Abstract
Study of geometries of 16 possible isomers for C76N2 based on C78(C 2v) by intermediate neglect of differential overlap (INDO) series of methods indicated that the most stable geometry 25,78-C76N2 where two nitrogen atoms substitute two apexes C(25) and C(78) near the shortest X axis and Y axis formed by two hexagons and a pentagon. Electronic structures and spectra of C76N2 were investigated. The reason for the red-shift for absorptions of C76N2 compared with that of C78(C 2v) is discussed.
Keywords: C76N2, Electronic spectra, INDO
INTRODUCTION
The synthesis and characterization of heterofullerenes are very challengeable research topics because of application in superconductivity, photoelectronics, organic magnetism and even nanotubes. Pradeep et al.(1991) studied the interaction between nitrogen and fullerenes and obtained nitrogen derivatives of C60 and C70 such as C59N2, C59N4, C59N6 and C70N2 by contact-arc vaporization of graphite in a partial N2 or NH3 atmosphere. Yu et al.(1995) synthesized carbon nanotubes and nitrogen-doped fullerenes by arcing a graphite rod in a pure nitrogen atmosphere and observed C59N− by mass spectra. Hummelen et al.(1995) isolated the heterofullerene C59N as its dimmer (C59N)2. Nuber and Hirsh (1996) found a new way to synthesize nitrogen heterofullerenes RC59N and RC69N and achieved (C69N)2 by heating butylamino adducts of diazafullerenes with toluene-p-sulfonic acid. Esfarjani et al.(1994) investigated the bonding and electronic properties of substituted fullerenes C58BN. Wang et al.(1995) theoretically analyzed C60−xNx and C60−xBx (x=1~2) and their study on the stability of heterohedral fullerenes showed that the 6/6 site is favorable for C58N2 while the 5/6 site is favorable for C58B2 according to molecular mechanics calculations. Lamparth et al.(1995) used bisazafulleroid as a precursor to prepare bisadducts, which directly fragment to form the heterofullerene ions C59N+ and C69N+–the isoelectronic heteroanalogues of C60 and C70, and gave the resonance structures of C59N+ using Austin model 1 (AM1) method. We used INDO series of methods to study stabilities of isomers and electronic spectra for C75N+ (Wu and Teng, 2002) and C75B− (Teng et al., 2003), which showed that the substitution of other atoms leads to the decrease in symmetry and the red-shift of absorptions in electronic spectra. Benz et al.(1996) characterized C78(C 2v) with 21 unique carbon atoms and C78(C 2v ′) with 22 unique carbon atoms by nuclear magnetic resonance (NMR), ultraviolet visible (UV), infra-red (IR) and Raman spectra, and indicated that the properties of higher fullerenes must be treated on an individual basis when they share the same number of atoms and symmetry. Based on C78(C 2v), here we study C76N2 to predict electronic structures and stabilities of isomers and calculate electronic spectra. We also discuss electronic transition theoretically and the red-shift of absorption peaks of C76N2 relative to that of C78(C 2v).
CALCULATIONAL METHODS
We used standard bond lengths as an initial input for C78(C 2v) and implemented full geometry optimization with the INDO/2 method without any symmetry restriction and obtained C78(C 2v) (Fig.1). Then we used a nitrogen atom to substitute 21 unique carbon atoms to get the most stable isomer where C(78) is substituted. After that we replaced other carbon atoms such as C(69), C(68) and so on using the second nitrogen atom to get 16 possible isomers. Full geometry optimization was carried out using the same method as described above to obtain equilibrium geometries. Electronic spectra were computed by intermediate neglect of differential overlap/configuration interaction for singlet (INDO/CIS) (Wu and Teng, 2002; Teng et al., 2003) as in the INDO program improved by Michael C. Zerner without any parameter adjustments. One-hundred ninety-seven configurations were generated by exciting electrons from the 14 highest occupied molecular orbitals (HOMO) into the 14 lowest unoccupied molecular orbitals (LUMO).
Fig. 1.
The optimized geometry of C78(C 2v)
RESULTS AND DISCUSSION
Stabilities of isomers
The relative energy and LUMO-HOMO energy gap of 16 isomers for C76N2 are given in Table 1 showing that the most stable isomer is 25,78-C76N2 where two nitrogen atoms locate at two apexes of two hexagons and a pentagon near the shortest X axis and Y axis of C78(C 2v) because the apexes are connected with relatively weak 6/5 bonds. Lengths of C-N bonds were 0.1312, 0.1317 and 0.1325 nm and bond orders were 1.0844, 1.0678 and 1.0496, forming C-N single bonds. The second stable isomer is 49,78-C76N2, N(49), which also substitutes near the X axis, and more stable than 28,78-C76N2 by 0.1949 eV; N(28) locates near the longest Z axis of C78(C 2v). The next four stable isomers are those where two nitrogen atoms are separated from each other. From 71,78-C76N2 and 73,78-C76N2 we can see that 1,4-substitution is more stable than 1,2-substitution on the hexagon. It is noted that the unstable isomers are those where two nitrogen atoms are connected with each other, which leads to higher energies from 29,30-C76N2 to 1,10-C76N2. Bond lengths and orders for C-N bonds in other isomers are 0.1281~0.1348 nm and 1.0138~1.1879.
