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A theoretical survey on the D7d [84]fullerene, a fullerene with two heptagon rings
Computational and Theoretical Chemistry 1009 (2013) 103–107
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A theoretical survey on the D7d [84]fullerene, a fullerene with two heptagon rings Zahra Badri a, Cina Foroutan-Nejad a,b, Parviz Rashidi-Ranjbar a,⇑ a b
School of Chemistry, College of Science, University of Tehran, Tehran, Iran National Center for Biomolecular Research, Faculty of Science, Masaryk University, Kamenice 5/A4, CZ-62500 Brno, Czech Republic
a r t i c l e
i n f o
Article history: Received 29 September 2012 Received in revised form 25 December 2012 Accepted 10 January 2013 Available online 18 January 2013 Keywords: Fullerene D7d point group DFT QTAIM Magnetizability Metallocenoid
a b s t r a c t Our theoretical studies suggest that a novel isomer of [84]fullerenes with D7d point group symmetry is kinetically stable. This novel structure contains two heptagons, 28 hexagons and 14 pentagons. Studying the electronic properties shows that the molecule has a Singlet ground state and the Singlet–Triplet energy gap is about 31.0 kcal mol1. In addition, the HOMO–LUMO energy gap of the molecule is 2.261 eV, which confirms kinetic stability of the molecule. Studying the magnetizability of the molecule suggests presence of strong diatropic electronic currents, i.e. magnetic aromaticity, in this molecule. Since our newly proposed structure is a high energy fullerene, we suggested a method for synthesis of the molecule based on the application of a template. The Mo2 molecule is suggested as a template for synthesis of the D7d–C84 since complexes containing two 7-membered carbon rings and a Mo2 system have been experimentally prepared before. Observation of such complexes suggests that Mo2 might be able to form metallocenoid complexes with large carbon rings. In addition, it is shown that the Mo2 molecule forms a stable complex with the formed D7d–C84. Bonding properties of the D7d–C84 and its complex with Mo2 were studied within the context of the quantum theory of atoms in molecules, QTAIM. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Since the discovery of buckyball fullerene, C60, in 1985 [1] a large number of fullerenes with different number of carbon atoms have been introduced either experimentally or theoretically. Most of these fullerenes are consisted of pentagon and hexagon rings and obey the isolated pentagon rule (IPR), i.e. every pentagon should not be attached to another pentagon ring in structure of fullerenes. Meanwhile, there are few reports regarding the fullerenes containing heptagon rings. Only three fullerene derivatives containing heptagons are reported experimentally; C58F18 and C58F17CF3 derivatives of C58, containing one heptagon, were identified by mass spectroscopy and 19F-NMR studies [2]. A chlorinated derivative of C84 containing heptagon ring was also reported recently [3]. The latter fullerene derivative, C84Cl32, was obtained from chlorination of C86 fullerene and characterized by X-ray crystallography. Theoretical studies also confirmed that some fullerenes containing heptagon rings are local minima on their potential energy hyper-surfaces. A study on C40 isomers has shown that in heptagon containing molecules, total energy decreases as the number of heptagon–pentagon fusions increases, in contrast to the pentagon– pentagon fusions [4]. A detailed study on the isomers of C62 suggested that the lowest energy isomer of this species is a non-classical, i.e. not just made of pentagons and hexagons, C62 fullerene with five azulenoid pentagon–heptagon contacts [5]. Surveying ⇑ Corresponding author. Tel.: +98 21 66495291; fax: +98 21 66405141. E-mail address: [email protected] (P. Rashidi-Ranjbar). 2210-271X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.comptc.2013.01.005
the relative energies of C58 fullerenes also confirmed that a heptagon containing isomer is a low-lying isomer which is just 2.5 kcal mol1 higher in energy compared with the lowest energy isomer at DFT, B3LYP/6-31G(d), computational level. Interestingly, studying the HOMO–LUMO gap among C58 fullerenes showed that the lowest energy isomer is not kinetically stable as it has a low HOMO–LUMO energy gap [6]. Such theoretical studies and experiments promise opportunities for finding non-classical fullerenes in future. In addition, recent advances in synthesis of fullerenes may provide a chance for successful synthesis of novel types of fullerenes [7–12]. In the present work, a novel highly-symmetric, D7d, non-classical [84]fullerene with two heptagons is described. Although, this strained molecule is relatively higher in energy than other [84] fullerenes, it is kinetically stable and has a Singlet ground state. Aromaticity and bonding of this novel species are also studied in detail and compared with aromatic hydrocarbons, C60 and several isomers of C84. The studied [84]fullerene has two heptagon rings, in a relatively close distance together. It is suggested that Mo2 molecule can interact simultaneously with both rings to form a stable metallocenoid species. It is also suggested that Mo2 might be used as a template for synthesizing the new fullerene. This is suggested mainly based on the tendency of molybdenum atoms toward forming numerous bonds and ability of Mo2 system for forming complex with the 7-membered carbon rings [13]. Bonding between the Mo2 molecule and the [84]fullerene is also studied in detail within the context of Quantum Theory of Atoms in Molecules, QTAIM [14].
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2. Computational methods All species were optimized at DFT level employing the B3LYP, hybrid functional combined with the 6-31G(d) basis set. The electron spin multiplicity of the ground state of D7d [84]fullerene was studied carefully. The second derivatives of energy with respect to the degrees of freedom of the system were computed to ensure the local minimum nature of the studied species at the studied level of theory. The magnetic aromaticity of the studied species was surveyed by means of the interatomic magnetizability probe in the context of QTAIM [14] as introduced recently [15]. The interatomic magnetizability values were obtained from processing the FCH files of NMR computations as described in the Supporting information. Bonding properties of the novel D7d [84]fullerene were also studied in the context of QTAIM and compared with those of C60, the most abundant fullerene. The D7d [84]fullerene is a high-energy fullerene due to the considerable strain around the edge of the molecule, Fig. 1. However, sometimes unforeseen fullerenes may form upon complexation with templates, which are present during the fullerene formation. A famous example of such species is the egg-shaped [84]fullerene with fused pentagon rings [16]. In the D7d [84]fullerene, two heptagon rings are relatively close to each other. Therefore, we guessed that an appropriate metal, which can form a sandwich-shaped complex, may serve as a template during the formation of this novel structure. It is necessary that the employed template also form a stable complex with the D7d [84]fullerene after formation. A suitable metal for this sandwichshaped metallocenoid must be a metal capable of forming many bonds. A vast number of metal atoms and di-atomic metallic molecules were considered (see Supplementary information). Frequencies of those species which formed a D7d complex were considered to probe the nature of local minima. Among all studied structures the Mo2@D7d–C84 conform to a D7d point group and is a
local minimum. In this complex, each molybdenum atom is bonded to seven carbon atoms of heptagon rings and the other molybdenum atom, Fig. 1. Several forms of the Mo2@D7d–C84 species were studied at B3LYP/MIDIX/Def2-TZVP level and local minimum structures were re-optimized at B3LYP/6-31G(d)/Def2TZVP level to identify the most stable conformer of Mo2@D7d– C84. The well-known tendency of Mo for forming several bonds could be the driving force for the formation of this species [17,18]. Bonding properties of this new complex, Mo2@C84, were also studied by the QTAIM approach. To examine the efficiency of using Mo2 as a template for preparation of D7d–C84, Mo2@D2C84 and Mo2@D2dC84 were also examined and the energy of these species were compared. Although, the energy of Mo2@D7dC84 still remains above the energy of classical Mo2@[84]fullerenes but compared to the free fullerenes, the complexed D7d [84]fullerene is 42 and 38 kcal mol1 more stabilized compared to D2–C84 and D2d–C84 fullerenes. This promises that species like Mo2 or a closely related species might be applied as a template for kinetically controlled preparation of our exotic species. However, this needs more comprehensive experimental studies to verify the role of template in real conditions. The DFT computations were performed by Gaussian 09 [19], version A02 and all QTAIM computations were done by AIMAll, version 11.12.19 [20].
