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C115: A coplanar double-C60-cage molecule with odd carbon atoms
Chemical Physics 296 (2004) 37–42 www.elsevier.com/locate/chemphys
C115: A coplanar double-C60-cage molecule with odd carbon atoms Feng-Ling Liu
*
Department of Chemistry, Shandong Normal University, Jinan 250014, PeopleÕs Republic of China Received 6 February 2003; accepted 29 September 2003
Abstract Using geometry optimization and semiempirical AM1 and PM3 methods for C115 , an equilibrium geometry is identified that has the form of a coplanar double-C60 cage. Vibrational frequencies and the infrared spectrum are computed at the same level of theory. The determined energy change for the reaction ð115=60ÞC60 ¼ C115 and the heat of formation of C115 as well as the vibrational analysis indicates that this system enjoys sufficient stability to allow its experimental preparation. Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction Since the discovery of C60 in 1985, numerous papers have been published on the investigation of fullerenes. Recently, connecting fullerene cages has been a subject of interest since the observations of fullerene coalescence upon laser irradiation of C60 films [1], and many fullerene dimers have been reported [2]. As we know, every carbon atom can form four bonds with other atoms. At the cage surface of fullerene molecule, each of carbon atoms only forms three bonds, so it may form another bond with other atoms. When two C60 cages share a pentagon, in this case every carbon atom at the pentagon forms four bonds with other carbon atoms, a coplanar double-cage molecule C115 could be formed [3]. This is similar to that two benzene rings sharing one C@C bond can form a naphthalene molecule. But until now, to our knowledge no coplanar polycagic molecule of fullerene has been reported. Whether these molecules can form or not? If they can form, what is their thermochemical stability? Another question is, while only even-numbered single cage fullerene molecules have been reported and no odd-numbered single cage fullerene molecule has been reported, whether coplanar polycagic fullerenes with odd-numbered can exist or not. In order to answer these questions, C115 , a molecule with coplanar double-C60 cage has been studied by using *
Tel.: +865316186772; fax: +865312615258. E-mail address: liufl@beelink.com (F.-L. Liu).
0301-0104/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2003.09.029
AM1 and PM3 quantum-chemical method. Vibrational frequencies of C115 have been calculated at the same method of theory. The results reveal C115 has no imaginary vibrational frequency and is a minimum at the potential energy hypersurface. In order to study the thermochemical stability of C115 , the energy change for the following reaction: 115 C60 ¼ C115 60 was estimated in this paper, and the results show that the reaction is exothermic, which demonstrates that C115 is more stable than C60 only from the thermochemical point of view.
2. Computational details When two C60 cages share a same pentagon, a coplanar double-cage molecule C115 can be formed. At both sides of shared pentagon in this molecule, a hexagon faces another hexagon. The structure of C115 has been calculated by using AM1 and PM3 methods. All calculations were performed with Gaussian 94 program [4] system. Using a numerical energy gradient in internal coordinates performed the full geometry optimization. The starting geometry of optimization was assumed that apart from shared pentagon, every C60 cage in C115 is similar to that of C60 , i.e. the lengths of 6–6 bonds were and those of 6–5 bonds 1.45 A the assumed 1.39 A
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F.-L. Liu / Chemical Physics 296 (2004) 37–42
angles of \C–C–C in hexagons were assumed 120° and those in pentagons 108°; the lengths of C–C bonds in the . This geometry of shared pentagon were assumed 1.54 A C115 has D5h symmetry. In the process of optimization for C115 , the symmetry is restricted to D5h . But when we changed symmetry of starting geometry of C115 from D5h to C1 , the final geometry of C115 also converged to D5h after optimization. This demonstrated that C115 with D5h symmetry is a minimum at the potential energy hypersurface. Vibrational frequencies of C115 with the optimized D5h geometry were calculated by using AM1 and PM3 methods. Vibrational frequencies were determined first to verify the nature of the stationary point structures, second to examine zero-point energy cor-
Fig. 1. Optimized geometry of C115 with D5h symmetry.
rections on calculating the heat of formation of the molecule, and third to predict vibrational frequencies for unknown stable species for the sake of their future experimental identification by infrared spectroscopy and the assignment of the observed frequencies.
3. Results and discussion 3.1. Geometries The optimized geometry of C115 by using AM1 and PM3 methods with the numbering system of the carbon atoms is shown in Fig. 1, and the geometry is of D5h symmetry. Some parameters of the geometry are given in Table 1. From Table 1, it can be seen that the difference between AM1 and PM3 parameters is very small. For the sake of comparison, the structure of C60 was optimized using AM1 and PM3 methods. The AM1 optimized and those of 6–5 bond lengths of 6–6 bonds are 1.3847 A bonds are 1.4639 A, respectively. This is corresponding to the experimental values. If PM3 method is employed, , rethe corresponding values are 1.3841 and 1.4576 A spectively. The optimized angles of all pentagons in C60 using AM1 and PM3 methods are all 108°, and those of hexagons are all 120°. Comparing the lengths of carbon– carbon bonds in C60 with those of corresponding bonds in C115 , it can be seen that when the bonds in C115 are far away from the shared pentagon, the difference of lengths is small; but when the bonds are near the shared pentagon, the difference is relatively large. This is similar to the difference of angles in C115 and in C60 . In the optimized geometry of C115 , the C3 forms a single bond with the C14 and the corresponding atoms form single bonds too. In another words, a C60 cage forms five single bonds C–C with another C60 cage besides two C60 cages sharing a same pentagon. This structure is a closed-shell system and has relative stability.
Table 1 Some geometrical parameters of C115 obtained by using AM1 and PM3 methods Parametera
AM1
PM3
Parameter
AM1
PM3
C1 –C2 C2 –C3 C3 –C4 C4 –C5 C5 –C6 C6 –C7 C6 –C8 C8 –C9 C9 –C10 C10 –C11 C11 –C12 C12 –C13 C3 –C14
1.4862 1.5241 1.5020 1.3748 1.4540 1.4604 1.3868 1.4548 1.4648 1.4633 1.3857 1.4635 1.5045
1.4896 1.5168 1.5032 1.3754 1.4454 1.4545 1.3866 1.4463 1.4592 1.4568 1.3853 1.4573 1.5132
\C1 C2 C3 \C2 C3 C4 \C3 C4 C5 \C4 C5 C6 \C5 C6 C7 \C5 C6 C8 \C6 C8 C9 \C8 C9 C10 \C9 C10 C11 \C10 C11 C12 \C11 C12 C13 \C3 C2 C14
120.7 114.8 123.8 119.6 108.5 121.1 119.8 108.1 107.9 120.0 120.0 59.2
120.6 115.2 123.5 119.6 108.7 120.9 119.4 108.2 107.9 120.0 120.0 59.8
a
and bond angles in degrees. Bond lengths are in A
F.-L. Liu / Chemical Physics 296 (2004) 37–42
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3.3. Vibrational frequencies In order to verify whether C115 is a minimum at the potential energy hypersurface or not, vibrational frequencies have been calculated by using AM1 and PM3 methods, the predicted AM1 and PM3 vibrational frequencies for C115 are listed in Table 3. Most of the AM1 vibrational frequencies are higher than those of PM3. All vibrational frequencies in Table 3 are not scaled. From Table 3, it can be seen that C115 has no imaginary vibrational frequency and is a minimum of the potential energy hypersurface. The irreducible representation of all vibrations for C115 is as follows: Cvib ¼ 19a01 þ 15a001 þ 34e01 ðIRÞ þ 33e001 þ 15a02 þ 18a002 ðIRÞ þ 35e02 þ 34e002 :
Fig. 2. C115 numbering systems for charge distributions.
