Article pubs.acs.org/JPCA
Aromatization Energy and Strain Energy of Buckminsterfullerene from Homodesmotic Reactions Cherumuttathu H. Suresh,*,†,‡ Thevarmadam Louis Lincy,† Neetha Mohan,† and Ramachandran Rakhi†,‡ †
Inorganic and Theoretical Chemistry Section, Chemical Sciences and Technology Division, ‡Academy of Scientific & Innovative Research, CSIR-National Institute for Interdisciplinary Science and Technology, Trivandrum 695 019, India S Supporting Information *
ABSTRACT: The amount of aromatic stabilization of C60 fullerene (Earoma) and the amount of its destabilizing strain effect (Estrain) are unknown quantities because both are intimately connected and difficult to separate. Based on experimentally known transformation of C60H30 to C60 and conversion of a polycyclic aromatic hydrocarbon C60H20 to the nonaromatic linear conjugated C60H62, new homodesmotic reaction schemes have been proposed to evaluate Earoma and Estrain. The Earoma values obtained at M06L/6-311G(d,p), M062X/6-311G(d,p), and B3LYP-D3/6-311G(d,p) levels of density functional theory are 122.3, 169.8, and 152.4 kcal/ mol, respectively, whereas Estrain values at these levels are 327.3, 382.0, and 381.4 kcal/mol, respectively. These data suggest that a CC bond of C60 is destabilized by ∼2.28−2.54 kcal/mol compared to that of benzene, and this minor energetic effect explains the existence of C60 as a stable molecule.
■
minimizes strain resulting from the misalignment of sp2 hybrid orbitals on the cage structure due to significant pyramidalization of the carbon atoms. The harmonic oscillator model of aromaticity (HOMA)22 is often used to assess the aromaticity using geometric criteria, and according to this index, the pentagons of fullerene bear antiaromatic character (HOMA = −0.26) while hexagons exhibit some amount of aromatic character (HOMA = 0.35).23 Similarly, nucleus-independent chemical shift (NICS),24 a magnetic criterion of aromaticity, predicts that pentagons in C60 are antiaromatic, with NICS of 6.3 ppm, while hexagons are aromatic, with NICS of −6.8 ppm.25 On the basis of the electronically based index of aromaticity, the para delocalization index (PDI), Sola and coworkers showed that among the polycyclic aromatic hydrocarbons and fullerenes, the rings with the smallest average pyramidalization angles possess the largest local aromaticities.25 Isodesmic reactions26 as well as homodesmotic reactions27 (HDRs) are suggested for the estimation of Earoma and Estrain of a variety of molecules.28,29 In isodesmic reactions, retention of the number of bonds of a given formal type, e.g., C−H, C−C, CC, has to be maintained. Homodesmotic reactions belong to a subset of isodesmic reactions where the number of bonds, type of bonds, and hybridization state of each atoms are conserved. HDRs ensure a very similar amount of electron correlation on both sides of the reaction, giving more accurate thermochemical values from even low-level computational methods because of cancellation of errors. Fowler et al. predicted that the cost of separating the bonds in C60 to 30
INTRODUCTION In 1985, Kroto and co-workers discovered C60 and suggested that it appears to be aromatic.1 Since then, the aromaticity of buckminsterfullerene has been a topic of considerable interest2−11 and various theoretical and experimental studies have been done on this subject.4,11−15 Bühl and Hirsch3 reviewed the aromaticity of fullerenes in depth and based on several criteria summarized that fullerene (C60) is definitely aromatic. In recent reviews on the related topic of aromaticty in endohedral fullerenes, Sola and co-workers concluded that aromatic stabilization energy associated with neutral and hollow fullerenes is relatively small, whereas it plays a fundamental role in determining the molecular structure and reactivity of endohedral metallofullerenes and negatively charged fullerenes.16,17 Though