Theoretical Studies On The Structure And Stability Of Large Fullerenes

Since the discovery of C₆₀ in 1985, the similar spherical molecules, fullerenes, have become a hot research topic, and more than 30 isomers of fullerenes C_N (N=76-96) have been isolated and characterized one after the other through experiments. However, for the larger fullerenes, due to the rapidly increasing fullerene isomers and their diminishing solubility in common solvents, the definitive experimental data of fullerenes beyond C₉₆ are still seldom so far. Thus, theoretical studies have become an indispensable tool in investigation on these larger fullerenes. By identifying thermodynamically favorable isomers and providing the spectra of individual structures, theoretical investigations can help experimentalists to analyze experimental results and predict new structures. In this dissertation, the fullerenes with carbon atoms between 80 and 180 were systematic studied, and the main contents include:1. Several basic aspects about fullerenes, such as the structural features, the synthesis methods and the applications in several fields, were introduced. The frequently used methods in fullerene calculations, the properties of fullerenes, and some factors to the fullerene stability were summarized as an emphasis, in which the progress was reviewed.2. Based on the fullerene generation program CaGe and the REBO potential (reactive empirical bond order potential), a prescreening algorithm CaGe_REBO was proposed. The main idea of CaGe_REBO is, generating all the fullerene isomers that meet the specified conditions, optimizing each generated structure based on the REBO potential, and selecting a given number of low-energy isomers based on all the REBO energies. CaGe_REBO was used on fullerenes C₈₀-C₉₀, and the top 20 low-energy isomers of each fullerenes were selected from all the non-IPR (isolated pentagon rule, IPR) isomers. These candidate isomers and all the IPR isomers of C₈₀-C₉₀ were further optimized at the B3LYP/6-31G*//B3LYP/3-21G level to determine the top 5 stable isomers of each fullerene. It was found that the calculated stable isomers of C₈₀-C₉₀ are in good agreement with the published results, and not like C₇₂, the IPR isomers are more stable than the non-IPR ones with large relative energies, which means that the IPR is still satisfied for C₈₀-C₉₀.3. Because of the limitation in experimental methods, theoretical calculations are the mainly used method in the investigations on fullerenes larger than C₉₀. To our limited knowledge, fullerenes C₉₀-C₁₀₀ C₁₁₆, C₁₁₈, and C₁₂₀ have been systematically studied before, however the reports on the larger fullerenes are still seldom. In this chapter, a QM/MM approach that consists of the prescreening algorithm CaGe_REBO and semiempirical method PM3 were proposed to predict the stable isomers of fullerenes C₉₀-C₁₄₀. First, all the IPR isomers of C₉₀-C₁₄₀ were systematically searched using CaGe_REBO to select the best 100 REBO low-energy isomers for each fullerene. Then, these candidate isomers were further optimized by PM3 to determine the stable isomers. Comparisons with the published results show that this QM/MM approach can be used to predict the stable isomers of the large fullerenes C₉₀-C₁₄₀ at the semiempirical level. It was also found that for the large fullerenes C₉₀-C₁₄₀, many fullerenes have several isomers with very close energies, which indicates that these isomers may be coexist in experiments; and the predicted stable isomers have relatively low symmetries. Furthermore, to investigate the possible factors to the stability of fullerenes, the H values which can be used to quantitatively describe HNR (hexagon neighbor rule) signature, and the PM3 HOMO-LUMO gaps were also calculated. The results show that the hexagon-neighbor rule is an important factor to the stability of fullerenes; the HOMO-LUMO gap also contributes to the stability but not a dominating factor.4. Many semiempirical methods have been widely used on fullerenes due to their fast calculation speed. Thus, it is necessary to assess the reliability of these semiempirical methods through comparison with higher-level quantum chemical results. To our limited knowledge, the performance of semiempirical methods has been assessed only for fullerenes below C₁₀₂. In this chapter, the