Scientific paper
Relative Stability and Spectroscopic Regularity of C80O Based on C80(D5rf)
Haomiao Zhang,1,2 Tanzhang Chen,2 Yingying Yu2 and Shi Wu1*
1 Department of Chemistry, Zhejiang University, 310027 Hangzhou,China
2 Department of Chemical Engineering & Bioengineering, Zhejiang University, 310027 Hangzhou, China
* Corresponding author: E-mail: wushi@zju.edu.cn Tel.: +86-57188206529
Received: 19-05-2010
Abstract
The relative stabilities of the nine possible isomers for C80O based on C80(D5d) were investigated via density function theory (DFT) at B3LYP/6-31G(d) level. The most stable geometry of C80O is predicted to be 23,24-C80O, where an an-nulene-like structure is formed. The stretching vibration frequencies of the C=C bonds in the IR spectrum of C80O compared with those of the C=C bonds in the IR spectrum of C80(D5d) are basically blue-shifted. The signals of the bridged carbon atoms in the NMR spectrum of C80O, computed at B3LYP/6-31G level, are changed upfield compared with those of the correspoding carbon atoms in the NMR spectrum of C80(D5d). The anti-aromaticity of rings in C80O relative to that of the corresponding rings in C80(D5d) is decreased according to the NICS values at the dummy centers of these rings calculated at B3LYP/6-31G level. A hexagon in 21,22-C80O even shows a tendency of aromaticity.
Keywords: C80O, B3LYP/6-31G(d), blue-shift, 13C NMR, NICS.
1. Introduction
The functionalization of fullerenes has been an interesting research field for recent years because the modified fullerenes can be widely used in medicine, pharmacy and material science. There are seven isomers of the fulle-rene cage C80 satisfying the isolated pentagon rule (IPR). These isomers are C80(C2v), C80(C2v,), C80(D2), C80(D3), C80(D5d), C80(D5h) and C80(/h), respectively. Q^) and C80(D5d) are predicted to be more stable than the other five isomers by using DFT.1 Furthermore, the C2 fragmentation energy of C80(D5d) is slightly higher than that of C80(D2).2 Despite this, C80(D5d) has been synthesized and characterized, which owns the five unique carbon atoms.3 For C80(D5d) has also been proven to possess a typical structure with pyrene-like tetracycle moieties on the ellipsoidal cage,4 which show a high reactivity.5'6 The conjugation system of C80(D5d) is able to accept extra electrons. When two electrons in the Ti atom of Ti2@C80(D5d) are transferred to the cage, the C804-(D5d) can be formed.7 The similar electron transfer occurs in Sc2@C80(D5d). Thus the energy gap of Sc2@C80(D5d) compared to that of C80(D5d) is reduced,8 which is favorable to elevating the semi-conductivity of the material. The thermodynamic stability of
C80(D5d) can be improved by the endohedral doping with the Be, C, Si, or Ge atoms.9 Simultaneously, the physical properties of C80(D5d) like the magnetic moment can be changed by increasing the number of the Er3+ ions in Er-Sc2N@C80.10 Besides the encapsulation inside the cage, the exohedral chemical functionalization on the cage also alters the characters of C80(D5d). The addition of methylamine onto the C80 cage is predicted to solve a low solubility problem of the fullerenes in water.11
Although C80O has been studied theoretically,12 the C80 cage with the Ih symmetry is emphasized. Herein, more efforts are concentrated to the binding features of C80(D5d). First, the nine possible geometries of C80O based on C80(D5d) are studied to find the most stable geometry of C80O. Then, the electronic structure and spectros-copic property of C80O are investigated. Finally, the aromaticity of rings on the C80O cage is explored.
2. Research Approach
Godly has recommended the IUPAC rule for the fullerenes.13 According to this rule, the numbering system of C80(D5d) was established as illustrated in Figure 1. The fi-
ve unique carbon atoms in C80(D5d) were named as C(I), C(II), C(III), C(IV) and C(V). Also, nine kinds of bonds in C80(D5d) were defined as the bonds a, b, c, d, e, f, g, h and i. On the basis of the geometry of C80(D5d), an oxygen atom was added to the nine kinds of bonds, and thus nine isomers of C80O were designed. These isomers were 1,2-C80O, 1,9-C80O, 6,7-C80O, 7,8-C80O, 7,22-C80O, 21,22-C80O, 22,23-C80O, 23,24-C80O and 23,42-C8°O, respectively. In the isomer 1,2-C80O, 1,2- stands for the bond added by the oxygen atom.
