大富勒烯结构与稳定性的理论研究
摘要
自从1985年C_(60)发现以后，对同类球形分子——富勒烯的研究就成为了一个热点。科学家们相继从实验中成功分离出30多个碳原子数在76-96间的富勒烯异构体。然而，随着富勒烯的增大，其异构体的数目飞速增加，并且在溶剂中的溶解度逐渐变小，因此在实验中对它们进行分离和表征也变得越来越难。到目前为止，实验中分离出的最大的富勒烯是C_(96)。这样一来，对于更大富勒烯的研究，理论方法就不可或缺了。理论研究能够预测热力学稳定的富勒烯异构体，并且能对这些稳定结构进行性能分析，提供各种光谱数据，对实验研究提供理论依据，是研究富勒烯的一种重要手段。本论文对碳原子数在80-180之间的富勒烯进行了系统的理论研究，主要内容包括：
1．介绍了富勒烯的结构特点、制备方法以及在不同领域中的应用，重点综述了富勒烯研究中常用的理论计算方法和富勒烯结构和性质研究方面所取得的进展，并对富勒烯的性质和影响其稳定性的各种因素进行了总结。
2．结合富勒烯生成程序CaGe和REBO势(reactive empirical bond order potential)，开发了富勒烯异构体的能量筛选算法CaGe_REBO。其基本原理是枚举产生富勒烯所有满足指定条件的异构体，并对每个异构体的结构进行REBO势能量优化，根据得到的REBO能量筛选出一定数目的低能异构体。将该算法用于富勒烯C_(80)-C_(90)的理论研究，从C_(80)-C_(90)的所有non-IPR(isolated pentagon rule，IPR)异构体中筛选出每个富勒烯前20个低能异构体；并对这些候选异构体和C_(80)-C_(90)的所有IPR异构体进行了进一步的B3LYP／6-31G~*／／B3LYP／3-21G计算。计算确定了C_(80)-C_(90)每一富勒烯较稳定的5个异构体，与文献报道的结果吻合。同时验证了五元环分离规则，即对于C_(80)-C_(90)，满足IPR规则的异构体仍然较non-IPR异构体稳定，并不象C_(72)一样，有更稳定的non-IPR异构体。
3．由于实验手段的局限，对于碳原子数大于90的富勒烯的研究主要集中在理论计算方面。文献报道的研究结果包括C_(90)-C_(100)，C_(116)，C_(118)，和C_(120)，而对更大富勒烯的系统研究，还未见报道。本章结合能量筛选算法CaGe_REBO和半经验PM3方法，提出了一种QM／MM方法用于大富勒烯C_(90)-C_(140)稳定结构的理论预测。首先，采用CaGe_REBO程序对C_(90)-C_(140)的所有IPR异构体进行系统地搜索，基于REBO能量对每个富勒烯筛选出100个低能量异构体，再用半经验PM3方法对筛选出来的异构体进行进一步优化以确定稳定异构体。与文献研究结果进行比较发现，这种QM／MM方法能够在半经验水平上预测大富勒烯的稳定异构体。故而，基于该方法预测了C_(90)-C_(140)中未被研究过的富勒烯前5个稳定异构体。通过比较稳定异构体的能量，发现对于大富勒烯C_(90)-C_(140)，许多富勒烯稳定异构体间的能量差别非常小，因此在实验中可能出现多个异构体共存的现象；这些稳定异构体一般拥有较低的对称性；另外，对影响富勒烯稳定性的可能因素进行了详细地研究：计算了用于定量描述六元环邻近规则HNR(hexagon neighbor rule)的H指数，以及HOMO-LUMO能隙。结果表明：HNR是影响富勒烯稳定性的一个重要因素；而PM3能隙对稳定性有一定的影响，但不是主要影响因素。
4．许多半经验方法由于计算速度较快已被广泛地应用于富勒烯研究中，而这些半经验方法的可靠性需要进一步研究。通常的方法是将各种半经验的计算结果与更高理论水平的量化计算结果进行比较。文献调研结果表明这种比较研究所针对的富勒烯都不超过C_(102)。本章结合分子力学方法(CaGe_REBO)、半经验方法(AM1，PM3，MNDO和TB)和更高理论水平的密度泛函理论方法(B3LYP)，在B3LYP／6-31G~*／／B3LYP／3-21G水平上预测了大富勒烯C_(116)-C_(120)的稳定异构体，并对不同半经验方法的可靠性进行了评估。结果表明，对于C_(116)-C_(120)，与精确的密度泛函理论方法B3LYP相比，半经验TB势方法能提供较为准确的定性半定量的计算结果；而AM1、PM3和MNDO这三种半经验方法计算得到的相对能量却非常不准确，和B3LYP相对能量之间相关性很差。另外，对稳定异构体的结构特点进行了研究，结果表明除上述HNR规则外，三种拓扑结构图形6656、6556和13／66对富勒烯稳定性的影响最大。
5．我们的计算经验表明，对于更大富勒烯如C_(160)，即使用分子力学方法进行预筛选，计算量也将无法承受。因此需要开发一种更快更有效的预筛选方法来避免复杂的能量计算。本章采用基于拓扑结构信息而非能量的方法对大富勒烯进行快速预筛选，以选出潜在的低能量异构体。这种拓扑方法就是Cioslowski等人提出的基于富勒烯所含30种局部拓扑结构的数目计算其标准生成焓ΔH°_f的经验拟合公式。结合CaGe开发了基于ΔH°_f进行预筛选的程序CaGe_Hf。利用CaGe_Hf对C_(132)-C_(160)的所有IPR集合进行筛选，对每个富勒烯选择出1000个候选异构体，再结合半经验的PM3和TB势方法以及更高精度的B3LYP／6-31G~*／／B3LYP／3-21G方法预测了C_(132)-C_(160)的热力学稳定异构体。B3LYP／6-31G~*能量分析表明，随着碳原子数由132增加到160，最低能量异构体的平均能量大体上呈单调递减趋势，其中C_(150)和C_(152)相对稍低。通过对计算得到的半经验结果进行系统地分析，发现异构体的局部拓扑结构图形对富勒烯的稳定性有重要的影响，HOMO-LUMO能隙对富勒烯稳定性的影响不太明显，而富勒烯的非球面性与稳定性没有相关性。此外，还在B3LYP／6-31G~*／／B3LYP／3-21G水平上计算了C_(132)-C_(160)最低能量异构体的电离能和电子亲和势。结果显示，C_(132)-C_(160)的电离能和电子亲和势分别在6.14和3.02 eV附近轻微波动，电离能和电子亲和势之差可用于估计异构体的HOMO-LUMO能隙。其中，C_(132)和C_(150)拥有较高的电离能和较低的电子亲和势，使得它们的HOMO-LUMO能隙较大。
6．文献调研结果表明采用高精度量子化学方法对大于C_(160)的富勒烯进行理论研究的报道非常少。本章在上一章研究的基础上提出了分层筛选的策略。首先根据我们以前计算的C_(60)-C_(160)的536个IPR异构体的数据，对Cioslowski等人提出的拓扑方法进行了重新拟合，得到新的筛选模型Ⅰ，标准偏差和相关系数分别为3.45和0.999。并将模型Ⅰ用于对C_(122)-C_(130)和C_(162)-C_(180)的IPR异构体进行第一步筛选；然后，在模型Ⅰ的基础上引入了TB势能量项得到模型Ⅱ，标准偏差和相关系数分别为1.70和0.999。显然，模型Ⅱ的预测精度有了明显改善，可用于对模型Ⅰ的筛选结果进行二次筛选。最后对模型Ⅱ的筛选结果进行B3LYP／6-31G~*优化以准确地预测C_(122)-C_(130)和C_(162)-C_(180)的热力学稳定异构体。研究结果表明，C_(174)和C_(180)的最稳定异构体不仅能量较低，而且拥有相当大的HOMO-LUMO能隙，这说明这两个异构体很可能从实验中分离出来。此外，还对预测的最低能量异构体的电子性质进行了计算。结果发现，对于C_(122)-C_(130)和C_(162)-C_(180)，其电离能和电子亲和势分别在6.079和3.156 eV附近轻微的波动。
Since the discovery of C_(60) 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 C_(96) 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 C_(80)-C_(90), 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 C_(80)-C_(90) 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 C_(80)-C_(90) are in good agreement with the published results, and not like C_(72), the IPR isomers are more stable than the non-IPR ones with large relative energies, which means that the IPR is still satisfied for C_(80)-C_(90).
3. Because of the limitation in experimental methods, theoretical calculations are the mainly used method in the investigations on fullerenes larger than C_(90). To our limited knowledge, fullerenes C_(90)-C_(100) C_(116), C_(118), and C_(120) 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 C_(90)-C_(140). First, all the IPR isomers of C_(90)-C_(140) 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 C_(90)-C_(140) at the semiempirical level. It was also found that for the large fullerenes C_(90)-C_(140), 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 C_(102). 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 C_(116)-C_(120) 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 C_(116)-C_(120), 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 C_(116)-C_(120) 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 C_(160). 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 C_(132)-C_(160) 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 C_(150) and C_(152) 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 C_(132)-C_(160) 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 C_(132) and C_(150) result in their large HOMO-LUMO gaps.
6. To our limited knowledge, for the fullerenes beyond C_(160), 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 C_(60)-C_(160), 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 C_(122)-C_(130) and C_(162)-C_(180), 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 C_(174) and C_(180) 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 C_(122)-C_(130) and C_(162)-C_(180) 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.
1．介绍了富勒烯的结构特点、制备方法以及在不同领域中的应用，重点综述了富勒烯研究中常用的理论计算方法和富勒烯结构和性质研究方面所取得的进展，并对富勒烯的性质和影响其稳定性的各种因素进行了总结。
2．结合富勒烯生成程序CaGe和REBO势(reactive empirical bond order potential)，开发了富勒烯异构体的能量筛选算法CaGe_REBO。其基本原理是枚举产生富勒烯所有满足指定条件的异构体，并对每个异构体的结构进行REBO势能量优化，根据得到的REBO能量筛选出一定数目的低能异构体。将该算法用于富勒烯C_(80)-C_(90)的理论研究，从C_(80)-C_(90)的所有non-IPR(isolated pentagon rule，IPR)异构体中筛选出每个富勒烯前20个低能异构体；并对这些候选异构体和C_(80)-C_(90)的所有IPR异构体进行了进一步的B3LYP／6-31G~*／／B3LYP／3-21G计算。计算确定了C_(80)-C_(90)每一富勒烯较稳定的5个异构体，与文献报道的结果吻合。同时验证了五元环分离规则，即对于C_(80)-C_(90)，满足IPR规则的异构体仍然较non-IPR异构体稳定，并不象C_(72)一样，有更稳定的non-IPR异构体。
3．由于实验手段的局限，对于碳原子数大于90的富勒烯的研究主要集中在理论计算方面。文献报道的研究结果包括C_(90)-C_(100)，C_(116)，C_(118)，和C_(120)，而对更大富勒烯的系统研究，还未见报道。本章结合能量筛选算法CaGe_REBO和半经验PM3方法，提出了一种QM／MM方法用于大富勒烯C_(90)-C_(140)稳定结构的理论预测。首先，采用CaGe_REBO程序对C_(90)-C_(140)的所有IPR异构体进行系统地搜索，基于REBO能量对每个富勒烯筛选出100个低能量异构体，再用半经验PM3方法对筛选出来的异构体进行进一步优化以确定稳定异构体。与文献研究结果进行比较发现，这种QM／MM方法能够在半经验水平上预测大富勒烯的稳定异构体。故而，基于该方法预测了C_(90)-C_(140)中未被研究过的富勒烯前5个稳定异构体。通过比较稳定异构体的能量，发现对于大富勒烯C_(90)-C_(140)，许多富勒烯稳定异构体间的能量差别非常小，因此在实验中可能出现多个异构体共存的现象；这些稳定异构体一般拥有较低的对称性；另外，对影响富勒烯稳定性的可能因素进行了详细地研究：计算了用于定量描述六元环邻近规则HNR(hexagon neighbor rule)的H指数，以及HOMO-LUMO能隙。结果表明：HNR是影响富勒烯稳定性的一个重要因素；而PM3能隙对稳定性有一定的影响，但不是主要影响因素。
4．许多半经验方法由于计算速度较快已被广泛地应用于富勒烯研究中，而这些半经验方法的可靠性需要进一步研究。通常的方法是将各种半经验的计算结果与更高理论水平的量化计算结果进行比较。文献调研结果表明这种比较研究所针对的富勒烯都不超过C_(102)。本章结合分子力学方法(CaGe_REBO)、半经验方法(AM1，PM3，MNDO和TB)和更高理论水平的密度泛函理论方法(B3LYP)，在B3LYP／6-31G~*／／B3LYP／3-21G水平上预测了大富勒烯C_(116)-C_(120)的稳定异构体，并对不同半经验方法的可靠性进行了评估。结果表明，对于C_(116)-C_(120)，与精确的密度泛函理论方法B3LYP相比，半经验TB势方法能提供较为准确的定性半定量的计算结果；而AM1、PM3和MNDO这三种半经验方法计算得到的相对能量却非常不准确，和B3LYP相对能量之间相关性很差。另外，对稳定异构体的结构特点进行了研究，结果表明除上述HNR规则外，三种拓扑结构图形6656、6556和13／66对富勒烯稳定性的影响最大。
5．我们的计算经验表明，对于更大富勒烯如C_(160)，即使用分子力学方法进行预筛选，计算量也将无法承受。因此需要开发一种更快更有效的预筛选方法来避免复杂的能量计算。本章采用基于拓扑结构信息而非能量的方法对大富勒烯进行快速预筛选，以选出潜在的低能量异构体。这种拓扑方法就是Cioslowski等人提出的基于富勒烯所含30种局部拓扑结构的数目计算其标准生成焓ΔH°_f的经验拟合公式。结合CaGe开发了基于ΔH°_f进行预筛选的程序CaGe_Hf。利用CaGe_Hf对C_(132)-C_(160)的所有IPR集合进行筛选，对每个富勒烯选择出1000个候选异构体，再结合半经验的PM3和TB势方法以及更高精度的B3LYP／6-31G~*／／B3LYP／3-21G方法预测了C_(132)-C_(160)的热力学稳定异构体。B3LYP／6-31G~*能量分析表明，随着碳原子数由132增加到160，最低能量异构体的平均能量大体上呈单调递减趋势，其中C_(150)和C_(152)相对稍低。通过对计算得到的半经验结果进行系统地分析，发现异构体的局部拓扑结构图形对富勒烯的稳定性有重要的影响，HOMO-LUMO能隙对富勒烯稳定性的影响不太明显，而富勒烯的非球面性与稳定性没有相关性。此外，还在B3LYP／6-31G~*／／B3LYP／3-21G水平上计算了C_(132)-C_(160)最低能量异构体的电离能和电子亲和势。结果显示，C_(132)-C_(160)的电离能和电子亲和势分别在6.14和3.02 eV附近轻微波动，电离能和电子亲和势之差可用于估计异构体的HOMO-LUMO能隙。其中，C_(132)和C_(150)拥有较高的电离能和较低的电子亲和势，使得它们的HOMO-LUMO能隙较大。
6．文献调研结果表明采用高精度量子化学方法对大于C_(160)的富勒烯进行理论研究的报道非常少。本章在上一章研究的基础上提出了分层筛选的策略。首先根据我们以前计算的C_(60)-C_(160)的536个IPR异构体的数据，对Cioslowski等人提出的拓扑方法进行了重新拟合，得到新的筛选模型Ⅰ，标准偏差和相关系数分别为3.45和0.999。并将模型Ⅰ用于对C_(122)-C_(130)和C_(162)-C_(180)的IPR异构体进行第一步筛选；然后，在模型Ⅰ的基础上引入了TB势能量项得到模型Ⅱ，标准偏差和相关系数分别为1.70和0.999。显然，模型Ⅱ的预测精度有了明显改善，可用于对模型Ⅰ的筛选结果进行二次筛选。最后对模型Ⅱ的筛选结果进行B3LYP／6-31G~*优化以准确地预测C_(122)-C_(130)和C_(162)-C_(180)的热力学稳定异构体。研究结果表明，C_(174)和C_(180)的最稳定异构体不仅能量较低，而且拥有相当大的HOMO-LUMO能隙，这说明这两个异构体很可能从实验中分离出来。此外，还对预测的最低能量异构体的电子性质进行了计算。结果发现，对于C_(122)-C_(130)和C_(162)-C_(180)，其电离能和电子亲和势分别在6.079和3.156 eV附近轻微的波动。
Since the discovery of C_(60) 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 C_(96) 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 C_(80)-C_(90), 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 C_(80)-C_(90) 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 C_(80)-C_(90) are in good agreement with the published results, and not like C_(72), the IPR isomers are more stable than the non-IPR ones with large relative energies, which means that the IPR is still satisfied for C_(80)-C_(90).
