Scientific paper
Theoretical Study on Stability and Spectroscopy of C84O 2 Based °n C84(D2d)
Jingcheng Fu,1'2 Jiangmiao Yuan,1 Anni Ren,1 Qiwen Teng1 and Shi Wu1'*
1 Department of Chemistry, ZhejiangUniversity, 310027 Hangzhou, China
2 School of Medical Engineering, HefeiUniversity of Technology, 230009 Hefei, China
* Corresponding author: E-mail: wushi@zju.edu.cn Tel.: +8657181634787
Received: 08-05-2012
Abstract
The relative stabilities of the twenty-three possible isomers for C84O2 based on C84(D2d) were studied by using density functional theory (DFT) at B3LYP/6-31G(d) level. The most stable isomer of C84O2 was found to be 1,5,8,9-C84O2 which contains annulene-like structures. In this isomer, two oxygen atoms are added on the same hexagon, which is called a same-ring adduct. The energy gap of C84O2 is narrower than that of C84(D2d). The chemical shifts of the bridged carbon atoms in C84O2 are changed upfield compared with those of the same carbon atoms in C84(D2d). The same-ring adduct possesses the higher aromaticity than C84(D2d). The area within the range of 0.2 nm from the cage center of C84(D2d) or C84O2 is the most suitable area for calculating NICS values.
Keywords: C84O2, energy gap, NICS, B3LYP/6-31G(d).
1. Introduction
The fullerene C84 is the most abundant empty cage extractable from arc-processed soot. Fullerene epoxides can be utilized to prepare fullerene-based films. These films own the ability to store electrons, thus they are widely used in an energy storage battery. The higher fullerene C84 exhibits the thermodynamic stability since fullerenes become more stable as the number of carbon atoms increases.1 The C84 cage with the D2d symmetry is a stable isomer compared with other isomers of C84.2 Both resonance and strain energy are used to predict stabilities of the higher fullerenes including C84(D2d).3 Besides the stabilities of the fullerenes, the aromaticity of the spherical species C84(D2d) has been studied using different methods, which extends the traditional concept of aromaticity on the two-dimensional annulenes.4 At the same time, there is a great progress on the spectroscopic study of C84(D2d). C84(D2d) shows a UV absorption at 600 nm.5 The broad ESR signal of C84(D2d) is caused by the degenerate LU-MO,6 and affected by temperature.7 The triplet lifetime of C84(D2d) is short even at low temperature.8 In addition, the electronic coupling of the endohedral complexes
Kx@C840D2<j) is proved in the EPR experiment.9 Also, some new exohedral adductsof C84(D2d) have been synthesized.10 Simultaneously, the possible additive sites of the oxygen atom in C84(D2d) are studied, and the most stable isomer of C84O is predicted.11
However, theoretical study on C84O2 based on C84(D2d) has not been reported. Herein, we design twenty-three geometries of C84O2. At first, we focus on looking for the most stable geometry. Also, we concentrate whether the additive bond is broken. Then, we distinguish annulene-like structures and epoxy structures by NMR calculations. Finally, we discuss the connection between the stability and aromaticity, which is also the novelty of the thesis.