3. Results and discussion Fullerenes, composed of pentagons and hexagons, tend to conform to a spherical geometry to distribute the strain energy almost equally among all carbon atoms. The D7d [84]fullerene is compressed along the main axis of symmetry of the molecule, Fig. 1. This introduces two types of strain to this species; (a) the poles of molecule (along the C7 axis of symmetry) are considerably flat
Fig. 1. (a–c) The structure of D7d–C84 from different views. The carbon atoms and bond critical points of QTAIM are marked by numbers to be easily addressable in tables. (d) The structure of Mo2@D7d–C84.
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and (b) hexagons and pentagons around the edge (equator) of the molecule are non-planar, see Fig. 1. In a recent account Khamatgalimov and Kovalenko mentioned that planar distortion destabilizes the Singlet electronic ground state of fullerenes [21]; since D7d [84]fullerene is highly flat (in poles) it might have a Triplet ground state. The stability of Singlet electronic ground state of the D7d [84]fullerene was examined and the molecule was optimized by unrestricted Triplet wave function to measure the energy gap between Singlet and Triplet states. Interestingly, the Singlet state of the D7d [84]fullerene is 31.0 kcal mol1 more stable than the first Triplet state (at 298 K by considering the thermal correction to energy, the S–T energy gap is 27.2 kcal mol1). In addition, the Triplet state also has the D7d symmetry, like the Singlet state. This novel fullerene is 296 kcal mol1 higher in energy compared to the most stable and the most abundant C84 fullerenes, i.e. the D2d and D2 [84]fullerenes. Although, the D7d [84]fullerene is considerably higher in energy compared to the most stable [84]fullerenes, still there might be a chance to be prepared but not from the routine ways for synthesizing fullerenes. This should be noted that two high-energy isomers of [84]fullerene with D2 and Td point groups have not been identified yet while computational studies confirm that these isomers are kinetically stable concerning their high HOMO–LUMO energy gaps. High S–T energy difference and notable HOMO–LUMO energy gap (2.261 eV) promises that D7d [84]fullerene is a kinetically stable species, particularly, because the smallest vibrational frequency of this species is 184 cm1 at the studied computational level. Interestingly, the HOMO–LUMO energy gap in this fullerene is even more than the most stable C84 fullerenes (D2 and D2d isomers) see Ref. [21] for HOMO–LUMO energy gap details in C84 fullerenes. Large HOMO–LUMO gap is characteristic of aromatic systems. To validate this hypothesis, aromaticity of this species was studied by interatomic magnetizability approach. Table 1 lists the bond magnetizability of different bonds in the D7d [84]fullerene molecule. Studying Table 1 clearly demonstrates that the D7d [84]fullerene is more aromatic than fullerene C60; in addition, bond magnetizability in most of rings in this species is almost comparable with that of well-known aromatic hydrocarbons. The interatomic magnetizability for the three bonds forming the 5membered ring moiety in the D7d [84]fullerene is less than those of its 6- and 7-membered counterparts. In order to obtain a complete picture of magnetic aromaticity in the D7d [84]fullerene, total bond magnetizability, i.e. summation of all bond magnetizabilities in this molecule was compared with that of C60 and two other [84]fullerenes, D2d and D6h [84]fullerenes; Table 2. The latter two [84]fullerenes were selected since the D2d isomer is the most stable [84]fullerene and the D6h isomer has a very similar structure to the
Table 1 The bond magnetizability values for C60, D7d–C84, benzene, cyclopentadienyl anion and tropylium cation. Molecule
Bond
v (C|C)a
C60
BCP (1) BCP (2)
0.60 1.35
C84(UFO)
BCP BCP BCP BCP BCP BCP BCP BCP BCP BCP
2.04 2.63 1.68 2.23 1.51 1.56 2.24 2.22 2.25 2.32
C6H6 C5 H 5 C7 Hþ 7 a
(1) (2) (3) (4) (5) (6) (7)
Average values for both carbon atoms in a bond.
Table 2 Total isotropic intra-atomic magnetizability, vtot iso (C), Total isotropic interatomic magnetizability, vtot iso (C|C), the ratio of inter to intra-atomic isotropic magnetizability and the total bond magnetizability per atom for C60 and three different isomers of C84. The data show that D7d–C84 is the most aromatic species among studied molecules. Molecule
vtot iso (C)
vtot iso (C|C)
tot vtot iso (C|C)/ viso (C)
vtot iso (C|C) per atom
C60 D2d–C84 D6h–C84 D7d–C84
103.584 148.112 144.466 135.363
152.992 274.360 384.040 478.379
1.477 1.852 2.658 3.534
2.550 3.226 4.572 5.695
D7d [84]fullerene. Indeed the D6h isomer has a relatively flat structure and has two coronene-like structures on the pole regions of the molecule. Table 2 clearly shows that the aromaticity of the D7d [84]fullerene is considerably higher than the other studied [84]fullerenes based on the bond magnetizability values, vtot iso (C|C). Although, comparing the magnetic aromaticity of molecules with different number of atoms, based on the total magnetizability, is not reasonable, one may compare the aromaticity of fullerenes with different sizes by dividing the total bond magnetizability of a molecule by the number of atoms in that molecule. As it is presented in Table 2, the studied [84]fullerenes are relatively more aromatic than C60. This could be due to the fact that as fullerenes grow larger, their constituent rings gradually become more and more flat so electrons can circulate easier in the fullerene moiety. Among the studied fullerenes, D7d [84]fullerene has the flattest structure so it is expected that electrons flow easier within this molecule compared to the rest of C84 isomers. It is interesting to note that among the [84]fullerenes the most aromatic species is the highest energy one. This shows that among this family of molecules magnetic aromaticity does not correlate with energy content of molecules. Studying the charge distribution and bonding in this novel structure can help to predict reactive sites of the molecule. As it is shown in Fig. 1, four different types of carbon atoms are distinguishable in the molecule. Table S-1 shows that atoms forming the heptagon ring bear 0.0081 a.u. positive charge. The positive charge of these atoms resemble the positive charge of carbon atoms in tropylium cation, though it should be mentioned that the amount of positive charge of these carbon atoms is less than that of the positive charge on tropylium cation carbon atoms, see Table S-1. The carbon–carbon bond length in heptagon ring is 1.52 Å, 0.12 Å more than the C–C bond length in tropylium cation computed at the same level of theory. The C2 carbon atom next to C1 (see Fig. 1b) is negatively charged, 0.0176 a.u. Carbon atoms marked by 3 and 4 in Fig. 1b are charged positively, 0.0113 a.u., and negatively, 0.0064 a.u., respectively. Electron delocalization is a measure of covalency between different atoms; in addition, delocalization index between carbons 1 and 4 in different aromatic hydrocarbons (para delocalization index, PDI) is a measure of electronic aromaticity [22–25]. PDI in benzene and tropilium cation are 0.1047 a.u. and 0.0541 a.u. respectively at B3LYP/6-31G(d) level of theory, Table S-2. A larger PDI means a higher aromaticity; accordingly, PDI, in contrast to magnetic probes of aromaticity [15], suggests that benzene is more aromatic than tropilium cation. PDI of the 6-membered rings in C60 suggests that their electronic aromaticty is reduced compared with benzene (PDI = 0.0453 a.u.). In D7d–C84, PDI of two different 6- and 7-membered rings are 0.0446 a.u. (for 6-membered rings on the top of molecule), 0.0431 a.u. (for 6-membered ring on the edge of molecule) and 0.0056 a.u. respectively. Indeed, distorted geometry of this molecule should affect p-electron delocalization and this is reflected in reduced PDI values. Particularly, long bond length of the 7-membered ring in this species reduces PDI compared to the tropilium cation.