numerous measures of aromaticity, viz. structural, electronic, magnetic, energetic, and reactivity-based, have been proposed, the absolute value of the aromatization energy (Earoma) of fullerene has never been calculated or measured experimentally. For an accurate treatment of aromaticity of fullerene, the strain energy (Estrain) of the molecule must be established because aromaticity and strain are intimately connected in C60, and their separation is difficult to achieve. Hence, an accurate estimation of Earoma and Estrain is elusive, both theoretically and experimentally. According to the isolated pentagon rule (IPR) proposed by Kroto,18 among the 1812 distinct C60 fullerene structures, the most stable is the one that displays icosahedral Ih symmetry as it presents the 12 pentagons isolated from each other. The Ih-C60 is the only isomer that can be predicted from the IPR rule,16,18−20 and it shows pronounced bond length alteration along the [6,6]- and [5,6]-bonds, suggesting partial localization of the π-orbitals and proportional loss of aromaticity. 11,21 This arrangement © 2015 American Chemical Society
Received: February 4, 2015 Revised: June 2, 2015 Published: June 3, 2015 6683
DOI: 10.1021/acs.jpca.5b01157 J. Phys. Chem. A 2015, 119, 6683−6688
Article
The Journal of Physical Chemistry A Scheme 1. Dehyrogenation Pathways for the Formation of C60
approximation, the π-orbital axis vector is defined as the vector that makes equal angles to the three bonds at a conjugated carbon atom. The common angle to the three σ bonds (which are assumed to lie along the internuclear axis) is denoted as θσπ. Bakowies and co-workers32,33 established the relation between θσπ and ΔHf for Cn fullerenes as ΔHf = a∑n1(θσπ − π/2)2 + nb. This equation suggests that 78% of the excess ΔHf of the carbons in C60 above those in graphite originates in the strain of pyramidalization.11 In the POAV1 approximation, Haddon relates the π-orbital hybridization (smp) to the pyramidalization angle θσπ as m = (2sin2(θσπ − π/2))/(1−3sin2(θσπ − π/2)). The POAV analysis sets the strain energy in the fullerenes to 484 kcal/mol and strain per carbon atom to 8 kcal/mol.11 There are several successful attempts to synthesize C60 from strain free condensed aromatic systems. Jenneskens and coworkers reported the synthesis of C60 by MALDI TOF-MS of tribenzo [l:l:l″]benzo[1,2-e:3,4-e′:5,6-e″]triacephenanthrylene (C60H30) by multiple intramolecular cyclodehydrogenation reactions.34 Otero et al. synthesized C60 from polycyclic aromatic hydrocarbons using platinum surface catalyzed cyclodehydogenation at 750 K.35 In 2001, Boorum et al. reported the synthesis of C60 by nitrogen laser irradiation of C60H30 (Scheme 1) at 337 nm36 which induced the loss of hydrogen from C60H30. The direct molecular transformation of C60 from C60H30 is verified by mass spectrometry and 13C isotope labeling.36 Herein we propose that the experimentally known transformation of C60H30 to C60 is useful for gaining insight into the computation of Estrain of C60. In Scheme 1, 1,3,5-tri(benzo[c]phenanthrene-5-yl)benzene (TBPB) is shown as a precursor to C60H30. A retro-synthetic approach will suggest that by cleaving the CC bond at the 1, 3, and 5 positions of the central phenyl ring of TBPB via hydrogenation can give us three benzophenanthrene molecules and one benzene. In fact one of the precursors for C60H30 was a benzophenanthrene derivative. Plater prepared TBPB and trinaphtho-annulated decacylene as precursor to C60.37−39 Thus, Scheme 1 suggests that one benzene and three benzophenanthrene molecules can be combined by dehydrogenation pathways to synthesize C60. Scheme 2 is useful for understanding the successive dehydrogenation steps (b−g) from TBPB to C60. Steps b, c, d, e, f and g will give C60H30, C60H24, C60H18, C60H12, C60H6, and C60, respectively, by eliminating three hydrogen molecules in each step.