Bond lengths of C–C bonds in the shared pentagon for AM1 and 1.4896 A for PM3, and they are 1.4862 A are shorter than common single C–C bond length ), which illustrates that these bonds are (1.535–1.541 A stronger than common single C–C bonds. Bond lengths of C3–C14 bond and the corresponding C–C bonds are for AM1 and 1.5132 A for PM3. These bonds 1.5045 A are slightly shorter than the common single C–C bond length too. We think that the shared pentagon causes C115 to be very rigid and this rigidity makes the single C– C bonds shorter than the common single C–C bond.
The a01 , a001 , e001 , a02 , e02 and e002 normal modes are IR forbidden by symmetry and their IR intensities are identical zero. The other modes e01 and a002 are IR allowed by symmetry, but many theoretical IR intensities of these modes are smaller than 1.0 km/mol. As it is well-known quantum-chemical methods tend to overestimate the values of vibrational frequencies. Such as C60 , the experimental values of IR allowed frequencies (symmetry t1u ) are 428, 577, 1183 and 1429 cm1 [5], but the AM1 values obtained here are 573.5, 775.6, 1405.3 and 1752.8 cm1 . According to the regression analysis theory, we found that the experimental values m~exp and the AM1 theoretical values m~AM1 of IR allowed vibrational frequencies for C60 satisfied the following relationship: m~exp ¼ 0:8728 m~AM1 79:2045:
ð1Þ
3.2. Charge distribution
The coefficient of correlation of formula (1) is 0.9984. The corresponding relationship from the PM3 data is
Since the symmetry of C115 is D5h , there are only eight kinds of different carbon atoms in the molecule. The eight kinds of different carbon atoms are numbered in Fig. 2. The charge distribution of C115 with atoms numbered in Fig. 2 is listed in Table 2. In the molecule C115 , the atoms 1, 3, 5, 7 are with negative charges and 2, 4, 6, 8 are with positive ones. The positive charges alternate with the negative charges in C115 , and this charge distribution increases the molecular stability. Since the symmetry of C115 is D5h , it has no dipole moment.
m~exp ¼ 0:8856 m~PM3 64:2874:
ð2Þ
The coefficient of correlation of formula (2) is 0.9991. Formula (1) and (2) can be used to scale AM1 and PM3 vibrational frequencies for the fullerene molecules. According to vibrational frequencies in Table 3, IR spectrum of C115 has been simulated and reported in Figs. 3 and 4. In Figs. 3 and 4, the IR allowed vibrational frequencies of C115 were scaled using formula (1) and (2), respectively.
Table 2 The charge distribution of C115 with atoms numbering in Fig. 2 Method
AM1 PM3
Atomic number 1
2
3
4
5
6
7
8
)0.0643 )0.0760
0.0331 0.0554
)0.0038 )0.0113
0.0059 0.0060
)0.0053 )0.0070
0.0030 0.0042
)0.0009 )0.0019
0.0003 0.0005
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F.-L. Liu / Chemical Physics 296 (2004) 37–42
Table 3 Harmonic vibrational frequencies (in cm1 ) and IR intensities (in km/mol, in parentheses) for C115 determined by using AM1 and PM3 methods Symmetry AM1 a01 a001 e01
e001 a02 a002 e02 e002 PM3 a01 a001 e01
e001 a02 a002 e02 e002 a
