 6.53S3N3

� D3h �9.4 �6.4 �3.2 �8.5 �22.4 �15.8 3.70

26 L. Lin et al. / Journal of Molecular Structure: THEOCHEM 943 (2010) 23–31

found in the spectra of C6H6BH, C6H6AlH and C6H6GaH, whichemerge by the split of C–H stretching peak resulting from a symme-try reduction from D7h to C2v upon substitution of CH+ by BH, AlHand GaH. Band shifts also take place for other vibrational modes.

To obtain another view on the electronic distribution of 1, weperformed an ELF analysis, which is a simple measure of the elec-tron localization in molecular system [23]. The ELF isosurface andits cutplane for the C7H7

+ cation 1 are illustrated in Fig. 2. The meanelectronic populations computed for the localized basins areshown with the ELF isosurface. Our computations suggest thatC7H7

+ contains 21 basins: since the molecule is highly symmetric(D7h), the 7 CH units are equivalent, and so is the same with the7 CC units. Each C(C) basin has an electronic population of �2.1electrons. The valence basins V(CC) and V(CH) basins contain�2.6 and �2.1 electrons, respectively.

3.2. Derivatives of tropylium cation by Si and Ge

Substitution of one carbon atom of 1 with the higher congenersilicon and germanium leads to the silatropylium C6H6SiH+ 5 and

Fig. 2. Cutplane and ELF isosurface of C7H7+ (isov

germatropylium C6H6GeH+ 6 cation, respectively. Their equilib-rium structures obtained by B3LYP/aug-cc-pVTZ calculations areshown in Fig. 3. Removal of H+ from C6H6SiH+ and C6H6GeH+ willproduce the neutral dicoordinated silylene C6H6Si and germyleneC6H6Ge molecules that also bear planar seven-membered ringswith C2v point group (Fig. 3). Geometries of the neutrals are chan-ged upon deprotonation: the C–Si bond of 1.784 Å in C6H6SiH+ iselongated to 1.875 Å in C6H6Si. A similar trend is found for theGe-counterparts, namely the C–Ge bond is elongated from 1.861to 1.967 Å upon deprotonation from Ge. As stated above, the planarseven-membered rings C6H6SiH+ and C6H6GeH+ are not the moststable isomers of the relevant systems [9].

The NICS(1)zz of C6H6SiH+ and C6H6GeH+ amount to �19.5 and�18.9 ppm, respectively, which are less negative than that ofC7H7

+ (�27.0 ppm), indicating that the aromatic character of theheterosubstituted derivatives of C7H7

+ gradually decreases upondescending the rows of the main group elements, which is inaccordance to the trend in benzene [1a,36]. This fact is due tothe weak electron delocalization in Si and Ge cations [9c]. TheNICS(1)zz of C6H6Si and C6H6Ge are even less negative (�16.0 and

alue = 0.75) at the B3LYP/aug-cc-pVTZ level.

Fig. 3. Geometries of C6H6Si, C6H6SiH+, C6H6Ge, C6H6GeH+, C6H6N+, C6H6P+ and C6H6As+, C5H5(BNH2)+, C3H3(BNH2)2+, CH (BNH2)3

+, CB7�, B8

2�, S4N3+, S3N4, S3N3CH and

S3N2(CH)2 with selected bond lengths (Å) at the B3LYP/aug-cc-pVTZ level. The colors stand for: heavy grey = C, light grey = H, blue = N, pink = B, yellow = S. (For interpretationof the references to colour in this figure legend, the reader is referred to the web version of this article.)

L. Lin et al. / Journal of Molecular Structure: THEOCHEM 943 (2010) 23–31 27

�14.6 ppm), and the NICS(0) values of them are only slightly neg-ative (�1.8 and �1.2 ppm), which are similar to the cases ofC6H6AlH and C6H6GaH, indicating a very low, if any, aromaticity.