2. Computational Details
In view of the IUPAC rule, a numbering system of C84(D2d) is applied.12 Full geometric optimization of C84(D2d) without any symmetrical restriction was carried out by using Becke three parameters plus Lee, Yang, and Parr's (B3LYP) method with the 6-31G basis set in DFT.13
This method, in GAUSSIAN 03 program,14 has been used to study electronic structures of supra-molecular complexes,15 hydrogen bonding systems,16,17 fluorescent materials,18 fullerene derivatives,19,20 and other compounds.21 Since there are numeral isomers of C84O2, it is important to reduce the number of these isomers so as to simplify the calculation. As the oxygen atom was added one by one in the synthetic experiment of C60On,22 the C84O2 isomers were designed based on the isomers of C84O. The most stable three isomers of C84O, which were 8,9-C84O, 13,31-C84O and 12,13-C84O,18 were used. To make comparison, the unstable isomer 1,2-C84O was considered. In addition, some isomers of C84O2 with two far oxygen atoms were also designed. As a result, twenty-three isomers of C84O2 were formed. Similar geometric optimization was performed and the equilibrium geometries were accomplished. After that, the energies at the single point were calculated at B3LYP/6-31G(d) level. Based on the B3LYP/6-31G optimized geometries, the 13C NMR spectra and NICS values were calculated at B3LYP/6-31G level on the GIAO method.23 These NICS
values were investigated by using a dummy center of the
geometry.24,25
3. Results and Discussion
3. 1. Relative Energies and Stabilities
The bond lengths in C84(D2d) are calculated to be within 0.137-0.147 nm, which are in agreement with those in literature.26 The distance between the two farthest atoms in C84(D2d) is 0.851 nm, which is consistent with the experiment.27 The three dimensional diameters of C84(D2d) are 0.799, 0.846 and 0.850 nm, respectively, which are also identical to the reference results.28
According to the relative energies of the C84O2 isomers (Table 1), C84O2(A) is the most stable isomer. The total energy of C84O2(A) is -91193.851 eV. In C84O2(A), the two oxygen atoms are added on the 1,5- and 8,9-bonds. These bonds are located on the same hexagon, and then this isomer is called same-ring adduct. Actually, C84O2(B)-C84O2(D) are all same-ring adducts. On the contrary, the unstable isomers C84O2(Q)-C84O2(S) are different-ring adducts, where the two oxygen atoms are added on different rings. Therefore, same-ring adducts are generally more stable than different-ring adducts. The conjugation system is destroyed owing to the addition of the first oxygen atom, and the bonds nearby are activated. Consequently, the second oxygen atom is easily added on the same hexagon. It has been proved experimentally that the second oxygen atom is added to the bonds near the first oxygen atom in C60O2,29 which supports our conclusion.
Isomers with annulene-like structures are more stable than those with epoxy structures. In C84O2(A), the lengths of the additive bonds C(1)-C(5) and C(8)-C(9)
Table 1. Several parameters of the C84O2 isomers at B3LYP/6-31G(d) level
Isomers	Er (eV)	Eg (eV)	NICSa (ppm)
1,5,8,9-C84O2(A)	0	2.011	-6.5
6,7,8,9-C84O2(B)	0.103	2.011	-6.5
11,29,13,31-C84O2(C)	0.196	1.781	-5.8
8,9,10,27-C84O2(D)	0.308	1.956	-6.2
8,9,36,57-C84O2(E)	0.362	1.969	-4.3
8,9,25,26-C84O2(F)	0.363	1.956	-6.1
8,9,62,79-C84O2(G)	0.395	1.969	-4.2
11,29,12,13-C84O2(H)	0.479	2.032	-7.1
8,9,74,83-C8402(I)	0.571	1.826	-4.0
13,31,62,79-C84O2(J)	0.642	1.826	-4.0
8,9,13,31-C84O2(K)	0.661	1.861	-4.1
8,9,19,40-C84O2(L)	0.708	1.953	-4.7
Isomers	Er (eV)	Eg (eV)	NICS (ppm)
13,31,44,45-C84O2(M)	0.868	1.733	-3.1
8,9,12,13-C84O2(N)	0.920	1.909	-3.9
12,13,44,45-C84O2(O)	0.980	1.856	-4.6
13,31,36,57-C84O2(P)	0.991	1.862	-3.9
8,9,18,19-C84O2(Q)	1.007	1.861	-3.9
3,4,8,9-C84O2(R)	1.067	1.923	-4.2
12,13,17,18-C84O2(S)	1.429	1.986	-4.9
2,12,13,31-C84O2(T)	1.826	1.713	-4.5
1,2,7,22-C^O^U)	1.869	1.957	-7.4
7,22,47,48-C^O^V)	2.016	1.974	-6.5
7,22,46,47-C^O^W)	2.351	1.914	-5.5
a: The NICS values were calculated at B3LYP/6-31G level.
are 0.228 and 0.235 nm. These bonds are broken, thus the annulene-like structures are formed (Figure 1). The lengths of the additive C-C bonds in the isomers C84O2(B)-C84O2(S) are located in the range of 0.2190.236 nm, and the C-O-C angles are larger than 100°. As a result, the annulene-like structures are formed. The cyclic tension on the cage is reduced in the annulene-like structures, thus these isomers are stable. Hitherto, the an-nulene-like isomers of C60O and C70O have been synthe-sized.30,31 Contrarily, the lengths of the additive bonds in
Figure 1. The optimized geometry of 1,5,8,9-C84O2 at B3LYP/6-31G level.
the unstable isomer C84O2(T)-C84O2(W) range from 0.156 to 0.158 nm, and the C-O-C angles are located around 60°. These bonds are not broken, thus the epoxy structures are produced.