3. Because of the limitation in experimental methods, theoretical calculations are the mainly used method in the investigations on fullerenes larger than C_(90). To our limited knowledge, fullerenes C_(90)-C_(100) C_(116), C_(118), and C_(120) 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 C_(90)-C_(140). First, all the IPR isomers of C_(90)-C_(140) 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 C_(90)-C_(140) at the semiempirical level. It was also found that for the large fullerenes C_(90)-C_(140), 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 C_(102). 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 C_(116)-C_(120) 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 C_(116)-C_(120), 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 C_(116)-C_(120) 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 C_(160). 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 C_(132)-C_(160) 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 C_(150) and C_(152) 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 C_(132)-C_(160) 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 C_(132) and C_(150) result in their large HOMO-LUMO gaps.
6. To our limited knowledge, for the fullerenes beyond C_(160), 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 C_(60)-C_(160), 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 C_(122)-C_(130) and C_(162)-C_(180), 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 C_(174) and C_(180) 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 C_(122)-C_(130) and C_(162)-C_(180) 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.
引文
[1] Kroto H. W., Heath J. R., O'Brien S. C., Curl R. F., Smalley R. E., C_(60); Buckminsterfullerene. Nature, 1985; 318, 162-163.
[2] Kratschmer W., Lamb L. D., Fostiropoulos K., Huffman D. R., Solid C_(60): A new form carbon. Nature, 1990, 347, 354-358,
[3] Sun G. Y., Kertesz M., ~(13)C NMR spectra for IPR isomers of fullerene C_(86). Chem. Phys., 2002, 276, 107-114.
[4] Kikuchi K., Nakahara N., Wakabayashi T., Suzuki S., Shiromaru H., Miyake Y., Saito K., Ikemoto I., Kainosho M., Achiba Y., NMR characterization of isomers of C_(72), C_(82) and C_(84) fullerenes. Nature, 1992, 357, 142-145.
[5] Kikuchi K., Nakahara N., Wakabayashi T., Honda M., Matsumiya H., Moriwaki T., Suzuki S., Shiromaru H., Saito K., Yamauchi K., Ikemoto I., Achiba Y., Isolation and identification of fullerene family: C_(76), C_(78), C_(82), C_(84), C_(90) and C_(96). Chem. Phys. Lett., 1992, 188, 177-180.
[6] Taylor R., Langley G. J., Avent A. G., Dennis T. J. S., Kroto H. W., Walton D. R. M., ~(13)C NMR-spectroscopy of C_(76), C_(78), C_(84) and mixtures of C_(86)-C_(102): Anomalous chromatographic behavior of C_(82), and evidence for C_(70)H_(12). J. Chem. Soc., Perkin Trans. 2, 1993, 1029-1036.
[7] Hennrich F. H., Michel R. H., Fischer A., RichardSchneider S., Gilb S., Kappes M. M., Fuchs D., Burk M., Kobayashi K., Nagase S., Isolation and characterization of C_(80). Angew. Chem., Int. Ed. Engl., 1996, 35, 1732-1734.
[8] Mitsumoto R., Oji H., Mori I., Yamamoto Y., Asato K., Ouchi Y., Shinohara H., Seki K., Umishita K., Hino S., Nagase S., Kikuchi K., Achiba Y., NEXAFS studies of higher fullerenes up to C_(96). J. Phys. Ⅳ, 1997, 7, 525-526.
[9] Diederich F., Ettl R., Rubin Y., Whetten R. L., Beck R., Alvarez M. M., Anz S., Sensharma D., Wudl F., Khemani K. C., Koch A., The higher fullerenes: Isolation and characterization of C_(76), C_(84), C_(90), C_(94), and C_(70)O, an oxide of D_(5H)-C_(70). Science, 1991, 252, 548-551.
[10] Crassous J., Rivera J., Fender N. S., Shu L. H., Echegoyen L., Thilgen C., Herrmann A., Diederich F., Chemistry of C_(84): Separation of three constitutional isomers and optical resolution of D_2-C_(84) by using the "Bingel-retro-Bingel" strategy. Angew. Chem., Int. Ed, 1999, 38, 1613-1617.
[11] Dennis T. J. S., Kai T., Asato K., Tomiyama T., Shinohara H., Yoshida T., Kobayashi Y., Ishiwatari H., Miyake Y., Kikuchi K., Achiba Y., Isolation and characterization by ~(13)C NMR spectroscopy of [84]fullerene minor isomers. J. Phys. Chem. A, 1999, 103, 8747-8752.
[12] Wang G. W., Saunders M., Khong A., Cross R. J., A new method for separating the isomeric C_(84) fullerenes. J. Am. Chem. Soc., 2000,122, 3216-3217.
[13] Kroto H. W., The stability of the fullerenes Cn, with n=24, 28, 32, 36, 50, 60 and 70. Nature, 1987, 329, 529-531.
[14] Fowler P. W., Fullerene stability and structure. Contemp. Phys., 1996, 37, 235-247.
[15] 李小罡，徐愉，刘云圻，朱道本，杨世和，富勒烯金属包合物的研究进展．化学进展，2000，12，385-390．
[16] 韩旭，李疏芬，富勒烯材料的催化作用研究进展．化学进展，2006，18，715-720．
[17] 刘书芝，唐光诗，[60]富勒烯衍生物的对称性、碳笼结构与~(13)C NMR谱．化学进展，2004，16，561-573．
[18] 滕启文，吴师，富勒烯离子Jahn-Teller畸变和光谱研究进展．化学进展，2005，17，949-954．
[19] 黄彬，郑启新，杨大志，郭晓东，吴永超，江贵长，富勒烯(C_(60))-甘氨酸衍生物对小鼠骨肉瘤细胞生长的影响．华中科技大学学报(医学版)，2006，35，493-496
[20] 倪瑾，蔡建明，吴秋业，富勒烯及其衍生物在核生物医学领域应用的研究现状．国际放射医学核医学杂志，2006，30，72-75．
[21] 姚姗姗，杨卫海，林修光，高建国，李炳海，陈滇宝，富勒烯衍生物的制备及其光催化杀菌研究．青岛科技大学学报(自然科学版)，2006，27，31-39．
[22] 鄂义峰，丁杨栋，方芳，刘佳川，内嵌金属富勒烯在生物医药中的应用．数理压药学杂志，2006，19，75-76．
[23] 王晓娟，魏传晚，刘传湘，富勒烯金属配合物的研究进展．化工时刊，2006，20，56-61．
[24] 官文超，曹远美，朱超，胡桢，C_(60)衍生物的合成及在水性成膜材料中的抗近红外和紫外性能．高分子材料科学与工程，2006，22，107-110．
[25] 李宏宇，陈志强，李效玉，活性聚合改性富勒烯C_(60)在新型聚合物材料中的应用．化工新型材料，2006，34，60-62．
[26] Parter D. H., Wurz P., Chatterjee K., Lykke K. R., Hunt J. E., Pellin M. J., Hemminger J. C., Gruen D. M., Stock L. M., High-yield synthesis, separation, and mass-spectrometric characterization of fullerenes C_(60) to C_(266). J. Am. Chem. Soc., 1991,113, 7499-7503.
[27] Parter D. H., Chatterjee K., Wurz P., Lykke K. R., Pellin M. J., Stock L. M., Fullerenes and giant fullerenes: synthesis, separation, and mass-spectrometric characterization. Carbon, 1992, 30, 1167-1182.
[28] Howard J. B., Mckinnon J. T., Makarovsky Y., Lafleur A. L., Johnson M. E., Fullerenes C_(60) and C_(70) in flames. Nature, 1991, 352, 139-141.
[29] Peters G., Jansen M., A new fullerene synthesis. Angew. Chem., Int. Ed Engl., 1992, 31,223-224.
[30] Chibante L. P. E, Thess A., Alford J. M., Diener M. D., Smalley R. E., Solar generation of the fullerenes. J. Phys. Chem., 1993, 97, 8696-8700.
[31] Taylor R., Langley G. J., Kroto H. W., Walton D. R. M., Formation of C_(60) by pyrolysis of naphthalene. Nature, 1993, 366, 728-731.
[32] Feng S. Q., Zhu X., Wu E., Superconductivity and structure of alkali-doped fullerenes: K_3C_(60) and Rb_3C_(60). Solid State Commun., 1991, 80, 639-642.
[33] Zhao W. B., Zhang X. D., Ye Z. Y., Synthesis of K_3C_(60) single crystal thin-films with high critical currents. Solid State Commun., 1993, 85,945-947.
[34] Allemand P. M., Khemani K. C., Koch A., Wudl F., Holczer K., Donovan S., Gruner G., Thompson J. D., Organic molecular soft ferromagnetism in a fullerene C_(60). Science, 1991, 253,301-303.
[35] 鲁照玲，官文超，富勒烯衍生物对神经细胞的凋亡作用．化学通报，2005，7，510-514．
[36] 李亚原，谭信，杨新林，乔新歌，王文晞，富勒烯膦酸衍生物对HeLa细胞生长的影响．生命科学仪器，2005，3，20-23．
[37] 单鹄声，倪瑾，蔡建明，富勒烯衍生物的生物学应用．生命的化学，2005，25，424-427．
[38] 李玉良，徐菊华，朱道本，我国C_(60)和碳纳米管的研究进展．化学通报，1999，10，10-13．
[39] Bendale R. D., Zerner M. C., Electronic-structure and spectroscopy of the most 5 stable isomers of C_(78) fullerene. J. Phys. Chem., 1995, 99, 13830-13833.
[40] Wang X. Q, Wang C. Z., Zhang B. L., Ho K. M., Electronic-structures of C_(82) fullerene isomers. Chem. Phys. Lett., 1994, 217, 199-203.
[41] 唐敖庆，李前树，柏拉图多面体与高碳原子簇．高等学校化学学报，1997，18， 1180-1184．
[42] 唐敖庆，李前树，高碳原子簇电子结构的计算方法及其应用．科学通报，1997，42，567-573．
[43] Tang A. C., Huang F. Q., Group theoretical applications to icosahedral fullerenes. Chem. Phys. Lett., 1995, 245, 561-565.
[44] Tang A. C., Huang F. Q., Electronic structures of dihedral (D_(5h), D_(4d), D_(6h), D_(6d)) fullerenes. Chem. Phys. Lett., 1996, 250, 528-536.
[45] Tang A. C., Huang F. Q., Liu R. Z., Electronic structures of fullerenes C_n with I_h symmetry and n=20k~2. Phys. Rev. B, 1996, 53, 7442-7450.
[46] Teng Q. W., Zhao X. Z., Cai Z. S., Tang A. C., Theoretical studies on the structures and electronic spectra of C_(70)CH_2. Int. J. Quantum Chem., 1997, 61, 815-822.
[47] Li A. Y., Tang A. C., Eigenvalue spectra geometric transformation of polyhedra. J. Mol. Struct. (Theochem), 2000, 530, 245-264.
[48] Li A. Y., Liao M. Z., Tang A. C., Site projection operator and its application: electronic structures and stability rules of tetrahedral fullerenes. Phys. Chem. Chem. Phys., 2000, 2, 2301-2307.
[49] Smalley R. E., Self-assembly of the fullerenes. Accounts. Chem. Res., 1992, 25, 98-105.
[50] Goeres A., Sedlmayr E., On the nucleation mechanism of effective fullerite condensation. Chem. Phys. Lett., 1991, 184, 310-317.
[51] Wakabayashi T., Achiba Y., A model for the C_(60) and C_(70) growth-mechanism. Chem. Phys. Lett., 1992, 190, 465-468.
[52] Wakabayashi T., Shiromaru H., Kikuchi K., Achiba Y., A selective isomer growth of fullerenes. Chem. Phys. Lett., 1993, 201,470-474.
[53] Curl R. F., Collapse and growth. Nature, 1993, 363, 14-15.
[54] Yamaguchi Y., Maruyama S., A molecular dynamics simulation of the fullerene formation process. Chem. Phys. Lett., 1998, 286, 336-342.
[55] Melker A. I., Romanov S. N., Kornilov D. A., Computer simulation of formation of carbon fullerenes. Mater. Phys. Mech., 2000, 2, 42-50.
[56] Turker L., A bucky onion from C_(20) and C_(60)—an AM1 treatment. J. Mol. Struct. (Theochem), 2001, 545, 207-214.
[57] Liu F. Y., Meng L. P., Zheng S. J., Density functional studies on a novel double-shell fullerene C_(20)@C_(60). J. Mol. Struct. (Theochem), 2005, 725, 17-21.
[58] Erkoc S., Stability of carbon nanoonion C_(20)@C_(60)@C_(240): Molecular dynamics simulations, Nano Lett., 2002, 2, 215-217.
[59] Kobayashi K., Nagase S., Akasaka T., A theoretical study of C_(80) and La_2@C_(80). Chem. Phys. Lett., 1995, 245, 230-236.
[60] Kobayashi K., Nagase S., Akasaka T., Endohedral dimetallofullerenes Sc_2@C_(84) and La_2@C_(80). Are the metal atoms still inside the fullerene cages? Chem. Phys. Lett., 1996, 261, 502-506.
[61] Kobayashi K., Nagase S., Structures and electronic states of endohedral dimetallofullerenes: M_2@C_(80) (M=Sc, Y, La, Ce, Pr, Eu, Gd, Yb and Lu). Chem. Phys. Lett., 1996, 262, 227-232.
[62] Nagase S., Kobayashi K., Structural study of endohedral dimetallofullerenes Sc_2@C_(84) and Sc_2@C_(74). Chem. Phys. Lett., 1997, 276, 55-61.
[63] Kobayashi K., Nagase S., Yoshida M., Osawa E., Endohedral metallofullerenes. Are the isolated pentagon rule and fullerene structures always satisfied? J. Am. Chem. Soc., 1997, 119, 12693-12694.
[64] Yan Q. B., Zheng Q. R., Su G., Structures, electronic properties, spectroscopies, and hexagonal monolayer phase of a family of unconventional fullerenes C_(64)X_4 (X=H, F, Cl, Br). J. Chem. Phys., 2007, 111, 549-554.
[65] Hemandez E., Meunier V., Smith B. W., Rurali R., Terrones H., Nardelli M. B., Terrones M., Luzzi D. E., Charlier J. C., Fullerene Coalescence in Nanopeapods: A Path to Novel Tubular Carbon, Nano Lett., 2003, 3, 1037-1042.
[66] Lin Y., Cai W. S., Shao X. G., Fullerenes Connected Nanotubes: An Approach to Build Multidimensional Carbon Nanocomposites. Chem. Phys., 2006, 331, 85-91.
[67] Brenner D. W., Empirical potential for hydrocarbons for use in simulating the chemical vapor-deposition of diamond films. Phys. Rev. B, 1990, 42, 9458-9471.
[68] Brenner D. W., Shenderova O. A., Harrison J. A., Stuart S. J., Ni B., Sinnott S. B., A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys.: Condens. Matter, 2002, 14, 783-802.
[69] Tersoff J., New empirical model for the structural properties of silicon. Phys. Rev. Lett., 1986, 56, 632-635.
[70] Cai W. S., Shao X. G., A fast annealing evolutionary algorithm for global optimization. J. Comp. Chem., 2002, 23,427-435.
[71] Cai W. S., Shao N., Shao X. G., Pan Z. X., Structural analysis of carbon clusters by using a global optimization algorithm with Brenner potential. J Mol. Struct. (Theochem), 2004, 678, 113-122.
[72] Liu D. C., Nocedal J., On the limited memory BFGS method for large-scale optimization. Math. Progm., 1989, 45,503-528.
[73] Cai W. S., Xu L., Shao N., Shao X. G., Guo Q. X., An efficient approach for theoretical study on the low-energy isomers of large fullerenes C_(90)-C_(140). J. Chem. Phys., 2005, 122, 184318.
[74] Ponomareva I. V., Chernozatonskii L. A., How can carbon onion transform into diamond-like structure. Microelectron. Eng., 2003, 69, 625-628.
[75] Sutton A. P., Finnis M. W., Pettifor D. G., Ohta Y., The tight-binding bond model. J. Phys. C: Solid State Physics, 1988, 21, 35-66.
[76] Xu C. H., Wang C. Z., Chan C. T., Ho K. M., A transferable tight-binding potential for carbon. J. Phys: Condens. Matter, 1992, 4, 6047-6054
[77] Elstner M., Porezag D., Jungnickel G., Eisner J., Haugk M., Frauenheim T., Suhai S., Seifert G., Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties. Phys. Rev. B, 1998, 58, 7260-7268.
[78] Porezag D., Frauenheim T., Kohler T., Seifert G., Kaschner R., Construction of tight-binding-like potentials on the basis of density-functional theory: Application to carbon. Phys. Rev. B, 1995, 51, 12947-12957.
[79] Frauenheim T., Seifert G., Elstner M., Niehaus T., Kohler C., Amkreutz M., Sternberg M., Hajnal Z., Carlo A. D., Suhai S., Atomistic simulations of complex materials: ground-state and excited-state properties. J. Phys. : Cond. Mater, 2002, 14, 3015-3047.