Vibrational frequencies and IR intensities 187.4, 374.6, 473.4, 552.6, 606.2, 726.0, 783.6, 832.4, 1002.1, 1250.2,1360.6, 1406.6, 1425.9, 1478.2, 1687.9, 1756.1, 1790.3, 1811.6, 1828.0 129.2, 480.2, 557.1, 622.6, 682.4, 800.1, 863.5, 879.2, 909.9, 1012.2, 1368.2, 1413.0, 1476.7, 1506.9, 1788.1 121.6(0.0),a 318.4(0.0), 421.4(0.0), 460.5(0.0), 482.9(0.0), 539.2(0.0), 582.2(8.7), 609.0(0.8), 652.8(3.0), 709.0(0.6), 758.7(0.4), 783.4(0.5), 783.6(0.3), 843.6(0.0), 883.1(0.6), 901.7(0.3), 925.3(2.2), 1024.1(6.5), 1151.0(1.1), 1291.4(6.1), 1329.5(1.0), 1340.2(1.9), 1416.4(10.3), 1433.4(5.3), 1457.9(0.1), 1462.1(1.9), 1497.5(0.6), 1505.8(0.1), 1653.6(1.8), 1703.5(9.9), 1727.8(0.1), 1765.9(24.9), 1793.8(3.2), 1836.0(0.1) 229.2, 321.4, 401.6, 456.2, 490.0, 552.6, 561.9, 572.1, 616.8, 714.8, 777.4, 790.4, 821.7, 823.6, 864.3, 901.4, 971.7, 1111.1, 1248.1, 1297.0, 1316.3, 1353.1, 1372.8, 1432.3, 1447.9, 1461.9, 1478.4, 1503.9, 1661.2, 1732.4, 1743.7, 1793.4, 1831.6 433.0, 546.8, 612.2, 626.5, 733.5, 835.4, 866.1, 893.7, 908.8, 1002.9, 1357.2, 1400.1, 1479.1, 1507.1, 1788.1 301.2(1.1), 388.0(0.7), 455.8(0.1), 573.6(32.7), 667.7(0.0), 772.6(2.8), 783.6(0.3), 840.8(55.9), 1002.1(5.9), 1212.9(1.1), 1297.8(0.1), 1374.1(0.1), 1412.9(46.3), 1462.1(3.7), 1700.3(0.7), 1779.8(74.2), 1803.6(2.1), 1820.9(9.0) 256.0, 358.2, 375.6, 434.9, 477.1, 577.0, 596.6, 668.7, 736.4, 781.0, 801.1, 829.1, 840.1, 852.1, 867.2, 905.9, 957.2, 1074.4, 1149.1, 1243.6, 1276.9, 1301.3, 1371.2, 1402.3, 1449.9, 1500.7, 1519.2, 1525.3, 1651.9, 1686.7, 1735.5, 1766.4, 1806.9, 1826.1 270.4, 354.0, 384.2, 439.0, 467.7, 522.9, 600.2, 626.8, 633.2, 640.7, 745.7, 780.8, 801.7, 826.8, 847.3, 859.9, 905.5, 938.4, 1001.1, 1091.2, 1183.6, 1239.5, 1343.3, 1386.3, 1410.2, 1467.8, 1480.9, 1518.7, 1522.2, 1651.4, 1694.6, 1758.7, 1801.8, 1823.8 175.5, 350.5, 448.8, 519.9, 585.9, 761.2, 803.3, 804.3, 956.3, 1185.6, 1315.6, 1362.7, 1390.8, 1465.5, 1648.6, 1698.5, 1739.2, 1776.6, 1815.3 123.8, 455.7, 531.9, 611.3, 655.4, 788.0, 814.2, 850.4, 913.8, 976.4, 1353.1, 1395.6, 1468.2, 1519.7, 1801.0 114.4(0.0), 299.4(0.1), 397.8(0.0), 437.2(0.0), 458.5(0.0), 515.3(0.1), 564.8(14.6), 584.5(3.8), 630.5(0.1), 681.8(1.0), 723.0(0.0), 761.7(1.2), 777.8(0.0), 835.6(0.6), 851.6(0.5), 876.8(3.7), 906.1(0.2), 1008.3(9.2), 1104.3(0.7), 1242.0(4.3), 1290.5(3.2), 1302.7(0.4), 1388.8(6.3), 1415.4(3.0), 1434.6(0.1), 1448.1(1.6), 1493.7(0.6), 1510.6(0.0), 1634.8(0.2), 1665.7(11.2), 1704.5(29.4), 1729.0(3.8), 1802.8(0.5), 1824.2(0.1) 218.2, 303.4, 381.0, 435.7, 464.5, 539.4, 553.1, 590.2, 612.6, 745.6, 760.3, 777.2, 823.2, 854.9, 870.4, 907.7, 946.1, 1081.0, 1208.6, 1272.5, 1323.0, 1345.6, 1416.7, 1428.7, 1447.8, 1465.6, 1491.0, 1511.5, 1652.3, 1692.6, 1728.9, 1806.0, 1822.6 407.7, 524.4, 595.8, 608.6, 712.0, 812.3, 825.2, 869.3, 914.9, 967.2, 1322.9, 1386.1, 1469.8, 1520.4, 1801.1 283.6(0.7), 363.1(0.7), 433.7(0.0), 558.3(48.1), 630.4(0.7), 736.0(1.42), 761.5(0.7), 807.7(61.5), 970.8(7.9), 1164.3(4.9), 1262.6(0.0), 1325.8(0.8), 1385.4(26.4), 1460.3(2.3), 1675.2(0.2), 1731.0(103.3), 1774.9(0.0), 1814.8(0.6) 241.4, 339.3, 354.7, 411.3, 454.7, 553.4, 573.1, 639.0, 705.5, 760.7, 771.9, 819.5, 846.4, 864.8, 910.2, 912.0, 1035.3, 1101.5, 1186.8, 1231.0, 1248.9, 1346.6, 1367.6, 1432.6, 1483.3, 1524.8, 1534.2, 1636.1, 1672.6, 1685.9, 1754.5, 1802.4, 1806.5, 1818.3, 255.4, 336.2, 361.6, 415.9, 446.2, 496.2, 523.8, 575.2, 605.7, 615.9, 687.3, 717.2, 760.3, 771.7, 800.3, 815.2, 909.5, 936.3, 953.7, 1083.5, 1146.7, 1183.4, 1253.6, 1306.2, 1348.2, 1393.3, 1449.5, 1479.1, 1523.4, 1536.1, 1637.0, 1682.8, 1753.3, 1816.2
Only e01 and a002 normal modes are IR allowed, their IR intensities are in the parentheses.
Fig. 3. The simulated IR spectrum of C115 using scaled AM1 vibrational frequencies.
Fig. 4. The simulated IR spectrum of C115 using scaled PM3 vibrational frequencies.
Apart from the IR intensities, the simulated AM1 IR spectrum for C115 is similar to that of PM3. In the simulated IR spectrum of C115 , only a few modes exhibit
higher IR intensities and the primary peaks are four groups. The four-group peaks could be used as evidence to identify C115 .