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However, studying the electron delocalization between the heptagon carbons and the Mo atoms (0.2783 a.u.) suggests some degrees of covalency compared with previously studied metallocenes (0.4518 for Fe(Cp)2, 0.1272 for Al+(Cp)2 and 0.2486 for Ge(Cp)2) [27]. The electron delocalization between Mo atoms in the free Mo2 molecule is 6.1151 a.u.; this value reduces to 3.3419 a.u. between Mo atoms in the complex with D7d–C84. Based on the magnitude of the electron delocalization, the bond order in between Mo2 in Mo2@D7d–C84 complex reduces to 3.3, if we assume that 6.1151 a.u. represents a sextuple bond. The change in electron delocalization is in line with bond length change in the Mo2 molecule. Similarly, studying the percent localization, i.e. the number of electrons localized in an atomic basin divided by the population of that atomic basin multiplied by a hundred [27] shows that percent localization of Mo atoms decrease from 78.16% upon complexation with C84, to 76.56%. This change beside decrease in electron delocalization between Mo atoms shows that electrons of Mo atoms are mainly distributed between Mo atoms and carbons of the C84 fullerene. Accordingly, the bond order of Mo2 within the C84 moiety has decreased, so, its bond length increased. The bond length of the free Mo2 at B3LYP/Def2-TZVP level is 1.907 Å (the experimental bond length, obtained from spectroscopy is 1.938 Å [18]). In the Mo2@D7d–C84 complex the bond length increases by 0.052 Å up to 1.959 Å. In addition, complexation with Mo2 affects the electronic properties of the molecule; the HOMO–LUMO energy gap drops to 0.912 eV in the Mo2@D7d–C84 complex. PDI in 6- and 7-membered rings of the Mo2@D7d–C84 complex decreases compared with the free fullerene, see Table S-2. In order to verify the effect of complexation with Mo2 on the energy content of D7d–C84, Mo2@D2– and D2d–C84 molecules were also studied. The energy of Mo2@D7d–C84 complex remains still more than the Mo2@D2– and D2d–C84 species by 254 and 258 kcal mol1 respectively. It is worth noting that free D2 and D2d [84]fullerenes were 296 kcal mol1 lower in energy compared with the complexed species. Accordingly, complexation decreases the energy difference to some degrees which could judge the suggestion of D7d–C84 synthesis by using the Mo2 as a template.
4. Mo2@D7d–C84 The application of metallic templates for organic synthesis is an old approach which has been vastly employed in the synthesis of crown ethers and cryptands [26]. As mentioned earlier the unprecedented fullerenes have also been synthesized by a similar technique [16]. Templates may form complexes with the synthesized organic hosts during the synthesis, so we tried to find a stable complex between the heptagon rings of the D7d–C84 and a metallic species and suggest that the metallic guest might be useful for synthesizing the D7d–C84 molecule. Among all studied guests the Mo2 molecule forms a sandwich shaped metallocenoid with the D7d–C84. As a matter of fact, surveying the literature shows that complexes between two tropylium rings and the Mo2 molecule, with a structure quite close to the structure of the poles of our proposed fullerene have been prepared [13]. The most stable structure of Mo2@C84 conforms to a molecular geometry with D7d symmetry. In this structure, the Mo2 molecule is positioned along the main axis of symmetry of the D7d–C84 fullerene, Fig. 1. This form is significantly more stable than the form in which the Mo2 is perpendicular to the main axis of symmetry at the B3LYP/6-31G(d) computational level. Complexation with Mo2 influences the charge content of carbon atoms of the D7d– C84; particularly, the atoms of the heptagon ring, which are directly bonded to the Mo atoms, are negatively charged in the complex while these atoms are positively charged in the free D7d–C84. This is evidently due to the charge transfer from the Mo atoms to the carbon moiety. Carbon atoms of the heptagon ring have lower energy compared to the carbon atoms of the free D7d–C84. The bond between carbon atoms of the heptagon ring and the Mo atoms should be classified among closed-shell interactions concerning the magnitude of the Laplacian of the electron density. In addition, the electron density of the (3, 1) critical points between Mo atoms and carbon atoms of the heptagons are lower than other (3, 1) critical points, between carbon atoms. Studying the critical point descriptors of carbon–carbon bonds in D7d–C84, Mo2@D7d–C84 and fullerenes as well as normal hydrocarbons shows that carbon–carbon bonds are almost of the same type, see Table 3.
Table 3 Descriptors of (3, 1) critical points for carbon–carbon bonds in different molecules. The electron density, q(r), virial field function, V(r), Lagrangian kinetic energy, G(r), Hamiltonian kinetic energy, K(r), Laplacian of electron density, L(r), the ratio of Lagrangian kinetic energy to electron density and ellipticity (e), of (3, 1) critical points. All parameters are presented in atomic units. For detailed description of these parameters please see Ref. [28].
q(r)
V(r)
G(r)
K(r)
G(r)/q(r)
e
0.2810 0.3102
0.3351 0.4111
0.0810 0.1023
0.2541 0.3088
0.1731 0.2065
0.2883 0.3298
0.1474 0.2229
(1)a (2)a (3)a (4)a (5)a (6)a (7)a
0.2447 0.2781 0.2878 0.3433 0.2784 0.3032 0.3057
0.2570 0.3349 0.3506 0.4922 0.3322 0.3832 0.4032
0.0625 0.0857 0.0845 0.1170 0.0814 0.0904 0.1016
0.1944 0.2492 0.2661 0.3753 0.2508 0.2928 0.3015
0.1319 0.1635 0.1817 0.2583 0.1694 0.2024 0.1999
0.2554 0.3082 0.2936 0.3408 0.2924 0.2982 0.3324
0.1600 0.3000 0.1425 0.2148 0.1429 0.1486 0.2092
(1)a (2)a (3)a (4)a (5)a (6)a (7)a (8)b (9)c
0.2338 0.2675 0.2954 0.3351 0.2481 0.3052 0.2983 0.0528 0.2488 0.3113 0.2949 0.3121
0.2453 0.3094 0.3705 0.4695 0.3288 0.3929 0.3852 0.0539 0.5794 0.4082 0.3807 0.4024
0.0642 0.0772 0.0893 0.1107 0.0803 0.0948 0.0960 0.0462 0.3876 0.0983 0.0987 0.0923
0.1811 0.2322 0.2812 0.3588 0.2486 0.2981 0.2892 0.0077 0.1919 0.3099 0.2820 0.3101
0.1169 0.1550 0.1919 0.2481 0.1683 0.2033 0.1932 0.0385 0.1957 0.2116 0.1833 0.2178
0.2746 0.3023 0.3023 0.3303 0.3237 0.3106 0.3218 0.8750 1.5579 0.3158 0.3347 0.2957
0.1954 0.1869 0.1524 0.2003 0.1406 0.1799 0.1890 1.6024 0.0003 0.2092 0.2892 0.1411
Molecule C60
BCP (1) BCP (2)
C84(UFO)
BCP BCP BCP BCP BCP BCP BCP
Mo2@UFO
BCP BCP BCP BCP BCP BCP BCP BCP BCP BCP BCP BCP
C6H6 C5 H 5 C7 Hþ 7 a b c
See Fig. 1 for identifying BCP numbers. (3, 1) Critical points between Mo atoms and carbon atoms of heptagons. (3, 1) Critical point between two Mo atoms.