[80] Slanina Z., Zhao X., Lee S. L., Osawa E., C_(90) temperature effects on relative stabilities of the IPR isomers. Chem. Phys. Lett., 1997, 219, 193-200.
[81] Slanina Z., Zhao X., Deota P., Osawa E., Relative stabilities of C_(92) IPR fullerenes. J. Mol. Model., 2000, 6, 312-317.
[82] Zhao X., Slanina Z., Goto H., Osawa E., Theoretical investigations on relative stabilities of fullerene C_(94). J. Chem. Phys., 2003, 118, 10534-10540.
[83] Zhao X., Slanina Z., Goto H., Theoretical studies on the relative stabilities of C_(96) IPR fullerenes. J. Phys. Chem. A, 2004, 108, 4479-4484.
[84] Zhao X., Slanina Z., C_(98) IPR isomers: Gibbs-energy based relative stabilities. J. Mol. Struct. (Theochem), 2003, 636, 195-201.
[85] Zhao X., Goto H., Slanina Z., C_(110) IPR fullerenes: temperature-dependent relative stabilities based on the Gibbs function. Chem. Phys., 2004, 306, 93-104.
[86] Zhang B. L., Wang C. Z., Ho K. M., Xu C. H., Chan C. T., The geometry of small fullerene cages: C_(20) to C_(70). J. Chem. Phys., 1992, 97, 5007-5011.
[87] Zhang B. L., Wang C. Z., Ho K. M., Xu C. H., Chan C. T., The geometry of large fullerene cages: C_(72) to C_(102). J. Chem. Phys., 1993, 98, 3095-3102.
[88] Achiba Y., Fowler P. W., Mitchell D., Zerbetto F., Structural predictions for the C_(116) molecule. J. Phys. Chem. A, 1998, 102, 6835-6841.
[89] Fowler P. W., Heine T., Zerbetto F., Competition between even and odd fullerenes: C_(118), C_(119) and C_(120). J. Phys. Chem. A, 2000, 104, 9625-9629.
[90] Shao N., Gao Y., Yoo S., An W., Zeng X. C., Search for lowest-energy fullerenes: C_(98)-C_(110). J. Phys. Chem. A, 2006, 110, 7672-7676.
[91] Xu L., Cai W. S., Shao X. G., Prediction of low-energy isomers of large fullerenes from C_(132)-C_(160). J. Phys. Chem. A, 2006, 110, 9247-9253.
[92] Furche F., Ahlrichs R., Fullerene C_(80): Are there still more isomers? J. Chem. Phys., 2001, 114, 10362-10367.
[93] Nishikawa T., Kinoshita T., Nanbu S., Aoyagi M., A theoretical study on vibrational spectra of C_(84) fullerenes: results for C_2, D_2, and D_(2d) isomers. J. Mol. Struct. (Theochem), 1999, 461-462, 453-461.
[94] Sun G., Kertesz M., Theoretical ~(13)C NMR spectra of IPR isomers of fullerenes C_(60), C_(70), C_(72), C_(74), C_(76), and C_(78) studied by density functional theory. J. Phys. Chem. A, 2000, 104, 7398-7403.
[95] Sun G., Kertesz M., Identification for IPR isomers of fullerene C_(82) by theoretical ~(13)C NMR spectra calculated by density functional theory. J. Phys. Chem. A, 2001, 105, 5468-5472.
[96] Cioslowski J., Rao N., Moncrieff D., Standard enthalpies of formation fo fullerenes and their dependence on structural motifs. J. Am. Chem. Soc., 2002, 122, 8265-8270.
[97] Xu L., Cai W. S., Shao X. G., Systematic search for energetically favored isomers of large fullerenes C_(122)-C_(130) and C_(162)-C_(180), Comp. Mater. Sci., accepted.
[98] Albertazzi E., Domene C., Fowler P. W., Heine T., Seifert G., Alsenoy C. V., Zerbetto F., Pentagon adjacency as a determinant of fullerene stability. Phys. Chem. Chem. Phys., 1999, 1, 2913-2918.
[99] Lin Y., Cai W. S., Shao X. G., Comparison studies of fullerenes C_(72), C_(74), C_(76) and C_(78) by tight-binding Monte Carlo and quantum chemical methods. J. Mol. Struct. (Theochem), 2006, 760, 153-158.
[100] Chen Z., Thiel W., Performance of semiempirical methods in fullerene chemistry: relative energies and nucleus-independent chemical shifts. Chem. Phys. Lett., 2003, 367, 15-25.
[101] Zheng G., Irle S., Morokuma K., Performance of the DFTB method in comparison to DFT and semiempirical methods for geometries and energies of C_(20)-C_(86) fullerene isomers. Chem. Phys. Lett., 2005, 412, 210-216.
[102] Xu L., Cai W. S., Shao X. G., Performance of the semiempirical AM1, PM3, MNDO, and tight-binding methods in comparison with DFT method for the large fullerenes C_(116)-C_(120). J. Mol. Struct.(Theochem), in press.
[103] Slanina Z., Ishimura K., Kobayashi K., Nagase S., C_(72) isomers: the IPR-satisfying cage is disfavored by both energy and entropy. Chem. Phys. Lett., 2004, 384, 114-118.
[104] Wu H. S., Xu X. H., Jiao H. J., Structure and stability of C_(48) fullerenes, J. Phys. Chem. A, 2004, 108, 3813-3816.
[105] Wu H. S., Tian X. X., Jian J. F., Feng R. J., Stability of fullerene cages: C_(30) to C_(70) and their dependence on shared pentagon bonds. Chinese J. Struct. Chem., 2006, 25, 1051-1056.
[106] Raghavachari K., Ground-state of C_(84):2 almost isoenergetic isomers. Chem. Phys. Lett., 1992, 190, 397-400.
[107] Yoshida M., Aihara J., Validity of the weighted HOMO-LUMO energy separation as an index of kinetic stability for fullerenes with up to 120 carbon atoms. Phys. Chem. Chem. Phys., 1999, 1,227-230.
[108] Yoshida M., Aihara J., Weighted HOMO-LUMO energy separations of properly closed-shell fullerene isomers. J. Mol. Graphics Modell., 2001, 19, 194-198.
[109] Seifert G., Vietze K., Schmidt R., Ionization energies of fullerenes—size and charge dependence. J. Phys. B: At. Mol. Opt. Phys., 1996, 29, 5183-5192.
[110] Boltalina O. V., Ioffe I. N., Sidorov L. N., Seifert G., Vietze K., Ionization energy of fullerenes, J. Am. Chem. Soc., 2000, 122, 9745-9749.
[1] Brinkmann G., Dress A. W. M., A constructive enumeration of fullerenes. J. Algorithms, 1997, 23,345-358.
[2] Brinkmann G., Dress A. W. M., A reliable and efficient top-down approach to fullerene-structure enumeration. Adv. Appl. Math., 1998, 21,473-480.
[3] Fowler P. W., Manolopoulos D. E., An Atlas of Fullerenes. Clarendon Press: Oxford, 1995.
[4] Manolopoulos D. E., May J. C., Down S. E., Theoretical studies of the fullerenes: C_(34) to C_(70). Chem. Phys. Lett., 1991, 181, 105-111.
[5] Kroto H. W., The stability of the fullerenes Cn, with n=24, 28, 32, 36, 50, 60 and 70. Nature, 1987, 329, 529-531.
[6] Brenner D. W., Shenderova O. A., Harrison J. A., Stuart S. J., Ni B., Sinnott S. B., A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys.: Condens. Matter, 2002, 14, 783-802.
[7] Liu D. C., Nocedal J., On the limited memory BFGS method for large-scale optimization. Math. Progm., 1989, 45, 503-528.
[8] Ettl R., Chao I., Diederich F., Whetten R. L., Isolation of C76: a chiral (D2) allotrope of carbon, Nature, 1991, 353, 149-153.
[9] Kikuchi K., Nakahara N., Wakabayashi T., Suzuki S., Shiromaru H., Miyake Y., Saito K., Ikemoto I., Kainosho M., Achiba Y., NMR characterization of isomers of C_(78), C_(82) and C_(84) fullerenes. Nature, 1992, 357, 142-145.
[10] Slanina Z., Lee S. L., Adamowicz L., C_(80), C_(86), C_(88): Semiempirical and ab initio SCF calculations. Int. J. Quantum. Chem., 1997, 63, 529-535.
[11] Sun G. Y., Kertesz M., Identification for IPR isomers of fullerene C_(82) by theoretical C-13 NMR spectra calculated by density functional theory. J. Phys. Chem. A, 2001, 105, 5468-5472.
[12] Buhl M., van Wullen C., Computational evidence for a new C_(84) isomer. Chem. Phys. Lett., 1995, 247, 63-68.
[13] Slanina Z., Zhao X., Lee S. L., Osawa E., C_(90) temperature effects on relative stabilities of the IPR isomers. Chem. Phys., 1997, 219, 193-200.
[14] Kobayashi K., Nagase S., Yoshida M., Osawa E., Endohedral metallofullerenes. Are the isolated pentagon rule and fullerene structures always satisfied? J. Am. Chem. Soc., 1997, 119, 12693-12694.
[15] Slanina Z., Ishimura K., Kobayashi K., Nagase S., C_(72) isomers: the IPR-satisfying cage is disfavored by both energy and entropy. Chem. Phys. Lett., 2004, 384, 114-118.
[16] Frisch M. J., Trucks G. W., Schlegel H. B., Scuseria G. E., Robb M. A., Cheeseman J. R., Montgomery J. A., Jr., Vreven T., Kudin K. N., Burant J. C., Millam J. M., Iyengar S. S., Tomasi J., Barone V., Mennucci B., Cossi M., Scalmani G., Rega N., Petersson G. A., Nakatsuji H., Hada M., Ehara M., Toyota K., Fukuda R., Hasegawa J., Ishida M., Nakajima T., Honda Y., Kitao O., Nakai H., Klene M., Li X., Knox J. E., Hratchian H. P., Cross J. B., Adamo C., Jaramillo J., Gomperts J., Stratmann R. E., Yazyev O., Austin A. J., Cammi R., Pomelli C., Ochterski J. W., Ayala P. Y., Morokuma K., Voth G. A., Salvador P., Dannenberg J. J., Zakrzewski V. G., Dapprich S., Daniels A. D., Strain M. C., Farkas O., Malick D. K., Rabuck A. D., Raghavachari K., Foresman J. B., Ortiz J. V., Cui Q., Baboul A. G., Clifford S., Cioslowski J., Stefanov B. B., Liu G., Liashenko A., Piskorz P., Komaromi I., Martin R. L., Fox D. J., Keith T., Al-Laham M. A., Peng C. Y., Nanayakkara A., Challacombe M., Gill P. M. W., Johnson B., Chen W., Wong M. W., Gonzalez C., Pople J. A., GAUSSIAN 03, Revision C.02, Gaussian, Inc., Wallingford CT, 2004.
[17] Sun G. Y., Kertesz M., Theoretical ~(13)C NMR spectra of IPR isomers of fullerene C_(80): a density functional theory study. Chem. Phys. Lett., 2000, 328, 387-395.
[18] Zhang B. L., Wang C. Z., Ho K. M., Xu C. H., Chan C. T., The geometry of large fullerene cages: C_(72) to C_(102). J. Chem. Phys., 1993, 98, 3095-3102.
[1] Kratschmer W., Lamb L. D., Fostiropoulos K., Huffman D. R., Solid C_(60): A new form carbon. Nature, 1990, 347, 354-358.
[2] Sun G. Y., Kertesz M., ~(13)C NMR spectra for IPR isomers of fullerene C_(86). Chem. Phys., 2002, 276, 107-114.
[3] Kikuchi K., Nakahara N., Wakabayashi T., Suzuki S., Shiromaru H., Miyake Y., Saito K., Ikemoto I., Kainosho M., Achiba Y., NMR characterization of isomers of C_(78), C_(82) and C_(84) fullerenes. Nature, 1992, 357, 142-145.
[4] Kikuchi K., Nakahara N., Wakabayashi T., Honda M., Matsumiya H., Moriwaki T., Suzuki S., Shiromaru H., Saito K., Yamauchi K., Ikemoto I., Achiba Y., Isolation and identification of fullerene family: C_(76), C_(78), C_(82), C_(84), C_(90) and C_(96). Chem. Phys. Lett., 1992, 188, 177-180.
[5] Taylor R., Langley G. J., Avent A. G., Dennis T. J. S., Kroto H. W., Walton D. R. M., ~(13)C NMR-spectroscopy of C_(76), C_(78), C_(84) and mixtures of C_(86)-C_(102): Anomalous chromatographic behavior of C_(82), and evidence for C_(70)H_(12). J Chem. Soc., Perkin Trans. 2, 1993, 1029-1036.
[6] Hennrich F. H., Michel R. H., Fischer A., RichardSchneider S., Gilb S., Kappes M. M., Fuchs D., Burk M., Kobayashi K., Nagase S., Isolation and characterization ofC_(80). Angew. Chem., Int. Ed. Engl., 1996, 35, 1732-1734.
[7] Mitsumoto R., Oji H., Mori I., Yamamoto Y., Asato K., Ouchi Y., Shinohara H., Seki K., Umishita K., Hino S., Nagase S., Kikuchi K., Achiba Y., NEXAFS studies of higher fullerenes up to C_(96). J. Phys. Ⅳ, 1997, 7, 525-526.
[8] Diederich F., Ettl R., Rubin Y., Whetten R. L., Beck R., Alvarez M. M., Anz S., Sensharma D., Wudl F., Khemani K. C., Koch A., The higher fullerenes: Isolation and characterization of C_(76), C_(84), C_(90), C_(94), and C_(70)O, an oxide of D_(5H)-C_(70). Science, 1991, 252, 548-551.
[9] Crassous J., Rivera J., Fender N. S., Shu L. H., Echegoyen L., Thilgen C., Herrmann A., Diederich F., Chemistry of C_(84): Separation of three constitutional isomers and optical resolution of D_2-C_(84) by using the "Bingel-retro-Bingel" strategy. Angew. Chem., Int. Ed., 1999, 38, 1613-1617.
[10] Dennis T. J. S., Kai T., Asato K., Tomiyama T., Shinohara H., Yoshida T., Kobayashi Y., Ishiwatari H., Miyake Y., Kikuchi K., Achiba Y., Isolation and characterization by ~(13)C NMR spectroscopy of [84]fullerene minor isomers. J. Phys. Chem. A, 1999, 103, 8747-8752.
[11] Cai W. S., Shao N., Shao X. G., Pan Z. X., Structural analysis of carbon clusters by using a global optimization algorithm with Brenner potential. J. Mol. Struct. (Theochem), 2004, 678, 113-122.
[12] Zhang B. L., Wang C. Z., Ho K. M., Xu C. H., Chan C. T., The geometry of small fullerene cages: C_(20) to C_(70). J. Chem. Phys., 1992, 97, 5007-5011.
[13] Zhang B. L., Wang C. Z., Ho K. M., Xu C. H., Chan C. T., The geometry of large fullerene cages: C_(72) to C_(102). ,J.. Chem. Phys., 1993, 98, 3095-3102.
[14] Slanina Z., Zhao X., Lee S. L., Osawa E., C_(90) temperature effects on relative stabilities of the IPR isomers. Chem. Phys. Lett., 1997, 219, 193-200.
[15] Slanina Z., Zhao X., Deota P., Osawa E., Relative stabilities of C_(92) IPR fullerenes. J. Mol. Model., 2000, 6, 312-317.
[16] Zhao X., Slanina Z., Goto H., Osawa E., Theoretical investigations on relative stabilities of fullerene C_(94). J. Chem. Phys., 2003, 118, 10534-10540.
[17] Zhao X., Slanina Z., Goto H., Theoretical studies on the relative stabilities of C_(96) IPR fullerenes. J. Phys. Chem. A, 2004, 108, 4479-4484.
[18] Zhao X., Slanina Z., C_(98) IPR isomers: Gibbs-energy based relative stabilities. J. Mol. Struct. ~heochem), 2003, 636, 195-201.
[19] Zhao X., Goto H., Slanina Z., C_(110) IPR fullerenes: temperature-dependent relative stabilities based on the Gibbs function. Chem. Phys., 2004, 306, 93-104.
[20] Achiba Y., Fowler P. W., Mitchell D., Zerbetto F., Structural predictions for the C_(116) molecule, J. Phys. Chem. A, 1998, 102, 6835-6841.
[21] Fowler P. W., Heine T., Zerbetto F., Competition between even and odd fullerenes: C_(118), C_(119) and C_(120). J. Phys. Chem. A, 2000, 104, 9625-9629.
[22] Brinkmann G., Dress A. W. M., A reliable and efficient top-down approach to fullerene-structure enumeration. Adv. Appl. Math., 1998, 21,473-480.
