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Scientific Paper
Modelling and Vibrational Structure of C60 and C
80
Medhat Ibrahim
Spectroscopy Department, National Research Center, Dokki, Cairo, Egypt E-mail: m.ibrahim@gom.com.eg
Received 15-09-2004
Abstract
Fullerene derivatives have been shown to contribute in many applications. As a result, both structural and vibra-tional properties of C60 and C80 fullerenes and their epoxides are studied by quantum mechanical semiempirical PM3 method. Results indicate a similarity betvveen the structures of fullerenes as compared with their epoxides in one hand and the studied dimers on the other hand. The final heat of formation is higher in čase of C80 and its epojride as compared with that of C60. Results showed that, the calculated C60 spectra are higher than experimental spectra in terms of both anharmonicity effects and electron correlation.
Key words: PM3, C60, C80, fullerene epoxide, vibrational spectra



Introduction
The structure of C60 was discovered, in 1985 by Harold Kroto et al.1 Five years later, Krätschmer et al.2 investigated a technique for synthesizing C60 as a bulk solid. Later on, C60 was prepared in both powder form and bulk quantities.3 The vibrational Raman spectra for both C60 and C70 were obtained.4 The fine intramolecu-lar vibrational modes of crvstalline C60 were elucidated using high-resolution FT Raman spectroscopy.5 The surface morphology, optical absorption characteristics and structure of C60 cluster thin films which were obtained by thermal evaporation have been investigated.6 C60 solid film was irradiated with pulsed UV-laser-light, as a result, a surface transformation of the irradiated films has been observed. A new carbon phase has been formed with diamond-like sp3 bonding through an oxygen-assisted fullerene cage opening.7 A modified method of Raman scattering study for C60 dimer was described by Lededkin et al.8 The vibrational spectrum of C60 has been obtained through quantum chemical calculations.9 The equilibrium geometry of C60 has been calculated.10 Electron correlations are shown to have a significant influence on the calculated bond distances (1.446 and 1.406 A). A program package for solving the vibrational Schrödinger equation in one and two dimen-sions was developed by Stare and Mavri.11 Accordingly, the IR spectra can be calculated beyond the limit of electrical harmoniciry. Furthermore, the Raman spectra can replace the dipole moment function by the cor-responding polarizability function. It is demonstrated that, the Grid basis set has several advantages over the Gaussian basis set for realistic, anharmonic systems.
Using a tight-binding potential model both structural and vibrational properties of C60 and C70 fullerenes were studied.12 It is shown that this tight-binding molecular-dynamics scheme has accuracy comparable to ab initio techniques. The structure, energetic, and vibrational properties of five different [C60]N oligomers (N=2, 3, and 4) were studied using Density Functional based nonorthogonal tight-binding (DF-TB).13 Quantum molecular dynamics are used to assign the predominant IhC60 symmetries of observed modes. The vibrational structure in the phosphorescence spectrum of C60 is studied using molecular modelling.14 The spectral stud-ies of the molecular dynamics of some adducts of C60 to TTF was investigated.15 Using ab initio calculations it is found that, g-C80 and g-C240 cages are less stable than their graphite isomers and have smaller HOMO-LUMO gaps.16 Terso potential molecular dynamics was used to investigate the interaction between C60 molecules and a diamond substrate. It is observed that the impact of C60 molecules on the diamond substrate seldom results in the formation of an sp3 structure.17 The C60 structure dependence on the C60 fullerene concentration in water was studied using UV-VIS, Raman, IR-spectroscopy and small-angle neutron scattering (SANS) as well as PM3 semiempirical calculations.18 Using AM1 (UHF) type calculations the substitutionally B, N and P doped C80 structures were found to be stable.19 Finally, either C60 or C80 are linked into polymeric chains, and as a result nanotubes are produced.20–22 The potential acute and sub chronic toxic effects of fullerenes (C60) applied in benzene on the mouse skin were studied. The obtained data indicate that fullerenes applied in benzene at a likely industrial exposure level do not cause acute toxic
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a.
b.
,O
C.
d.
e.
f.