L(r)
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5. Conclusions In the present account a novel isomer for [84]fullerenes is introduced theoretically. The structure of this novel isomer has a D7d point group composed of two heptagons, 28 hexagons and 14 pentagons. Based on the HOMO–LUMO gap, vibrational frequencies and tendency of the molecule toward Singlet ground state (Singlet–Triplet energy difference of 31.0 kcal mol1) it is proposed that this strained structure, though high energy, is kinetically stable. The aromaticity of this novel molecule was studied by the bond magnetizability probe. It is suggested that this molecule is relatively more aromatic in the context of magnetic aromaticity than C60 and normal [84]fullerenes that were considered here. However, PDI values do not confirm a higher aromaticity relative to C60, within the electronic paradigm of aromaticity. A method for probable synthesis of this molecule is also suggested based on application of Mo2 template. It should be mentioned that high energy difference between this molecule and normal [84]fullerenes complexed with Mo2 molecule shows that there is almost no chance for observation of D7d [84]fullerene in thermodynamic control synthetic approaches. It is shown that Mo2 molecule can form a stable complex with this fullerene, which resembles a sandwich shaped metallocenoid. Studying QTAIM parameters, in particular delocalization index, suggests that bonding between the fullerene and the metallic core, Mo2, is covalence in nature. To the bests of our knowledge this molecule is the first proposed fullerene with two heptagon rings which is kinetically stable. Acknowledgments Authors gratefully thank to Prof. M. Sola, Universitat de Girona, Campus de Montilivi, Girona, Spain, for providing computational time (hardware and software) for computations. Authors also thank to the University of Tehran for financial support. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.comptc.2013. 01.005. References [1] H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl, R.E. Smalley, C60: buckminsterfullerene, Nature 318 (1985) 162–163. [2] P.A. Troshin, A.G. Avent, A.D. Darwish, N. Martsinovich, A.K. Abdul-Sada, J.M. Street, R. Taylor, Chemistry: isolation of two seven-membered ring C58 fullerene derivatives: C58F17CF3 and C58F18, Science 309 (2005) 278–281. [3] I.N. Ioffe, C. Chen, S. Yang, L.N. Sidorov, E. Kemnitz, S.I. Troyanov, Chlorination of C86 to C84Cl32 with nonclassical heptagon-containing fullerene cage formed by cage shrinkage, Angew. Chem. Int. Ed. 49 (2010) 4784–4787. [4] P.W. Fowler, T. Heine, D. Mitchell, G. Orlandi, R. Schmidt, G. Seifert, F. Zerbetto, Boron-nitrogen analogues of the fullerenes: the isolated-square rule, J. Chem. Soc., Faraday Trans. 92 (1996) 2203–2210. [5] A. Ayuela, P.W. Fowler, D. Mitchell, R. Schmidt, G. Seifert, F. Zerbetto, C62: theoretical evidence for a nonclassical fullerene with a heptagonal ring, J. Phys. Chem. A 100 (1996) 15634–15636.
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[6] D.-L. Chen, W.Q. Tian, J.-K. Feng, C.-C. Sun, Structures, stabilities, and electronic and optical properties of C58 fullerene isomers, ions, and metallofullerenes, Chem. Phys. Chem. 8 (2007) 1029–1036. [7] K.Y. Amsharov, M.A. Kabdulov, M. Jansen, Facile bucky-bowl synthesis by regiospecific cove-region closure by HF elimination, Angew. Chem. Int. Ed. 51 (2012) 4594–4597. [8] F. Vines, A. Gorling, Template-assisted formation of fullerenes from shortchain hydrocarbons by supported platinum nanoparticles, Angew. Chem. Int. Ed. 50 (2011) 4611–4614. [9] I.B. Lebedeva, A.A. Knizhnik, A.M. Popov, B.V. Potapkin, Ni-assisted transformation of graphene flakes to fullerenes, J. Phys. Chem. C 116 (2012) 6572–6584. [10] J.A. Martin-Gago, Polycyclic aromatics: on-surface molecular engineering, Nat. Chem. 3 (2011) 11–12. [11] K. Amsharov, N. Abdurakhmanova, S. Stepanow, S. Rauschenbach, M. Jansen, K. Kern, Towards the isomer-specific synthesis of higher fullerenes and buckybowls by the surface-catalyzed cyclodehydrogenation of aromatic precursors, Angew. Chem. Int. Ed. 49 (2010) 9392–9396. [12] G. Otero, G. Biddau, C. Sanchez-Sanchez, R. Caillard, M.F. Lopez, C. Rogero, F.J. Palomares, N. Cabello, M.A. Basanta, J. Ortega, J. Mendez, A.M. Echavarren, R. Perez, B. Gomez-Lor, J.A. Martin-Gago, Fullerenes from aromatic precursors by surface-catalysedcyclodehydrogenation, Nature 454 (2008) 865–868. [13] M. Tamm, T. Bannenberg, R. Frohlich, S. Grimme, M. Gerenkamp, Mono- and dinuclear molybdenum complexes with sterically demanding cycloheptatrienyl ligands, Dalton Trans. (2004) 482–491. [14] R.F.W. Bader, Atoms in Molecules: A Quantum Theory, Oxford University Press, Oxford, UK, 1990. [15] C. Foroutan-Nejad, Interatomic magnetizability: a QTAIM-based approach toward deciphering magnetic aromaticity, J. Phys. Chem. A115 (2011) 12555– 12560. [16] C.M. Beavers, T. Zuo, J.C. Duchamp, K. Harich, H.C. Dorn, M.M. Olmstead, A.L. Balch, Tb3N@C84: an improbable, egg-shaped endohedral fullerene that violates the isolated pentagon rule, J. Am. Chem. Soc. 128 (2006) 11352– 11353. [17] B.E. Bursten, F.A. Cotton, M.B. Hall, Dimolybdenum: nature of the sextuple bond, J. Am. Chem. Soc. 20 (1980) 6348–6349. [18] A.C. Borin, J.P. Gobbo, B.O. Roos, A theoretical study of the binding and electronic spectrum of the Mo2 molecule, Chem. Phys. 343 (2008) 210–216. [19] Gaussian 09, Revision A.02, M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G.A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H.P. Hratchian, A.F. Izmaylov, J. Bloino, G. Zheng, J.L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven Jr., J.A. Montgomery, J.E. Peralta, F. Ogliaro, M. Bearpark. J.J. Heyd, E. Brothers, K.N. Kudin, V.N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J.C. Burant, S.S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J.M. Millam, M. Klene, J.E. Knox, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, R.L. Martin, K. Morokuma, V.G. Zakrzewski, G.A. Voth, P. Salvador, J.J. Dannenberg, S. Dapprich, A.D. Daniels, O. Farkas, J.B. Foresman, J.V. Ortiz, J. Cioslowski, D.J. Fox, Gaussian, Inc., Wallingford, CT, 2009. [20] AIMAll (version 11.02.27), Keith, T.A., 2011.. [21] A.R. Khamatgalimov, V.I. Kovalenko, Deformation and thermodynamic instability of a C84 fullerene cage, Russ. J. Phys. Chem. A 84 (2010) 636–641. [22] R.F.W. Bader, A. Streitwieser, A. Neuhaus, K.E. Laidig, P. Speers, Electron delocalization and the Fermi hole, J. Am. Chem. Soc. 118 (1996) 4959–4965. [23] X. Fradera, M.A. Austen, R.F.W. Bader, The Lewis model and beyond, J. Phys. Chem. A 103 (1999) 304–314. [24] J. Poater, X. Fradera, M. Duran, M. Sola, The delocalization index as an electronic aromaticity criterion: application to a series of planar polycyclic aromatic hydrocarbons, Chem. Eur. J. 9 (2003) 400–406. [25] J. Poater, M. Duran, M. Sola, B. Silvi, Electron localization function at the correlated level, Chem. Rev. 105 (2005) 3911. [26] J.M. Lehn, Supramolecular Chemistry: Concepts and Perspectives, VCH, Weinheim, 1995. [27] F. Cortes-Guzman, R.F.W. Bader, Complementarity of QTAIM and MO theory in the study of bonding in donor–acceptor complexes, Coord. Chem. Rev. 249 (2005) 633–662. [28] C. Foroutan-Nejad, P. Rashidi-Ranjbar, Chemical bonding in the lightest triþ atomic clusters; Hþ 3 , Li3 and B3 , J. Mol. Struct. Theochem 901 (2009) 243–248.