Fig. 1. The optimized geometry of C80(D5d) at B3LYP/6-31G(d) level.
Full geometric optimization without any symmetric restriction for these nine isomers of C80O was firstly performed using PM3 method. Further optimization of these isomers was carried out employing Becke three parameters plus Lee, Yang and Parr's (B3LYP) method14 with the STO-3G, 3-21G and 6-31G(d) basis sets in density function theory (DFT), step by step, in order to save computation time. These methods, in Gaussian 03 program package,15 have been used to study electronic structures of the supramolecular complexes,16 fluorescent materials,17 ful-lerenes,18 and other compounds.19 Then the equilibrium geometries with the minimum energies of the C80O isomers were obtained. According to Koopmans' theory, vertical ionization potential (IP) is approximately defined as the negative value of HOMO (the highest occupied molecular orbital) energy. Similarly, vertical electron affinity (EA) is defined as the negative value of LUMO (the lowest unoccupied molecular orbital) energy. Absolute hardness (n) is equal to the half of the difference between IP and EA. Absolute electron negativity (%) is defined as the half of the sum for IP and EA. All these variables were calculated at B3LYP/6-31G(d) level.
Based on the B3LYP/6-31G(d) geometry optimized C80O isomers, the IR spectra of the C80O isomers were calculated using PM3 method. The 13C NMR spectra and NICS (nucleus independent chemical shift) values of rings in the C80O isomers were investigated at B3LYP/6-
31G level using GIAO (gauge-including atomic orbital) method.20 The NICS values of the several hexagons and pentagons in the stable C80O isomers were studied by using a dummy center of the ring on the cage. These NICS values were used to measure the aromaticity of the rings, which was proposed by P. v. R. Schleyer et al..21
3. Results and Discussion
3. 1. Relative Energies at B3LYP/6-31G(d) Level
The optimized results of C80(D5d) were compared with the experimental values and other calculation results. The lengths of the nine kinds of bonds a-i in C80(D5d) optimized at B3LYP/6-31G(d) level are 0.146, 0.139, 0.145, 0.140, 0.143, 0.147, 0.140, 0.146 and 0.146 nm, respectively. The bond lengths in C80(D5d), calculated by using RHF/STO-3G method are within the range of 0.136-0.147 nm,5 which supports our results. The length and width of the C80(D5d) cage are 0.914 and 0.705 nm, respectively, and they are in agreement with other calculated results; namely 0.946 and 0.716 nm, respectively.22 The ratio between the long and short axes of C80(D5d) is 1.296, which is compatible with the experimental value 1.3.3
The most stable geometries of C80O are found to be 23,24-C80O and 21,22-C80O. The total energy of 23,24-C80O optimized at B3LYP/6-31G(d) level of theory is -849978.879 eV. The relative energy of 23,24-C80O is the lowest among the nine isomers of C80O (Table 1), thus 23,24-C80O is the most stable isomer thermodynamically. While the relative energy of 21,22-C80O is 0.310 eV higher than in 23,24-C80O, the 21,22-C80O can be listed as the second most stable isomer of the nine isomers of C80O.
The former stability order can be explained by the position of the added oxygen atom, which is located near the equatorial belt of C80(D5d). This position is preferable because of the lengths of the C(23)-C(24) and C(21)-C(22) bonds in C80(D5d), 0.146 and 0.147 nm, respectively, which are relatively long. These weak bonds can be easily broken when the oxygen atom approaches, and then the annulene-like open structures are formed in 23,24-C80O and 21,22-C80O. The formation of the annulene-like structure is favorable for reducing the tension of rings in the cage. At last, 23,24-C80O and 21,22-C80O own the Cs symmetry. Thereby, 23,24-C80O and 2^022-C80O are stable isomers.
The third stable isomer of C80O is 1,2-C80O with Cs symmetry. The length 0.146 nm of the bond C(1)-C(2) in C80(D5d) before the addition of the oxygen atom is long and weak; thus the annulene-like structure is formed in 1,2-C80O. But the bond C(1)-C(2) is located near the pole of C80(D5d), thus 1,2-C80O is less stable than the former two isomers of C80O. The forth stable isomer of C80O is 1,9-C80O with the Cs symmetry. The bond C(1)-C(9) is
also located near the pole of C80(D5d). Whereas the length 0.139 nm of the bond C(1)-C(9) in C 80(D5d) before the addition of the oxygen atom is short and strong, thus the epoxy structure is formed in 1,9-C80O. Therefore, 1,9-C80O is less stable than 1,2-C80O.