3. 2. Energy Gap
The kinetic stability of C84O2 is affected by energy gaps. The energy gap of C84(D2d) is 2.046 eV, which is consistent with the calculation result 2.05 eV.27 The energy gap of C84O2(A) is 2.011 eV. The energy gaps of the other isomers vary from 1.713 to 2.032 eV. Thus C84O2 owns the narrower energy gap than C84(D2d). Since the valence electrons of the oxygen atoms are filled into the anti-bonded orbitals of C84(D2d), the symmetry of C84(D2d) is decreased and degeneracy of the energy levels is eliminated. Then C84O2 shows a low kinetic stability and high chemical reactivity compared with C84(D2d). Although C84O2 has not been synthesized, C60O2 exhibits a narrow energy gap and good reactivity as well as the first red-shifted absorption compared with C60.32
The energy gap of the thermodynamically stable isomer C84O2(C) is narrow, whereas that of the unstable isomer C84O2(S) is wide. Therefore, the thermodynamic
stability of C84O2 does not correlate with the kinetic stability, as Slanina et al. proposed.33
3. 3. 13C NMR Spectra
The anisotropic chemical shifts of the carbon atoms in C84(D2d) are located in the range of 143.6-169.0 ppm (Figure 2), which are basically compatible with the experimental results.34 The chemical shifts of C(1), C(5), C(8) and C(9) in C84O2(A) are located at 117.2, 129.1, 110.8 and 101.0 ppm; whereas those of the same carbon atoms in C84(D2d) appear at 148.8, 149.8, 168.0 and 166.5 ppm. Thus the chemical shifts of the bridged carbon atoms in C84O2(A) are changed upfield compared with those of the same carbon atoms in C84(D2d). The similar regularity has been observed in the other annulene-like isomers. The electron density on the bridged carbon atoms in the annu-lene-like structures is intensified due to the strong electronegativity of the oxygen atoms, thus the shielding effect is improved. The experimental chemical shift of the bridged carbon atom in the annulene isomer of C70CH2 is 118.7 ppm,31 which supports our results.
The chemical shifts of C(7), C(22), C(46) and C(47) in C84O2(W) appear at 66.1, 62.3, 55.4 and 66.0 ppm,
Figure 2. The 13C NMR spectra of C84(D2d) and C84O2 isomers at B3LYP/6-31G level.
which are transferred upfield compared with those of the same carbon atoms in C84(D2d). The analogous phenomenon is found in the other epoxy structures owing to the presence of the bridged carbon atoms with the sp3-hy-bridyzation. The experimental chemical shifts of the bridged carbon atoms in the cyclopropane isomer of
C70CH2 are 62.6 and 64.1 ppm,3 sion.
supporting our conclu- —
3. 4. Aromaticity
The NICS value at the cage center of C84(D2d) is -4.6 ppm at B3LYP/6-31G level,11 which is coincident with the calculation results -3.9, -5.2, -9.5 and -11.4 ppm at B3LYP/3-21G, B3LYP/6-31G*, HF/3-21G and HF/6-31G* levels.4 The experimental 3He chemical shift of C84(D2d) is -7.5 ppm.35 The NICS values of C84O2(A)-C84O2(D) (Table 1) are lower than that of C84(D2d). Thus, the annulene-like same-ring adducts of C84O2 are highly aromatic compared with C84(D2d). The conjugation system in these isomers is well maintained, and the shielding effect is intensified. The 3He chemical shifts at -8.2 and -6.6 ppm of the annulene isomers for C60O and C60CH2 are lower than the value at -6.4 of C60(Ih),36 which supports our results. Other annulene-like isomers such as C84O2(E) and C84O2(G) are lowly aromatic, relative to C84(D2d). They are different-ring adducts.