isolated double bonds is 536.6 kcal/mol by the isodesmic reaction given in eq 1.30 This amount of energy is not Earoma because in this reaction, the number of Csp3−Csp3 bonds and Csp2−Csp2 bonds are not conserved.30 In other words, 90 Csp2− Csp2 bonds on the reactant side cannot be energetically equated with 60 Csp3−Csp3 single bonds and 30 Csp2−Csp2 double bonds on the product side. Furthermore, strain is not balanced on both sides of the reaction. The reactions proposed by Slayden and Liebman given in eqs 2a and 2b are homodesmotic. On the basis of the homodesmotic stabilization energy of 90.8 kcal/mol obtained from eq 2a (exothermic), they proposed that C60 is not aromatic and better described it as antiaromatic.4,15 In these homodesmotic formalisms, the extracted values are strongly biased by strain, which is impossible to separate out; hence, the actual value of aromatic stabilization cannot be determined. Also, if trans-butadiene is used instead of cis-butadiene, the energy will differ by 213 kcal/mol. In 2007, Salcedo et al. used another homodesmotic reaction scheme in eq 3 and evaluated that the aromatic stabilization energy of C60 is 560.7 kcal/ mol.13,14 Reactions in eqs 2a, 2b, and 3 are fundamentally the same because the product side consists of noncyclic conjugated hydrocarbons. However, the enormous difference in the energy value of eq 3 compared to that of 2a and 2b can be attributed largely to intrinsic strain effect in the nonplanar structure of tetra vinyl ethylene. This result means that proper accounting of strain in C60 is very important for obtaining accurate estimation of its aromatic stabilization energy.
Cyrański et al. formulated a set of homodesmotic reactions (eqs 4a and 4b) in which the reference systems used in the reactant side and product side matched closely to the topology and strain.4 The reference compounds in the product side of the reactions are fragments of fullerene with one six- or one five-membered ring omitted while the reactant sides of the equations are fulfilled by fullerene fragments with top and bottom six- (or five-) membered rings omitted to satisfy the standard homodesmotic reaction requirements. They calculated a value of 93.6 kcal/mol for the strain energy of fullerene.4 Schmalz et al.20 reported an index of strain based on the πorbital axis vector (POAV) analysis11,31 for fullerenes. For a Cn fullerene, POAV is given as ∑n1(θσπ − π/2)2 = 4π/(3√3) = 2.41, where (θσπ − π/2) is in radians.20 In the POAV1
■
COMPUTATIONAL METHODS Geometry optimization of all the reported molecules is carried out using the local meta-GGA exchange−correlation density functional theory (DFT) M06L40 and 6-311G(d,p) basis set. The M06L level of theory developed by Truhlar and Zhao40 includes dispersion effect, and a recent benchmark study from our group41 recommended it for geometry optimization and interaction energy calculation of organic molecular dimers. On 6684
DOI: 10.1021/acs.jpca.5b01157 J. Phys. Chem. A 2015, 119, 6683−6688
Article
The Journal of Physical Chemistry A
very good approximation to the energy change associated with the transformation of six Csp2-H bonds to three formal Csp2− Csp2 single bonds and three H−H bonds. The optimized geometries of the product structures from step b−g reactions, viz., C60H30, C60H24, C60H18, C60H12, C60H6, and C60 and C60H36 are presented in Figure 1.
Scheme 2. Successive Dehydrogenation Steps (b−g) from TBPB to C60
Figure 1. Optimized geometries of C60 and precursors for C60.
the basis of the comments made by one of the reviewers, we also did a benchmark calculation on the energetics of the reported reactions using five more methods, viz., M06L/ccpVDZ, B3LYP/6-311G(d,p),42,43 M062X/6-311G(d,p),44 and B3LYP-D3/6-311G(d,p).45 Among these methods, M06L/ccpVDZ is useful for assessing the effect of basis set on energetics. We also note that the initial structure used for the DFT level optimizations were M06L/6-31G(d) level optimized structures, confirmed as minimum-energy configurations (zero imaginary frequency) in the vibrational frequency calculation at the same level. This compromise on calculation is made to afford the computational cost of frequency calculation. Because almost all the structures are quite rigid and well-defined by interconnected Csp2 atoms, it is very unlikely to find any structures with saddle point character. To verify this, we did the frequency calculation on B3LYP/6-311G(d,p) level geometries and found that they are all energy minima. All the calculations are performed using the Gaussian09 suite46 of programs. The default “FineGrid” option is selected for DFT integration grid. The geometry optimization is completed when the default threshold values used by Gaussian09 for maximum force, RMS force, maximum displacement, and RMS displacement are converged.