F.-L. Liu / Chemical Physics 296 (2004) 37–42
3.4. Heat of formation
41
the following reaction (3). First, the energy change DHr for the following reaction:
Some properties of C115 carried out by using AM1 and PM3 methods are listed in Table 4. The corresponding properties of C60 are also listed in Table 4 for comparison. The energies of HOMO and LUMO for C115 were calculated with AM1 and PM3 methods, the results are given in Table 4. According to KoopmanÕs theorem, the energy of HOMO approximates the first ionization potential of the molecule. In practice, orbital energies usually give estimates that are large compared to experimental ionization energies [6]. For example, the HOMO energies obtained with AM1 and PM3 methods for C60 are )9.64 and )9.48 eV, respectively, but the experimental ionization energy for C60 is 7.61 eV [7]. The HOMO energies obtained with AM1 and PM3 for C115 are )9.56 and )9.40 eV, respectively. Compared with C60 , the experimental ionization energy for C115 approximates 7.53 eV (for AM1 value is 9:56 9:64 þ 7:61 ¼ 7:53 eV, and for PM3 value is 9:40 9:48 þ 7:61 ¼ 7:53 eV). In fact, the energy of LUMO is sometimes considered as an approximation to the electron affinity. The LUMO energies obtained with AM1 and PM3 methods for C60 are )2.95 and )2.90 eV, respectively. The experimental electron affinity for C60 is 2.6–2.8 eV [8]. So we think the experimental electron affinity for C115 approximates 2.4– 2.6 eV. Since the symmetry of the LUMO is E001 , we think that C115 can obtain four electrons to form a C4 115 anions. A large HOMO–LUMO gap has long been recognized as being correlated with kinetic and structural stability while a small gap is associated with reactivity [9–14]. The HOMO–LUMO gaps with AM1 and PM3 methods for C60 are 6.79 and 6.58 eV, respectively. As for C115 , the HOMO–LUMO gaps are 6.80 and 6.70 eV, respectively. Since the HOMO–LUMO gap of C115 is larger than that of C60 and C60 is very stable, we think that C115 may be very stable. Since heat of formation DHf0 is an important parameter, the DHf0 for C115 was estimated according to
115 C60 ¼ C115 60
ð3Þ
was estimated using the final iteration energies E and the zero-point vibrational energies ZPE for C60 and C115 gained in this paper. As for AM1 method, the energy change DHr of reaction (3) was calculated as follows: 115 ðEC60 þ ZPEC60 Þ 60 ðkcal=mol:Þ
DHr ¼ ðEC115 þ ZPEC115 Þ ¼ 30:08
The corresponding value from the PM3 data is DHr ¼ )41.51 kcal/mol. According to the results of DHr obtained above, the reaction ð115=60ÞC60 ¼ C115 is exothermic. This illustrates that the energy of C115 generated from C60 would be reduced. So only from the thermochemical point of view, C115 is more stable than C60 . When the energy change DHr of reaction (3) and the heat of formation DHf0 for C60 are known, the heat of formation DHf0 for C115 can be estimated according to the reaction (3). The calculation formula for the heat of formation of C115 is as follows: 0 ¼ DHf;C 115
115 0 DHf;C þ DHr : 60 60
ð4Þ
The experimental heat of formation DHf0 for C60 is 609.6 kcal/mol [15], and the energy change DHr of reaction (3) has been calculated above. So we can estimate the heat of formation DHf0 for C115 . When the value of DHr is 0 determined by using the AM1, the DHf;C is 115 115 0 DHf;C þ DHr;AM1 60 60 ¼ 1138:32 ðkcal=mol:Þ
0 ¼ DHf;C 115
Table 4 Some properties of C115 obtained by using AM1 and PM3 methods Properties
EHOMO (eV) ELUMO (eV) DEL–H b (eV) Ec (eV) Electronic state Point group ZPEd (kcal/mol) a
C115
C60
AM1
PM3
AM1
PM3
)9.56 (A001 )a )2.76 (E001 ) 6.80 79.39529 1 0 A1 D5h 512.60
)9.40 (A001 ) )2.70 (E001 ) 6.70 65.48822 1 0 A1 D5h 501.82
)9.64 (Hu ) )2.95 (T1u ) 6.79 42.16692 1 Ag Ih 265.999
)9.48 (Hu ) )2.90 (T1u ) 6.58 35.16078 1 Ag Ih 260.577
The orbital symmetry of HOMO and LUMO is given in parentheses. DEL–H is the energy gap between HOMO and LUMO. c E is the final iteration energy of the molecule computed by using Gaussian 94 program. d ZPE is the zero-point vibrational energy of the molecule, and the value were not scaled. b
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F.-L. Liu / Chemical Physics 296 (2004) 37–42
Table 5 The heat of formation DHf0 for C115 Method
DHf0 (kcal/mol)
DHf0 per C atom (kcal/mol)
AM1 PM3
1138.32 1126.89
9.90 9.80
The corresponding value from the PM3 data is 0 DHf;C ¼ 1126.89 kcal/mol. The heat of formation DHf0 115 obtained above is given in Table 5. According to DHf0 for C60 (609.6 kcal/mol), DHf0 per C atom of C60 is 10.16 kcal/mol. In Table 5, the DHf0 per C atom for C115 is 9.90 kcal/mol (AM1 value) and 9.80 kcal/mol (PM3 value), respectively. This also illustrates that C115 is more stable than C60 . Since C115 is more stable than C60 and C60 has been prepared, only from the thermochemical point of view, C115 may be prepared in the future. 3.5. Energy changes for decay channels C115 ! C115 n + Cn , 1 6 n 6 57 In order to study the thermochemical stability of C115 , the energy changes for all possible decay channels C115 ! C115 n + Cn (1 6 n 6 57) have been calculated. Some typical results are listed in Table 6. From Table 6, it can be seen that the energy changes for all possible decay channels C115 ! C115 n + Cn (1 6 n 6 57) are all endothermic, so C115 is a thermochemical stable molecule. 3.6. Discussion Using AM1 and PM3 methods, the geometry of the coplanar double-C60 -cage molecule C115 has been optimized. Its structure is of D5h symmetry and has relative rigidity. According to the results of this paper, only from the thermochemical point of view, C115 is more stable than C60 . So we think C115 can be prepared in the future. Table 6 Some typical energy changes for possible decay channels C115 ! C115 n + Cn (1 6 n 6 57) Decay channels
C115 ! C114 + C C115 ! C113 + C2 C115 ! C112 + C3 C115 ! C111 + C4 C115 ! C110 + C5 C115 ! C75 + C40 C115 ! C60 + C55 C115 ! C59 + C56 C115 ! C58 + C57
Energy change (kcal/mol) AM1
PM3
301.3 296.6 420.4 419.3 504.3 833.1 335.0 309.5 341.7
299.0 331.4 405.4 407.1 489.4 738.6 323.4 301.5 331.3
Two C60 cages sharing a same pentagon forms a coplanar double-C60 -cage molecule C115 . C115 has only one kind of cage. We think that the coplanar polycagic molecules could be formed with the same or different kind of cages. When the cages are the same, the molecules can be called homologous coplanar polycagic molecule, such as C115 studied in this paper. When the cages are different, the molecule can be called heterologous coplanar polycagic molecule, such as a C60 cage and a C70 cage sharing a same pentagon, can be form a molecule C125 . So the variety of the coplanar polycagic molecules of fullerenes is a large number. If the coplanar polycagic molecule could be prepared, species of fullerenes might be extremely increased.
Acknowledgements We appreciate the financial support of this work that was provided by Natural Science Foundation Committee of China (20271043). The author thanks to English associate professor J.S. Zhang for correcting the manuscript.