Some epoxy isomers C84O2(U) and C84O2(V) even display the lower NICS values than the annulene-like isomers C84O2(A)-C84O2(D). Then C84O2(U) and C84O2(V) are highly aromatic. The 3He chemical shifts at -8.1 and -28.1 ppm of the cyclopropane isomers for C60CH2 and C70CH2 are lower than those at -6.6 and -27.5 ppm of the annulene isomers,36 which supports our results.
The NICS curves in C84(D2d) (Figure 3) and C84O2(A) (Figure 3, curve A-D) were obtained by moving the dummy center from ring A or B-D (Figure 1) to the opposite ring, through the cage center. The NICS values in the range of 0.2 nm from the cage center of C84(D2d) are all near -4.6 ppm. Therefore, this range is an insensitive area for calculating the NICS values. The NICS values within 0.2 nm from the cage center of C84O2(A) are lower than those of C84(D2d). The aromaticity of C84O2(A) is improved owing to the extension of the conjugation system caused by the annulene-like structures. The NICS value at 4.9, 8.6 or 10.6 ppm at the center of pentagon B, C or D is higher than that at -0.2, -0.5 or -1.6 ppm at the center of the opposite hexagon, respectively. The conjugation effect on the pentagon with low n-electron cloud is weaker than that on the hexagon. The NICS minimum on curve B, C or D appears at -0.3 nm from the cage center, different from that on curve A. Curve A shows a higher symmetry than curve B, C or D since the two oxygen atoms are added on ring A. Therefore, the shielding effects of different paths in the cage are anisotropic owing to the addition of the oxygen atoms.
Figure 3. The NICS curves in C84(D2d) and C84O2(A).
4. Conclusion
In summary, annulene-like isomers of C84O2 are more stable than the epoxy ones. For the annulene-like isomers, same-ring adducts are more stable than different-ring adducts. The C-C bonds near the oxygen atoms are activated, which will be easily added by the next oxygen atom. C84O2 owns the narrower energy gap than C84(D2d). The chemical shifts of the bridged carbon atoms in C84O2 are changed upfield compared with those of the same carbon atoms in C84(D2d). Same-ring annulene-like adducts exhibit the higher aromaticity than different-ring annu-lene-like adducts. The hexagons in C84O2(A) are highly aromatic relative to the pentagons, and the shielding effects in different paths show the anisotropic characters.
5. Acknowledgements
We would like to thank Prof. Jikang Feng at Jilin University for helpful discussion.
6. References
1.	A. Rojas, M. Martinez, P. Amador, L. A. Torres, J. Phys. Chem. B 2007, 111, 9031-9035.
2.	N. Tagmatarchis, A. G. Avent, K. Prassides, T. J. S. Dennis, H. Shinohara, Chem. Commun. 1999, 1023-1024.
3.	C. H. Sun, G. Q. Lu, H. M. Cheng, J. Phys. Chem. A 2006, 110, 299-302.
4.	Z. Chen, R. B. King, Chem. Rev. 2005, 105, 3613-3642.
5.	T. J. S. Dennis, T. Kai, K. Asato, T. Tomiyama, H. Shinohara, T. Yoshida, Y. Kobayashi, H. Ishiwatari, Y. Miyake, K. Kikuchi, Y. Achiba, J. Phys. Chem. A 1999, 103, 8747-8752.
6.	M. Zalibera, P. Rapta, A. A. Popov, L. Dunsch, J. Phys. Chem. C 2009, 113, 5141-5149.
7.	J. A. Azamar-Barrios, T. J. S. Dennis, S. Sadhukan, H. Shinohara, G. E. Scuseria, A. Penicaud, J. Phys. Chem. A 2001, 105, 4627-4632.
8.	E. C. Booth, S. M. Bachilo, M. Kanai, T. J. S. Dennis, R. B. Weisman, J. Phys. Chem. C 2007, 111, 17720-17724.
9.	K. M. Allen, T. J. S. Dennis, M. J. Rosseinsky, H. Shinohara, J. Am. Chem. Soc. 1998, 120, 6681-6689.
10.	F. B. Kooistra, V. D. Mihailetchi, L. M. Popescu, D. Kronholm, P. W. M. Blom, J. C. Hummelen, Chem. Mater. 2006, 18, 3068-3073.