Figure 1. Optimized structure of a.: C60, b.: C80, c.: C60-O, d.: C80-O, e.: C60 dimer, and finally f.: C80 dimer which are calculated at Mopac PM3 semiempirical level.
effects on the mouse skin epidermis.23 Genotoxicity of fullerene C60 has been determined in a prokaryotic in vitro test and in an eukaryotic in vivo system. Only at the highest possible fullerene concentration of 2.24 micrograms per 1 mL medium, a slight genotoxic effect was observed in wing cells. Fullerol demonstrates no mutagenic effect at a concentration of 2.46 mg/mL.24 In the present work both the structure and vibra-tional spectra were evaluated for two fullerenes C60, C80 with their dimers as well as their epoxide isomers.
Calculation details
Calculations were carried out on a personal computer, using semiempirical quantum mechan-ics package, MOPAC 2002 which implemented with the version 1.33 CAChe Program (by Fujitsu), at the Spectroscopy Department, National Research Center, Egypt. The initial geometry optimization of both C60 and C80 was performed with the molecular mechanics (MM+) force field. The lowest energy conformations obtained by MM+, the method were further optimized at semiempirical methods PM3.25
Results and discussion
MOPAC is used directly to predict numerous chemi-cal and physical properties, such as geometry and infrared spectra. Ali the studied molecules were first subjected to geometry optimization at semiempirical PM3 level then the vibrational spectra were calculated at the same level.
Optimized geometry parameters: The geometry of both C60, C80 and their dimers as well as their epoxides are optimized. The optimized geometries of which are shown in Figurel. It is found from the optimized structure that, the molecular point group of C60 is corre-sponding to Ih symmetry. For C80 the symmetry number for point group Ci is equal to 1. On the other hand, the symmetry number for point group Cs is also 1, for both of C60-O and C80-O. In addition, both molecules are in ground state and are not linear. For each of the studied fullerenes ali carbons atoms are equivalent.
Table 1. Calculated bond lengths in angstrom for both Cm, C80 and their epoxides as well as their dimers which are optimized at MOPAC, PM3 semiempirical level.
Bond              C60			C80		
distance, A monomer	epoxide	dimer	monomer	epoxide	dimer
C-C                1.4045 C-0 COC angle	1.3839 2.3934 152.7	1.3927	1.4322	1.4322 2.9536 111.5	1.4324
The distances betvveen the carbon atoms are calculated as in Table 1. For both C60 and C80, the C-C distance increased from 1.4045 A to 1.4322 A respec-tively. Oxygen is binded to the two six rings, 6-6 bond, potentially forming a three COC ring. The isomer under investigation is the epoxide 6-6 bonded. The distance C-C was nearly quite similar in čase of C60 and its epoxide. Furthermore, C-C shows identical bonds for C80 and its epoxide. Again, the distance C-O is longer for C80 epoxide than C60 epoxide in contrast to the angle COC. This means that C80 epoxide is characterized by
O
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a very long bridging carbon distance as compared with C60. Studying the structure of carbon dimer is the first step towards understating the structure of carbon crys-tal. Regarding Table 1 and comparing C-C distances of both dimer as well as monomer, it is clear that the C-C distance was not affected as a result of dimmerization.
Infrared spectra: The calculated spectra are tabu-lated in both Table 2 and Table 3, and the spectra are illustrated in Figure 2. According to the calculated vibra-tional spectra the number of genuine vibrations is 174 and 177 for C60 and its epoxide. The similar vibrations for C80 and its epoxide were 234 and 237 respectivelv. Ali the vibrational modes are mentioned and tabulated.
Although C60 possesses 174 (3x60-6) normal vibrations, it exhibits only 4 characteristic vibrational modes according to their higher IR intensitv, and hence there are only 4 active bands. A C60 line at 591.94 crrT1 is observed, and assigned as lowest frequency Hg “squash-ing” mode of Buckminsterfullerene. Accordingh/ the Ag (1) mode was obtained at around 781.83 crrT1. The two strong C60 lines, found at 1444.65 crrT1 and 1797.99 cm-1, can accordingh/ be assigned to the two totalh/ symmetric Ag (2) modes. As compared to C60, C60-O showed a shift in the four characteristic bands towards the lower frequencies, in addition two bands appear at 393.61 crrT1 and 1138.96 cm_1 due to the existing of oxygen. It is worth to mention that, C80 has 8 intense vibrational modes. The spectra of C80 showed the same vibrational feature of C60 with a noticeable shift towards a lower frequency. C80-O showed 10 intense vibrational bands, the four characteristic bands are considerabh/ shifted towards lower frequencies. Finally, the striking reduction in the number of active bands as compared with the total calculated bands is evidently due to the molecule’s extremely high symmetry (Ih point group).