Table 1.
Relative energy and LUMO-HOMO energy gap (eV) of C76N2
| Isomers | Energy | L-H gap |
| 25,78-C76N2 | 0 | 3.4578 |
| 49,78-C76N2 | 0.1910 | 3.5315 |
| 28,78-C76N2 | 0.1949 | 3.4883 |
| 24,78-C76N2 | 0.2201 | 3.4749 |
| 6,78-C76N2 | 0.4185 | 3.4804 |
| 7,78-C76N2 | 0.5220 | 3.4461 |
| 48,78-C76N2 | 0.6620 | 3.5040 |
| 71,78-C76N2 | 0.6708 | 3.4325 |
| 68,78-C76N2 | 0.7798 | 3.3710 |
| 29,30-C76N2 | 2.4413 | 3.5174 |
| 70,71-C76N2 | 3.0077 | 3.5430 |
| 69,78-C76N2 | 3.3090 | 3.1795 |
| 73,78-C76N2 | 3.5660 | 3.5516 |
| 52,53-C76N2 | 4.0588 | 3.4670 |
| 47,48-C76N2 | 4.1177 | 3.6110 |
| 1,10-C76N2 | 4.8244 | 3.3802 |
Electronic structures
25,78-C76N2 is a stable closed-shell molecule where LUMO-HOMO energy gap is 3.4578 eV. Other isomers in Table 1 possess much less LUMO-HOMO energy gap than that of C78(C 2v) (4.7534 eV). Molecular orbitals for C76N2 isomers are non-degenerate owing to the lower symmetry. In 25,78-C76N2, two nitrogen atoms carry positive Mülliken charges 1.589 and 1.590 whereas the adjacent carbon atoms are of negative charges from −0.467 to −0.557, leading to the formation of polar covalent bonds. At the same time, the positive charge is chiefly concentrated on two nitrogen atoms, which makes them become further reaction centers for nuclearphilic reagents. For the rest of the isomers, Mülliken charges of nitrogen atoms and successive carbon atoms are within the regions of 1.171~1.602 and −0.443~0.620.
Electronic spectroscopy
The INDO/CIS method can be used successfully for computing electronic spectra of carbon clusters (Wu and Teng, 2002; Teng et al., 2003). UV bands of C78(C 2v) are at 289.9, 310.2, 328.8, 370.7, 434.4, 466.7, 527.6 and 614.0 nm, and are consistent with the experiment values of 290, 310, 330, 370, 430, 470, 530 and 590 nm (Benz et al., 1996). The first absorption of 25,78-C76N2 is at 1484.6 nm (Table 2), generated by electronic transition from HOMO (157) to LUMO (158). Strong absorption appearing at 913.2 nm, resulted from electronic excitation from (157) to (161). The first peak of 49,78-C76N2 locates at 1456.6 nm, generated by electronic transition from (157) to (158). The absorptions for 25,78-C76N2 and 49,78-C76N2 are red-shifted relative to that of C78(C 2v) due to less LUMO-HOMO energy gaps.
Table 2.
The calculated electronic spectra for 25,78-C76N2 and 49,78-C76N2
| Isomers | λ (nm) | Oscill. | Trans. nature | coeffic. |
| 25,78-C76N2 | 1484.6 | 0.0297 | (157)→(158) | 0.7700 |
| 25,78-C76N2 | 1209.7 | 0.0033 | (157)→(159) | 0.7527 |
| 25,78-C76N2 | 985.2 | 0.0381 | (157)→(160) | 0.8554 |
| 25,78-C76N2 | 913.2 | 0.1334 | (157)→(161) | −0.7561 |
| 25,78-C76N2 | 807.6 | 0.0279 | (157)→(162) | −0.8754 |
| 25,78-C76N2 | 692.3 | 0.0032 | (157)→(163) | 0.6966 |
| 49,78-C76N2 | 1456.6 | 0.0205 | (157)→(158) | 0.7914 |
| 49,78-C76N2 | 1183.6 | 0.0135 | (157)→(159) | 0.7251 |
| 49,78-C76N2 | 952.2 | 0.0339 | (157)→(160) | −0.8013 |
| 49,78-C76N2 | 891.4 | 0.1236 | (157)→(161) | −0.8059 |
| 49,78-C76N2 | 787.9 | 0.0195 | (157)→(162) | 0.8972 |
| 49,78-C76N2 | 630.0 | 0.0609 | (156)→(158) | 0.8019 |
The first peak of 28,78-C76N2 is at 1387.7 nm (Table 3), generated by electronic transition from (157) to (159). The strong band is at 928.4 nm, owing to electronic transition from (157) to (161). The first band of 24,78-C76N2 is at 1559.2 nm, generated by electronic transition from (157) to (158). The near infra-red (NIR) absorptions for 25,78-C76N2 and 24,78-C76N2 are caused by decrease in LUMO-HOMO energy gaps.