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Computational and Theoretical Chemistry journal homepage: www.elsevier.com/locate/comptc
A theoretical survey on the D7d [84]fullerene, a fullerene with two heptagon rings Zahra Badri a, Cina Foroutan-Nejad a,b, Parviz Rashidi-Ranjbar a,⇑ a b
School of Chemistry, College of Science, University of Tehran, Tehran, Iran National Center for Biomolecular Research, Faculty of Science, Masaryk University, Kamenice 5/A4, CZ-62500 Brno, Czech Republic
a r t i c l e
i n f o
Article history: Received 29 September 2012 Received in revised form 25 December 2012 Accepted 10 January 2013 Available online 18 January 2013 Keywords: Fullerene D7d point group DFT QTAIM Magnetizability Metallocenoid
a b s t r a c t Our theoretical studies suggest that a novel isomer of [84]fullerenes with D7d point group symmetry is kinetically stable. This novel structure contains two heptagons, 28 hexagons and 14 pentagons. Studying the electronic properties shows that the molecule has a Singlet ground state and the Singlet–Triplet energy gap is about 31.0 kcal mol1. In addition, the HOMO–LUMO energy gap of the molecule is 2.261 eV, which confirms kinetic stability of the molecule. Studying the magnetizability of the molecule suggests presence of strong diatropic electronic currents, i.e. magnetic aromaticity, in this molecule. Since our newly proposed structure is a high energy fullerene, we suggested a method for synthesis of the molecule based on the application of a template. The Mo2 molecule is suggested as a template for synthesis of the D7d–C84 since complexes containing two 7-membered carbon rings and a Mo2 system have been experimentally prepared before. Observation of such complexes suggests that Mo2 might be able to form metallocenoid complexes with large carbon rings. In addition, it is shown that the Mo2 molecule forms a stable complex with the formed D7d–C84. Bonding properties of the D7d–C84 and its complex with Mo2 were studied within the context of the quantum theory of atoms in molecules, QTAIM. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Since the discovery of buckyball fullerene, C60, in 1985 [1] a large number of fullerenes with different number of carbon atoms have been introduced either experimentally or theoretically. Most of these fullerenes are consisted of pentagon and hexagon rings and obey the isolated pentagon rule (IPR), i.e. every pentagon should not be attached to another pentagon ring in structure of fullerenes. Meanwhile, there are few reports regarding the fullerenes containing heptagon rings. Only three fullerene derivatives containing heptagons are reported experimentally; C58F18 and C58F17CF3 derivatives of C58, containing one heptagon, were identified by mass spectroscopy and 19F-NMR studies [2]. A chlorinated derivative of C84 containing heptagon ring was also reported recently [3]. The latter fullerene derivative, C84Cl32, was obtained from chlorination of C86 fullerene and characterized by X-ray crystallography. Theoretical studies also confirmed that some fullerenes containing heptagon rings are local minima on their potential energy hyper-surfaces. A study on C40 isomers has shown that in heptagon containing molecules, total energy decreases as the number of heptagon–pentagon fusions increases, in contrast to the pentagon– pentagon fusions [4]. A detailed study on the isomers of C62 suggested that the lowest energy isomer of this species is a non-classical, i.e. not just made of pentagons and hexagons, C62 fullerene with five azulenoid pentagon–heptagon contacts [5]. Surveying ⇑ Corresponding author. Tel.: +98 21 66495291; fax: +98 21 66405141. E-mail address: [email protected] (P. Rashidi-Ranjbar). 2210-271X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.comptc.2013.01.005
the relative energies of C58 fullerenes also confirmed that a heptagon containing isomer is a low-lying isomer which is just 2.5 kcal mol1 higher in energy compared with the lowest energy isomer at DFT, B3LYP/6-31G(d), computational level. Interestingly, studying the HOMO–LUMO gap among C58 fullerenes showed that the lowest energy isomer is not kinetically stable as it has a low HOMO–LUMO energy gap [6]. Such theoretical studies and experiments promise opportunities for finding non-classical fullerenes in future. In addition, recent advances in synthesis of fullerenes may provide a chance for successful synthesis of novel types of fullerenes [7–12]. In the present work, a novel highly-symmetric, D7d, non-classical [84]fullerene with two heptagons is described. Although, this strained molecule is relatively higher in energy than other [84] fullerenes, it is kinetically stable and has a Singlet ground state. Aromaticity and bonding of this novel species are also studied in detail and compared with aromatic hydrocarbons, C60 and several isomers of C84. The studied [84]fullerene has two heptagon rings, in a relatively close distance together. It is suggested that Mo2 molecule can interact simultaneously with both rings to form a stable metallocenoid species. It is also suggested that Mo2 might be used as a template for synthesizing the new fullerene. This is suggested mainly based on the tendency of molybdenum atoms toward forming numerous bonds and ability of Mo2 system for forming complex with the 7-membered carbon rings [13]. Bonding between the Mo2 molecule and the [84]fullerene is also studied in detail within the context of Quantum Theory of Atoms in Molecules, QTAIM [14].
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2. Computational methods All species were optimized at DFT level employing the B3LYP, hybrid functional combined with the 6-31G(d) basis set. The electron spin multiplicity of the ground state of D7d [84]fullerene was studied carefully. The second derivatives of energy with respect to the degrees of freedom of the system were computed to ensure the local minimum nature of the studied species at the studied level of theory. The magnetic aromaticity of the studied species was surveyed by means of the interatomic magnetizability probe in the context of QTAIM [14] as introduced recently [15]. The interatomic magnetizability values were obtained from processing the FCH files of NMR computations as described in the Supporting information. Bonding properties of the novel D7d [84]fullerene were also studied in the context of QTAIM and compared with those of C60, the most abundant fullerene. The D7d [84]fullerene is a high-energy fullerene due to the considerable strain around the edge of the molecule, Fig. 1. However, sometimes unforeseen fullerenes may form upon complexation with templates, which are present during the fullerene formation. A famous example of such species is the egg-shaped [84]fullerene with fused pentagon rings [16]. In the D7d [84]fullerene, two heptagon rings are relatively close to each other. Therefore, we guessed that an appropriate metal, which can form a sandwich-shaped complex, may serve as a template during the formation of this novel structure. It is necessary that the employed template also form a stable complex with the D7d [84]fullerene after formation. A suitable metal for this sandwichshaped metallocenoid must be a metal capable of forming many bonds. A vast number of metal atoms and di-atomic metallic molecules were considered (see Supplementary information). Frequencies of those species which formed a D7d complex were considered to probe the nature of local minima. Among all studied structures the Mo2@D7d–C84 conform to a D7d point group and is a
local minimum. In this complex, each molybdenum atom is bonded to seven carbon atoms of heptagon rings and the other molybdenum atom, Fig. 1. Several forms of the Mo2@D7d–C84 species were studied at B3LYP/MIDIX/Def2-TZVP level and local minimum structures were re-optimized at B3LYP/6-31G(d)/Def2TZVP level to identify the most stable conformer of Mo2@D7d– C84. The well-known tendency of Mo for forming several bonds could be the driving force for the formation of this species [17,18]. Bonding properties of this new complex, Mo2@C84, were also studied by the QTAIM approach. To examine the efficiency of using Mo2 as a template for preparation of D7d–C84, Mo2@D2C84 and Mo2@D2dC84 were also examined and the energy of these species were compared. Although, the energy of Mo2@D7dC84 still remains above the energy of classical Mo2@[84]fullerenes but compared to the free fullerenes, the complexed D7d [84]fullerene is 42 and 38 kcal mol1 more stabilized compared to D2–C84 and D2d–C84 fullerenes. This promises that species like Mo2 or a closely related species might be applied as a template for kinetically controlled preparation of our exotic species. However, this needs more comprehensive experimental studies to verify the role of template in real conditions. The DFT computations were performed by Gaussian 09 [19], version A02 and all QTAIM computations were done by AIMAll, version 11.12.19 [20].