6,7-C80O, 22,23-C80O, 7,22-C80O and 23,42-C80O without any symmetry are less stable than the former four isomers of C80O. The length 0.146 nm of the bond C(23)-C(42) in C80(D5d) before the addition of the oxygen atom is long, and the annulene-like structure is formed in 23,42-C80O, which is near the equatorial belt of C80(D5d). In spite of these, 23,42-C80O possesses no symmetry, thus it is the most unstable isomer of C80O. Although 7,8-C80O displays the Cs symmetry, it is less stable than the former four isomers of C80O. The length 0.140 nm of the bond C(7)-C(8) in C80(D5d) before the addition of the oxygen atom is short, thus the epoxy structure is formed in 7,8-C80O.
0.688 eV computed by using RHF/STO-3G method.5 The energies of HOMO and LUMO of 23,24-C80O are -5.022 and -3.977 eV. The energy gap of 23,24-C8°O is 1.045 eV, which is higher than 0.988 eV of C80(D5d). The energy gaps of 21,22-C80O, 1,2-C80O, and 1,9-C80O are 1.194, 0.999, and 1.020 eV, respectively, which are also higher than that of C80(D5d). As a consequence, the kinetic stability of the stable C80O isomers to the excitation of electrons in HOMO increases in contrast to that of C80(D5d).
The IP, EA, n, and x values of C80(D5d) are 4.941, 3.953, 0.494, and 4.447 eV, respectively. The IP values of the C80O isomers except 7,8-C80O are higher than that of C80(D5d). Then these C80O isomers are unlikely to lose the electrons in HOMOs in the presence of the oxygen atom. The EA values of the C80O isomers except 21,22-C80O and 22,23-C80O are higher than that of C80(D5d). Thus most of the C80O isomers are ready to accept the electrons in LUMOs. The n values of the C80O isomers except
Table 1. Relative energies (Er) and some parameters (eV) of C80O isomers at B3LYP/6-31G(d) level
Compounds	Er	ehomo	elumo	Eg	IP	EA	n	X
23,24-C80O	0	-5.022	-3.977	1.045	5.022	3.977	0.522	4.500
21,22-C^O	0.310	-5.083	-3.890	1.194	5.083	3.890	0.597	4.487
1,2-CmO	0.467	-4.959	-3.959	0.999	4.959	3.959	0.500	4.459
1,9-CmO	0.516	-4.990	-3.969	1.020	4.990	3.969	0.510	4.479
6,7-C8OO	0.554	-4.984	-3.985	0.998	4.984	3.985	0.499	4.485
7,8-C8OO	0.812	-4.920	-4.029	0.891	4.920	4.029	0.445	4.474
22,23-C80O	0.909	-5.120	-3.923	1.198	5.120	3.923	0.599	4.522
7,22-C8OO	1.118	-5.143	-3.957	1.186	5.143	3.957	0.593	4.550
23,42-C80O	1.405	-5.011	-3.971	1.040	5.011	3.971	0.520	4.491
Fig. 2. The optimized geometries of 23,24-C80O and 21,22-C80O at B3LYP/6-31G(d) level.
3. 2. Electronic Structures at the Ground State
The energy gap (Eg) of C80(D5d) is calculated to be 0.988 eV at B3LYP/6-31G(d) level, which is higher than
7,8-C80O are higher than that of C80(D5d). Then the C80O isomers are basically more stable thermodynamically than C80(D5d). The x values of all the C80O isomers are higher than that of C80(D5d). Thus, the C80O isomers are oxidized with difficulty compared to C80(D5d).