[23] Kroto H. W., The stability of the fullerenes Cn, with n=24, 28, 32, 36, 50, 60 and 70. Nature, 1987, 329, 529-531.
[24] Brenner D. W., Shenderova O. A., Harrison J. A., Stuart S. J., Ni B., Sinnott S. B., A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys.: Condens. Matter, 2002, 14, 783-802.
[25] Albertazzi E., Domene C., Fowler P. W., Heine T., Seifert G., Alsenoy C. V., Zerbetto F., Pentagon adjacency as a determinant of fullerene stability. Phys. Chem. Chem. Phys., 1999, 1, 2913-2918.
[26] Raghavachari K., Ground-state of Cs4:2 almost isoenergetic isomers. Chem. Phys. Lett., 1992, 190, 397-400.
[27] Liu D. C., Nocedal J., On the limited memory BFGS method for large-scale optimization. Math. Progm., 1989, 45, 503-528.
[28] Frisch M. J., Trucks G. W., Schlegel H. B., Scuseria G. E., Robb M. A., Cheeseman J. R., Zakrzewski V. G., Montgomery J. A., Stratmann R. E., Burant J. C., Dapprich S., Millam J. M., Daniels A. D., Kudin K. N., Strain M. C., Farkas O., Tomasi J., Barone V., Cossi M., Cammi R., Mennucci B., Pomelli C., Adamo C., Clifford S., Ochterski J., Petersson G. A., Ayala P. Y., Cui Q., Morokuma K., Salvador P., Dannenberg J. J., Malick D. K., Rabuck A. D., Raghavachari K., Foresman J. B., Cioslowski J., Ortiz J. V., Baboul A. G., Stefanov B. B., Liu G., Liashenko A., Piskorz P., Komaromi I., Gomperts R., Martin R. L., Fox D. J., Keith T., Al-Laham M. A., Peng C. Y., Nanayakkara A., Challacombe M., Gill P. M. W., Johnson B., Chen W., Wong M. W., Andres J. L., Gonzalez C., Head-Gordon M., Replogle E. S., and Pople J. A., Gaussian 98, Revision A.7, Gaussian, Inc., Pittsburgh, PA (1998).
[29] Fowler P. W., Manolopoulos D. E., An Atlas of Fullerenes. Clarendon Press: Oxford, 1995.
[1] Zhang B. L., Wang C. Z., Ho K. M., Xu C. H., Chan C. T., The geometry of large fullerene cages: C_(72) to C_(102). J. Chem. Phys., 1993, 98, 3095-3102.
[2] Slanina Z., Zhao X., Lee S. L., Osawa E., C_(90) temperature effects on relative stabilities of the IPR isomers. Chem. Phys. Lett., 1997, 219, 193-200.
[3] Slanina Z., Zhao X., Deota P., Osawa E., Relative stabilities of C_(92) IPR fullerenes. J. Mol. Model., 2000, 6, 312-317.
[4] Zhao X., Slanina Z., Goto H., Osawa E., Theoretical investigations on relative stabilities of fullerene C_(94). J. Chem. Phys., 2003, 118, 10534-10540.
[5] Zhao X., Slanina Z., Goto H., Theoretical studies on the relative stabilities of C_(96) IPR fullerenes. J. Phys. Chem. A, 2004, 108, 4479-4484.
[6] Zhao X., Slanina Z., C98 IPR isomers: Gibbs-energy based relative stabilities. J. Mol. Struct. (Theochem), 2003, 636, 195-201.
[7] Zhao X., Goto H., Slanina Z., C_(110) IPR fullerenes: temperature-dependent relative stabilities based on the Gibbs function. Chem. Phys., 2004, 306, 93-104.
[8] Cioslowski J., Electronic structure calculations on fullerenes and their derivatives. Oxford University Press: New York, 1995.
[9] Thiel W., Perspectives on semiempirical molecular orbital theory. Adv. Chem. Phys., 1996, 93, 703-757.
[10] Chen Z., Thiel W., Performance of semiempirical methods in fullerene chemistry: relative energies and nucleus-independent chemical shifts. Chem. Phys. Lett., 2003, 367, 15-25.
[11] Zheng G., Irle S., Morokuma K., Performance of the DFTB method in comparison to DFT and semiempirical methods for geometries and energies of C_(20)-C_(86) fullerene isomers. Chem. Phys. Lett., 2005, 412, 210-216.
[12] Elstner M., Porezag D., Jungnickel G., Eisner J., Haugk M., Frauenheim T., Suhai S., Seifert G., Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties. Phys. Rev. B, 1998, 58, 7260-7268.
[13] Porezag D., Frauenheim T., Kohler T., Seifert G., Kaschner R., Construction of tight-binding-like potentials on the basis of density-functional theory: Application to carbon. Phys. Rev. B, 1995, 51, 12947-12957.
[14] Frauenheim T., Seifert G., Elstner M., Niehaus T., Kohler C., Amkreutz M., Sternberg M., Hajnal Z., Carlo A. D., Suhai S., Atomistic simulations of complex materials: ground-state and excited-state properties. J. Phys.: Cond Mater, 2002, 14, 3015-3047.
[15] Achiba Y., Fowler P. W., Mitchell D., Zerbetto F., Structural predictions for the C_(116) molecule. J. Phys. Chem. A, 1998, 102, 6835-6841.
[16] Fowler P. W., Heine T., Zerbetto F., Competition between even and odd fullerenes: C_(118), C_(119) and C_(120). J.. Phys. Chem. A, 2000, 104, 9625-9629.
[17] Xu C. H., Wang C. Z., Chan C. T., Ho K. M., A transferable tight-binding potential for carbon. J. Phys: Condens. Matter, 1992, 4, 6047-6054.
[18] Brenner D. W., Shenderova O. A., Harrison J. A., Stuart S. J., Ni B., Sinnott S. B., A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys.: Condens. Matter, 2002, 14, 783-802.
[19] Cai W. S., Xu L., Shao N., Shao X. G., Guo Q. X., An efficient approach for theoretical study on the low-energy isomers of large fullerenes C_(90)-C_(140). J. Chem. Phys., 2005, 122, 184318.
[20] Brinkmann G., Dress A. W. M., A reliable and efficient top-down approach to fullerene-structure enumeration. Adv. Appl. Math., 1998, 21, 473-480.
[21] Fowler P. W., Manolopoulos D. E., An Atlas of Fullerenes. Clarendon Press: Oxford, 1995.
[22] Manolopoulos D. E., May J. C., Down S. E., Theoretical studies of the fullerenes: C_(34) to C_(70). Chem. Phys. Lett., 1991, 181, 105-111.
[23] Frisch M. J., Trucks G. W., Schlegel H. B., Scuseria G. E., Robb M. A., Cheeseman J. R., Montgomery J. A., Jr., Vreven T., Kudin K. N., Burant J. C., Millam J. M., Iyengar S. S., Tomasi J., Barone V., Mennucci B., Cossi M., Scalmani G., Rega N., Petersson G. A., Nakatsuji H., Hada M., Ehara M., Toyota K., Fukuda R., Hasegawa J., Ishida M., Nakajima T., Honda Y., Kitao O., Nakai H., Klene M., Li X., Knox J. E., Hratchian H. P., Cross J. B., Adamo C., Jaramillo J., Gomperts J., Stratmann R. E., Yazyev O., Austin A. J., Cammi R., Pomelli C., Ochterski J. W., Ayala P. Y., Morokuma K., Voth G. A., Salvador P., Dannenberg J. J., Zakrzewski V. G., Dapprich S., Daniels A. D., Strain M. C., Farkas O., Malick D. K., Rabuck A. D., Raghavachari K., Foresman J. B., Ortiz J. V., Cui Q., Baboul A. G., Clifford S., Cioslowski J., Stefanov B. B., Liu (3., Liashenko A., Piskorz P., Komaromi I., Martin R. L., Fox D. J., Keith T., Al-Laham M. A., Peng C. Y., Nanayakkara A., Challacombe M., Gill P. M. W., Johnson B., Chen W., Wong M. W., Gonzalez C., Pople J. A., GAUSSIAN 03, Revision C.02, Gaussian, Inc., Wallingford CT, 2004.
[24] Xu L., Cai W. S., Shao X. G., Prediction of low-energy isomers of large fullerenes from C_(132)-C_(160). J. Phys. Chem. A, 2006, 110, 9247-9253.
[25] Raghavachari K., Ground-state of C_(84):2 almost isoenergetic isomers. Chem. Phys. Lett., 1992, 190, 397-400.
[26] Cioslowski J., Rao N., Moncrieff D., Standard enthalpies of formation fo fullerenes and their dependence on structural motifs. J. Am. Chem. Soc., 2002, 122, 8265-8270.
[1] Sun G. Y., Kertesz M., ~(13)C NMR spectra for IPR isomers of fullerene C_(86). Chem. Phys., 2002, 276, 107-114.
[2] Kikuchi K., Nakahara N., Wakabayashi T., Suzuki S., Shiromaru H., Miyake Y., Saito K., Ikemoto I., Kainosho M., Achiba Y., NMR characterization of isomers of C_(78), C_(82) and C_(84) fullerenes. Nature, 1992, 357, 142-145.
[3] Kikuchi K., Nakahara N., Wakabayashi T., Honda M., Matsumiya H., Moriwaki T., Suzuki S., Shiromaru H., Saito K., Yamauchi K., Ikemoto I., Achiba Y., Isolation and identification of fullerene family: C_(76), C_(78), C_(82), C_(84), C_(90) and C_(96). Chem. Phys. Lett., 1992, 188, 177-180.
[4] Taylor R., Langley G. J., Avent A. G., Dennis T. J. S., Kroto H. W., Walton D. R. M., ~(13)C NMR-spectroscopy of C_(76), C_(78), C_(84) and mixtures of C_(86)-C_(102): Anomalous chromatographic behavior of C_(82), and evidence for C_(70)H_(12). J. Chem. Soc., Perkin Trans. 2, 1993, 1029-1036.
[5] Hennrich F. H., Michel R. H., Fischer A., RichardSchneider S., Gilb S., Kappes M. M., Fuchs D., Burk M., Kobayashi K., Nagase S., Isolation and characterization ofC_(80). Angew. Chem., Int. Ed. Engl., 1996, 35, 1732-1734.
[6] Mitsumoto R., Oji H., Mori I., Yamamoto Y., Asato K., Ouchi Y., Shinohara H., Seki K., Umishita K., Hino S., Nagase S., Kikuchi K., Achiba Y., NEXAFS studies of higher fullerenes up to C_(96). J. Phys. Ⅳ, 1997, 7, 525-526.
[7] Diederich F., Ettl R., Rubin Y., Whetten R. L., Beck R., Alvarez M. M., Anz S., Sensharma D., Wudl F., Khemani K. C., Koch A., The higher fullerenes: Isolation and characterization of C_(76), C_(84), C_(90), C_(94), and C_(70)O, an oxide of D_(5H)-C_(70). Science, 1991, 252, 548-551.
[8] Crassous J., Rivera J., Fender N. S., Shu L. H., Echegoyen L., Thilgen C., Herrmarm A., Diederich F, Chemistry of C_(84): Separation of three constitutional isomers and optical resolution of D_2-C_(84) by using the "Bingel-retro-Bingel" strategy. Angew. Chem., Int. Ed, 1999, 38, 1613-1617.
[9] Dennis T. J. S., Kai T., Asato K., Tomiyama T., Shinohara H., Yoshida T., Kobayashi Y., Ishiwatari H., Miyake Y., Kikuchi K., Achiba Y., Isolation and characterization by ~(13)C NMR spectroscopy of [84]fullerene minor isomers. J. Phys. Chem. A, 1999, 103, 8747-8752.
[10] Kroto H. W., The stability of the fullerenes Cn, with n=24, 28, 32, 36, 50, 60 and 70. Nature, 1987, 329, 529-531.
[11] Schmalz T. G., Seitz W. A., Klein D. J., Hite G. E., Elemental carbon cages. J Am. Chem. Soc., 1988, 110, 1113-1127.
[12] Cai W. S., Shao N., Shao X. G., Pan Z. X., Structural analysis of carbon clusters by using a global optimization algorithm with Brenner potential. J. Mol. Struct. (Theochem), 2004, 678, 113-122.
[13] Zhang B. L., Wang C. Z., Ho K. M., Xu C. H., Chan C. T., The geometry of small fullerene cages: C_(20) to C_(70). J Chem. Phys., 1992, 97, 5007-5011.
[14] Zhang B. L., Wang C. Z., Ho K. M., Xu C. H., Chan C. T., The geometry of large fullerene cages: C_(72) to C_(102). J Chem. Phys., 1993, 98, 3095-3102.
[15] Slanina Z., Zhao X., Lee S. L., Osawa E., C_(90) temperature effects on relative stabilities of the IPR isomers. Chem. Phys. Lett., 1997, 219, 193-200.
[16] Slanina Z., Zhao X., Deota P., Osawa E., Relative stabilities of C_(92) IPR fullerenes. J Mol. Model., 2000, 6, 312-317.
[17] Zhao X., Slanina Z., Goto H., Osawa E., Theoretical investigations on relative stabilities of fullerene C_(94). J. Chem. Phys., 2003, 118, 10534-10540.
[18] Zhao X., Slanina Z., Goto H., Theoretical studies on the relative stabilities of C_(96) IPR fullerenes. J. Phys. Chem. A, 2004, 108, 4479-4484.
[19] Zhao X., Slanina Z., C_(98) IPR isomers: Gibbs-energy based relative stabilities. J. Mol. Struct. (Theochem), 2003, 636, 195-201.
[20] Zhao X., Goto H., Slanina Z., C_(110) IPR fullerenes: temperature-dependent relative stabilities based on the Gibbs function. Chem. Phys., 2004, 306, 93-104.
[21] Achiba Y., Fowler P. W., Mitchell D., Zerbetto F., Structural predictions for the C_(116) molecule. J. Phys. Chem. A, 1998, 102, 6835-6841.
[22] Fowler P. W., Heine T., Zerbetto F., Competition between even and odd fullerenes: C_(118), C_(119) and C_(120). J. Phys. Chem. A, 2000, 104, 9625-9629.
[23] Cai W. S., Xu L., Shao N., Shao X. G., Guo Q. X., An efficient approach for theoretical study on the low-energy isomers of large fullerenes C_(90)-C_(140). J. Chem. Phys., 2005, 122, 184318.
[24] Brenner D. W., Shenderova O. A., Harrison J. A., Stuart S. J., Ni B., Sinnott S. B., A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys.: Condens. Matter, 2002, 14, 783-802.
[25] Brinkmann G., Dress A. W. M., A reliable and efficient top-down approach to fullerene-structure enumeration. Adv. Appl. Math., 1998, 21, 473-480.
[26] Cioslowski J., Rao N., Moncrieff D., Standard enthalpies of formation fo fullerenes and their dependence on structural motifs. J. Am. Chem. Soc., 2002, 122, 8265-8270.
[27] Xu C. H., Wang C. Z., Chan C. T., Ho K. M., A transferable tight-binding potential for carbon. J. Phys: Condens. Matter, 1992, 4, 6047-6054
[28] Frisch M. J., Trucks G. W., Schlegel H. B., Scuseria G. E., Robb M. A., Cheeseman J. R., Montgomery J. A., Jr., Vreven T., Kudin K. N., Burant J. C., Millam J. M., Iyengar S. S., Tomasi J., Barone V., Mennucci B., Cossi M., Scalmani G., Rega N., Petersson G. A., Nakatsuji H., Hada M., Ehara M., Toyota K., Fukuda R., Hasegawa J., Ishida M., Nakajima T., Honda Y., Kitao O., Nakai H., Klene M., Li X., Knox J. E., Hratchian H. P., Cross J. B., Adamo C., Jaramillo J., Gomperts J., Stratmann R. E., Yazyev O., Austin A. J., Cammi R., Pomelli C., Ochterski J. W., Ayala P. Y., Morokuma K., Voth G. A., Salvador P., Dannenberg J. J., Zakrzewski V. G., Dapprich S., Daniels A. D., Strain M. C., Farkas O., Malick D. K., Rabuck A. D., Raghavachari K., Foresman J. B., Ortiz J. V., Cui Q., Baboul A. G., Clifford S., Cioslowski J., Stefanov B. B., Liu G., Liashenko A., Piskorz P., Komaromi I., Martin R. L., Fox D. J., Keith T., Al-Laham M. A., Peng C. Y., Nanayakkara A., Challacombe M., Gill P. M. W., Johnson B., Chen W., Wong M. W., Gonzalez C., Pople J. A., GAUSSIAN 03, Revision C.02, Gaussian, Inc., Wallingford CT, 2004.
[29] Liu D. C., Nocedal J., On the limited memory BFGS method for large-scale optimization. Math. Progm., 1989, 45,503-528.
[30] Fowler P, W., Manolopoulos D. E., An Atlas of Fullerenes. Clarendon Press: Oxford, 1995.