3. Results and discussion Fullerenes, composed of pentagons and hexagons, tend to conform to a spherical geometry to distribute the strain energy almost equally among all carbon atoms. The D7d [84]fullerene is compressed along the main axis of symmetry of the molecule, Fig. 1. This introduces two types of strain to this species; (a) the poles of molecule (along the C7 axis of symmetry) are considerably flat
Fig. 1. (a–c) The structure of D7d–C84 from different views. The carbon atoms and bond critical points of QTAIM are marked by numbers to be easily addressable in tables. (d) The structure of Mo2@D7d–C84.
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and (b) hexagons and pentagons around the edge (equator) of the molecule are non-planar, see Fig. 1. In a recent account Khamatgalimov and Kovalenko mentioned that planar distortion destabilizes the Singlet electronic ground state of fullerenes [21]; since D7d [84]fullerene is highly flat (in poles) it might have a Triplet ground state. The stability of Singlet electronic ground state of the D7d [84]fullerene was examined and the molecule was optimized by unrestricted Triplet wave function to measure the energy gap between Singlet and Triplet states. Interestingly, the Singlet state of the D7d [84]fullerene is 31.0 kcal mol1 more stable than the first Triplet state (at 298 K by considering the thermal correction to energy, the S–T energy gap is 27.2 kcal mol1). In addition, the Triplet state also has the D7d symmetry, like the Singlet state. This novel fullerene is 296 kcal mol1 higher in energy compared to the most stable and the most abundant C84 fullerenes, i.e. the D2d and D2 [84]fullerenes. Although, the D7d [84]fullerene is considerably higher in energy compared to the most stable [84]fullerenes, still there might be a chance to be prepared but not from the routine ways for synthesizing fullerenes. This should be noted that two high-energy isomers of [84]fullerene with D2 and Td point groups have not been identified yet while computational studies confirm that these isomers are kinetically stable concerning their high HOMO–LUMO energy gaps. High S–T energy difference and notable HOMO–LUMO energy gap (2.261 eV) promises that D7d [84]fullerene is a kinetically stable species, particularly, because the smallest vibrational frequency of this species is 184 cm1 at the studied computational level. Interestingly, the HOMO–LUMO energy gap in this fullerene is even more than the most stable C84 fullerenes (D2 and D2d isomers) see Ref. [21] for HOMO–LUMO energy gap details in C84 fullerenes. Large HOMO–LUMO gap is characteristic of aromatic systems. To validate this hypothesis, aromaticity of this species was studied by interatomic magnetizability approach. Table 1 lists the bond magnetizability of different bonds in the D7d [84]fullerene molecule. Studying Table 1 clearly demonstrates that the D7d [84]fullerene is more aromatic than fullerene C60; in addition, bond magnetizability in most of rings in this species is almost comparable with that of well-known aromatic hydrocarbons. The interatomic magnetizability for the three bonds forming the 5membered ring moiety in the D7d [84]fullerene is less than those of its 6- and 7-membered counterparts. In order to obtain a complete picture of magnetic aromaticity in the D7d [84]fullerene, total bond magnetizability, i.e. summation of all bond magnetizabilities in this molecule was compared with that of C60 and two other [84]fullerenes, D2d and D6h [84]fullerenes; Table 2. The latter two [84]fullerenes were selected since the D2d isomer is the most stable [84]fullerene and the D6h isomer has a very similar structure to the
Table 1 The bond magnetizability values for C60, D7d–C84, benzene, cyclopentadienyl anion and tropylium cation. Molecule
Bond
v (C|C)a
C60
BCP (1) BCP (2)
0.60 1.35
C84(UFO)
BCP BCP BCP BCP BCP BCP BCP BCP BCP BCP
2.04 2.63 1.68 2.23 1.51 1.56 2.24 2.22 2.25 2.32
C6H6 C5 H 5 C7 Hþ 7 a
(1) (2) (3) (4) (5) (6) (7)
Average values for both carbon atoms in a bond.
Table 2 Total isotropic intra-atomic magnetizability, vtot iso (C), Total isotropic interatomic magnetizability, vtot iso (C|C), the ratio of inter to intra-atomic isotropic magnetizability and the total bond magnetizability per atom for C60 and three different isomers of C84. The data show that D7d–C84 is the most aromatic species among studied molecules. Molecule
vtot iso (C)
vtot iso (C|C)
tot vtot iso (C|C)/ viso (C)
vtot iso (C|C) per atom
C60 D2d–C84 D6h–C84 D7d–C84
103.584 148.112 144.466 135.363
152.992 274.360 384.040 478.379
1.477 1.852 2.658 3.534
2.550 3.226 4.572 5.695
D7d [84]fullerene. Indeed the D6h isomer has a relatively flat structure and has two coronene-like structures on the pole regions of the molecule. Table 2 clearly shows that the aromaticity of the D7d [84]fullerene is considerably higher than the other studied [84]fullerenes based on the bond magnetizability values, vtot iso (C|C). Although, comparing the magnetic aromaticity of molecules with different number of atoms, based on the total magnetizability, is not reasonable, one may compare the aromaticity of fullerenes with different sizes by dividing the total bond magnetizability of a molecule by the number of atoms in that molecule. As it is presented in Table 2, the studied [84]fullerenes are relatively more aromatic than C60. This could be due to the fact that as fullerenes grow larger, their constituent rings gradually become more and more flat so electrons can circulate easier in the fullerene moiety. Among the studied fullerenes, D7d [84]fullerene has the flattest structure so it is expected that electrons flow easier within this molecule compared to the rest of C84 isomers. It is interesting to note that among the [84]fullerenes the most aromatic species is the highest energy one. This shows that among this family of molecules magnetic aromaticity does not correlate with energy content of molecules. Studying the charge distribution and bonding in this novel structure can help to predict reactive sites of the molecule. As it is shown in Fig. 1, four different types of carbon atoms are distinguishable in the molecule. Table S-1 shows that atoms forming the heptagon ring bear 0.0081 a.u. positive charge. The positive charge of these atoms resemble the positive charge of carbon atoms in tropylium cation, though it should be mentioned that the amount of positive charge of these carbon atoms is less than that of the positive charge on tropylium cation carbon atoms, see Table S-1. The carbon–carbon bond length in heptagon ring is 1.52 Å, 0.12 Å more than the C–C bond length in tropylium cation computed at the same level of theory. The C2 carbon atom next to C1 (see Fig. 1b) is negatively charged, 0.0176 a.u. Carbon atoms marked by 3 and 4 in Fig. 1b are charged positively, 0.0113 a.u., and negatively, 0.0064 a.u., respectively. Electron delocalization is a measure of covalency between different atoms; in addition, delocalization index between carbons 1 and 4 in different aromatic hydrocarbons (para delocalization index, PDI) is a measure of electronic aromaticity [22–25]. PDI in benzene and tropilium cation are 0.1047 a.u. and 0.0541 a.u. respectively at B3LYP/6-31G(d) level of theory, Table S-2. A larger PDI means a higher aromaticity; accordingly, PDI, in contrast to magnetic probes of aromaticity [15], suggests that benzene is more aromatic than tropilium cation. PDI of the 6-membered rings in C60 suggests that their electronic aromaticty is reduced compared with benzene (PDI = 0.0453 a.u.). In D7d–C84, PDI of two different 6- and 7-membered rings are 0.0446 a.u. (for 6-membered rings on the top of molecule), 0.0431 a.u. (for 6-membered ring on the edge of molecule) and 0.0056 a.u. respectively. Indeed, distorted geometry of this molecule should affect p-electron delocalization and this is reflected in reduced PDI values. Particularly, long bond length of the 7-membered ring in this species reduces PDI compared to the tropilium cation.