3.3. Derivatives of tropylium cation by N, P and As

The C6H6N+, C6H6P+ and C6H6As+ cations are formed by replac-ing one CH unit of C7H7

+ by the N, P and As atom, respectively. It

was not our intention to search here for the entire potential energysurface of each system. We rather considered the seven-memberedcyclic structures even though it is possible that the latter does notcorrespond to the global equilibrium structure. Their calculated C2v

geometries are displayed in Fig. 3.The NICS(1)zz values of the cations C6H6N+, C6H6P+ and C6H6As+

are �26.0, �24.3 and �22.9 ppm, respectively, which are morenegative than the corresponding values of the other derivatives

28 L. Lin et al. / Journal of Molecular Structure: THEOCHEM 943 (2010) 23–31

of C7H7+ mentioned above (Table 1). This suggests that these cat-

ions exhibit a certain aromaticity and therefore, it is worth inves-tigating in future studies the corresponding energy surfaces.These are the parents of the class of nitrenium, phospheniumand arsenium cations, that can be generated as transientintermediates.

3.4. Derivatives of tropylium cation by substitution of CC by BN unit

Derivatives of C7H7+ formed by replacing a CC unit by an iso-

electronic BN unit form a potentially interesting series of mole-cules as recently a BN-substituted benzene has experimentallybeen prepared [13,37]. In the present work, we successively re-placed the (CC)n of C7H7

+ by the (B–N)n (n = 1–3) groups. Thereare several isomers resulting from each substitution, but onlystructures of the most stable planar isomers are shown in Fig. 3.

The NICS(0) and NICS(1) values of �2.4 and �5.8 ppm calcu-lated for C5H5BNH2

+ are small, suggesting its lower degree of aro-maticity with respect to C7H7

+ whose corresponding values are�6.0 and �9.2 ppm. As for C3H3(BNH2)2

+ and CH(BNH2)3+ cations,

the NICS(0) values are slightly positive (0.8 and 0.7 ppm), whilethe NICS(1) values are slightly negative (�2.5 and �1.9), whichagain point toward a non-aromaticity of C3H3(BNH2)2

+ andCH(BNH2)3

+. Accordingly, as the number of BN units in the ring in-creases, the molecule becomes less aromatic until it loses at theend the aromatic character.

In summary, the C7H7+ cation remains the most aromatic species

among its ring-substituted derivatives. Different ways of substitu-tion do not induce much improvement on this property of the ring.

3.5. Derivatives from boron anions

We now consider a different set of anions. Both the B82� and

CB7� derivatives have been studied extensively [10–15] and we

mainly focus hereafter on their structure (Fig. 3) and aromaticcharacter (Table 1). The B–B and C–B bonds of the CB7

� (D7h) anionare predicted to be 1.525 and 1.757 Å, respectively, which areshorter than the corresponding bond lengths of B8

2� (1.546 and1.782 Å), implying that the ring shrinks upon substitution of thecentral boron of B8

2� by a carbon atom.The values of �61.3 and �58.8 ppm calculated for NICS(1)zz of

both D7h and C2v CB7� anions, respectively (Table 1) are quite close

to the corresponding value of �60.1 ppm for B82�, and accordingly,

they are predicted to be similarly aromatic, in agreement with ear-lier studies [12].

Attempts have been done to replace the central carbon atom ofCB7

� (D7h) with the heavier Si, and Ge atoms, but both resultingmolecules prefer pyramidal C7v shape, which also agrees with pre-vious report [12b]. The main reason for such behavior is that the B7

ring turns out to be too small to accommodate the heavier carboncongeners. These are also not the energetically lowest-lyingstructures.

3.6. Derivatives of S3N4

We now examine the trithiatetrazepine S3N4 molecule and itsderivatives obtained by substituting one or two N atoms by CHunits, and also the thiotrithiazyl cation S4N3

+. Some of these com-pounds have been prepared experimentally [38]. Relevant struc-tures with selected bond lengths are also displayed in Fig. 3.