Compared to step a reaction, the step b−g reactions produce highly strained molecules. Moreover, for such reactions, the aromatic character of the molecules in the product side may differ from that in the reactant side. As far as the number and type of bonds cleaved and formed are concerned, step b−g reactions are very similar to the step a reaction. Hence, any deviation of the energy of the reactions b−g from the reference value 38.0 kcal/mol for the step a reaction can be accounted for by the combined effect of aromaticity and strain energy of their product molecule. It is found that the energy of step b−g reactions are all higher than step a reaction, indicating that strain effect is dominating in all the product structures and the aromatic character of all of them may be lowered compared to TBPB. At this point we make an assumption that among the structures depicted in Figure 1, the aromatic character is the highest for TBPB and the lowest for fullerene. Furthermore, the decrease in the aromatic stabilization along the series C60H30, C60H24, C60H18, C60H12, C60H6, and C60 is mainly attributed to strain effect. Hence, the cumulative sum of the deviation of the energy of step b−g reactions from the value 38.0 kcal/mol can be accounted for as an upper bound to the total strain energy. C60H30 is planar and suggests that the strain effect due to the formation of three five-membered rings in step b could be very small. In fact, the energy of this step of the reaction, Eb, is 48.5 kcal/mol, meaning that 10.5 kcal/mol can be assigned for the strain energy associated with the formation of C60H30 from TBPB. The energy of the reaction corresponding to steps c, d, e, f, and g (Ec−Eg) are 112.4, 113.4, 119.2, 90.2, and 54.2 kcal/ mol, respectively (Figure 1). The increase in the reaction energy compared to Ea accounts for the strain energy for steps c, d, e, f, and g, which are 74.4, 75.4, 81.2, 52.2, and 16.2 kcal/ mol, respectively. The sum of all the strain energies (steps b−g) will yield the total strain energy 309.9 kcal/mol for the formation of fullerene from benzene and three benzophenanthrene. It may be noted that benzophenanthrene is nonplanar and possesses some strain due to the close proximity of C−H bonds at the terminal rings, whereas its isomer chrysene is planar and possesses no strain. Hence, the energy difference between benzophenenathrene and chrysene (5.8 kcal/mol) is
■
RESULTS AND DISCUSSION First, we discuss the results obtained using the M06L/6311G(d,p) level. When one benzene and three benzophenanthrenes are combined to form TBPB, six C−H bonds are broken and three formal Csp2−Csp2 single bonds are formed along with three molecules of hydrogen (Scheme 1). This reaction is named as step a. Exactly the same chemical changes occur in steps b−g (Scheme 2). The energy of the step a reaction (Ea) is 38.0 kcal/mol. In TBPB, benzophenanthrene moiety shows a twist angle of 49.2° with the central benzene ring. It is almost safe to assume that in step a the aromaticity of benzene and three benzophenanthrene moieties in the reactant side can be equated to the that of TBPB in the product side. Furthermore, no significant strain effect is present in the reaction. Hence, the value 38.0 kcal/mol can be considered as a 6685
DOI: 10.1021/acs.jpca.5b01157 J. Phys. Chem. A 2015, 119, 6683−6688
Article
The Journal of Physical Chemistry A used as a correction factor to account for the strain energy of benzophenanthrene. According to Scheme 1, three times the strain energy of benzophenanthrene has to be added as energy correction factor (Ecorr) to 309.9 kcal/mol to obtain the total strain energy, Estrain, of C60 (327.3 kcal/mol). In Scheme 3, a homodesmotic reaction (HDR-1) is presented for C60. C60 has 30 formal Csp2−Csp2 double bonds
as a stable molecule despite showing a large global value for the strain energy. The energy data presented in Table 1 is useful for comparing the energetics obtained using the M06L/6-311G(d,p) level Table 1. Energy of Step a−g Reactions, Homodesmotic Reactions, and Other Energy Parametersa energy terms
Scheme 3. Homodesmotic Reaction (HDR-1) for C60
step step step step step step step
and 60 formal Csp2−Csp2 single bonds. C60H20 given in the reactant side of the reaction is characterized by 30 formal Csp2− Csp2 double bonds and 50 formal Csp2−Csp2 single bonds. The addition of 10 biphenyl molecules in the reactant side will account for 10 more formal Csp2−Csp2 single bonds to balance the total number of such bonds in the reaction. The number of Csp2−H bonds is also conserved in the reaction. What is not conserved is the strain and aromaticity. Scheme 3 shows that the strained and partially aromatic C60 is converted to unstrained and fully aromatic C60H20. Hence, the energy change associated with the reaction (EHDR‑1) in Scheme 3 will account for the release of strain as well as aromatic stabilization energy. The reaction is exothermic by 437.4 kcal/mol. Because Estrain is 327.3 kcal/mol, we can say that C60H20 possesses 110.1 kcal/mol more aromatic stabilization than C60. The total aromatic stabilization of C60H20 can be evaluated using the homodesmotic reaction (HDR-2) given in Scheme 4.