References [1] C. Yeretzian, K. Hauser, F. Diederich, R. Whetten, Nature 359 (1992) 44. [2] J.L. Segura, N. Martin, Chem. Soc. Rev. 29 (2000) 13. [3] C60 has 12 pentagons and 20 hexagons, two C60 cages using same hexagon might form a coplanar double-cagic molecule C114 , two C60 cages using same pentagon can form another coplanar doublecagic molecule C115 . [4] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T.A. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. Al-Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P. Stewart, M. Head-Gordon, C. Gonzalez, and J.A. Pople, Gaussian94, Gaussian, Inc., Pittsburgh, PA, Carnegie Office Park, Building 6, Pittsburgh, PA 15106, USA, 1995. [5] W. Kr€atschmer, L.D. Lamb, K. Fostiropoilos, D.R. Huffman, Nature 347 (1990) 354. [6] J.P. Lowe, Quantum Chemistry, Academic Press, New York, p. 321. [7] J.A. Zimerman, J.R. Eyler, S.B.H. Bach, J. Phys. Chem. 94 (1991) 3556. [8] S.H. Yang, C.L. Pettiette, J. Conceicao, Chem. Phys. Lett. 139 (1987) 233. [9] L.S. Bartell, J. Chem. Educ. 45 (1968) 745. [10] R. Hoffmann, J. Chem. Soc., Chem. Commun. (1969) 240. [11] E.L. Muetterties, B.F. Beier, Bull. Soc. Chim. Belg. 84 (1975) 397. [12] R.G. Pearson, J. Org. Chem. 54 (1989) 1423. [13] J.K. Burdett, B.A. Coddens, Inorg. Chem. 27 (1988) 3259. [14] Z. Zhou, R.G. Parr, J. Am. Chem. Soc. 112 (1990) 5720. [15] H-D. Beckhaus, S. Verevkin, C. R€ uchardt, F. Diederich, C. Thilgen, H.-U. ter Meer, H. Mohn, W. M€ uller, Angew. Chem., Int. Ed. Engl. 33 (1994) 996.
C115: A coplanar double-C60-cage molecule with odd carbon atoms Feng-Ling Liu
*
Department of Chemistry, Shandong Normal University, Jinan 250014, PeopleÕs Republic of China Received 6 February 2003; accepted 29 September 2003
Abstract Using geometry optimization and semiempirical AM1 and PM3 methods for C115 , an equilibrium geometry is identified that has the form of a coplanar double-C60 cage. Vibrational frequencies and the infrared spectrum are computed at the same level of theory. The determined energy change for the reaction ð115=60ÞC60 ¼ C115 and the heat of formation of C115 as well as the vibrational analysis indicates that this system enjoys sufficient stability to allow its experimental preparation. Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction Since the discovery of C60 in 1985, numerous papers have been published on the investigation of fullerenes. Recently, connecting fullerene cages has been a subject of interest since the observations of fullerene coalescence upon laser irradiation of C60 films [1], and many fullerene dimers have been reported [2]. As we know, every carbon atom can form four bonds with other atoms. At the cage surface of fullerene molecule, each of carbon atoms only forms three bonds, so it may form another bond with other atoms. When two C60 cages share a pentagon, in this case every carbon atom at the pentagon forms four bonds with other carbon atoms, a coplanar double-cage molecule C115 could be formed [3]. This is similar to that two benzene rings sharing one C@C bond can form a naphthalene molecule. But until now, to our knowledge no coplanar polycagic molecule of fullerene has been reported. Whether these molecules can form or not? If they can form, what is their thermochemical stability? Another question is, while only even-numbered single cage fullerene molecules have been reported and no odd-numbered single cage fullerene molecule has been reported, whether coplanar polycagic fullerenes with odd-numbered can exist or not. In order to answer these questions, C115 , a molecule with coplanar double-C60 cage has been studied by using *
Tel.: +865316186772; fax: +865312615258. E-mail address: liufl@beelink.com (F.-L. Liu).
0301-0104/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2003.09.029
AM1 and PM3 quantum-chemical method. Vibrational frequencies of C115 have been calculated at the same method of theory. The results reveal C115 has no imaginary vibrational frequency and is a minimum at the potential energy hypersurface. In order to study the thermochemical stability of C115 , the energy change for the following reaction: 115 C60 ¼ C115 60 was estimated in this paper, and the results show that the reaction is exothermic, which demonstrates that C115 is more stable than C60 only from the thermochemical point of view.
2. Computational details When two C60 cages share a same pentagon, a coplanar double-cage molecule C115 can be formed. At both sides of shared pentagon in this molecule, a hexagon faces another hexagon. The structure of C115 has been calculated by using AM1 and PM3 methods. All calculations were performed with Gaussian 94 program [4] system. Using a numerical energy gradient in internal coordinates performed the full geometry optimization. The starting geometry of optimization was assumed that apart from shared pentagon, every C60 cage in C115 is similar to that of C60 , i.e. the lengths of 6–6 bonds were and those of 6–5 bonds 1.45 A the assumed 1.39 A
38
F.-L. Liu / Chemical Physics 296 (2004) 37–42
angles of \C–C–C in hexagons were assumed 120° and those in pentagons 108°; the lengths of C–C bonds in the . This geometry of shared pentagon were assumed 1.54 A C115 has D5h symmetry. In the process of optimization for C115 , the symmetry is restricted to D5h . But when we changed symmetry of starting geometry of C115 from D5h to C1 , the final geometry of C115 also converged to D5h after optimization. This demonstrated that C115 with D5h symmetry is a minimum at the potential energy hypersurface. Vibrational frequencies of C115 with the optimized D5h geometry were calculated by using AM1 and PM3 methods. Vibrational frequencies were determined first to verify the nature of the stationary point structures, second to examine zero-point energy cor-
Fig. 1. Optimized geometry of C115 with D5h symmetry.
rections on calculating the heat of formation of the molecule, and third to predict vibrational frequencies for unknown stable species for the sake of their future experimental identification by infrared spectroscopy and the assignment of the observed frequencies.
3. Results and discussion 3.1. Geometries The optimized geometry of C115 by using AM1 and PM3 methods with the numbering system of the carbon atoms is shown in Fig. 1, and the geometry is of D5h symmetry. Some parameters of the geometry are given in Table 1. From Table 1, it can be seen that the difference between AM1 and PM3 parameters is very small. For the sake of comparison, the structure of C60 was optimized using AM1 and PM3 methods. The AM1 optimized and those of 6–5 bond lengths of 6–6 bonds are 1.3847 A bonds are 1.4639 A, respectively. This is corresponding to the experimental values. If PM3 method is employed, , rethe corresponding values are 1.3841 and 1.4576 A spectively. The optimized angles of all pentagons in C60 using AM1 and PM3 methods are all 108°, and those of hexagons are all 120°. Comparing the lengths of carbon– carbon bonds in C60 with those of corresponding bonds in C115 , it can be seen that when the bonds in C115 are far away from the shared pentagon, the difference of lengths is small; but when the bonds are near the shared pentagon, the difference is relatively large. This is similar to the difference of angles in C115 and in C60 . In the optimized geometry of C115 , the C3 forms a single bond with the C14 and the corresponding atoms form single bonds too. In another words, a C60 cage forms five single bonds C–C with another C60 cage besides two C60 cages sharing a same pentagon. This structure is a closed-shell system and has relative stability.