[31] Manolopoulos D. E., May J. C., Down S. E., Theoretical studies of the fullerenes: C_(34) to C_(70). Chem. Phys. Lett., 1991, 181,105-111.
[32] Seifert G., Vietze K., Schmidt R., Ionization energies of fullerenes—size and charge dependence. J. Phys. B: At. Mol. Opt. Phys., 1996, 29, 5183-5192.
[33] Boltalina O. V., Ioffe I. N., Sidorov L. N., Seifert G., Vietze K., Ionization energy of fullerenes. J. Am. Chem. Soc., 2000, 122, 9745-9749.
[1] Sun G. Y., Kertesz M., ~(13)C NMR spectra for IPR isomers of fullerene C_(86). Chem. Phys., 2002, 276, 107-114.
[2] Kikuchi K., Nakahara N., Wakabayashi T., Suzuki S., Shiromaru H., Miyake Y., Saito K., Ikemoto I., Kainosho M., Achiba Y., NMR characterization of isomers of C_(78), C_(82) and C_(84) fullerenes. Nature, 1992, 357, 142-145.
[3] Kikuchi K., Nakahara N., Wakabayashi T., Honda M., Matsumiya H., Moriwaki T., Suzuki S., Shiromaru H., Saito K., Yamauchi K., Ikemoto I., Achiba Y., Isolation and identification of fullerene family: C_(76), C_(78), C_(82), C_(84), C_(90) and C_(96). Chem. Phys. Lett., 1992, 188, 177-180.
[4] Taylor R., Langley G. J., Avent A. G., Dennis T. J. S., Kroto H. W., Walton D. R. M., ~(13)C NMR-spectroscopy of C_(76), C_(78), C_(84) and mixtures of C_(86)-C_(102): Anomalous chromatographic behavior of C_(82), and evidence for C_(70)H_(12). J.. Chem. Soc., Perkin Trans. 2, 1993, 1029-1036.
[5] Hennrich F. H., Michel R. H., Fischer A., RichardSchneider S., Gilb S., Kappes M. M., Fuchs D., Burk M., Kobayashi K., Nagase S., Isolation and characterization of C_(80). Angew. Chem., Int. Ed. Engl., 1996, 35, 1732-1734.
[6] Mitsumoto R., Oji H., Mori I., Yamamoto Y., Asato K., Ouchi Y., Shinohara H., Seki K., Umishita K., Hino S., Nagase S., Kikuchi K., Achiba Y., NEXAFS studies of higher fullerenes up to C_(96). J. Phys. Ⅳ, 1997, 7, 525-526.
[7] Diederich F., Ettl R., Rubin Y., Whetten R. L., Beck R., Alvarez M. M., Anz S., Sensharma D., Wudl F., Khemani K. C., Koch A., The higher fullerenes: Isolation and characterization of C_(76), C_(84), C_(90), C_(94), and C_(70)O, an oxide of D_(5H)-C_(70). Science, 1991, 252, 548-551.
[8] Crassous J., Rivera J., Fender N. S., Shu L. H., Echegoyen L., Thilgen C., Herrmann A., Diederich F., Chemistry of C_(84): Separation of three constitutional isomers and optical resolution of D_2-C_(84) by using the "Bingel-retro-Bingel" strategy. Angew. Chem., Int. Ed., 1999, 38, 1613-1617.
[9] Dennis T. J. S., Kai T., Asato K., Tomiyama T., Shinohara H., Yoshida T., Kobayashi Y., Ishiwatari H., Miyake Y., Kikuchi K., Achiba Y., Isolation and characterization by ~(13)C NMR spectroscopy of [84]fullerene minor isomers. J. Phys. Chem. A, 1999, 103, 8747-8752.
[10] Achiba Y., Fowler P. W., Mitchell D., Zerbetto F., Structural predictions for the C_(116) molecule. J. Phys. Chem. A, 1998, 102, 6835-6841.
[11] Fowler P. W., Heine T., Zerbetto F., Competition between even and odd fullerenes: C_(118), C_(119) and C_(120). J. Phys. Chem. A, 2000, 104, 9625-9629.
[12] Cai W. S., Xu L., Shao N., Shao X. G., Guo Q. X., An efficient approach for theoretical study on the low-energy isomers of large fullerenes C_(90)-C_(140). J. Chem. Phys., 2005, 122, 184318.
[13] Shao N., Gao Y., Yoo S., An W., Zeng X. C., Search for lowest-energy fullerenes: C_(98)-C_(110). J. Phys. Chem. A, 2006, 110, 7672-7676.
[14] Xu L., Cai W. S., Shao X. G., Prediction of low-energy isomers of large fullerenes from C_(132)-C_(160). J. Phys. Chem. A, 2006, 110, 9247-9253.
[15] Kroto H. W., The stability of the fullerenes Cn, with n=24, 28, 32, 36, 50, 60 and 70. Nature, 1987, 329, 529-531.
[16] Brinkmann G., Dress A. W. M., A reliable and efficient top-down approach to fullerene-structure enumeration. Adv. Appl. Math., 1998, 21,473-480.
[17] Cioslowski J., Rao N., Moncrieff D., Standard enthalpies of formation fo fullerenes and their dependence on structural motifs. J. Am. Chem. Soc., 2002, 122, 8265-8270.
[18] Xu C. H., Wang C. Z., Chan C. T., Ho K. M., A transferable tight-binding potential for carbon. J. Phys: Condens. Matter, 1992, 4, 6047-6054.
[19] Zhang B. L., Wang C. Z., Ho K. M., Xu C. H., Chan C. T., The geometry of small fullerene cages: C_(20) to C_(70). J. Chem. Phys., 1992, 97, 5007-5011.
[20] Zhang B. L., Wang C. Z., Ho Ko M., Xu C. H., Chan C. T., The geometry of large fullerene cages: C_(72) to C_(102). J. Chem. Phys., 1993, 98, 3095-3102.
[21] Lin Y., Cai W. S., Shao X. G., Comparison studies of fullerenes C72, C74, C76 and C78 by tight-binding Monte Carlo and quantum chemical methods. J. Mol. Struct. (Theochem), 2006, 760, 153-158.
[22] Cioslowski J., Heats of formation of higher fullerenes from ab initio hartree-fock and correlation-energy functional calculations. Chem. Phys. Lett., 1993, 216, 389-393.
[23] Liu D. C., Nocedal J., On the limited memory BFGS method for large-scale optimization. Math. Progm., 1989, 45, 503-528.
[24] Frisch M. J., Trucks G. W., Schlegel H. B., Scuseria G. E., Robb M. A., Cheeseman J. R., Montgomery J. A., Jr., Vreven T., Kudin K. N., Burant J. C., Millam J. M., Iyengar S. S., Tomasi J., Barone V., Mennucci B., Cossi M., Scalmani G., Rega N., Petersson G. A., Nakatsuji H., Hada M., Ehara M., Toyota K., Fukuda R., Hasegawa J., Ishida M., Nakajima T., Honda Y., Kitao O., Nakai H., Klene M., Li X., Knox J. E., Hratchian H. P., Cross J. B., Adamo C., Jaramillo J., Gomperts J., Stratmann R. E., Yazyev O., Austin A. J., Cammi R., Pomelli C., Ochterski J. W., Ayala P. Y., Morokuma K., Voth G. A., Salvador P., Dannenberg J. J., Zakrzewski V. G., Dapprich S., Daniels A. D., Strain M. C., Farkas O., Malick D. K., Rabuck A. D., Raghavachari K., Foresman J. B., Ortiz J. V., Cui Q., Baboul A. G., Clifford S., Cioslowski J., Stefanov B. B., Liu G., Liashenko A., Piskorz P., Komaromi I., Martin R. L., Fox D. J., Keith T., Al-Laham M. A., Peng C. Y., Nanayakkara A., Challacombe M., Gill P. M. W., Johnson B., Chen W., Wong M. W., Gonzalez C., Pople J. A., GAUSSIAN 03, Revision C.02, Gaussian, Inc., Wallingford CT, 2004.
[25] Fowler P. W., Manolopoulos D. E., An Atlas of Fullerenes. Clarendon Press: Oxford, 1995.
[26] Manolopoulos D. E., May J. C., Down S. E., Theoretical studies of the fullerenes: C_(34) to C_(70). Chem. Phys. Lett., 1991, 181, 105-111.
[27] Elstner M., Porezag D., Jungnickel G., Elsner J., Haugk M., Frauenheim Yh., Suhai S., Seifert G., Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties. Phys. Rev. B, 1998, 58, 7260-7268.
[28] Zhang B. L., Xu C. H., Wang C. Z., Chan C. T., Ho K. M., Systematic study of structures and stabilities of fullerenes. Phys. Rev. B, 1992, 46, 7333-7336.
[29] Seifert G., Vietze K., Schmidt R., Ionization energies of fullerenes—size and charge dependence. J. Phys. B: At. Mol. Opt. Phys., 1996, 29, 5183-5192.
[30] Boltalina O. V., Ioffe I. N., Sidorov L. N., Seifert G., Vietze K., Ionization energy of fullerenes. J. Am. Chem. Soc., 2000, 122, 9745-9749.
[2] Kratschmer W., Lamb L. D., Fostiropoulos K., Huffman D. R., Solid C_(60): A new form carbon. Nature, 1990, 347, 354-358,
[3] Sun G. Y., Kertesz M., ~(13)C NMR spectra for IPR isomers of fullerene C_(86). Chem. Phys., 2002, 276, 107-114.
[4] Kikuchi K., Nakahara N., Wakabayashi T., Suzuki S., Shiromaru H., Miyake Y., Saito K., Ikemoto I., Kainosho M., Achiba Y., NMR characterization of isomers of C_(72), C_(82) and C_(84) fullerenes. Nature, 1992, 357, 142-145.
[5] Kikuchi K., Nakahara N., Wakabayashi T., Honda M., Matsumiya H., Moriwaki T., Suzuki S., Shiromaru H., Saito K., Yamauchi K., Ikemoto I., Achiba Y., Isolation and identification of fullerene family: C_(76), C_(78), C_(82), C_(84), C_(90) and C_(96). Chem. Phys. Lett., 1992, 188, 177-180.
[6] Taylor R., Langley G. J., Avent A. G., Dennis T. J. S., Kroto H. W., Walton D. R. M., ~(13)C NMR-spectroscopy of C_(76), C_(78), C_(84) and mixtures of C_(86)-C_(102): Anomalous chromatographic behavior of C_(82), and evidence for C_(70)H_(12). J. Chem. Soc., Perkin Trans. 2, 1993, 1029-1036.
[7] Hennrich F. H., Michel R. H., Fischer A., RichardSchneider S., Gilb S., Kappes M. M., Fuchs D., Burk M., Kobayashi K., Nagase S., Isolation and characterization of C_(80). Angew. Chem., Int. Ed. Engl., 1996, 35, 1732-1734.
[8] Mitsumoto R., Oji H., Mori I., Yamamoto Y., Asato K., Ouchi Y., Shinohara H., Seki K., Umishita K., Hino S., Nagase S., Kikuchi K., Achiba Y., NEXAFS studies of higher fullerenes up to C_(96). J. Phys. Ⅳ, 1997, 7, 525-526.
[9] Diederich F., Ettl R., Rubin Y., Whetten R. L., Beck R., Alvarez M. M., Anz S., Sensharma D., Wudl F., Khemani K. C., Koch A., The higher fullerenes: Isolation and characterization of C_(76), C_(84), C_(90), C_(94), and C_(70)O, an oxide of D_(5H)-C_(70). Science, 1991, 252, 548-551.
[10] Crassous J., Rivera J., Fender N. S., Shu L. H., Echegoyen L., Thilgen C., Herrmann A., Diederich F., Chemistry of C_(84): Separation of three constitutional isomers and optical resolution of D_2-C_(84) by using the "Bingel-retro-Bingel" strategy. Angew. Chem., Int. Ed, 1999, 38, 1613-1617.
[11] Dennis T. J. S., Kai T., Asato K., Tomiyama T., Shinohara H., Yoshida T., Kobayashi Y., Ishiwatari H., Miyake Y., Kikuchi K., Achiba Y., Isolation and characterization by ~(13)C NMR spectroscopy of [84]fullerene minor isomers. J. Phys. Chem. A, 1999, 103, 8747-8752.
[12] Wang G. W., Saunders M., Khong A., Cross R. J., A new method for separating the isomeric C_(84) fullerenes. J. Am. Chem. Soc., 2000,122, 3216-3217.
[13] Kroto H. W., The stability of the fullerenes Cn, with n=24, 28, 32, 36, 50, 60 and 70. Nature, 1987, 329, 529-531.
[14] Fowler P. W., Fullerene stability and structure. Contemp. Phys., 1996, 37, 235-247.
[15] 李小罡，徐愉，刘云圻，朱道本，杨世和，富勒烯金属包合物的研究进展．化学进展，2000，12，385-390．
[16] 韩旭，李疏芬，富勒烯材料的催化作用研究进展．化学进展，2006，18，715-720．
[17] 刘书芝，唐光诗，[60]富勒烯衍生物的对称性、碳笼结构与~(13)C NMR谱．化学进展，2004，16，561-573．
[18] 滕启文，吴师，富勒烯离子Jahn-Teller畸变和光谱研究进展．化学进展，2005，17，949-954．
[19] 黄彬，郑启新，杨大志，郭晓东，吴永超，江贵长，富勒烯(C_(60))-甘氨酸衍生物对小鼠骨肉瘤细胞生长的影响．华中科技大学学报(医学版)，2006，35，493-496
[20] 倪瑾，蔡建明，吴秋业，富勒烯及其衍生物在核生物医学领域应用的研究现状．国际放射医学核医学杂志，2006，30，72-75．
[21] 姚姗姗，杨卫海，林修光，高建国，李炳海，陈滇宝，富勒烯衍生物的制备及其光催化杀菌研究．青岛科技大学学报(自然科学版)，2006，27，31-39．
[22] 鄂义峰，丁杨栋，方芳，刘佳川，内嵌金属富勒烯在生物医药中的应用．数理压药学杂志，2006，19，75-76．
[23] 王晓娟，魏传晚，刘传湘，富勒烯金属配合物的研究进展．化工时刊，2006，20，56-61．
[24] 官文超，曹远美，朱超，胡桢，C_(60)衍生物的合成及在水性成膜材料中的抗近红外和紫外性能．高分子材料科学与工程，2006，22，107-110．
[25] 李宏宇，陈志强，李效玉，活性聚合改性富勒烯C_(60)在新型聚合物材料中的应用．化工新型材料，2006，34，60-62．
[26] Parter D. H., Wurz P., Chatterjee K., Lykke K. R., Hunt J. E., Pellin M. J., Hemminger J. C., Gruen D. M., Stock L. M., High-yield synthesis, separation, and mass-spectrometric characterization of fullerenes C_(60) to C_(266). J. Am. Chem. Soc., 1991,113, 7499-7503.
[27] Parter D. H., Chatterjee K., Wurz P., Lykke K. R., Pellin M. J., Stock L. M., Fullerenes and giant fullerenes: synthesis, separation, and mass-spectrometric characterization. Carbon, 1992, 30, 1167-1182.
[28] Howard J. B., Mckinnon J. T., Makarovsky Y., Lafleur A. L., Johnson M. E., Fullerenes C_(60) and C_(70) in flames. Nature, 1991, 352, 139-141.
[29] Peters G., Jansen M., A new fullerene synthesis. Angew. Chem., Int. Ed Engl., 1992, 31,223-224.
[30] Chibante L. P. E, Thess A., Alford J. M., Diener M. D., Smalley R. E., Solar generation of the fullerenes. J. Phys. Chem., 1993, 97, 8696-8700.
[31] Taylor R., Langley G. J., Kroto H. W., Walton D. R. M., Formation of C_(60) by pyrolysis of naphthalene. Nature, 1993, 366, 728-731.
[32] Feng S. Q., Zhu X., Wu E., Superconductivity and structure of alkali-doped fullerenes: K_3C_(60) and Rb_3C_(60). Solid State Commun., 1991, 80, 639-642.
[33] Zhao W. B., Zhang X. D., Ye Z. Y., Synthesis of K_3C_(60) single crystal thin-films with high critical currents. Solid State Commun., 1993, 85,945-947.
[34] Allemand P. M., Khemani K. C., Koch A., Wudl F., Holczer K., Donovan S., Gruner G., Thompson J. D., Organic molecular soft ferromagnetism in a fullerene C_(60). Science, 1991, 253,301-303.
[35] 鲁照玲，官文超，富勒烯衍生物对神经细胞的凋亡作用．化学通报，2005，7，510-514．
[36] 李亚原，谭信，杨新林，乔新歌，王文晞，富勒烯膦酸衍生物对HeLa细胞生长的影响．生命科学仪器，2005，3，20-23．
[37] 单鹄声，倪瑾，蔡建明，富勒烯衍生物的生物学应用．生命的化学，2005，25，424-427．
[38] 李玉良，徐菊华，朱道本，我国C_(60)和碳纳米管的研究进展．化学通报，1999，10，10-13．
[39] Bendale R. D., Zerner M. C., Electronic-structure and spectroscopy of the most 5 stable isomers of C_(78) fullerene. J. Phys. Chem., 1995, 99, 13830-13833.