a
M06L/6311g(D,P)
M06l/ Cc-Pvdz
M062X/6311g(D,P)
B3lyp/6311g(D,P)
B3lyp-D3/6 -311g(D,P)
a b c d e f g
38.0 48.5 112.4 113.4 119.2 90.2 54.2
28.6 38.2 103.9 104.4 109.6 80.5 45.0
27.5 52.3 106.6 114.4 120.9 84.0 53.1
44.6 46.5 116.7 113.2 121.8 94.9 49.3
24.9 46.6 107.1 110.1 115.2 84.2 51.5
Ecorr Estrain EHDRr‑1 EHDR‑2 Earoma
17.4 327.3 −437.4 232.4 122.3
17.8 327.8 −441.4 234.0 120.4
15.6 382.0 −461.6 249.4 169.8
18.0 292.7 −432.8 280.4 140.3
15.9 381.4 −461.0 232.1 152.4
All values are in kilocalories per mole.
with other benchmark methods selected for this study. Changing the basis set from 6-311G(d,p) to cc-pVDZ has only a minor effect on the Estrain and Earoma values as both the quantities are nearly unchanged. Overall, the energy of step a to g reactions shows the same trend at all levels of theory. Considering all levels of theory, compared to step a reaction, endothermic character of step b and step g reactions shows an average increase of 17.5 kcal/mol, whereas that of steps c, d, e, and f reactions are 75.7, 79.4, 85.0, and 53.5 kcal/mol, respectively. The Ecorr (three times the energy difference between benzophenanthrene and chrysene) shows a minor variation in the range of 15.6−18.0 kcal/mol at different levels of theory. The Estrain at B3LYP/6-311G(d,p) is significantly smaller than that of all other dispersion-included DFT methods. Almost the same Estrain values, viz., 382.0 and 381.4 kcal/mol, are observed for the dispersion-included levels M062X/6-311G(d,p) and B3LYP-D3/6-311G(d,p), respectively. Similarly, the energy of the homodesmotic reactions 1 and 2 (EHRD‑1 and EHDR‑2) are comparable at M062X/6311G(d,p) and B3LYP-D3/6-311G(d,p) levels. Compared to B3LYP/6-311G(d,p) level, Earoma obtained at the dispersionincluded B3LYP-D3/6-311G(d,p) shows a 12.2 kcal/mol higher value. The Earoma obtained at M062X/6-311G(d,p) is the highest, 169.8 kcal/mol, which is 17.2 kcal/mol higher than that at B3LYP-D3/6-311G(d,p).