2000
1500
1000
500
Wavelength(cm1)
Comparison with Experimental results: Figure 3 presents the experimental FTIR spectrum.26 of 1.4 mm thick film of C60. The figure shows the four characteristic bands of C60. The comparison bervveen calculated and experimental frequencies revealed that, the calculated bands are shifted to higher frequencies. The reason is that, the harmonic vibrational frequencies are typically higher than the fundamental ones which are observed experimentally. A major source of this disagreement is the neglect of anharmonicity effects in the theoretical treatment. In addition, an error also arises because of incorporation of electron correlation.
2000            1500         1000
Wavenumber /cm"1
Figure 3. FTIR spectra of 1.44 mm thick film of C60.
Final heat of formation: Other important physical parameter which is calculated for the studied fullerene is the final heat of formation. It is relates to the ele-ments in their standard state at 298 K. The final heat of formation is calculated as –811.087 kcal/mol at 298 K.
-750
-800
-850
-900
-950
-1000
-1050
200   250   300   350   400
Temperature , K
450
500
Figure 2. Active vibrational modes for C60 as well as its epoxide C60-O and C80 and its epoxide C80-O.
Figure 4. The change in final heat of formation in kcal/mol, as a function of temperature in K for C60, C80, C60–O and finally C80–O respectively.
0
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Table 2. Calculated vibrational spectra for C60 and its epoxide.
C60
266.38	266.38	266.38	266.38	266.38
354.94	354.94	354.94	356.00	356.00
356.00	356.00	406.43	406.43	406.43
406.43	406.43	440.18	440.18	440.18
440.18	440.18	488.09	488.09	488.09
488.09	546.77	546.77	546.77	546.77
546.77	557.93	557.93	557.93	584.80
584.80	584.80	591.94	591.94	591.94
591.94	612.71	612.71	612.71	622.75
699.58	699.58	699.58	699.58	699.58
732.98	732.98	732.98	757.57	757.57
757.57	757.57	757.57	762.34	762.34
762.34	781.83	781.83	781.83	781.83
815.28	815.28	815.28	815.28	815.28
816.34	816.34	816.34	850.21	850.21
850.21	850.21	865.28	865.28	865.28
908.84	908.84	908.84	908.84	912.56
912.56	912.56	940.96	940.96	940.96
940.96	940.96	977.11	1124.37	1124.37
1124.37	1124.37	1158.55	1158.55	1158.55
1245.80	1245.80	1245.80	1245.80	1290.04
1290.04	1290.04	1290.04	1290.04	1337.55
1337.55	1337.55	1376.21	1376.21	1376.21
1377.86	1377.86	1377.86	1377.86	1377.86
1435.53	1435.53	1435.53	1435.53	1435.53
1438.83	1438.83	1438.83	1444.65	1444.65
1444.65	1444.65	1474.87	1474.87	1474.87
1474.87	1499.72	1499.72	1499.72	1499.72
1499.72	1516.50	1516.50	1516.50	1654.03
1654.03	1654.03	1654.03	1668.52	1668.52
1668.52	1668.52	1668.52	1707.18	1707.18
1707.18	1728.13	1728.13	1728.13	1728.13
1750.29	1775.45	1775.45	1775.45	1797.99
1797.99	1797.99	1797.99	1812.47	1812.47
1812.47	1812.47	1812.47	1812.47	

Figure 4 shows the final heat of formation, studied as a function of temperature from 200 K up to 500 K. The calculated heat of formation was –803.142 kcal/mol at 200 K then changed gradually to reach –841.127 kcal/mol at 500 K. Regarding C80, the calculated heat of formation was –1021.204 kcal/mol at 298 K. As seen in Figure 4 the calculated heat of formation has changed from –1010.100 kcal/mol, up to –1062.175 kcal/mol over a temperature range from 200 up to 500 K. Finally it is clear that, the final heat of formation changes as a function of temperature for both C60 and C80. Com-paring between both types of carbons, the final heat of formation of C80 is lower than that of C60 by 210.0 kcal/mol. The calculated final heat of formation has slightly increased by 30 kcal/mol, in case of C60 epoxide