molecular mechanics method (CaGe_REBO), four semiempirical methods (AM1, PM3, MNDO, and TB), and the higher-level density functional theory method (B3LYP) were combined to predict the stable isomers of C₁₁₆-C₁₂₀ at the B3LYP/6-31G*//B3LYP/3-21G level of theory. Meanwhile, the reliability of these four semiempirical methods was also assessed. It was found that for C₁₁₆-C₁₂₀, the TB method can provide relatively accurate qualitative results, while AM1, PM3, and MNDO are notably less accurate for the prediction of the relative energies when compared with the B3LYP/6-31G* results. Furthermore, analysis on the stable isomers suggests that in addition to HNR, the most important structural motifs to the stability of C₁₁₆-C₁₂₀ are 6656, 6556, and 13/66.5. According to our calculation experience, even the molecular mechanics method CaGe_REBO is too time-consuming for the larger fullerenes such as C₁₆₀. Thus, a more efficient prescreening method is necessary to avoid the time-consuming energy calculations. In this chapter, the larger fullerenes were prescreened using a scheme based on the topological information to select the potential low-energy isomers. The scheme is the fitted empirical formula proposed by Cioslowski et al., which can be used to calculate the predicted standard enthalpies of formationΔH°_f based upon counts of 30 local topological structures. A prescreening program CaGe_Hf were developed based on CaGe and the empirical formula in this chapter. All the IPR isomers of C₁₃₂-C₁₆₀ were first systematically searched using CaGe_Hf to select 1000 candidate isomers for each fullerene, and then semiempirical PM3, TB, and higher-level B3LYP/6-31G*//B3LYP/3-21G calculations were performed to predict the energetically favored isomers. It was found that, by and large, the average B3LYP/6-31G* energy of the lowest energy isomers decreases monotonically as the cluster size increases from 132 to 160, only C₁₅₀ and C₁₅₂ have relatively low energies. And thorough analysis of the semiempirical results suggested that the local topological structures play an important role to the fullerene stability, and the contribution of the HOMO-LUMO gap to the stability is not obvious, whereas the asphericity of the isomers does not seem to correlate with the stability. Furthermore, the IE (ionization energy) and EA (electron affinity) of the lowest energy isomers of C₁₃₂-C₁₆₀ were also calculated at the B3LYP/6-31G*//B3LYP/3-21G level. It was found that their IE and EA values slightly fluctuates near 6.14 and 3.07 eV, respectively, and the difference of IE-EA can be used as a measure for the HOMO-LUMO gap. Among these fullerenes, the relatively high IE and low EA of C₁₃₂ and C₁₅₀ result in their large HOMO-LUMO gaps.6. To our limited knowledge, for the fullerenes beyond C₁₆₀, theoretical studies that involved higher-level quantum chemical calculations are seldom. In this chapter, a two-level screening approach was proposed on the basis of the previous chapter. First, according to the calculated data of 536 IPR isomers of C₆₀-C₁₆₀, the empirical formula proposed by Cioslowski et al. was modified and re-parameterized to achieve model I, which was used as the preliminary screening tool. For model I, the correlation coefficient is 0.999 and the standard deviation is 3.45 kcal/mol. Then, a new screening model (model II) was established based on model I and additional TB energy term, of which the standard error was substantially lowered to 1.70 kcal/mol. It would be used as a second-level screening tool applied on the preliminary candidates screened out by model I. This two-level screening approach described above was applied in the systematic search of fullerenes C₁₂₂-C₁₃₀ and C₁₆₂-C₁₈₀, and the selected candidate isomers were further optimized at the B3LYP/6-31G* level to accurately predict the energetically favored isomers. It was found that the lowest energy isomers of C₁₇₄ and C₁₈₀ are notably lower in energy and have rather large HOMO-LUMO gaps, suggesting that the two isomers are more likely to be isolated experimentally. Furthermore, the electronic properties of the lowest energy isomers of C₁₂₂-C₁₃₀ and C₁₆₂-C₁₈₀ were also calculated at the B3LYP/6-31G* level. The results show that for these fullerenes, the IE and EA values slightly fluctuate near 6.079 and 3.156 eV respectively.