Each of the four cycles exhibits ten p-electrons, thus formallysatisfying the Hückel rule. Previous studies [38,39] postulated thatS3N4, S3N3CH, S3N2(CH)2 and S4N3

+ are aromatic. On the basis ofraw current values, it was predicted that S3N4, S3N3CH andS3N2(CH)2 may have the same, or even higher, aromaticity as ben-zene [38]. The S4N3

+ cation seemingly contains a diatropic p-cur-

rent, which is reinforced by r-circulations [39], therefore, S4N3+

is considered as doubly aromatic. Table 1 points out that theNICS(1)zz values of S3N4, S3N3CH and S3N2(CH)2 of �28.7, �27.4and �26.4 ppm, respectively, are in the same order of magnitudeas the corresponding value of �29.6 ppm for benzene, suggestingthey are similarly aromatic. This agrees well with a previous studyusing a different theoretical approach [39].

As the number of –CH group increases in the S3N4 derivatives,the NICS(1)zz value becomes slightly less negative, emphasizing adecrease in the ring aromaticity upon replacement of N by CH.Influence of the N by CH substitution on the aromaticity of S3N4

is, however, less important than that of the replacement of CHfor C7H7

+ by B atom and etc. discussed above. The S4N3+ cation

turns out to be slightly less aromatic than the series of S3N4, as ithas a less negative NICS(1)zz value of �24.9 ppm.

Concerning the HOMO–LUMO gaps, substitution of N by CHdoes not influence it significantly, as the gaps amount to aboutthe same value of �4.3 eV for S3N4 and its two CH-derivatives,and of �4.2 eV for the S4N3

+ cation.

3.7. Derivatives of Cu7Sc cluster

In a recent study [16], we demonstrated that the pure copperCu7

3� anion and the neutral Sc-doped cluster Cu7Sc possess anr-aromatic character in their seven-membered cyclic shape(D7h). This has been determined on the basis of electron counts,as well as the ELI-D and NICS analyses [16]. According to the phe-nomenological shell model [40], enhanced stabilities in circularclusters are expected for structures having 2, 6, 10, 12, 16 or 20delocalized valence s-electrons. The highly symmetrical D7h struc-ture of Cu7

3� and Cu7Sc can be considered to be circular, and bothof them have closed electronic shell structure as each contains 10delocalized electrons [16].

Among the pure and doped transition metal clusters having 10valence electrons in a seven-membered ring structure, we foundthat the Ag7

3� and Au73� anions are characterized by a D7h shape,

just like Cu73�. Regarding the doped clusters, it appears that the

Ag7 ring is too large to accommodate an atom such as Sc, Ti+ orZr+ at its center. Although they are supposed to be stable [41], ageometrical distortion actually occurs leading to a Cs structure.On the contrary, a Y atom can comfortably be incorporated withinthe Ag7 ring, resulting in a D7h Ag7Y species.

In the group of doped gold clusters, we found that Au7Y isslightly distorted from the D7h symmetry. The Au7Y (D7h) is foundto be a sixth-order saddle point, which is however located at only0.02 eV higher in energy than the global Cs minimum. This speciesalso has a highly fluctional character, and it can be expected thatthe D7h form ends up to be the vibrationally averaged equilibriumstructure. Selected geometrical parameters of the rings consideredand their IR spectra are summarized in Fig. 4.

The Cu–Cu, Ag–Ag and Au–Au bonds in the pure Cu73�, Ag7

3�

and Au73� cyclic clusters are predicted to be 2.446, 2.799 and

2.727 Å, respectively, from which one may find that the size ofthe Au7

3� ring surprisingly lies between those of Cu73� and

Ag73�. This can be attributed to be a larger relativistic effect of

Au [42]. The Cu–Cu bond in Cu7Sc and Cu7Y are 2.363 and2.429 Å, respectively, which are shorter than the correspondingbond length in Cu7

3�. In Cu73�, as all the Cu atoms carry a negative

charge (�0.43 electron), they repel each other, whereas in Cu7Scand Cu7Y, the Cu and the doped atoms (Sc and Y) attract each otherbecause Cu atoms are positively charged, while Sc and Y are nega-tively charged. In the same vein, the Ag–Ag and Au–Au bonds areshortened from 2.799 and 2.727 Å to 2.685 and 2.643 Å upon dop-ing a Y atom into the Ag7

3� and Au73� systems.