Table 1 Some geometrical parameters of C115 obtained by using AM1 and PM3 methods Parametera
AM1
PM3
Parameter
AM1
PM3
C1 –C2 C2 –C3 C3 –C4 C4 –C5 C5 –C6 C6 –C7 C6 –C8 C8 –C9 C9 –C10 C10 –C11 C11 –C12 C12 –C13 C3 –C14
1.4862 1.5241 1.5020 1.3748 1.4540 1.4604 1.3868 1.4548 1.4648 1.4633 1.3857 1.4635 1.5045
1.4896 1.5168 1.5032 1.3754 1.4454 1.4545 1.3866 1.4463 1.4592 1.4568 1.3853 1.4573 1.5132
\C1 C2 C3 \C2 C3 C4 \C3 C4 C5 \C4 C5 C6 \C5 C6 C7 \C5 C6 C8 \C6 C8 C9 \C8 C9 C10 \C9 C10 C11 \C10 C11 C12 \C11 C12 C13 \C3 C2 C14
120.7 114.8 123.8 119.6 108.5 121.1 119.8 108.1 107.9 120.0 120.0 59.2
120.6 115.2 123.5 119.6 108.7 120.9 119.4 108.2 107.9 120.0 120.0 59.8
a
and bond angles in degrees. Bond lengths are in A
F.-L. Liu / Chemical Physics 296 (2004) 37–42
39
3.3. Vibrational frequencies In order to verify whether C115 is a minimum at the potential energy hypersurface or not, vibrational frequencies have been calculated by using AM1 and PM3 methods, the predicted AM1 and PM3 vibrational frequencies for C115 are listed in Table 3. Most of the AM1 vibrational frequencies are higher than those of PM3. All vibrational frequencies in Table 3 are not scaled. From Table 3, it can be seen that C115 has no imaginary vibrational frequency and is a minimum of the potential energy hypersurface. The irreducible representation of all vibrations for C115 is as follows: Cvib ¼ 19a01 þ 15a001 þ 34e01 ðIRÞ þ 33e001 þ 15a02 þ 18a002 ðIRÞ þ 35e02 þ 34e002 :
Fig. 2. C115 numbering systems for charge distributions.
Bond lengths of C–C bonds in the shared pentagon for AM1 and 1.4896 A for PM3, and they are 1.4862 A are shorter than common single C–C bond length ), which illustrates that these bonds are (1.535–1.541 A stronger than common single C–C bonds. Bond lengths of C3–C14 bond and the corresponding C–C bonds are for AM1 and 1.5132 A for PM3. These bonds 1.5045 A are slightly shorter than the common single C–C bond length too. We think that the shared pentagon causes C115 to be very rigid and this rigidity makes the single C– C bonds shorter than the common single C–C bond.
The a01 , a001 , e001 , a02 , e02 and e002 normal modes are IR forbidden by symmetry and their IR intensities are identical zero. The other modes e01 and a002 are IR allowed by symmetry, but many theoretical IR intensities of these modes are smaller than 1.0 km/mol. As it is well-known quantum-chemical methods tend to overestimate the values of vibrational frequencies. Such as C60 , the experimental values of IR allowed frequencies (symmetry t1u ) are 428, 577, 1183 and 1429 cm1 [5], but the AM1 values obtained here are 573.5, 775.6, 1405.3 and 1752.8 cm1 . According to the regression analysis theory, we found that the experimental values m~exp and the AM1 theoretical values m~AM1 of IR allowed vibrational frequencies for C60 satisfied the following relationship: m~exp ¼ 0:8728 m~AM1 79:2045:
ð1Þ
3.2. Charge distribution
The coefficient of correlation of formula (1) is 0.9984. The corresponding relationship from the PM3 data is
Since the symmetry of C115 is D5h , there are only eight kinds of different carbon atoms in the molecule. The eight kinds of different carbon atoms are numbered in Fig. 2. The charge distribution of C115 with atoms numbered in Fig. 2 is listed in Table 2. In the molecule C115 , the atoms 1, 3, 5, 7 are with negative charges and 2, 4, 6, 8 are with positive ones. The positive charges alternate with the negative charges in C115 , and this charge distribution increases the molecular stability. Since the symmetry of C115 is D5h , it has no dipole moment.
m~exp ¼ 0:8856 m~PM3 64:2874:
ð2Þ
The coefficient of correlation of formula (2) is 0.9991. Formula (1) and (2) can be used to scale AM1 and PM3 vibrational frequencies for the fullerene molecules. According to vibrational frequencies in Table 3, IR spectrum of C115 has been simulated and reported in Figs. 3 and 4. In Figs. 3 and 4, the IR allowed vibrational frequencies of C115 were scaled using formula (1) and (2), respectively.
Table 2 The charge distribution of C115 with atoms numbering in Fig. 2 Method
AM1 PM3
Atomic number 1
2
3
4
5
6
7
8
)0.0643 )0.0760
0.0331 0.0554
)0.0038 )0.0113
0.0059 0.0060
)0.0053 )0.0070
0.0030 0.0042
)0.0009 )0.0019
0.0003 0.0005
40
F.-L. Liu / Chemical Physics 296 (2004) 37–42