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However, studying the electron delocalization between the heptagon carbons and the Mo atoms (0.2783 a.u.) suggests some degrees of covalency compared with previously studied metallocenes (0.4518 for Fe(Cp)2, 0.1272 for Al+(Cp)2 and 0.2486 for Ge(Cp)2) [27]. The electron delocalization between Mo atoms in the free Mo2 molecule is 6.1151 a.u.; this value reduces to 3.3419 a.u. between Mo atoms in the complex with D7d–C84. Based on the magnitude of the electron delocalization, the bond order in between Mo2 in Mo2@D7d–C84 complex reduces to 3.3, if we assume that 6.1151 a.u. represents a sextuple bond. The change in electron delocalization is in line with bond length change in the Mo2 molecule. Similarly, studying the percent localization, i.e. the number of electrons localized in an atomic basin divided by the population of that atomic basin multiplied by a hundred [27] shows that percent localization of Mo atoms decrease from 78.16% upon complexation with C84, to 76.56%. This change beside decrease in electron delocalization between Mo atoms shows that electrons of Mo atoms are mainly distributed between Mo atoms and carbons of the C84 fullerene. Accordingly, the bond order of Mo2 within the C84 moiety has decreased, so, its bond length increased. The bond length of the free Mo2 at B3LYP/Def2-TZVP level is 1.907 Å (the experimental bond length, obtained from spectroscopy is 1.938 Å [18]). In the Mo2@D7d–C84 complex the bond length increases by 0.052 Å up to 1.959 Å. In addition, complexation with Mo2 affects the electronic properties of the molecule; the HOMO–LUMO energy gap drops to 0.912 eV in the Mo2@D7d–C84 complex. PDI in 6- and 7-membered rings of the Mo2@D7d–C84 complex decreases compared with the free fullerene, see Table S-2. In order to verify the effect of complexation with Mo2 on the energy content of D7d–C84, Mo2@D2– and D2d–C84 molecules were also studied. The energy of Mo2@D7d–C84 complex remains still more than the Mo2@D2– and D2d–C84 species by 254 and 258 kcal mol1 respectively. It is worth noting that free D2 and D2d [84]fullerenes were 296 kcal mol1 lower in energy compared with the complexed species. Accordingly, complexation decreases the energy difference to some degrees which could judge the suggestion of D7d–C84 synthesis by using the Mo2 as a template.
4. Mo2@D7d–C84 The application of metallic templates for organic synthesis is an old approach which has been vastly employed in the synthesis of crown ethers and cryptands [26]. As mentioned earlier the unprecedented fullerenes have also been synthesized by a similar technique [16]. Templates may form complexes with the synthesized organic hosts during the synthesis, so we tried to find a stable complex between the heptagon rings of the D7d–C84 and a metallic species and suggest that the metallic guest might be useful for synthesizing the D7d–C84 molecule. Among all studied guests the Mo2 molecule forms a sandwich shaped metallocenoid with the D7d–C84. As a matter of fact, surveying the literature shows that complexes between two tropylium rings and the Mo2 molecule, with a structure quite close to the structure of the poles of our proposed fullerene have been prepared [13]. The most stable structure of Mo2@C84 conforms to a molecular geometry with D7d symmetry. In this structure, the Mo2 molecule is positioned along the main axis of symmetry of the D7d–C84 fullerene, Fig. 1. This form is significantly more stable than the form in which the Mo2 is perpendicular to the main axis of symmetry at the B3LYP/6-31G(d) computational level. Complexation with Mo2 influences the charge content of carbon atoms of the D7d– C84; particularly, the atoms of the heptagon ring, which are directly bonded to the Mo atoms, are negatively charged in the complex while these atoms are positively charged in the free D7d–C84. This is evidently due to the charge transfer from the Mo atoms to the carbon moiety. Carbon atoms of the heptagon ring have lower energy compared to the carbon atoms of the free D7d–C84. The bond between carbon atoms of the heptagon ring and the Mo atoms should be classified among closed-shell interactions concerning the magnitude of the Laplacian of the electron density. In addition, the electron density of the (3, 1) critical points between Mo atoms and carbon atoms of the heptagons are lower than other (3, 1) critical points, between carbon atoms. Studying the critical point descriptors of carbon–carbon bonds in D7d–C84, Mo2@D7d–C84 and fullerenes as well as normal hydrocarbons shows that carbon–carbon bonds are almost of the same type, see Table 3.
Table 3 Descriptors of (3, 1) critical points for carbon–carbon bonds in different molecules. The electron density, q(r), virial field function, V(r), Lagrangian kinetic energy, G(r), Hamiltonian kinetic energy, K(r), Laplacian of electron density, L(r), the ratio of Lagrangian kinetic energy to electron density and ellipticity (e), of (3, 1) critical points. All parameters are presented in atomic units. For detailed description of these parameters please see Ref. [28].
q(r)
V(r)
G(r)
K(r)
G(r)/q(r)
e
0.2810 0.3102
0.3351 0.4111
0.0810 0.1023
0.2541 0.3088
0.1731 0.2065
0.2883 0.3298
0.1474 0.2229
(1)a (2)a (3)a (4)a (5)a (6)a (7)a
0.2447 0.2781 0.2878 0.3433 0.2784 0.3032 0.3057
0.2570 0.3349 0.3506 0.4922 0.3322 0.3832 0.4032
0.0625 0.0857 0.0845 0.1170 0.0814 0.0904 0.1016
0.1944 0.2492 0.2661 0.3753 0.2508 0.2928 0.3015
0.1319 0.1635 0.1817 0.2583 0.1694 0.2024 0.1999
0.2554 0.3082 0.2936 0.3408 0.2924 0.2982 0.3324
0.1600 0.3000 0.1425 0.2148 0.1429 0.1486 0.2092
(1)a (2)a (3)a (4)a (5)a (6)a (7)a (8)b (9)c
0.2338 0.2675 0.2954 0.3351 0.2481 0.3052 0.2983 0.0528 0.2488 0.3113 0.2949 0.3121
0.2453 0.3094 0.3705 0.4695 0.3288 0.3929 0.3852 0.0539 0.5794 0.4082 0.3807 0.4024
0.0642 0.0772 0.0893 0.1107 0.0803 0.0948 0.0960 0.0462 0.3876 0.0983 0.0987 0.0923
0.1811 0.2322 0.2812 0.3588 0.2486 0.2981 0.2892 0.0077 0.1919 0.3099 0.2820 0.3101
0.1169 0.1550 0.1919 0.2481 0.1683 0.2033 0.1932 0.0385 0.1957 0.2116 0.1833 0.2178
0.2746 0.3023 0.3023 0.3303 0.3237 0.3106 0.3218 0.8750 1.5579 0.3158 0.3347 0.2957
0.1954 0.1869 0.1524 0.2003 0.1406 0.1799 0.1890 1.6024 0.0003 0.2092 0.2892 0.1411
Molecule C60
BCP (1) BCP (2)
C84(UFO)
BCP BCP BCP BCP BCP BCP BCP
Mo2@UFO
BCP BCP BCP BCP BCP BCP BCP BCP BCP BCP BCP BCP
C6H6 C5 H 5 C7 Hþ 7 a b c
See Fig. 1 for identifying BCP numbers. (3, 1) Critical points between Mo atoms and carbon atoms of heptagons. (3, 1) Critical point between two Mo atoms.