11.	H. Sun, X. Yun, S. Wu, Q. Teng, J. Mol. Struct. (Theochem) 2008, 868, 71-77.
12.	E. W. Godly, R. Taylor, Pure Appl. Chem. 1997, 69, 14111434.
13.	A. D. Becke, J. Chem. Phys. 1993, 98, 5648-5652.
14.	M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, T. Vreven Jr., K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima,Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, C. Adamo, J. Jaramillo, R. Gom-perts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Ma-lick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, J. A. Pople, Gaussian 03, Revision B. 01, Gaussian Inc., Pittsburgh, PA, 2003.
15.	Z. Wang, S. Wu, Chem. Pap. 2007, 61, 313-320.
16.	I. Majerz, I. Olovsson, Acta Chim. Slov. 2011, 58, 379-384.
17.	B. de Oliveira, R. de, A. Acta Chim. Slov. 2009, 56, 704-711.
18.	L. Ding, Y. Ding, Q. Teng, K. Wang, Chin. J. Chem. 2008, 26, 97-100.
19.	X. Wen, X. Ren, S. Wu, Acta Chim. Slov. 2008, 55, 419-42.
20.	H. Zhang, T. Chen, Y. Yu, S. Wu, Acta Chim. Slov. 2011, 58, 217-222.
21.	L. Turker, S. Gumus, Acta Chim. Slov. 2009, 56, 246-253.
22.	T. Hamano, T. Mashino, M. Hirobe, Chem. Commun. 1995, 1537-1538.
23.	K. Wolinski, J. F. Hinton, P. Pulay, J. Am. Chem. Soc. 1990, 112, 8251-8260.
24.	Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta, P. v. R. Schleyer, Chem. Rev. 2005, 105, 3842-3888.
25.	P. v. R. Schleyer, C. Maerker, A. Dransfeld, H. Jiao, N. J. R. v. E. Hommes, J. Am. Chem. Soc. 1996, 118, 6317-6318.
26.	G. Y. Sun, M. Kertesz, J. Phys. Chem. A 2001, 105, 52125220.
27.	C. E. Moore, B. H. Cardelino, X. Q. Wang, J. Phys. Chem. 1996, 100, 4685-4688.
28.	X. Q. Wang, C. Z. Wang, B. L. Zhang, K. M. Ho, Chem. Phys. Lett. 1993, 207, 349-353.
29.	J. P. Deng, C. Y. Mou, C. C. Han, J. Phys. Chem. 1995, 99, 14907-14910.
30.	R. B. Weisman, D. Heymann, S. M. Bachilo, J. Am. Chem. Soc. 2001, 123, 9720-9721.
31.	A. B. Smith III, R. M. Strongin, L. Brard, G. T. Furst, W. J. Romanow, K. G. Owens, R. J. Goldschmidt, R. C. King, J. Am. Chem. Soc. 1995, 117, 5492-5502.
32.	A. L. Balch, D. A. Costa, B. C. Noll, M. M. Olmstead, J. Am. Chem. Soc. 1995, 117, 8926-8932.
33.	Z. Slanina, L. Stobinski, P. Tomasik, H. Lin, L. Adamo-wicze, J. Nanosci. Nanotechnol. 2003, 3, 193-198.
34.	T. J. S. Dennis, T. Kai, T. Tomiyama, H. Shinohara, Chem. Commun. 1998, 619-620.
35.	G. W. Wang, M. Saunders, A. Khong, R. J. Cross, J. Am. Chem. Soc. 2000, 122, 3216-3217.
36.	A. B. Smith III, R. M. Strongin, L. Brard, W. J. Romanow, J. Am. Chem. Soc. 1994, 116, 10831-10832.
Povzetek
S teorijo gostotnega potenciala (DFT) na B3LYPD6-31G(d) nivoju smo na osnovi C84(D2d) raziskovali relativne energije in stabilnost nekaterih možnih izomer C84O2. Izkazalo se je, da je najbolj stabilna izomera 1,5,8,9-C84O2, v kateri se tvorijo anulenu podobne strukture, kjer sta dva kisikova atoma dodana na isti heksagon. Te izomere imajo tudi bolj aro-matski značaj kot C84(D2d). Jedrno neodvisni kemijski premik (NICS) v1,5,8,9-C84O2 se manjša in doseže minimum v bližini centra, narašča pa proti površini kletke.