[40] Wang X. Q, Wang C. Z., Zhang B. L., Ho K. M., Electronic-structures of C_(82) fullerene isomers. Chem. Phys. Lett., 1994, 217, 199-203.
[41] 唐敖庆，李前树，柏拉图多面体与高碳原子簇．高等学校化学学报，1997，18， 1180-1184．
[42] 唐敖庆，李前树，高碳原子簇电子结构的计算方法及其应用．科学通报，1997，42，567-573．
[43] Tang A. C., Huang F. Q., Group theoretical applications to icosahedral fullerenes. Chem. Phys. Lett., 1995, 245, 561-565.
[44] Tang A. C., Huang F. Q., Electronic structures of dihedral (D_(5h), D_(4d), D_(6h), D_(6d)) fullerenes. Chem. Phys. Lett., 1996, 250, 528-536.
[45] Tang A. C., Huang F. Q., Liu R. Z., Electronic structures of fullerenes C_n with I_h symmetry and n=20k~2. Phys. Rev. B, 1996, 53, 7442-7450.
[46] Teng Q. W., Zhao X. Z., Cai Z. S., Tang A. C., Theoretical studies on the structures and electronic spectra of C_(70)CH_2. Int. J. Quantum Chem., 1997, 61, 815-822.
[47] Li A. Y., Tang A. C., Eigenvalue spectra geometric transformation of polyhedra. J. Mol. Struct. (Theochem), 2000, 530, 245-264.
[48] Li A. Y., Liao M. Z., Tang A. C., Site projection operator and its application: electronic structures and stability rules of tetrahedral fullerenes. Phys. Chem. Chem. Phys., 2000, 2, 2301-2307.
[49] Smalley R. E., Self-assembly of the fullerenes. Accounts. Chem. Res., 1992, 25, 98-105.
[50] Goeres A., Sedlmayr E., On the nucleation mechanism of effective fullerite condensation. Chem. Phys. Lett., 1991, 184, 310-317.
[51] Wakabayashi T., Achiba Y., A model for the C_(60) and C_(70) growth-mechanism. Chem. Phys. Lett., 1992, 190, 465-468.
[52] Wakabayashi T., Shiromaru H., Kikuchi K., Achiba Y., A selective isomer growth of fullerenes. Chem. Phys. Lett., 1993, 201,470-474.
[53] Curl R. F., Collapse and growth. Nature, 1993, 363, 14-15.
[54] Yamaguchi Y., Maruyama S., A molecular dynamics simulation of the fullerene formation process. Chem. Phys. Lett., 1998, 286, 336-342.
[55] Melker A. I., Romanov S. N., Kornilov D. A., Computer simulation of formation of carbon fullerenes. Mater. Phys. Mech., 2000, 2, 42-50.
[56] Turker L., A bucky onion from C_(20) and C_(60)—an AM1 treatment. J. Mol. Struct. (Theochem), 2001, 545, 207-214.
[57] Liu F. Y., Meng L. P., Zheng S. J., Density functional studies on a novel double-shell fullerene C_(20)@C_(60). J. Mol. Struct. (Theochem), 2005, 725, 17-21.
[58] Erkoc S., Stability of carbon nanoonion C_(20)@C_(60)@C_(240): Molecular dynamics simulations, Nano Lett., 2002, 2, 215-217.
[59] Kobayashi K., Nagase S., Akasaka T., A theoretical study of C_(80) and La_2@C_(80). Chem. Phys. Lett., 1995, 245, 230-236.
[60] Kobayashi K., Nagase S., Akasaka T., Endohedral dimetallofullerenes Sc_2@C_(84) and La_2@C_(80). Are the metal atoms still inside the fullerene cages? Chem. Phys. Lett., 1996, 261, 502-506.
[61] Kobayashi K., Nagase S., Structures and electronic states of endohedral dimetallofullerenes: M_2@C_(80) (M=Sc, Y, La, Ce, Pr, Eu, Gd, Yb and Lu). Chem. Phys. Lett., 1996, 262, 227-232.
[62] Nagase S., Kobayashi K., Structural study of endohedral dimetallofullerenes Sc_2@C_(84) and Sc_2@C_(74). Chem. Phys. Lett., 1997, 276, 55-61.
[63] Kobayashi K., Nagase S., Yoshida M., Osawa E., Endohedral metallofullerenes. Are the isolated pentagon rule and fullerene structures always satisfied? J. Am. Chem. Soc., 1997, 119, 12693-12694.
[64] Yan Q. B., Zheng Q. R., Su G., Structures, electronic properties, spectroscopies, and hexagonal monolayer phase of a family of unconventional fullerenes C_(64)X_4 (X=H, F, Cl, Br). J. Chem. Phys., 2007, 111, 549-554.
[65] Hemandez E., Meunier V., Smith B. W., Rurali R., Terrones H., Nardelli M. B., Terrones M., Luzzi D. E., Charlier J. C., Fullerene Coalescence in Nanopeapods: A Path to Novel Tubular Carbon, Nano Lett., 2003, 3, 1037-1042.
[66] Lin Y., Cai W. S., Shao X. G., Fullerenes Connected Nanotubes: An Approach to Build Multidimensional Carbon Nanocomposites. Chem. Phys., 2006, 331, 85-91.
[67] Brenner D. W., Empirical potential for hydrocarbons for use in simulating the chemical vapor-deposition of diamond films. Phys. Rev. B, 1990, 42, 9458-9471.
[68] Brenner D. W., Shenderova O. A., Harrison J. A., Stuart S. J., Ni B., Sinnott S. B., A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys.: Condens. Matter, 2002, 14, 783-802.
[69] Tersoff J., New empirical model for the structural properties of silicon. Phys. Rev. Lett., 1986, 56, 632-635.
[70] Cai W. S., Shao X. G., A fast annealing evolutionary algorithm for global optimization. J. Comp. Chem., 2002, 23,427-435.
[71] Cai W. S., Shao N., Shao X. G., Pan Z. X., Structural analysis of carbon clusters by using a global optimization algorithm with Brenner potential. J Mol. Struct. (Theochem), 2004, 678, 113-122.
[72] Liu D. C., Nocedal J., On the limited memory BFGS method for large-scale optimization. Math. Progm., 1989, 45,503-528.
[73] Cai W. S., Xu L., Shao N., Shao X. G., Guo Q. X., An efficient approach for theoretical study on the low-energy isomers of large fullerenes C_(90)-C_(140). J. Chem. Phys., 2005, 122, 184318.
[74] Ponomareva I. V., Chernozatonskii L. A., How can carbon onion transform into diamond-like structure. Microelectron. Eng., 2003, 69, 625-628.
[75] Sutton A. P., Finnis M. W., Pettifor D. G., Ohta Y., The tight-binding bond model. J. Phys. C: Solid State Physics, 1988, 21, 35-66.
[76] Xu C. H., Wang C. Z., Chan C. T., Ho K. M., A transferable tight-binding potential for carbon. J. Phys: Condens. Matter, 1992, 4, 6047-6054
[77] Elstner M., Porezag D., Jungnickel G., Eisner J., Haugk M., Frauenheim T., Suhai S., Seifert G., Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties. Phys. Rev. B, 1998, 58, 7260-7268.
[78] Porezag D., Frauenheim T., Kohler T., Seifert G., Kaschner R., Construction of tight-binding-like potentials on the basis of density-functional theory: Application to carbon. Phys. Rev. B, 1995, 51, 12947-12957.
[79] Frauenheim T., Seifert G., Elstner M., Niehaus T., Kohler C., Amkreutz M., Sternberg M., Hajnal Z., Carlo A. D., Suhai S., Atomistic simulations of complex materials: ground-state and excited-state properties. J. Phys. : Cond. Mater, 2002, 14, 3015-3047.
[80] Slanina Z., Zhao X., Lee S. L., Osawa E., C_(90) temperature effects on relative stabilities of the IPR isomers. Chem. Phys. Lett., 1997, 219, 193-200.
[81] Slanina Z., Zhao X., Deota P., Osawa E., Relative stabilities of C_(92) IPR fullerenes. J. Mol. Model., 2000, 6, 312-317.
[82] Zhao X., Slanina Z., Goto H., Osawa E., Theoretical investigations on relative stabilities of fullerene C_(94). J. Chem. Phys., 2003, 118, 10534-10540.
[83] Zhao X., Slanina Z., Goto H., Theoretical studies on the relative stabilities of C_(96) IPR fullerenes. J. Phys. Chem. A, 2004, 108, 4479-4484.
[84] Zhao X., Slanina Z., C_(98) IPR isomers: Gibbs-energy based relative stabilities. J. Mol. Struct. (Theochem), 2003, 636, 195-201.
[85] Zhao X., Goto H., Slanina Z., C_(110) IPR fullerenes: temperature-dependent relative stabilities based on the Gibbs function. Chem. Phys., 2004, 306, 93-104.
[86] Zhang B. L., Wang C. Z., Ho K. M., Xu C. H., Chan C. T., The geometry of small fullerene cages: C_(20) to C_(70). J. Chem. Phys., 1992, 97, 5007-5011.
[87] Zhang B. L., Wang C. Z., Ho K. M., Xu C. H., Chan C. T., The geometry of large fullerene cages: C_(72) to C_(102). J. Chem. Phys., 1993, 98, 3095-3102.
[88] Achiba Y., Fowler P. W., Mitchell D., Zerbetto F., Structural predictions for the C_(116) molecule. J. Phys. Chem. A, 1998, 102, 6835-6841.
[89] Fowler P. W., Heine T., Zerbetto F., Competition between even and odd fullerenes: C_(118), C_(119) and C_(120). J. Phys. Chem. A, 2000, 104, 9625-9629.
[90] Shao N., Gao Y., Yoo S., An W., Zeng X. C., Search for lowest-energy fullerenes: C_(98)-C_(110). J. Phys. Chem. A, 2006, 110, 7672-7676.
[91] Xu L., Cai W. S., Shao X. G., Prediction of low-energy isomers of large fullerenes from C_(132)-C_(160). J. Phys. Chem. A, 2006, 110, 9247-9253.
[92] Furche F., Ahlrichs R., Fullerene C_(80): Are there still more isomers? J. Chem. Phys., 2001, 114, 10362-10367.
[93] Nishikawa T., Kinoshita T., Nanbu S., Aoyagi M., A theoretical study on vibrational spectra of C_(84) fullerenes: results for C_2, D_2, and D_(2d) isomers. J. Mol. Struct. (Theochem), 1999, 461-462, 453-461.
[94] Sun G., Kertesz M., Theoretical ~(13)C NMR spectra of IPR isomers of fullerenes C_(60), C_(70), C_(72), C_(74), C_(76), and C_(78) studied by density functional theory. J. Phys. Chem. A, 2000, 104, 7398-7403.
[95] Sun G., Kertesz M., Identification for IPR isomers of fullerene C_(82) by theoretical ~(13)C NMR spectra calculated by density functional theory. J. Phys. Chem. A, 2001, 105, 5468-5472.
[96] Cioslowski J., Rao N., Moncrieff D., Standard enthalpies of formation fo fullerenes and their dependence on structural motifs. J. Am. Chem. Soc., 2002, 122, 8265-8270.
[97] Xu L., Cai W. S., Shao X. G., Systematic search for energetically favored isomers of large fullerenes C_(122)-C_(130) and C_(162)-C_(180), Comp. Mater. Sci., accepted.
[98] Albertazzi E., Domene C., Fowler P. W., Heine T., Seifert G., Alsenoy C. V., Zerbetto F., Pentagon adjacency as a determinant of fullerene stability. Phys. Chem. Chem. Phys., 1999, 1, 2913-2918.
[99] Lin Y., Cai W. S., Shao X. G., Comparison studies of fullerenes C_(72), C_(74), C_(76) and C_(78) by tight-binding Monte Carlo and quantum chemical methods. J. Mol. Struct. (Theochem), 2006, 760, 153-158.
[100] Chen Z., Thiel W., Performance of semiempirical methods in fullerene chemistry: relative energies and nucleus-independent chemical shifts. Chem. Phys. Lett., 2003, 367, 15-25.
[101] Zheng G., Irle S., Morokuma K., Performance of the DFTB method in comparison to DFT and semiempirical methods for geometries and energies of C_(20)-C_(86) fullerene isomers. Chem. Phys. Lett., 2005, 412, 210-216.
[102] Xu L., Cai W. S., Shao X. G., Performance of the semiempirical AM1, PM3, MNDO, and tight-binding methods in comparison with DFT method for the large fullerenes C_(116)-C_(120). J. Mol. Struct.(Theochem), in press.
[103] Slanina Z., Ishimura K., Kobayashi K., Nagase S., C_(72) isomers: the IPR-satisfying cage is disfavored by both energy and entropy. Chem. Phys. Lett., 2004, 384, 114-118.
[104] Wu H. S., Xu X. H., Jiao H. J., Structure and stability of C_(48) fullerenes, J. Phys. Chem. A, 2004, 108, 3813-3816.
[105] Wu H. S., Tian X. X., Jian J. F., Feng R. J., Stability of fullerene cages: C_(30) to C_(70) and their dependence on shared pentagon bonds. Chinese J. Struct. Chem., 2006, 25, 1051-1056.
[106] Raghavachari K., Ground-state of C_(84):2 almost isoenergetic isomers. Chem. Phys. Lett., 1992, 190, 397-400.
[107] Yoshida M., Aihara J., Validity of the weighted HOMO-LUMO energy separation as an index of kinetic stability for fullerenes with up to 120 carbon atoms. Phys. Chem. Chem. Phys., 1999, 1,227-230.
[108] Yoshida M., Aihara J., Weighted HOMO-LUMO energy separations of properly closed-shell fullerene isomers. J. Mol. Graphics Modell., 2001, 19, 194-198.
[109] Seifert G., Vietze K., Schmidt R., Ionization energies of fullerenes—size and charge dependence. J. Phys. B: At. Mol. Opt. Phys., 1996, 29, 5183-5192.
[110] Boltalina O. V., Ioffe I. N., Sidorov L. N., Seifert G., Vietze K., Ionization energy of fullerenes, J. Am. Chem. Soc., 2000, 122, 9745-9749.
[1] Brinkmann G., Dress A. W. M., A constructive enumeration of fullerenes. J. Algorithms, 1997, 23,345-358.
[2] Brinkmann G., Dress A. W. M., A reliable and efficient top-down approach to fullerene-structure enumeration. Adv. Appl. Math., 1998, 21,473-480.
[3] Fowler P. W., Manolopoulos D. E., An Atlas of Fullerenes. Clarendon Press: Oxford, 1995.
[4] Manolopoulos D. E., May J. C., Down S. E., Theoretical studies of the fullerenes: C_(34) to C_(70). Chem. Phys. Lett., 1991, 181, 105-111.
[5] Kroto H. W., The stability of the fullerenes Cn, with n=24, 28, 32, 36, 50, 60 and 70. Nature, 1987, 329, 529-531.
[6] Brenner D. W., Shenderova O. A., Harrison J. A., Stuart S. J., Ni B., Sinnott S. B., A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys.: Condens. Matter, 2002, 14, 783-802.
[7] Liu D. C., Nocedal J., On the limited memory BFGS method for large-scale optimization. Math. Progm., 1989, 45, 503-528.
[8] Ettl R., Chao I., Diederich F., Whetten R. L., Isolation of C76: a chiral (D2) allotrope of carbon, Nature, 1991, 353, 149-153.
[9] Kikuchi K., Nakahara N., Wakabayashi T., Suzuki S., Shiromaru H., Miyake Y., Saito K., Ikemoto I., Kainosho M., Achiba Y., NMR characterization of isomers of C_(78), C_(82) and C_(84) fullerenes. Nature, 1992, 357, 142-145.
[10] Slanina Z., Lee S. L., Adamowicz L., C_(80), C_(86), C_(88): Semiempirical and ab initio SCF calculations. Int. J. Quantum. Chem., 1997, 63, 529-535.
[11] Sun G. Y., Kertesz M., Identification for IPR isomers of fullerene C_(82) by theoretical C-13 NMR spectra calculated by density functional theory. J. Phys. Chem. A, 2001, 105, 5468-5472.
[12] Buhl M., van Wullen C., Computational evidence for a new C_(84) isomer. Chem. Phys. Lett., 1995, 247, 63-68.
[13] Slanina Z., Zhao X., Lee S. L., Osawa E., C_(90) temperature effects on relative stabilities of the IPR isomers. Chem. Phys., 1997, 219, 193-200.