of the oxygen atom, thus the shielding effect is intensified. Actually, the signals at 111.3, 111.3, 120.6, 154.7, 153.0, and 122.8 ppm of the nearby carbon atoms C(22), C(25), C(26), C(27), C(28), and C(29) with the reference to 125.2, 125.2, 125.2, 156.6, 156.6, and 125.2 ppm of the corresponding carbon atoms in C80(D5d) are all transferred upfield. The range of the 13C signals in 21,22-C80O is 125.5-189.7 ppm, which is also wider than that of the 13C
3. 3. IR Spectra
The absorptions in the IR spectrum of a molecule are affected by the crystal field, thermal fluctuations and quantization of the nuclear motion.23,24 Herein the absorptions in the IR spectrum of a single molecule for C80(D5d) in vacuum were studied. There are several moderate bands within 500-1000 cm-1, weak bands within 1000-1400
cm-1 and strong bands within 1400-1700 cm-1 in the IR signals in C80(D5d). More 13C signals in 21,22-C80O than spectrum of C80(D5d). The main IR absorptions at 931.9, those in C80(D5d) are produced. 1573.9 and 1709.8 cm"1 of CS0(D5d) are ascribed to puckering vibrations of aryl rings, stretching vibrations of C-C bonds and stretching vibrations of C=C bonds.
The stretching vibrations of the C=C bonds in the IR spectra of the C80O isomers with the annulene-like structure compared with those of the C=C bonds in the IR spectrum of C80(D5d) are blue-shifted. The main IR absorptions at 1712.3,1712.5, 1714.4, 1713.9, 1713.8 and 1727.5 cm-1 of 1,2-C80O, 6,7-C80O, 7,8-C80O, 7,22-C80O, 21,22-C80O and 23,42-C80O compared with the IR absorption at 1709.8 cm-1 of C80(D5d) are blue-shifted. The Mulliken charge of the oxygen atom in C80O is negative. For example, the Mulliken charge of the oxygen atom in 1,2-C80O is -0.519. Since the electrons in C80O are attracted from the C80 cage to the oxygen atom, the electron density on the C=C bonds near the oxygen atom is elevated. Thus, these C=C bonds are strengthened. There are some other main absorptions within the range of 1000-1400 cm-1 in the IR spectra of the C80O isomers. These absorptions split compared to those of C80(D5d). The symmetry of C80O is decreased owing to the addition of the oxygen atom.
3. 4. NMR Spectra
The solvent effect and quantum average play important roles in the investigation on signals of the carbon atoms in the NMR spectrum of a molecule.25 Herein the anisotropic signals of the carbon atoms in the NMR spectrum of a single molecule for C80(D5d) in vacuum were studied. The 13C signals of the five unique carbon atoms in C80(D5d) are 151.7, 164.6, 164.0, 125.2 and 156.6 ppm, which are basically identical to the experimental values 156.3, 163.9, 152.4, 128.9 and 130.2 ppm, respectively.3 The 13C signals of 23,24-C80O are located within the range of 111.3-172.5 ppm (Figure 3), which are caused by the sp2-C atoms on the cage. This range is wider than the range of 125.2-164.6 ppm for C80(D5d). Also, more signals in the NMR spectrum of 23,24-C80O are produced than those in the NMR spectrum of C80(D5d). These results are attributed to the decrease in symmetry of 23,24-C80O compared to that of C80(D5d). The signals at 119.9 ppm of the bridged carbon a8oms C(23) and C(24) in 23,24-C80O, compared with the signal at 156.6 ppm of the corresponding carbon atoms in C80(D5d), are changed upfield. The electron density on these carbon atoms is increased owing to the strong electron-withdrawing effect
Fig. 3. The 13C NMR spectra of 23,24-C80O and 21,22-C80O isomers at B3LYP/6-31G level.
The signals of the bridged carbon atoms in 1,2-C80O with the annulene-like structure are located at 105.8 and 104.5 ppm, which are moved upfield relative to 151.7 and 151.7 ppm of the corresponding carbon atoms in C80(D5d). The signals at 148.0 and 147.9 ppm of the bridged carbon atoms in 6,7-C80O with the annulene-like structure are also transferred upfield relative to 164.6 and 164.0 ppm of the corresponding carbon atoms in C80(D5d).
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The signals of the bridged carbon atoms in 1,9-C80O with the epoxy structure are situated at 82.6 and 93.1 ppm, which are changed upfield relative to 151.7 and 164.6 ppm of the corresponding carbon atoms in C80(D5d). The signals at 99.1 ppm of the bridged carbon atoms in 7,8-C80O with the epoxy structure relative to 164.0 ppm of the corresponding carbon atoms in C80(D5d) are changed upfield. The signals at 70.9 and 65.1 ppm of the bridged carbon atoms in 7,22-C80O with the epoxy structure relative to 164.0 and 125.2 ppm of the corresponding carbon atoms in C80(D5d) are also changed upfield. The signals at 90.2 and 74.3 ppm in 22,23-C80O with the epoxy structure relative to 125.2 and 156.6 ppm of the corresponding carbon atoms in C80(D5d) are changed upfield as well. These are caused by the formation of the sp3-C atoms in the epoxy structure of the above C80O isomers.