Table 3 Harmonic vibrational frequencies (in cm1 ) and IR intensities (in km/mol, in parentheses) for C115 determined by using AM1 and PM3 methods Symmetry AM1 a01 a001 e01
e001 a02 a002 e02 e002 PM3 a01 a001 e01
e001 a02 a002 e02 e002 a
Vibrational frequencies and IR intensities 187.4, 374.6, 473.4, 552.6, 606.2, 726.0, 783.6, 832.4, 1002.1, 1250.2,1360.6, 1406.6, 1425.9, 1478.2, 1687.9, 1756.1, 1790.3, 1811.6, 1828.0 129.2, 480.2, 557.1, 622.6, 682.4, 800.1, 863.5, 879.2, 909.9, 1012.2, 1368.2, 1413.0, 1476.7, 1506.9, 1788.1 121.6(0.0),a 318.4(0.0), 421.4(0.0), 460.5(0.0), 482.9(0.0), 539.2(0.0), 582.2(8.7), 609.0(0.8), 652.8(3.0), 709.0(0.6), 758.7(0.4), 783.4(0.5), 783.6(0.3), 843.6(0.0), 883.1(0.6), 901.7(0.3), 925.3(2.2), 1024.1(6.5), 1151.0(1.1), 1291.4(6.1), 1329.5(1.0), 1340.2(1.9), 1416.4(10.3), 1433.4(5.3), 1457.9(0.1), 1462.1(1.9), 1497.5(0.6), 1505.8(0.1), 1653.6(1.8), 1703.5(9.9), 1727.8(0.1), 1765.9(24.9), 1793.8(3.2), 1836.0(0.1) 229.2, 321.4, 401.6, 456.2, 490.0, 552.6, 561.9, 572.1, 616.8, 714.8, 777.4, 790.4, 821.7, 823.6, 864.3, 901.4, 971.7, 1111.1, 1248.1, 1297.0, 1316.3, 1353.1, 1372.8, 1432.3, 1447.9, 1461.9, 1478.4, 1503.9, 1661.2, 1732.4, 1743.7, 1793.4, 1831.6 433.0, 546.8, 612.2, 626.5, 733.5, 835.4, 866.1, 893.7, 908.8, 1002.9, 1357.2, 1400.1, 1479.1, 1507.1, 1788.1 301.2(1.1), 388.0(0.7), 455.8(0.1), 573.6(32.7), 667.7(0.0), 772.6(2.8), 783.6(0.3), 840.8(55.9), 1002.1(5.9), 1212.9(1.1), 1297.8(0.1), 1374.1(0.1), 1412.9(46.3), 1462.1(3.7), 1700.3(0.7), 1779.8(74.2), 1803.6(2.1), 1820.9(9.0) 256.0, 358.2, 375.6, 434.9, 477.1, 577.0, 596.6, 668.7, 736.4, 781.0, 801.1, 829.1, 840.1, 852.1, 867.2, 905.9, 957.2, 1074.4, 1149.1, 1243.6, 1276.9, 1301.3, 1371.2, 1402.3, 1449.9, 1500.7, 1519.2, 1525.3, 1651.9, 1686.7, 1735.5, 1766.4, 1806.9, 1826.1 270.4, 354.0, 384.2, 439.0, 467.7, 522.9, 600.2, 626.8, 633.2, 640.7, 745.7, 780.8, 801.7, 826.8, 847.3, 859.9, 905.5, 938.4, 1001.1, 1091.2, 1183.6, 1239.5, 1343.3, 1386.3, 1410.2, 1467.8, 1480.9, 1518.7, 1522.2, 1651.4, 1694.6, 1758.7, 1801.8, 1823.8 175.5, 350.5, 448.8, 519.9, 585.9, 761.2, 803.3, 804.3, 956.3, 1185.6, 1315.6, 1362.7, 1390.8, 1465.5, 1648.6, 1698.5, 1739.2, 1776.6, 1815.3 123.8, 455.7, 531.9, 611.3, 655.4, 788.0, 814.2, 850.4, 913.8, 976.4, 1353.1, 1395.6, 1468.2, 1519.7, 1801.0 114.4(0.0), 299.4(0.1), 397.8(0.0), 437.2(0.0), 458.5(0.0), 515.3(0.1), 564.8(14.6), 584.5(3.8), 630.5(0.1), 681.8(1.0), 723.0(0.0), 761.7(1.2), 777.8(0.0), 835.6(0.6), 851.6(0.5), 876.8(3.7), 906.1(0.2), 1008.3(9.2), 1104.3(0.7), 1242.0(4.3), 1290.5(3.2), 1302.7(0.4), 1388.8(6.3), 1415.4(3.0), 1434.6(0.1), 1448.1(1.6), 1493.7(0.6), 1510.6(0.0), 1634.8(0.2), 1665.7(11.2), 1704.5(29.4), 1729.0(3.8), 1802.8(0.5), 1824.2(0.1) 218.2, 303.4, 381.0, 435.7, 464.5, 539.4, 553.1, 590.2, 612.6, 745.6, 760.3, 777.2, 823.2, 854.9, 870.4, 907.7, 946.1, 1081.0, 1208.6, 1272.5, 1323.0, 1345.6, 1416.7, 1428.7, 1447.8, 1465.6, 1491.0, 1511.5, 1652.3, 1692.6, 1728.9, 1806.0, 1822.6 407.7, 524.4, 595.8, 608.6, 712.0, 812.3, 825.2, 869.3, 914.9, 967.2, 1322.9, 1386.1, 1469.8, 1520.4, 1801.1 283.6(0.7), 363.1(0.7), 433.7(0.0), 558.3(48.1), 630.4(0.7), 736.0(1.42), 761.5(0.7), 807.7(61.5), 970.8(7.9), 1164.3(4.9), 1262.6(0.0), 1325.8(0.8), 1385.4(26.4), 1460.3(2.3), 1675.2(0.2), 1731.0(103.3), 1774.9(0.0), 1814.8(0.6) 241.4, 339.3, 354.7, 411.3, 454.7, 553.4, 573.1, 639.0, 705.5, 760.7, 771.9, 819.5, 846.4, 864.8, 910.2, 912.0, 1035.3, 1101.5, 1186.8, 1231.0, 1248.9, 1346.6, 1367.6, 1432.6, 1483.3, 1524.8, 1534.2, 1636.1, 1672.6, 1685.9, 1754.5, 1802.4, 1806.5, 1818.3, 255.4, 336.2, 361.6, 415.9, 446.2, 496.2, 523.8, 575.2, 605.7, 615.9, 687.3, 717.2, 760.3, 771.7, 800.3, 815.2, 909.5, 936.3, 953.7, 1083.5, 1146.7, 1183.4, 1253.6, 1306.2, 1348.2, 1393.3, 1449.5, 1479.1, 1523.4, 1536.1, 1637.0, 1682.8, 1753.3, 1816.2
Only e01 and a002 normal modes are IR allowed, their IR intensities are in the parentheses.
Fig. 3. The simulated IR spectrum of C115 using scaled AM1 vibrational frequencies.
Fig. 4. The simulated IR spectrum of C115 using scaled PM3 vibrational frequencies.
Apart from the IR intensities, the simulated AM1 IR spectrum for C115 is similar to that of PM3. In the simulated IR spectrum of C115 , only a few modes exhibit
higher IR intensities and the primary peaks are four groups. The four-group peaks could be used as evidence to identify C115 .