c60-o
241.44	250.58	261.79	266.82	269.05
329.71	331.13	346.10	349.03	351.29
355.91	356.99	363.33	380.59	393.61
398.08	404.95	423.36	423.36	432.36
434.59	437.21	440.85	449.40	474.99
480.59	483.24	489.76	522.55	527.77
531.22	537.88	542.43	543.93	546.87
550.70	558.42	575.09	576.89	585.78
590.11	591.71	601.75	606.97	607.38
611.96	613.35	659.47	684.26	685.76
697.05	701.96	703.81	711.92	725.17
732.42	732.72	746.89	752.93	757.03
759.29	759.42	760.59	779.11	779.79
788.41	795.80	798.64	803.26	804.94
809.60	813.97	816.61	817.44	835.91
837.64	840.34	850.11	850.30	865.07
865.31	872.54	890.38	907.52	908.46
910.16	910.94	912.00	916.57	920.23
921.93	932.77	942.11	946.06	970.61
1073.59	1104.78	1124.38	1124.86	1138.96
1146.69	1162.08	1198.88	1235.83	1241.89
1245.46	1253.70	1272.89	1273.20	1288.00
1296.40	1304.00    1324.00		1325.82	1338.95
1354.59	1365.69	1373.57	1375.11	1375.90
1382.61	1386.82	1387.01	1412.85	1420.75
1429.96	1433.49	1437.02	1438.85	1442.75
1443.29	1445.84	1450.14	1453.70	1456.24
1470.24	1476.24	1481.25	1493.21	1494.31
1500.35	1502.79	1502.99	1512.01	1517.43
1525.34	1528.33	1624.27	1635.48	1641.74
1660.41	1661.75	1665.84	1666.60	1676.52
1680.59	1691.87	1708.36	1709.11	1720.95
1724.51	1731.07	1740.58	1749.50	1767.44
1774.10	1785.32	1791.56	1793.53	800.26
1800.97	1801.30	1808.97	1809.27	1810.24
1815.76	1819.36			
and 20 kcal/mol, for the case of C80 epoxide. The change in the values of final heat of formation for the studied fullerenes indicates that, this property can be consid-ered as a function of fullerenes molecular structure.
Conclusions
In this work both structure and vibrational proper-ties of both C60 and C80 were studied using semiempirical PM3 calculations. The obtained results of vibrational frequencies are shifted to higher frequencies as a re-sult of anharmonicity effects in theoretical treatment as well as the incorporation of electron correlation. On the other hand, PM3 results are considered to be fast and satisfactory as compared to other methods.
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Table 3.Calculated vibrational spectra for C80 and its epoxide.
c80					c80-o				
162.92	207.92	224.91	225.06	225.85	199.63	210.81	220.93	222.21	222.57
227.54	274.64	286.40	288.26	294.21	271.47	279.95	286.09	287.57	292.23
306.89	326.27	331.29	341.45	342.28	294.93	296.73	309.05	327.11	332.99
353.04	354.71	356.09	363.54	368.35	339.02	347.11	356.15	359.21	363.12
376.13	380.87	395.70	401.48	422.39	363.46	364.60	366.99	376.23	381.54
442.04	449.40	451.01	458.31	464.02	385.93	397.06	439.42	443.25	445.80
470.59	476.64	478.32	483.88	489.29	452.15	454.31	454.66	460.10	465.15
492.65	498.25	502.52	507.08	509.44	473.74	478.01	481.41	485.93	494.65
513.87	521.40	527.98	531.93	538.28	501.56	502.73	505.27	508.39	509.55
540.74	544.34	549.38	555.17	563.38	521.05	526.76	531.39	535.11	538.49
607.34	623.59	625.75	631.06	633.27	542.28	545.62	557.76	595.14	599.00
638.44	640.73	642.57	644.86	650.98	613.31	620.15	622.55	625.60	626.93