[14] Kobayashi K., Nagase S., Yoshida M., Osawa E., Endohedral metallofullerenes. Are the isolated pentagon rule and fullerene structures always satisfied? J. Am. Chem. Soc., 1997, 119, 12693-12694.
[15] Slanina Z., Ishimura K., Kobayashi K., Nagase S., C_(72) isomers: the IPR-satisfying cage is disfavored by both energy and entropy. Chem. Phys. Lett., 2004, 384, 114-118.
[16] Frisch M. J., Trucks G. W., Schlegel H. B., Scuseria G. E., Robb M. A., Cheeseman J. R., Montgomery J. A., Jr., Vreven T., Kudin K. N., Burant J. C., Millam J. M., Iyengar S. S., Tomasi J., Barone V., Mennucci B., Cossi M., Scalmani G., Rega N., Petersson G. A., Nakatsuji H., Hada M., Ehara M., Toyota K., Fukuda R., Hasegawa J., Ishida M., Nakajima T., Honda Y., Kitao O., Nakai H., Klene M., Li X., Knox J. E., Hratchian H. P., Cross J. B., Adamo C., Jaramillo J., Gomperts J., Stratmann R. E., Yazyev O., Austin A. J., Cammi R., Pomelli C., Ochterski J. W., Ayala P. Y., Morokuma K., Voth G. A., Salvador P., Dannenberg J. J., Zakrzewski V. G., Dapprich S., Daniels A. D., Strain M. C., Farkas O., Malick D. K., Rabuck A. D., Raghavachari K., Foresman J. B., Ortiz J. V., Cui Q., Baboul A. G., Clifford S., Cioslowski J., Stefanov B. B., Liu G., Liashenko A., Piskorz P., Komaromi I., Martin R. L., Fox D. J., Keith T., Al-Laham M. A., Peng C. Y., Nanayakkara A., Challacombe M., Gill P. M. W., Johnson B., Chen W., Wong M. W., Gonzalez C., Pople J. A., GAUSSIAN 03, Revision C.02, Gaussian, Inc., Wallingford CT, 2004.
[17] Sun G. Y., Kertesz M., Theoretical ~(13)C NMR spectra of IPR isomers of fullerene C_(80): a density functional theory study. Chem. Phys. Lett., 2000, 328, 387-395.
[18] Zhang B. L., Wang C. Z., Ho K. M., Xu C. H., Chan C. T., The geometry of large fullerene cages: C_(72) to C_(102). J. Chem. Phys., 1993, 98, 3095-3102.
[1] Kratschmer W., Lamb L. D., Fostiropoulos K., Huffman D. R., Solid C_(60): A new form carbon. Nature, 1990, 347, 354-358.
[2] Sun G. Y., Kertesz M., ~(13)C NMR spectra for IPR isomers of fullerene C_(86). Chem. Phys., 2002, 276, 107-114.
[3] Kikuchi K., Nakahara N., Wakabayashi T., Suzuki S., Shiromaru H., Miyake Y., Saito K., Ikemoto I., Kainosho M., Achiba Y., NMR characterization of isomers of C_(78), C_(82) and C_(84) fullerenes. Nature, 1992, 357, 142-145.
[4] Kikuchi K., Nakahara N., Wakabayashi T., Honda M., Matsumiya H., Moriwaki T., Suzuki S., Shiromaru H., Saito K., Yamauchi K., Ikemoto I., Achiba Y., Isolation and identification of fullerene family: C_(76), C_(78), C_(82), C_(84), C_(90) and C_(96). Chem. Phys. Lett., 1992, 188, 177-180.
[5] Taylor R., Langley G. J., Avent A. G., Dennis T. J. S., Kroto H. W., Walton D. R. M., ~(13)C NMR-spectroscopy of C_(76), C_(78), C_(84) and mixtures of C_(86)-C_(102): Anomalous chromatographic behavior of C_(82), and evidence for C_(70)H_(12). J Chem. Soc., Perkin Trans. 2, 1993, 1029-1036.
[6] Hennrich F. H., Michel R. H., Fischer A., RichardSchneider S., Gilb S., Kappes M. M., Fuchs D., Burk M., Kobayashi K., Nagase S., Isolation and characterization ofC_(80). Angew. Chem., Int. Ed. Engl., 1996, 35, 1732-1734.
[7] Mitsumoto R., Oji H., Mori I., Yamamoto Y., Asato K., Ouchi Y., Shinohara H., Seki K., Umishita K., Hino S., Nagase S., Kikuchi K., Achiba Y., NEXAFS studies of higher fullerenes up to C_(96). J. Phys. Ⅳ, 1997, 7, 525-526.
[8] Diederich F., Ettl R., Rubin Y., Whetten R. L., Beck R., Alvarez M. M., Anz S., Sensharma D., Wudl F., Khemani K. C., Koch A., The higher fullerenes: Isolation and characterization of C_(76), C_(84), C_(90), C_(94), and C_(70)O, an oxide of D_(5H)-C_(70). Science, 1991, 252, 548-551.
[9] Crassous J., Rivera J., Fender N. S., Shu L. H., Echegoyen L., Thilgen C., Herrmann A., Diederich F., Chemistry of C_(84): Separation of three constitutional isomers and optical resolution of D_2-C_(84) by using the "Bingel-retro-Bingel" strategy. Angew. Chem., Int. Ed., 1999, 38, 1613-1617.
[10] Dennis T. J. S., Kai T., Asato K., Tomiyama T., Shinohara H., Yoshida T., Kobayashi Y., Ishiwatari H., Miyake Y., Kikuchi K., Achiba Y., Isolation and characterization by ~(13)C NMR spectroscopy of [84]fullerene minor isomers. J. Phys. Chem. A, 1999, 103, 8747-8752.
[11] Cai W. S., Shao N., Shao X. G., Pan Z. X., Structural analysis of carbon clusters by using a global optimization algorithm with Brenner potential. J. Mol. Struct. (Theochem), 2004, 678, 113-122.
[12] Zhang B. L., Wang C. Z., Ho K. M., Xu C. H., Chan C. T., The geometry of small fullerene cages: C_(20) to C_(70). J. Chem. Phys., 1992, 97, 5007-5011.
[13] Zhang B. L., Wang C. Z., Ho K. M., Xu C. H., Chan C. T., The geometry of large fullerene cages: C_(72) to C_(102). ,J.. Chem. Phys., 1993, 98, 3095-3102.
[14] Slanina Z., Zhao X., Lee S. L., Osawa E., C_(90) temperature effects on relative stabilities of the IPR isomers. Chem. Phys. Lett., 1997, 219, 193-200.
[15] Slanina Z., Zhao X., Deota P., Osawa E., Relative stabilities of C_(92) IPR fullerenes. J. Mol. Model., 2000, 6, 312-317.
[16] Zhao X., Slanina Z., Goto H., Osawa E., Theoretical investigations on relative stabilities of fullerene C_(94). J. Chem. Phys., 2003, 118, 10534-10540.
[17] Zhao X., Slanina Z., Goto H., Theoretical studies on the relative stabilities of C_(96) IPR fullerenes. J. Phys. Chem. A, 2004, 108, 4479-4484.
[18] Zhao X., Slanina Z., C_(98) IPR isomers: Gibbs-energy based relative stabilities. J. Mol. Struct. ~heochem), 2003, 636, 195-201.
[19] Zhao X., Goto H., Slanina Z., C_(110) IPR fullerenes: temperature-dependent relative stabilities based on the Gibbs function. Chem. Phys., 2004, 306, 93-104.
[20] Achiba Y., Fowler P. W., Mitchell D., Zerbetto F., Structural predictions for the C_(116) molecule, J. Phys. Chem. A, 1998, 102, 6835-6841.
[21] Fowler P. W., Heine T., Zerbetto F., Competition between even and odd fullerenes: C_(118), C_(119) and C_(120). J. Phys. Chem. A, 2000, 104, 9625-9629.
[22] Brinkmann G., Dress A. W. M., A reliable and efficient top-down approach to fullerene-structure enumeration. Adv. Appl. Math., 1998, 21,473-480.
[23] Kroto H. W., The stability of the fullerenes Cn, with n=24, 28, 32, 36, 50, 60 and 70. Nature, 1987, 329, 529-531.
[24] Brenner D. W., Shenderova O. A., Harrison J. A., Stuart S. J., Ni B., Sinnott S. B., A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys.: Condens. Matter, 2002, 14, 783-802.
[25] Albertazzi E., Domene C., Fowler P. W., Heine T., Seifert G., Alsenoy C. V., Zerbetto F., Pentagon adjacency as a determinant of fullerene stability. Phys. Chem. Chem. Phys., 1999, 1, 2913-2918.
[26] Raghavachari K., Ground-state of Cs4:2 almost isoenergetic isomers. Chem. Phys. Lett., 1992, 190, 397-400.
[27] Liu D. C., Nocedal J., On the limited memory BFGS method for large-scale optimization. Math. Progm., 1989, 45, 503-528.
[28] Frisch M. J., Trucks G. W., Schlegel H. B., Scuseria G. E., Robb M. A., Cheeseman J. R., Zakrzewski V. G., Montgomery J. A., Stratmann R. E., Burant J. C., Dapprich S., Millam J. M., Daniels A. D., Kudin K. N., Strain M. C., Farkas O., Tomasi J., Barone V., Cossi M., Cammi R., Mennucci B., Pomelli C., Adamo C., Clifford S., Ochterski J., Petersson G. A., Ayala P. Y., Cui Q., Morokuma K., Salvador P., Dannenberg J. J., Malick D. K., Rabuck A. D., Raghavachari K., Foresman J. B., Cioslowski J., Ortiz J. V., Baboul A. G., Stefanov B. B., Liu G., Liashenko A., Piskorz P., Komaromi I., Gomperts R., Martin R. L., Fox D. J., Keith T., Al-Laham M. A., Peng C. Y., Nanayakkara A., Challacombe M., Gill P. M. W., Johnson B., Chen W., Wong M. W., Andres J. L., Gonzalez C., Head-Gordon M., Replogle E. S., and Pople J. A., Gaussian 98, Revision A.7, Gaussian, Inc., Pittsburgh, PA (1998).
[29] Fowler P. W., Manolopoulos D. E., An Atlas of Fullerenes. Clarendon Press: Oxford, 1995.
[1] Zhang B. L., Wang C. Z., Ho K. M., Xu C. H., Chan C. T., The geometry of large fullerene cages: C_(72) to C_(102). J. Chem. Phys., 1993, 98, 3095-3102.
[2] Slanina Z., Zhao X., Lee S. L., Osawa E., C_(90) temperature effects on relative stabilities of the IPR isomers. Chem. Phys. Lett., 1997, 219, 193-200.
[3] Slanina Z., Zhao X., Deota P., Osawa E., Relative stabilities of C_(92) IPR fullerenes. J. Mol. Model., 2000, 6, 312-317.
[4] Zhao X., Slanina Z., Goto H., Osawa E., Theoretical investigations on relative stabilities of fullerene C_(94). J. Chem. Phys., 2003, 118, 10534-10540.
[5] Zhao X., Slanina Z., Goto H., Theoretical studies on the relative stabilities of C_(96) IPR fullerenes. J. Phys. Chem. A, 2004, 108, 4479-4484.
[6] Zhao X., Slanina Z., C98 IPR isomers: Gibbs-energy based relative stabilities. J. Mol. Struct. (Theochem), 2003, 636, 195-201.
[7] Zhao X., Goto H., Slanina Z., C_(110) IPR fullerenes: temperature-dependent relative stabilities based on the Gibbs function. Chem. Phys., 2004, 306, 93-104.
[8] Cioslowski J., Electronic structure calculations on fullerenes and their derivatives. Oxford University Press: New York, 1995.
[9] Thiel W., Perspectives on semiempirical molecular orbital theory. Adv. Chem. Phys., 1996, 93, 703-757.
[10] Chen Z., Thiel W., Performance of semiempirical methods in fullerene chemistry: relative energies and nucleus-independent chemical shifts. Chem. Phys. Lett., 2003, 367, 15-25.
[11] Zheng G., Irle S., Morokuma K., Performance of the DFTB method in comparison to DFT and semiempirical methods for geometries and energies of C_(20)-C_(86) fullerene isomers. Chem. Phys. Lett., 2005, 412, 210-216.
[12] Elstner M., Porezag D., Jungnickel G., Eisner J., Haugk M., Frauenheim T., Suhai S., Seifert G., Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties. Phys. Rev. B, 1998, 58, 7260-7268.
[13] Porezag D., Frauenheim T., Kohler T., Seifert G., Kaschner R., Construction of tight-binding-like potentials on the basis of density-functional theory: Application to carbon. Phys. Rev. B, 1995, 51, 12947-12957.
[14] Frauenheim T., Seifert G., Elstner M., Niehaus T., Kohler C., Amkreutz M., Sternberg M., Hajnal Z., Carlo A. D., Suhai S., Atomistic simulations of complex materials: ground-state and excited-state properties. J. Phys.: Cond Mater, 2002, 14, 3015-3047.
[15] Achiba Y., Fowler P. W., Mitchell D., Zerbetto F., Structural predictions for the C_(116) molecule. J. Phys. Chem. A, 1998, 102, 6835-6841.
[16] Fowler P. W., Heine T., Zerbetto F., Competition between even and odd fullerenes: C_(118), C_(119) and C_(120). J.. Phys. Chem. A, 2000, 104, 9625-9629.
[17] Xu C. H., Wang C. Z., Chan C. T., Ho K. M., A transferable tight-binding potential for carbon. J. Phys: Condens. Matter, 1992, 4, 6047-6054.
[18] Brenner D. W., Shenderova O. A., Harrison J. A., Stuart S. J., Ni B., Sinnott S. B., A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys.: Condens. Matter, 2002, 14, 783-802.
[19] Cai W. S., Xu L., Shao N., Shao X. G., Guo Q. X., An efficient approach for theoretical study on the low-energy isomers of large fullerenes C_(90)-C_(140). J. Chem. Phys., 2005, 122, 184318.
[20] Brinkmann G., Dress A. W. M., A reliable and efficient top-down approach to fullerene-structure enumeration. Adv. Appl. Math., 1998, 21, 473-480.
[21] Fowler P. W., Manolopoulos D. E., An Atlas of Fullerenes. Clarendon Press: Oxford, 1995.
[22] Manolopoulos D. E., May J. C., Down S. E., Theoretical studies of the fullerenes: C_(34) to C_(70). Chem. Phys. Lett., 1991, 181, 105-111.
[23] Frisch M. J., Trucks G. W., Schlegel H. B., Scuseria G. E., Robb M. A., Cheeseman J. R., Montgomery J. A., Jr., Vreven T., Kudin K. N., Burant J. C., Millam J. M., Iyengar S. S., Tomasi J., Barone V., Mennucci B., Cossi M., Scalmani G., Rega N., Petersson G. A., Nakatsuji H., Hada M., Ehara M., Toyota K., Fukuda R., Hasegawa J., Ishida M., Nakajima T., Honda Y., Kitao O., Nakai H., Klene M., Li X., Knox J. E., Hratchian H. P., Cross J. B., Adamo C., Jaramillo J., Gomperts J., Stratmann R. E., Yazyev O., Austin A. J., Cammi R., Pomelli C., Ochterski J. W., Ayala P. Y., Morokuma K., Voth G. A., Salvador P., Dannenberg J. J., Zakrzewski V. G., Dapprich S., Daniels A. D., Strain M. C., Farkas O., Malick D. K., Rabuck A. D., Raghavachari K., Foresman J. B., Ortiz J. V., Cui Q., Baboul A. G., Clifford S., Cioslowski J., Stefanov B. B., Liu (3., Liashenko A., Piskorz P., Komaromi I., Martin R. L., Fox D. J., Keith T., Al-Laham M. A., Peng C. Y., Nanayakkara A., Challacombe M., Gill P. M. W., Johnson B., Chen W., Wong M. W., Gonzalez C., Pople J. A., GAUSSIAN 03, Revision C.02, Gaussian, Inc., Wallingford CT, 2004.
[24] Xu L., Cai W. S., Shao X. G., Prediction of low-energy isomers of large fullerenes from C_(132)-C_(160). J. Phys. Chem. A, 2006, 110, 9247-9253.
[25] Raghavachari K., Ground-state of C_(84):2 almost isoenergetic isomers. Chem. Phys. Lett., 1992, 190, 397-400.
[26] Cioslowski J., Rao N., Moncrieff D., Standard enthalpies of formation fo fullerenes and their dependence on structural motifs. J. Am. Chem. Soc., 2002, 122, 8265-8270.
[1] Sun G. Y., Kertesz M., ~(13)C NMR spectra for IPR isomers of fullerene C_(86). Chem. Phys., 2002, 276, 107-114.
[2] Kikuchi K., Nakahara N., Wakabayashi T., Suzuki S., Shiromaru H., Miyake Y., Saito K., Ikemoto I., Kainosho M., Achiba Y., NMR characterization of isomers of C_(78), C_(82) and C_(84) fullerenes. Nature, 1992, 357, 142-145.