Scheme 4. Homodesmotic Reaction for the Evaluation of Total Aromatic Stabilization of C60H20
Herein, C60H20 is converted to the nonaromatic linear conjugated C60H62. In this reaction, too, the number of formal Csp2−Csp2 single and double bonds are conserved as well as the number of Csp2−H bonds. Because all the bonding aspects are conserved except aromaticity, the reaction energy (EHDR‑2), endothermic by 232.4 kcal/mol, accounts for the loss of aromaticity during the conversion of C60H20 to C60H62. In other words, the value 232.4 kcal/mol is the aromatic stabilization energy of C60H20. Because the aromatization energy of C60 is 110.1 kcal/mol less than that of C60H20, we can say that the total aromatic stabilization energy, Earoma, of C60 is 122.3 kcal/ mol. Because Earoma is stabilizing by 122.3 kcal/mol and Estrain is destabilizing by 327.3 kcal/mol, the total destabilizing thermodynamic effect in C60 is 205.0 kcal/mol, which means that one CC bond of C60 is only 2.28 kcal/mol destabilized compared to a CC bond in benzene. This partitioning of the energy to each bond is justified because the strain and aromaticity effects are delocalized in this highly symmetric molecule. This energy factor can put only a minor effect on the stability of the system, and it also explains the existence of C60
■
CONCLUSIONS On the basis of the experimentally known dehydrogenation reactions of an aromatic hydrocarbon molecule to fullerene and new type of homodesmotic reaction schemes, the aromatic stabilization energy and strain energy of C60 is computed for the first time. Among the DFT methods used for this study, viz. M06L, M062X, B3LYP, and B3LYP-D3, more similarities and close agreement in energy data are seen between M062X and B3LYP-D3. Hence, on the basis of M062X and B3LYP-D3 energy data, we suggest that C60 experiences a strain energy ∼2.25−2.50 fold higher than its aromatic stabilization. However, on average, each C−C bond of C60 shows only a 6686
DOI: 10.1021/acs.jpca.5b01157 J. Phys. Chem. A 2015, 119, 6683−6688
Article
The Journal of Physical Chemistry A
Reactivity of (Endohedral Metallo)fullerenes. Chem. Soc. Rev. 2014, 43, 5089−5105. (17) Garcia-Borras, M.; Osuna, S.; Swart, M.; Luis, J. M.; Sola, M. Maximum Aromaticity as a Guiding Principle for the Most Suitable Hosting Cages in Endohedral Metallofullerenes. Angew. Chem., Int. Ed. 2013, 52, 9275−9278. (18) Kroto, H. W. The Stability of the Fullerenes Cn, with n = 24, 28, 32, 36, 50, 60 and 70. Nature 1987, 329, 529−531. (19) Schmalz, T. G.; Seitz, W. A.; Klein, D. J.; Hite, G. E. C60 Carbon Cages. Chem. Phys. Lett. 1986, 130, 203−207. (20) Schmalz, T. G.; Seitz, W. A.; Klein, D. J.; Hite, G. E. Elemental Carbon Cages. J. Am. Chem. Soc. 1988, 110, 1113−1127. (21) Haddon, R. C.; Raghavachari, K. Electronic Sructure of the Fulleroids: Homoconjugation in Bridged C60 Derivatives. Tetrahedron 1996, 52, 5207−5220. (22) Krygowski, T. M. Crystallographic Studies of Inter- and Intramolecular Interactions Reflected in Aromatic Character of πElectron Systems. J. Chem. Inf. Model. 1993, 33, 70−78. (23) Krygowski, T. M.; Ciesielski, A. Local Aromatic Character of C60 and C70 and their Derivatives. J. Chem. Inf. Model. 