F.-L. Liu / Chemical Physics 296 (2004) 37–42
3.4. Heat of formation
41
the following reaction (3). First, the energy change DHr for the following reaction:
Some properties of C115 carried out by using AM1 and PM3 methods are listed in Table 4. The corresponding properties of C60 are also listed in Table 4 for comparison. The energies of HOMO and LUMO for C115 were calculated with AM1 and PM3 methods, the results are given in Table 4. According to KoopmanÕs theorem, the energy of HOMO approximates the first ionization potential of the molecule. In practice, orbital energies usually give estimates that are large compared to experimental ionization energies [6]. For example, the HOMO energies obtained with AM1 and PM3 methods for C60 are )9.64 and )9.48 eV, respectively, but the experimental ionization energy for C60 is 7.61 eV [7]. The HOMO energies obtained with AM1 and PM3 for C115 are )9.56 and )9.40 eV, respectively. Compared with C60 , the experimental ionization energy for C115 approximates 7.53 eV (for AM1 value is 9:56 9:64 þ 7:61 ¼ 7:53 eV, and for PM3 value is 9:40 9:48 þ 7:61 ¼ 7:53 eV). In fact, the energy of LUMO is sometimes considered as an approximation to the electron affinity. The LUMO energies obtained with AM1 and PM3 methods for C60 are )2.95 and )2.90 eV, respectively. The experimental electron affinity for C60 is 2.6–2.8 eV [8]. So we think the experimental electron affinity for C115 approximates 2.4– 2.6 eV. Since the symmetry of the LUMO is E001 , we think that C115 can obtain four electrons to form a C4 115 anions. A large HOMO–LUMO gap has long been recognized as being correlated with kinetic and structural stability while a small gap is associated with reactivity [9–14]. The HOMO–LUMO gaps with AM1 and PM3 methods for C60 are 6.79 and 6.58 eV, respectively. As for C115 , the HOMO–LUMO gaps are 6.80 and 6.70 eV, respectively. Since the HOMO–LUMO gap of C115 is larger than that of C60 and C60 is very stable, we think that C115 may be very stable. Since heat of formation DHf0 is an important parameter, the DHf0 for C115 was estimated according to
115 C60 ¼ C115 60
ð3Þ
was estimated using the final iteration energies E and the zero-point vibrational energies ZPE for C60 and C115 gained in this paper. As for AM1 method, the energy change DHr of reaction (3) was calculated as follows: 115 ðEC60 þ ZPEC60 Þ 60 ðkcal=mol:Þ
DHr ¼ ðEC115 þ ZPEC115 Þ ¼ 30:08
The corresponding value from the PM3 data is DHr ¼ )41.51 kcal/mol. According to the results of DHr obtained above, the reaction ð115=60ÞC60 ¼ C115 is exothermic. This illustrates that the energy of C115 generated from C60 would be reduced. So only from the thermochemical point of view, C115 is more stable than C60 . When the energy change DHr of reaction (3) and the heat of formation DHf0 for C60 are known, the heat of formation DHf0 for C115 can be estimated according to the reaction (3). The calculation formula for the heat of formation of C115 is as follows: 0 ¼ DHf;C 115
115 0 DHf;C þ DHr : 60 60
ð4Þ
The experimental heat of formation DHf0 for C60 is 609.6 kcal/mol [15], and the energy change DHr of reaction (3) has been calculated above. So we can estimate the heat of formation DHf0 for C115 . When the value of DHr is 0 determined by using the AM1, the DHf;C is 115 115 0 DHf;C þ DHr;AM1 60 60 ¼ 1138:32 ðkcal=mol:Þ
0 ¼ DHf;C 115
Table 4 Some properties of C115 obtained by using AM1 and PM3 methods Properties
EHOMO (eV) ELUMO (eV) DEL–H b (eV) Ec (eV) Electronic state Point group ZPEd (kcal/mol) a
C115
C60
AM1
PM3
AM1
PM3
)9.56 (A001 )a )2.76 (E001 ) 6.80 79.39529 1 0 A1 D5h 512.60
)9.40 (A001 ) )2.70 (E001 ) 6.70 65.48822 1 0 A1 D5h 501.82
)9.64 (Hu ) )2.95 (T1u ) 6.79 42.16692 1 Ag Ih 265.999
)9.48 (Hu ) )2.90 (T1u ) 6.58 35.16078 1 Ag Ih 260.577
The orbital symmetry of HOMO and LUMO is given in parentheses. DEL–H is the energy gap between HOMO and LUMO. c E is the final iteration energy of the molecule computed by using Gaussian 94 program. d ZPE is the zero-point vibrational energy of the molecule, and the value were not scaled. b
42
F.-L. Liu / Chemical Physics 296 (2004) 37–42
Table 5 The heat of formation DHf0 for C115 Method
DHf0 (kcal/mol)
DHf0 per C atom (kcal/mol)
AM1 PM3
1138.32 1126.89
9.90 9.80
The corresponding value from the PM3 data is 0 DHf;C ¼ 1126.89 kcal/mol. The heat of formation DHf0 115 obtained above is given in Table 5. According to DHf0 for C60 (609.6 kcal/mol), DHf0 per C atom of C60 is 10.16 kcal/mol. In Table 5, the DHf0 per C atom for C115 is 9.90 kcal/mol (AM1 value) and 9.80 kcal/mol (PM3 value), respectively. This also illustrates that C115 is more stable than C60 . Since C115 is more stable than C60 and C60 has been prepared, only from the thermochemical point of view, C115 may be prepared in the future. 3.5. Energy changes for decay channels C115 ! C115 n + Cn , 1 6 n 6 57 In order to study the thermochemical stability of C115 , the energy changes for all possible decay channels C115 ! C115 n + Cn (1 6 n 6 57) have been calculated. Some typical results are listed in Table 6. From Table 6, it can be seen that the energy changes for all possible decay channels C115 ! C115 n + Cn (1 6 n 6 57) are all endothermic, so C115 is a thermochemical stable molecule. 3.6. Discussion Using AM1 and PM3 methods, the geometry of the coplanar double-C60 -cage molecule C115 has been optimized. Its structure is of D5h symmetry and has relative rigidity. According to the results of this paper, only from the thermochemical point of view, C115 is more stable than C60 . So we think C115 can be prepared in the future. Table 6 Some typical energy changes for possible decay channels C115 ! C115 n + Cn (1 6 n 6 57) Decay channels
C115 ! C114 + C C115 ! C113 + C2 C115 ! C112 + C3 C115 ! C111 + C4 C115 ! C110 + C5 C115 ! C75 + C40 C115 ! C60 + C55 C115 ! C59 + C56 C115 ! C58 + C57
Energy change (kcal/mol) AM1
PM3
301.3 296.6 420.4 419.3 504.3 833.1 335.0 309.5 341.7
299.0 331.4 405.4 407.1 489.4 738.6 323.4 301.5 331.3
Two C60 cages sharing a same pentagon forms a coplanar double-C60 -cage molecule C115 . C115 has only one kind of cage. We think that the coplanar polycagic molecules could be formed with the same or different kind of cages. When the cages are the same, the molecules can be called homologous coplanar polycagic molecule, such as C115 studied in this paper. When the cages are different, the molecule can be called heterologous coplanar polycagic molecule, such as a C60 cage and a C70 cage sharing a same pentagon, can be form a molecule C125 . So the variety of the coplanar polycagic molecules of fullerenes is a large number. If the coplanar polycagic molecule could be prepared, species of fullerenes might be extremely increased.
Acknowledgements We appreciate the financial support of this work that was provided by Natural Science Foundation Committee of China (20271043). The author thanks to English associate professor J.S. Zhang for correcting the manuscript.
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