L(r)
Z. Badri et al. / Computational and Theoretical Chemistry 1009 (2013) 103–107
5. Conclusions In the present account a novel isomer for [84]fullerenes is introduced theoretically. The structure of this novel isomer has a D7d point group composed of two heptagons, 28 hexagons and 14 pentagons. Based on the HOMO–LUMO gap, vibrational frequencies and tendency of the molecule toward Singlet ground state (Singlet–Triplet energy difference of 31.0 kcal mol1) it is proposed that this strained structure, though high energy, is kinetically stable. The aromaticity of this novel molecule was studied by the bond magnetizability probe. It is suggested that this molecule is relatively more aromatic in the context of magnetic aromaticity than C60 and normal [84]fullerenes that were considered here. However, PDI values do not confirm a higher aromaticity relative to C60, within the electronic paradigm of aromaticity. A method for probable synthesis of this molecule is also suggested based on application of Mo2 template. It should be mentioned that high energy difference between this molecule and normal [84]fullerenes complexed with Mo2 molecule shows that there is almost no chance for observation of D7d [84]fullerene in thermodynamic control synthetic approaches. It is shown that Mo2 molecule can form a stable complex with this fullerene, which resembles a sandwich shaped metallocenoid. Studying QTAIM parameters, in particular delocalization index, suggests that bonding between the fullerene and the metallic core, Mo2, is covalence in nature. To the bests of our knowledge this molecule is the first proposed fullerene with two heptagon rings which is kinetically stable. Acknowledgments Authors gratefully thank to Prof. M. Sola, Universitat de Girona, Campus de Montilivi, Girona, Spain, for providing computational time (hardware and software) for computations. Authors also thank to the University of Tehran for financial support. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.comptc.2013. 01.005. References [1] H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl, R.E. Smalley, C60: buckminsterfullerene, Nature 318 (1985) 162–163. [2] P.A. Troshin, A.G. Avent, A.D. Darwish, N. Martsinovich, A.K. Abdul-Sada, J.M. Street, R. Taylor, Chemistry: isolation of two seven-membered ring C58 fullerene derivatives: C58F17CF3 and C58F18, Science 309 (2005) 278–281. [3] I.N. Ioffe, C. Chen, S. Yang, L.N. Sidorov, E. Kemnitz, S.I. Troyanov, Chlorination of C86 to C84Cl32 with nonclassical heptagon-containing fullerene cage formed by cage shrinkage, Angew. Chem. Int. Ed. 49 (2010) 4784–4787. [4] P.W. Fowler, T. Heine, D. Mitchell, G. Orlandi, R. Schmidt, G. Seifert, F. Zerbetto, Boron-nitrogen analogues of the fullerenes: the isolated-square rule, J. Chem. Soc., Faraday Trans. 92 (1996) 2203–2210. [5] A. Ayuela, P.W. Fowler, D. Mitchell, R. Schmidt, G. Seifert, F. Zerbetto, C62: theoretical evidence for a nonclassical fullerene with a heptagonal ring, J. Phys. Chem. A 100 (1996) 15634–15636.
107
[6] D.-L. Chen, W.Q. Tian, J.-K. Feng, C.-C. Sun, Structures, stabilities, and electronic and optical properties of C58 fullerene isomers, ions, and metallofullerenes, Chem. Phys. Chem. 8 (2007) 1029–1036. [7] K.Y. Amsharov, M.A. Kabdulov, M. Jansen, Facile bucky-bowl synthesis by regiospecific cove-region closure by HF elimination, Angew. Chem. Int. Ed. 51 (2012) 4594–4597. [8] F. Vines, A. Gorling, Template-assisted formation of fullerenes from shortchain hydrocarbons by supported platinum nanoparticles, Angew. Chem. Int. Ed. 50 (2011) 4611–4614. [9] I.B. Lebedeva, A.A. Knizhnik, A.M. Popov, B.V. Potapkin, Ni-assisted transformation of graphene flakes to fullerenes, J. Phys. Chem. C 116 (2012) 6572–6584. [10] J.A. Martin-Gago, Polycyclic aromatics: on-surface molecular engineering, Nat. Chem. 3 (2011) 11–12. [11] K. Amsharov, N. Abdurakhmanova, S. Stepanow, S. Rauschenbach, M. Jansen, K. Kern, Towards the isomer-specific synthesis of higher fullerenes and buckybowls by the surface-catalyzed cyclodehydrogenation of aromatic precursors, Angew. Chem. Int. Ed. 49 (2010) 9392–9396. [12] G. Otero, G. Biddau, C. Sanchez-Sanchez, R. Caillard, M.F. Lopez, C. Rogero, F.J. Palomares, N. Cabello, M.A. Basanta, J. Ortega, J. Mendez, A.M. Echavarren, R. Perez, B. Gomez-Lor, J.A. Martin-Gago, Fullerenes from aromatic precursors by surface-catalysedcyclodehydrogenation, Nature 454 (2008) 865–868. [13] M. Tamm, T. Bannenberg, R. Frohlich, S. Grimme, M. Gerenkamp, Mono- and dinuclear molybdenum complexes with sterically demanding cycloheptatrienyl ligands, Dalton Trans. (2004) 482–491. [14] R.F.W. Bader, Atoms in Molecules: A Quantum Theory, Oxford University Press, Oxford, UK, 1990. [15] C. Foroutan-Nejad, Interatomic magnetizability: a QTAIM-based approach toward deciphering magnetic aromaticity, J. Phys. Chem. A115 (2011) 12555– 12560. [16] C.M. Beavers, T. Zuo, J.C. Duchamp, K. Harich, H.C. Dorn, M.M. Olmstead, A.L. Balch, Tb3N@C84: an improbable, egg-shaped endohedral fullerene that violates the isolated pentagon rule, J. Am. Chem. Soc. 128 (2006) 11352– 11353. [17] B.E. Bursten, F.A. Cotton, M.B. Hall, Dimolybdenum: nature of the sextuple bond, J. Am. Chem. Soc. 20 (1980) 6348–6349. [18] A.C. Borin, J.P. Gobbo, B.O. Roos, A theoretical study of the binding and electronic spectrum of the Mo2 molecule, Chem. Phys. 343 (2008) 210–216. [19] Gaussian 09, Revision A.02, M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G.A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H.P. Hratchian, A.F. Izmaylov, J. Bloino, G. Zheng, J.L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven Jr., J.A. Montgomery, J.E. Peralta, F. Ogliaro, M. Bearpark. J.J. Heyd, E. Brothers, K.N. Kudin, V.N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J.C. Burant, S.S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J.M. Millam, M. Klene, J.E. Knox, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, R.L. Martin, K. Morokuma, V.G. Zakrzewski, G.A. Voth, P. Salvador, J.J. Dannenberg, S. Dapprich, A.D. Daniels, O. Farkas, J.B. Foresman, J.V. Ortiz, J. Cioslowski, D.J. Fox, Gaussian, Inc., Wallingford, CT, 2009. [20] AIMAll (version 11.02.27), Keith, T.A., 2011.