Let us consider vibrational spectra to probe their differences.Most of the active modes range in the far infrared region. There

Fig. 4. Structures (bond length in Å) of Cu73�, Cu7Sc, Cu7Y, Ag7

3�, Ag7Y and Au73�, and corresponding far IR spectra (B3LYP/aug-cc-pVDZ-PP). The colors stand for: red = Cu,

silver = Ag, and yellow = Au. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

L. Lin et al. / Journal of Molecular Structure: THEOCHEM 943 (2010) 23–31 29

is only one peak for each pure trianion, located at 125 cm�1

(Cu73�), 83 cm�1 (Ag7

3�) and 91 cm�1 (Au73�), and they all corre-

spond to the in-plane bending of M–M–M (M = Cu, Ag and Au).For the binary Cu7Sc, Cu7Y and Ag7Y clusters, each contains twodistinct bands. Cu7Sc includes the bands centered at 83 and224 cm�1, that can be assigned to the Sc out-of plane deformationand Cu–Sc stretching modes, respectively, and they are similarlyintense. For Cu7Y, the out-of plane deformation of Y correspondsto the peak at 26 cm�1, which is much more intense than thepeak at 200 cm�1 originated from the Cu–Y stretching. Concern-ing Ag7Y, the peaks centered at 57 and 143 cm�1 are similarly as-signed to the Y-out-of plane deformation and Ag–Y stretching.The vibrational spectrum of Au7Y differs sensibly from those ofCu7Y and Ag7Y, in the sense that there are in this case three activepeaks, and the Au–Y stretching band centered at 134 cm�1 isintense.

As the aromatic character and electronic properties of copperclusters have been investigated before [16], we now mainly focus

on the Ag73�, Ag7Y, Au7

3� and Au7Y clusters. Both Ag73� and

Au73� have 10 valence electrons. In Ag7Y and Au7Y, together with

the three d-electrons of the Y atom, there are also 10 electrons.The resulting D7h structure can be considered as circular, andaccording to the shell model, the 1s, 1px, 1py, 1dxy and 1dx2–y2 shellorbitals are expected to be filled, similar to the situation in Cu7Sc[16].

The 10 valence electrons of Ag7Y are mainly composed of thosein 5s atomic orbitals, which can clearly be seen from the density ofstates (DOS) plotted in Fig. 5. The MOs having the highest contribu-tions from 5s-AOs have been assigned. Beside the important con-tributions of 5s AOs, there are also quantitative contributionsfrom other AOs as well. Similar patterns are also identified in Au7Y.

For the clusters Ag73�, Ag7Y, Au7

3� and Au7Y, the 10 valenceelectrons formally satisfy both the electron shell model and classi-cal Hückel’s rule, therefore whether they are aromatic is anotherimportant question to be considered. The NICS calculations showthat the NICS(1)zz of Ag7

3� and Au73� are �29.4 and �32.2 ppm,

Fig. 5. Total (black) and partial, computed from the s AOs (red), density of states and shell model MOs of the Ag7Y having high contributions from 5s AOs of Ag and Y (B3LYP/aug-cc-pVDZ-PP). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

30 L. Lin et al. / Journal of Molecular Structure: THEOCHEM 943 (2010) 23–31

respectively, which are slightly less negative than that of Cu3�

(�34.2 ppm). While the corresponding values for the doped clus-ters Cu7Y (�64.3 ppm), Ag7Y (�69.6 ppm) and Au7Y (�55.8 ppm)appear thus to be more negative than that of Cu7Sc (�46.0 ppm).It should be noticed that while the NICS(1)zz values are predictedto be similar for the pure Cu3�, Ag7