1995, 35, 1001− 1003. (24) Schleyer, P. v. R.; Maerker, C.; Dransfeld, A.; Jiao, H.; van Eikema Hommes, N. J. R. Nucleus-Independent Chemical Shifts: A Simple and Efficient Aromaticity Probe. J. Am. Chem. Soc. 1996, 118, 6317−6318. (25) Poater, J.; Fradera, X.; Duran, M.; Sola, M. An Insight into the Local Aromaticities of Polycyclic Aromatic Hydrocarbons and Fullerenes. Chem. - Eur. J. 2003, 9, 1113−1122. (26) Hehre, W. J.; Ditchfield, R.; Radom, L.; Pople, J. A. Molecular Orbital Theory of the Electronic Structure of Organic Compounds. V. Molecular Theory of Bond Separation. J. Am. Chem. Soc. 1970, 92, 4796−4801. (27) Wheeler, S. E.; Houk, K. N.; Schleyer, P. v. R.; Allen, W. D. A Hierarchy of Homodesmotic Reactions for Thermochemistry. J. Am. Chem. Soc. 2009, 131, 2547−2560. (28) Suresh, C. H.; Koga, N. Accurate Calculation of Aromaticity of Benzene and Antiaromaticity of Cyclobutadiene: New Homodesmotic Reactions. J. Org. Chem. 2002, 67, 1965−1968. (29) Suresh, C. H.; Koga, N. An Isodesmic Reaction Based Approach to Aromaticity of a Large Spectrum of Molecules. Chem. Phys. Lett. 2006, 419, 550−556. (30) Fowler, P. W.; Collins, D. J.; Austin, S. J. Is Aromaticity a Useful Concept for C60 and Its Derivatives - Aromatization of C60 by Regioselective Addition. J. Chem. Soc., Perkin Trans. 2 1993, 275−277. (31) Haddon, R. C. π-Electrons in Three Dimensions. Acc. Chem. Res. 1988, 21, 243−249. (32) Bakowies, D.; Thiel, W. MNDO Study of Large Carbon Clusters. J. Am. Chem. Soc. 1991, 113, 3704−3714. (33) Bakowies, D.; Gelessus, A.; Thiel, W. Quantum Chemical Study of C78 Fullerene Isomers. Chem. Phys. Lett. 1992, 197, 324−329. (34) Gómez-Lor, B.; Koper, C.; Fokkens, R. H.; Vlietstra, E. J.; Cleij, T. J.; Jenneskens, L. W.; Nibberinge, N. M. M.; Echavarrena, A. M. Zipping Up ‘The Crushed Fullerene’ C60H30: C60 by Fifteen-Fold, Consecutive Intramolecular H2 Losses. Chem. Commun. 2002, 370− 371. (35) Otero, G.; Biddau, G.; Sánchez-Sánchez, C.; Caillard, R.; López, M. F.; Rogero, C.; Palomares, F. J.; Cabello, N.; Basanta, M. A.; Ortega, J.; et al. Fullerenes from Aromatic Precursors by SurfaceCatalysed Cyclodehydrogenation. Nature 2008, 454, 865−868. (36) Boorum, M. M.; Vasil’ev, Y. V.; Drewello, T.; Scott, L. T. Groundwork for a Rational Synthesis of C60: Cyclodehydrogenation of a C60H30 Polyarene. Science 2001, 294, 828−831. (37) Plater, M. J.; Praveen, M.; Schmidt, D. M. Buckybowl Synthesis: A Novel Application of Flash Vacuum Pyrolysis. Fullerene Sci. Technol. 1997, 5, 781−800. (38) Plater, M. J. Fullerene Tectonics. Part 1. A Programmed Precursor to C60. J. Chem. Soc., Perkin Trans. 1 1997, 1, 2897−2901. (39) Mehta, G.; Rao, H. S. P. Synthesis Studies Directed Towards Bucky-Balls and Bucky-Bowls. Tetrahedron 1998, 54, 13325−13370.
marginal decrease in strength compared to a CC bond of benzene.
■
ASSOCIATED CONTENT
S Supporting Information *
Total energy of optimized structures at various levels of DFT (Table S1); first three low vibrational frequencies of the optimized structures at B3LYP/6-311G(d,p) level of DFT (Table S2); and energies and X,Y,Z-coordinates of all the optimized structures at the M06L/6-311G(d,p) level. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b01157.
■
AUTHOR INFORMATION
Corresponding Author
*Email:
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS This research is supported by the Council of Scientific and Industrial Research (CSIR), Govt. of India, through the MSM Project CSC0129.