655.08	668.59	673.77	676.48	681.55	635.52	640.12	641.82	644.40	650.00
684.37	690.00	694.22	697.37	701.15	655.01	666.55	672.13	677.46	682.53
704.19	720.31	724.53	726.72	732.53	685.82	687.70	689.93	692.05	698.64
733.64	738.90	742.88	764.03	766.39	700.81	722.98	725.38	726.93	731.47
768.40	773.27	775.60	777.12	778.83	735.01	736.43	747.70	756.37	761.55
787.92	791.39	792.41	793.75	830.27	769.12	771.03	772.69	781.09	785.87
833.73	836.03	840.80	843.00	846.98	787.41	790.17	791.20	793.84	795.09
857.28	858.60	859.91	862.10	867.85	799.06	810.27	820.32	821.41	829.35
868.71	870.30	873.79	879.21	881.40	831.51	833.68	834.50	836.59	840.41
901.56	903.82	908.59	910.15	911.04	849.00	854.17	859.09	860.03	864.39
912.58	913.62	914.88	920.66	921.05	866.96	870.37	872.51	876.54	879.48
957.21	1004.95	1007.89	1022.45	1050.01	897.25	900.89	902.32	906.82	909.12
1066.85	1079.50	1082.54	1124.02	1161.26	911.19	912.10	912.17	916.27	917.11
1183.11	1194.77	1201.47	1208.48	1214.49	969.49	991.04	1001.19	1009.14	1031.56
1214.91	1222.54	1236.50	1267.39	1269.37	1048.32	1065.16	1090.39	1133.05	1150.54
1271.06	1294.61	1298.92	1305.58	1308.78	1165.79	1181.53	1191.24	199.96	1203.58
1310.77	1319.49	1326.98	1329.14	1342.06	1205.06	1209.72	1230.05	1238.69	1258.93
1343.83	1352.29	1360.76	1369.86	1372.70	1266.00	1280.06	1282.92	1285.92	1297.53
1379.20	1382.42	1390.80	1399.99	1403.12	1300.17	1311.12	1324.15	1330.71	1332.59
1416.69	1421.10	1423.97	1442.72	1447.79	1338.21	1339.60	1350.48	1354.55	1362.07
1450.31	1457.36	1471.52	1472.41	1483.62	1365.25	1377.51	1387.85	1392.99	1405.65
1483.70	1494.73	1499.72	1501.94	1509.47	1414.29	1421.21	1425.40	1436.96	1443.86
1514.37	1516.96	1520.72	1526.46	1532.75	1448.59	1448.59	1451.00	1460.04	1462.86
1541.70	1541.74	1557.56	1564.24	1565.15	1462.86	1473.88	1475.71	1479.98	1491.75
1572.68	1573.13	1580.62	1583.96	1589.00	1492.87	1505.47	1508.49	1515.06	1519.75
1590.98	1604.74	1607.72	1610.83	1618.36	1521.05	1522.51	1532.66	1537.35	1540.64
1621.21	1629.69	1632.11	1633.04	1644.69	1543.64	1555.37	1566.59	1572.58	1573.90
1646.25	1654.82	1655.53	1662.30	1668.01	1577.54	1581.38	1582.95	1595.36	1602.07
1683.17	1672.83	1675.26	1693.58	1694.39	1604.57	1610.58	1618.27	1627.35	1635.30
1701.25	1706.57	1708.21	1718.32	1721.78	1638.34	1694.91	1700.55	1705.63	1710.17
1723.64	1724.96	1733.78	1735.94	1743.35	1719.42	1724.13	1726.19	1737.30	1738.10
1745.36	1748.41	1752.33	1757.14	1757.69	1739.74	1742.75	1747.70	1752.42	1755.24
1760.24	1760.39	1763.80	1767.63	1769.43	1758.85	1761.48	1762.09	1763.40	1763.97
1776.44					1767.22	1769.12	1773.03	1777.39	
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Povzetek

Derivati fulerenov so se pokazali za zelo uporabne v različne namene in so zato predmet številnih raziskav. S kvantnomehansko semiempirično metodo PM3 smo raziskali strukturne in vibracijske lastnosti fulerenov C60 in C80 ter njunih epoksidov. Rezultati kažejo na podobnosti med strukturami fulerenov in epoksidov ter med njihovimi dimerami. Tvorbena entalpija tako C80 kot tudi njegovega epoksida je višja od tvorbene entalpije ustreznih struktur s C60. Če upoštevamo anharmoničnost in elektronsko korelacijo, so vrednosti frekvenc v izračunanih spektrih za C60 višje od eksperimentalnih.
Ibrahim  Modelling and Vibrational Structure of C60 and C