[3] Kikuchi K., Nakahara N., Wakabayashi T., Honda M., Matsumiya H., Moriwaki T., Suzuki S., Shiromaru H., Saito K., Yamauchi K., Ikemoto I., Achiba Y., Isolation and identification of fullerene family: C_(76), C_(78), C_(82), C_(84), C_(90) and C_(96). Chem. Phys. Lett., 1992, 188, 177-180.
[4] Taylor R., Langley G. J., Avent A. G., Dennis T. J. S., Kroto H. W., Walton D. R. M., ~(13)C NMR-spectroscopy of C_(76), C_(78), C_(84) and mixtures of C_(86)-C_(102): Anomalous chromatographic behavior of C_(82), and evidence for C_(70)H_(12). J. Chem. Soc., Perkin Trans. 2, 1993, 1029-1036.
[5] Hennrich F. H., Michel R. H., Fischer A., RichardSchneider S., Gilb S., Kappes M. M., Fuchs D., Burk M., Kobayashi K., Nagase S., Isolation and characterization ofC_(80). Angew. Chem., Int. Ed. Engl., 1996, 35, 1732-1734.
[6] Mitsumoto R., Oji H., Mori I., Yamamoto Y., Asato K., Ouchi Y., Shinohara H., Seki K., Umishita K., Hino S., Nagase S., Kikuchi K., Achiba Y., NEXAFS studies of higher fullerenes up to C_(96). J. Phys. Ⅳ, 1997, 7, 525-526.
[7] Diederich F., Ettl R., Rubin Y., Whetten R. L., Beck R., Alvarez M. M., Anz S., Sensharma D., Wudl F., Khemani K. C., Koch A., The higher fullerenes: Isolation and characterization of C_(76), C_(84), C_(90), C_(94), and C_(70)O, an oxide of D_(5H)-C_(70). Science, 1991, 252, 548-551.
[8] Crassous J., Rivera J., Fender N. S., Shu L. H., Echegoyen L., Thilgen C., Herrmarm A., Diederich F, Chemistry of C_(84): Separation of three constitutional isomers and optical resolution of D_2-C_(84) by using the "Bingel-retro-Bingel" strategy. Angew. Chem., Int. Ed, 1999, 38, 1613-1617.
[9] Dennis T. J. S., Kai T., Asato K., Tomiyama T., Shinohara H., Yoshida T., Kobayashi Y., Ishiwatari H., Miyake Y., Kikuchi K., Achiba Y., Isolation and characterization by ~(13)C NMR spectroscopy of [84]fullerene minor isomers. J. Phys. Chem. A, 1999, 103, 8747-8752.
[10] Kroto H. W., The stability of the fullerenes Cn, with n=24, 28, 32, 36, 50, 60 and 70. Nature, 1987, 329, 529-531.
[11] Schmalz T. G., Seitz W. A., Klein D. J., Hite G. E., Elemental carbon cages. J Am. Chem. Soc., 1988, 110, 1113-1127.
[12] Cai W. S., Shao N., Shao X. G., Pan Z. X., Structural analysis of carbon clusters by using a global optimization algorithm with Brenner potential. J. Mol. Struct. (Theochem), 2004, 678, 113-122.
[13] Zhang B. L., Wang C. Z., Ho K. M., Xu C. H., Chan C. T., The geometry of small fullerene cages: C_(20) to C_(70). J Chem. Phys., 1992, 97, 5007-5011.
[14] Zhang B. L., Wang C. Z., Ho K. M., Xu C. H., Chan C. T., The geometry of large fullerene cages: C_(72) to C_(102). J Chem. Phys., 1993, 98, 3095-3102.
[15] Slanina Z., Zhao X., Lee S. L., Osawa E., C_(90) temperature effects on relative stabilities of the IPR isomers. Chem. Phys. Lett., 1997, 219, 193-200.
[16] Slanina Z., Zhao X., Deota P., Osawa E., Relative stabilities of C_(92) IPR fullerenes. J Mol. Model., 2000, 6, 312-317.
[17] Zhao X., Slanina Z., Goto H., Osawa E., Theoretical investigations on relative stabilities of fullerene C_(94). J. Chem. Phys., 2003, 118, 10534-10540.
[18] Zhao X., Slanina Z., Goto H., Theoretical studies on the relative stabilities of C_(96) IPR fullerenes. J. Phys. Chem. A, 2004, 108, 4479-4484.
[19] Zhao X., Slanina Z., C_(98) IPR isomers: Gibbs-energy based relative stabilities. J. Mol. Struct. (Theochem), 2003, 636, 195-201.
[20] Zhao X., Goto H., Slanina Z., C_(110) IPR fullerenes: temperature-dependent relative stabilities based on the Gibbs function. Chem. Phys., 2004, 306, 93-104.
[21] Achiba Y., Fowler P. W., Mitchell D., Zerbetto F., Structural predictions for the C_(116) molecule. J. Phys. Chem. A, 1998, 102, 6835-6841.
[22] Fowler P. W., Heine T., Zerbetto F., Competition between even and odd fullerenes: C_(118), C_(119) and C_(120). J. Phys. Chem. A, 2000, 104, 9625-9629.
[23] Cai W. S., Xu L., Shao N., Shao X. G., Guo Q. X., An efficient approach for theoretical study on the low-energy isomers of large fullerenes C_(90)-C_(140). J. Chem. Phys., 2005, 122, 184318.
[24] Brenner D. W., Shenderova O. A., Harrison J. A., Stuart S. J., Ni B., Sinnott S. B., A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys.: Condens. Matter, 2002, 14, 783-802.
[25] Brinkmann G., Dress A. W. M., A reliable and efficient top-down approach to fullerene-structure enumeration. Adv. Appl. Math., 1998, 21, 473-480.
[26] Cioslowski J., Rao N., Moncrieff D., Standard enthalpies of formation fo fullerenes and their dependence on structural motifs. J. Am. Chem. Soc., 2002, 122, 8265-8270.
[27] Xu C. H., Wang C. Z., Chan C. T., Ho K. M., A transferable tight-binding potential for carbon. J. Phys: Condens. Matter, 1992, 4, 6047-6054
[28] Frisch M. J., Trucks G. W., Schlegel H. B., Scuseria G. E., Robb M. A., Cheeseman J. R., Montgomery J. A., Jr., Vreven T., Kudin K. N., Burant J. C., Millam J. M., Iyengar S. S., Tomasi J., Barone V., Mennucci B., Cossi M., Scalmani G., Rega N., Petersson G. A., Nakatsuji H., Hada M., Ehara M., Toyota K., Fukuda R., Hasegawa J., Ishida M., Nakajima T., Honda Y., Kitao O., Nakai H., Klene M., Li X., Knox J. E., Hratchian H. P., Cross J. B., Adamo C., Jaramillo J., Gomperts J., Stratmann R. E., Yazyev O., Austin A. J., Cammi R., Pomelli C., Ochterski J. W., Ayala P. Y., Morokuma K., Voth G. A., Salvador P., Dannenberg J. J., Zakrzewski V. G., Dapprich S., Daniels A. D., Strain M. C., Farkas O., Malick D. K., Rabuck A. D., Raghavachari K., Foresman J. B., Ortiz J. V., Cui Q., Baboul A. G., Clifford S., Cioslowski J., Stefanov B. B., Liu G., Liashenko A., Piskorz P., Komaromi I., Martin R. L., Fox D. J., Keith T., Al-Laham M. A., Peng C. Y., Nanayakkara A., Challacombe M., Gill P. M. W., Johnson B., Chen W., Wong M. W., Gonzalez C., Pople J. A., GAUSSIAN 03, Revision C.02, Gaussian, Inc., Wallingford CT, 2004.
[29] Liu D. C., Nocedal J., On the limited memory BFGS method for large-scale optimization. Math. Progm., 1989, 45,503-528.
[30] Fowler P, W., Manolopoulos D. E., An Atlas of Fullerenes. Clarendon Press: Oxford, 1995.
[31] Manolopoulos D. E., May J. C., Down S. E., Theoretical studies of the fullerenes: C_(34) to C_(70). Chem. Phys. Lett., 1991, 181,105-111.
[32] Seifert G., Vietze K., Schmidt R., Ionization energies of fullerenes—size and charge dependence. J. Phys. B: At. Mol. Opt. Phys., 1996, 29, 5183-5192.
[33] Boltalina O. V., Ioffe I. N., Sidorov L. N., Seifert G., Vietze K., Ionization energy of fullerenes. J. Am. Chem. Soc., 2000, 122, 9745-9749.
[1] Sun G. Y., Kertesz M., ~(13)C NMR spectra for IPR isomers of fullerene C_(86). Chem. Phys., 2002, 276, 107-114.
[2] Kikuchi K., Nakahara N., Wakabayashi T., Suzuki S., Shiromaru H., Miyake Y., Saito K., Ikemoto I., Kainosho M., Achiba Y., NMR characterization of isomers of C_(78), C_(82) and C_(84) fullerenes. Nature, 1992, 357, 142-145.
[3] Kikuchi K., Nakahara N., Wakabayashi T., Honda M., Matsumiya H., Moriwaki T., Suzuki S., Shiromaru H., Saito K., Yamauchi K., Ikemoto I., Achiba Y., Isolation and identification of fullerene family: C_(76), C_(78), C_(82), C_(84), C_(90) and C_(96). Chem. Phys. Lett., 1992, 188, 177-180.
[4] Taylor R., Langley G. J., Avent A. G., Dennis T. J. S., Kroto H. W., Walton D. R. M., ~(13)C NMR-spectroscopy of C_(76), C_(78), C_(84) and mixtures of C_(86)-C_(102): Anomalous chromatographic behavior of C_(82), and evidence for C_(70)H_(12). J.. Chem. Soc., Perkin Trans. 2, 1993, 1029-1036.
[5] Hennrich F. H., Michel R. H., Fischer A., RichardSchneider S., Gilb S., Kappes M. M., Fuchs D., Burk M., Kobayashi K., Nagase S., Isolation and characterization of C_(80). Angew. Chem., Int. Ed. Engl., 1996, 35, 1732-1734.
[6] Mitsumoto R., Oji H., Mori I., Yamamoto Y., Asato K., Ouchi Y., Shinohara H., Seki K., Umishita K., Hino S., Nagase S., Kikuchi K., Achiba Y., NEXAFS studies of higher fullerenes up to C_(96). J. Phys. Ⅳ, 1997, 7, 525-526.
[7] Diederich F., Ettl R., Rubin Y., Whetten R. L., Beck R., Alvarez M. M., Anz S., Sensharma D., Wudl F., Khemani K. C., Koch A., The higher fullerenes: Isolation and characterization of C_(76), C_(84), C_(90), C_(94), and C_(70)O, an oxide of D_(5H)-C_(70). Science, 1991, 252, 548-551.
[8] Crassous J., Rivera J., Fender N. S., Shu L. H., Echegoyen L., Thilgen C., Herrmann A., Diederich F., Chemistry of C_(84): Separation of three constitutional isomers and optical resolution of D_2-C_(84) by using the "Bingel-retro-Bingel" strategy. Angew. Chem., Int. Ed., 1999, 38, 1613-1617.
[9] Dennis T. J. S., Kai T., Asato K., Tomiyama T., Shinohara H., Yoshida T., Kobayashi Y., Ishiwatari H., Miyake Y., Kikuchi K., Achiba Y., Isolation and characterization by ~(13)C NMR spectroscopy of [84]fullerene minor isomers. J. Phys. Chem. A, 1999, 103, 8747-8752.
[10] Achiba Y., Fowler P. W., Mitchell D., Zerbetto F., Structural predictions for the C_(116) molecule. J. Phys. Chem. A, 1998, 102, 6835-6841.
[11] Fowler P. W., Heine T., Zerbetto F., Competition between even and odd fullerenes: C_(118), C_(119) and C_(120). J. Phys. Chem. A, 2000, 104, 9625-9629.
[12] Cai W. S., Xu L., Shao N., Shao X. G., Guo Q. X., An efficient approach for theoretical study on the low-energy isomers of large fullerenes C_(90)-C_(140). J. Chem. Phys., 2005, 122, 184318.
[13] Shao N., Gao Y., Yoo S., An W., Zeng X. C., Search for lowest-energy fullerenes: C_(98)-C_(110). J. Phys. Chem. A, 2006, 110, 7672-7676.
[14] Xu L., Cai W. S., Shao X. G., Prediction of low-energy isomers of large fullerenes from C_(132)-C_(160). J. Phys. Chem. A, 2006, 110, 9247-9253.
[15] Kroto H. W., The stability of the fullerenes Cn, with n=24, 28, 32, 36, 50, 60 and 70. Nature, 1987, 329, 529-531.
[16] Brinkmann G., Dress A. W. M., A reliable and efficient top-down approach to fullerene-structure enumeration. Adv. Appl. Math., 1998, 21,473-480.
[17] Cioslowski J., Rao N., Moncrieff D., Standard enthalpies of formation fo fullerenes and their dependence on structural motifs. J. Am. Chem. Soc., 2002, 122, 8265-8270.
[18] Xu C. H., Wang C. Z., Chan C. T., Ho K. M., A transferable tight-binding potential for carbon. J. Phys: Condens. Matter, 1992, 4, 6047-6054.
[19] Zhang B. L., Wang C. Z., Ho K. M., Xu C. H., Chan C. T., The geometry of small fullerene cages: C_(20) to C_(70). J. Chem. Phys., 1992, 97, 5007-5011.
[20] Zhang B. L., Wang C. Z., Ho Ko M., Xu C. H., Chan C. T., The geometry of large fullerene cages: C_(72) to C_(102). J. Chem. Phys., 1993, 98, 3095-3102.
[21] Lin Y., Cai W. S., Shao X. G., Comparison studies of fullerenes C72, C74, C76 and C78 by tight-binding Monte Carlo and quantum chemical methods. J. Mol. Struct. (Theochem), 2006, 760, 153-158.
[22] Cioslowski J., Heats of formation of higher fullerenes from ab initio hartree-fock and correlation-energy functional calculations. Chem. Phys. Lett., 1993, 216, 389-393.
[23] Liu D. C., Nocedal J., On the limited memory BFGS method for large-scale optimization. Math. Progm., 1989, 45, 503-528.
[24] Frisch M. J., Trucks G. W., Schlegel H. B., Scuseria G. E., Robb M. A., Cheeseman J. R., Montgomery J. A., Jr., Vreven T., Kudin K. N., Burant J. C., Millam J. M., Iyengar S. S., Tomasi J., Barone V., Mennucci B., Cossi M., Scalmani G., Rega N., Petersson G. A., Nakatsuji H., Hada M., Ehara M., Toyota K., Fukuda R., Hasegawa J., Ishida M., Nakajima T., Honda Y., Kitao O., Nakai H., Klene M., Li X., Knox J. E., Hratchian H. P., Cross J. B., Adamo C., Jaramillo J., Gomperts J., Stratmann R. E., Yazyev O., Austin A. J., Cammi R., Pomelli C., Ochterski J. W., Ayala P. Y., Morokuma K., Voth G. A., Salvador P., Dannenberg J. J., Zakrzewski V. G., Dapprich S., Daniels A. D., Strain M. C., Farkas O., Malick D. K., Rabuck A. D., Raghavachari K., Foresman J. B., Ortiz J. V., Cui Q., Baboul A. G., Clifford S., Cioslowski J., Stefanov B. B., Liu G., Liashenko A., Piskorz P., Komaromi I., Martin R. L., Fox D. J., Keith T., Al-Laham M. A., Peng C. Y., Nanayakkara A., Challacombe M., Gill P. M. W., Johnson B., Chen W., Wong M. W., Gonzalez C., Pople J. A., GAUSSIAN 03, Revision C.02, Gaussian, Inc., Wallingford CT, 2004.
[25] Fowler P. W., Manolopoulos D. E., An Atlas of Fullerenes. Clarendon Press: Oxford, 1995.
[26] Manolopoulos D. E., May J. C., Down S. E., Theoretical studies of the fullerenes: C_(34) to C_(70). Chem. Phys. Lett., 1991, 181, 105-111.
[27] Elstner M., Porezag D., Jungnickel G., Elsner J., Haugk M., Frauenheim Yh., Suhai S., Seifert G., Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties. Phys. Rev. B, 1998, 58, 7260-7268.
[28] Zhang B. L., Xu C. H., Wang C. Z., Chan C. T., Ho K. M., Systematic study of structures and stabilities of fullerenes. Phys. Rev. B, 1992, 46, 7333-7336.
[29] Seifert G., Vietze K., Schmidt R., Ionization energies of fullerenes—size and charge dependence. J. Phys. B: At. Mol. Opt. Phys., 1996, 29, 5183-5192.
[30] Boltalina O. V., Ioffe I. N., Sidorov L. N., Seifert G., Vietze K., Ionization energy of fullerenes. J. Am. Chem. Soc., 2000, 122, 9745-9749.