3. 5. Aromaticity
The NICS value is the negative value of the absolute magnetic shielding effect calculated using a dummy centre in an aromatic system. There are five kinds of rings in C80(D5d), which are determined by the five unique carbon atoms. Of these rings, three kinds of hexagons are marked with I, II and III, respectively; and two kinds of pentagons are signed with IV and V. The NICS values at the dummy centre of rings I-V in C80(D5d) are positive (Figure 4), thus these rings possess the anti-aromaticity. At the same time, there exists an apparent inhomogeneity of the magnetic field produced by n electrons on the C80(D5d) cage. The NICS values of the pentagons are higher than those of the hexagons, thus the anti-aromaticity of the pentagons is stronger than that of the hexagons. This is because the conjugation effect in the pentagons is not as good as that in the hexagons. The NICS value of ring III is the highest of all the three hexagons, thus ring III exhibits the strongest
anti-aromaticity. The strong anti-aromaticity generally results in the high reactivity; therefore, ring III is the most reactive site of all the hexagons in C80(D5d), which is exactly located on the equatorial belt of the cage.
The NICS values at the dummy centre of rings I-V in 23,24-C80O are positive, and thus these rings are also anti-aromatic. The NICS values of rings I, III, IV and V in 23,24-C80O are decreased compared with those of the same rings in C80(D5d), respectively. Thus the anti-aromaticity of these rings is weakened. The presence of the oxygen atom is favourable to depressing the anti-aromaticity of these rings. The strong electronegativity of the oxygen atom increases the electron density and thus elevates the shielding effect of these rings. The NICS values of rings II, III, IV and V in 21,22-C80O in view of those of the corresponding rings in C80(D5d) are depressed, thus the anti-aromaticity of these rings is reduced. Especially, the NICS value of ring II is negative, thus ring II displays a tendency of the aromaticity owing to the addition of the oxygen atom.
4. Conclusions
In summary, the most stable isomer of C80O was predicted to be 23,24-C80O with Cs symmetry. The bond C(23)-C(24) added by the oxygen atom is located near the equatorial belt of C80(D5d). This bond is weak, thus the annulene-like structure is formed in 23,24-C80O. The signals of the bridged carbon atoms in the NMR spectrum of C80O are changed upfield relative to those of the corresponding carbon atoms in the NMR spectrum of C80(D5d). The anti-aromaticity of the rings in 23,24-C80O and 21,22-C80O is decreased compared with that of the corresponding rings in C80(D5d). Therefore, the kinetic stability of the C80(D5d) cage can be improved upon the addition of the oxygen atom.
Fig. 4. The NICS values of the given rings in C80(D5d) and 23,24-C80O at B3LYP/6-31G level.
5. Acknowledgements
We are very grateful to Prof. Jikang Feng at Jilin University for providing ZINDO program.
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S pomočjo teorije gostotnih funkcionalov (DFT) na nivoju B3LYP/6-31G(d) so bile raziskane ravnotežne geometrijske strukture in relativne stabilnosti devetih možnih izomernih oblik C80O, ki temeljijo na strukturi C80(D5d). Najbolj stabilna napovedana geometrija za C80O je anulenu pododna struktura, 23,24-C80O, katere vezavno mesto je vez 6/6 blizu ekvatorialnega pasu molekule C80(D5d). Prvi absorpcijski vrh pri 634.1 nm v elektronskem spektru 23,24-C80O je relativno z elektronskim spektrom C80(D5d) pomaknjen v bolj modro območje spektra. Najmočnejši IR vrh molekule C80O je v primerjavi z vrhom C80(D5d) pomaknjen v bolj rdeče območje spektra. Kemijski premiki v 13C so za mostovne ogljikove atome v epoksidnih strukturah C80O glede na premike v anulenu podobnih strukturah pomaknjeni v višje polje. Anti-aromatičnost nekaterih heksagonov in pentagonov s površine kletke, ki tvoriC80O, pada v skladu z izračunanimi NICS vrednostmi ustreznih heksagonov in pentagonov v C80(D5d).