■
REFERENCES
(1) Kroto, H. W.; Heath, J. R.; O’Brien, S. C.; Curl, R. F.; Smalley, R. E. C60: Buckminsterfullerene. Nature 1985, 318, 162−163. (2) Bühl, M. The Relation Between Endohedral Chemical Shifts and Local Aromaticities in Fullerenes. Chem.Eur. J. 1998, 4, 734−739. (3) Bühl, M.; Hirsch, A. Spherical Aromaticity of Fullerenes. Chem. Rev. 2001, 101, 1153−1183. (4) Cyrański, M. K.; Howard, S. T.; Chodkiewicz, M. L. Bond Energy, Aromatic Stabilization Energy and Strain in IPR Fullerenes. Chem. Commun. 2004, 7, 2458−2459. (5) Elser, V.; Haddon, R. C. Icosahedral C60 - An Aromatic Molecule With a Vanishingly Small Ring Current Magnetic Susceptibility. Nature 1987, 325, 792−794. (6) Hirsch, A.; Chen, Z. F.; Jiao, H. J. Spherical Aromaticity in Ih Symmetrical Fullerenes: The 2(N+1)2 Rule. Angew. Chem., Int. Ed. 2000, 39, 3915−3917. (7) Johansson, M. P.; Juselius, J.; Sundholm, D. Sphere Currents of Buckminsterfullerene. Angew. Chem., Int. Ed. 2005, 44, 1843−1846. (8) Pasquarello, A.; Schluter, M.; Haddon, R. C. Ring Currents in Topologically Complex-Molecules - Application to C60, C70, and their Hexa-Anions. Phys. Rev. A: At., Mol., Opt. Phys. 1993, 47, 1783−1789. (9) Poater, J.; Duran, M.; Sola, M. Analysis of Electronic Delocalization in Buckminster Fullerene (C60). Int. J. Quantum Chem. 2004, 98, 361−366. (10) Pasquarello, A.; Schluter, M.; Haddon, R. C. Ring Currents in Icosahedral C60. Science 1992, 257, 1660−1661. (11) Haddon, R. C. Chemistry of the Fullerenes - The Manifestation of Strain in a Class of Continuous Aromatic-Molecules. Science 1993, 261, 1545−1550. (12) Austin, S. J.; Fowler, P. W.; Hansen, P.; Manolopoulos, D. E.; Zheng, M. Fullerene Isomers of C60 Kekule Counts Versus Stability. Chem. Phys. Lett. 1994, 228, 478−484. (13) Salcedo, R.; Fomina, L. Homodesmotic Reaction for Fullerenes. Tetrahedron Lett. 2007, 48, 7731−7731. (14) Salcedo, R.; Fomina, L. Homodesmotic Reaction for Fullerenes. Tetrahedron Lett. 2007, 48, 3949−3951. (15) Slayden, S. W.; Liebman, J. F. The Energetics of Aromatic Hydrocarbons: An Experimental Thermochemical Perspective. Chem. Rev. 2001, 101, 1541−1566. (16) Garcia-Borras, M.; Osuna, S.; Luis, J. M.; Swart, M.; Sola, M. The Role of Aromaticity in Determining the Molecular Structure and 6687
DOI: 10.1021/acs.jpca.5b01157 J. Phys. Chem. A 2015, 119, 6683−6688
Article
The Journal of Physical Chemistry A (40) Zhao, Y.; Truhlar, D. G. A New Local Density Functional for Main-Group Thermochemistry, Transition Metal Bonding, Thermochemical Kinetics, and Noncovalent Interactions. J. Chem. Phys. 2006, 125, 194101−194118. (41) Remya, K.; Suresh, C. H. Which Density Functional is Close to CCSD Accuracy to Describe Geometry and Interaction Energy of Small Noncovalent Dimers? A Benchmark Study Using Gaussian09. J. Comput. Chem. 2013, 34, 1341−1353. (42) Becke, A. D. Density-Functional Thermochemistry III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648−5652. (43) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 37, 785−789. (44) Zhao, Y.; Truhlar, D. G. Comparative DFT Study of Van der Waals Complexes: Rare-Gas Dimers, Alkaline-Earth Dimers, Zinc Dimer, and Zinc-Rare-Gas Dimers. J. Phys. Chem. A 2006, 110, 5121− 5529. (45) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A. Consistent and Accurate ab initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132, 154104. (46) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.et al.; Gaussian 09, revision D.01; Gaussian, Inc.: Wallingford, CT, 2013.
6688
DOI: 10.1021/acs.jpca.5b01157 J. Phys. Chem. A 2015, 119, 6683−6688