Table 3.
The calculated electronic spectra for 28,78-C76N2 and 24,78-C76N2
| Isomers | λ (nm) | Oscill. | Trans. nature | coeffic. |
| 28,78-C76N2 | 1387.7 | 0.0329 | (157)→(159) | 0.9023 |
| 28,78-C76N2 | 1325.4 | 0.0263 | (157)→(158) | −0.9534 |
| 28,78-C76N2 | 990.7 | 0.0280 | (157)→(160) | 0.8837 |
| 28,78-C76N2 | 928.4 | 0.1211 | (157)→(161) | 0.8932 |
| 28,78-C76N2 | 762.2 | 0.0243 | (157)→(162) | −0.9014 |
| 28,78-C76N2 | 700.5 | 0.0057 | (157)→(163) | −0.6439 |
| 24,78-C76N2 | 1559.2 | 0.0226 | (157)→(158) | 0.9109 |
| 24,78-C76N2 | 1187.0 | 0.0233 | (157)→(159) | 0.8704 |
| 24,78-C76N2 | 990.3 | 0.0254 | (157)→(160) | −0.9220 |
| 24,78-C76N2 | 930.4 | 0.1057 | (157)→(161) | −0.8769 |
| 24,78-C76N2 | 793.6 | 0.0431 | (157)→(162) | 0.8832 |
| 24,78-C76N2 | 701.9 | 0.0107 | (157)→(163) | 0.7287 |
First peaks of electronic spectra for 6,78-C76N2 and 7,78-C76N2 (Fig.2) appearing at 1534.4 and 1518.0 nm are produced by electronic transitions from (157) to (158) and (157) to (159). The red-shift of the first peaks for 6,78-C76N2 and 7,78-C76N2 compared with that of C78(C 2v) happens owing to less LUMO-HOMO energy gaps.
Fig. 2.
Electronic spectra of 6,78-C76N2 (a) and 7,78-C76N2 (b)
Table 4 indicates that first peaks of electronic spectra for other C76N2 isomers are red-shifted relative to that of C78(C 2v), which is attributable to less LUMO-HOMO energy gaps. These NIR peaks are characteristics for recognizing different isomers in the experiment.
Table 4.
Wavelength (nm) and oscillation of other isomers for C76N2
| Isomers | λ (nm) | Oscill. |
| 48,78-C76N2 | 1474.4 | 0.0196 |
| 48,78-C76N2 | 1250.8 | 0.0220 |
| 48,78-C76N2 | 972.3 | 0.0346 |
| 71,78-C76N2 | 1587.7 | 0.0191 |
| 71,78-C76N2 | 1297.7 | 0.0160 |
| 71,78-C76N2 | 1023.9 | 0.0221 |
| 68,78-C76N2 | 1711.7 | 0.0174 |
| 68,78-C76N2 | 1449.9 | 0.0158 |
| 68,78-C76N2 | 1039.3 | 0.0384 |
| 29,30-C76N2 | 1306.9 | 0.0028 |
| 29,30-C76N2 | 1042.9 | 0.0123 |
| 29,30-C76N2 | 1032.1 | 0.0258 |
| 70,71-C76N2 | 1463.6 | 0.0178 |
| 70,71-C76N2 | 1061.1 | 0.0031 |
| 70,71-C76N2 | 957.7 | 0.0107 |
| 69,78-C76N2 | 2399.5 | 0.0122 |
| 69,78-C76N2 | 1593.6 | 0.0033 |
| 69,78-C76N2 | 1251.2 | 0.0658 |
| 73,78-C76N2 | 1344.1 | 0.0103 |
| 73,78-C76N2 | 989.6 | 0.0017 |
| 73,78-C76N2 | 861.6 | 0.2220 |
| 52,53-C76N2 | 1647.5 | 0.0289 |
| 52,53-C76N2 | 1054.8 | 0.0229 |
| 52,53-C76N2 | 927.6 | 0.0427 |
| 47,48-C76N2 | 1280.3 | 0.0293 |
| 47,48-C76N2 | 935.0 | 0.0320 |
| 47,48-C76N2 | 894.0 | 0.1232 |
| 1,10-C76N2 | 1470.3 | 0.0120 |
| 1,10-C76N2 | 1253.0 | 0.0266 |
| 1,10-C76N2 | 1126.3 | 0.0012 |
CONCLUSION
ZINDO methods can be successfully used for optimizing geometries and electronic spectra of C76N2 isomers. The most stable isomer is 25,78-C76N2 where two nitrogen atoms are separated and located near two shorter axes. The red-shift of absorptions in electronic spectra for C76N2 compared with that of C78(C 2v) takes place because of less LUMO-HOMO energy gap for C76N2.
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