3� and Au73� anions, these val-

ues become more negative after doping the clusters by Sc and Yatoms. The negative values for NICS(1)zz and NICS(2)zz suggest thatAg7

3�, Ag7Y, Au73� and Au7Y are actually aromatic. Furthermore,

the NICS(1) and NICS(1)zz values, that are found to be more nega-tive than the NICS(2) and NICS(2)zz (Table 1), point toward a factthat Ag7

3�, Ag7Y, Au73� and Au7Y have a r-aromatic character, in

a same way as the copper clusters Cu3�, Cu7Sc and Cu7Y.The electron localization indicator (ELI-D) isosurface and partial

p-ELI-D computed from MOs corresponding to the phenomenolog-ical shell of Ag7Y are shown in Fig. 6. There are localization do-mains not only around the nuclei, but also between every twoneighboring Ag atoms and also between Ag and the central Y inthe ELI-D isosurface. The partial-ELI-D analysis points out thatthe seven localization domains between Ag atoms in the ring arisemainly from the MOs composed of the 5s-AOs, while the remainingdomains are caused mainly by core orbitals and valence orbitalshaving high contributions from 4d-atomic orbitals of yttrium. Sim-ilar to the situation in Cu7Sc and Au6Y�, the MOs composed of thevalence s AO’s are responsible for the stability of the Ag7Y, which isagain consistent with a r-aromaticity.

The HOMO–LUMO gaps of Cu73�, Ag7

3� and Au73� amount to 1.0,

1.0 and 1.3 eV, respectively. The Sc- and Y-doped copper clusters(Cu7Sc and Cu7Y) have larger HOMO–LUMO gaps, being 2.7 and3.0 eV. A similar sequence has been found for Ag7Y (2.4 eV) andAu7Y (3.0 eV). Due to the larger HOMO–LUMO gaps, the doped clus-ters are expected to achieve a higher stability than the correspondingpure Cu7

3�, Ag73� and Au7

3� clusters. Furthermore, the gaps of thebinary clusters considered here are even larger than those of somedoped transition metal clusters known as having high HOMO–LUMOgaps, for example, Au14Zr (HOMO–LUMO gap: 2.2 eV) [43].

4. Concluding remarks

In the present theoretical study, we employed quantum chemicalcalculations to search for seven-membered rings having a certainaromatic character. The derivatives of C7H7

+ were considered andit has been found that substitution does not induce a higher degreeof aromaticity as compared to that of the parent C7H7

+ cation. Asfor the series of S3N4 molecules, substitution of N by CH marginallyinfluences the aromaticity of the system, in such a way that S3N4

and its CH-derivatives are similarly aromatic. Regarding the all-me-tal clusters, the binary clusters Cu7Sc, Cu7Y, Ag7Y and Au7Y achieve ahigher degree of aromaticity than the pure metal trianions Cu7

3�,Ag7

3�and Au73�. Origin of the 10 valence electrons, which are mainly

composed of the valence s AOs of the ring metal, confers to thesemetallic clusters an r-aromatic character.

Fig. 6. (a) ELI-D isosurface (isovalue = 1.18) and (b) partial ELI-D (isovalue = 0.78) computed from MOs corresponding to the phenomenological shell model for Ag7Y.

L. Lin et al. / Journal of Molecular Structure: THEOCHEM 943 (2010) 23–31 31

5. Supporting information available

Cartesian coordinates of optimized geometries of the moleculesconsidered are given. This material is available free of charge viathe Internet.

Acknowledgements

The authors are indebted to the KU Leuven Research Council(GOA, IUAP and IDO programs) and the Flemish Fund for ScientificResearch (FWO-Vlaanderen) for continuing support. LL thanks IN-PAC for a post-doctoral fellowship.

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