【作者】 许磊；

【导师】 蔡文生；

【作者基本信息】 中国科学技术大学 ， 分析化学， 2007， 博士

【摘要】 自从1985年C₆₀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C₉₆。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C₈₀-C₉₀的理论研究，从C₈₀-C₉₀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C₈₀-C₉₀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C₈₀-C₉₀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C₈₀-C₉₀，满足IPR规则的异构体仍然较non-IPR异构体稳定，并不象C₇₂一样，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C₉₀-C₁₀₀，C₁₁₆，C₁₁₈，和C₁₂₀，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C₉₀-C₁₄₀稳定结构的理论预测。首先，采用CaGe_REBO程序对C₉₀-C₁₄₀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C₉₀-C₁₄₀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C₉₀-C₁₄₀，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C₁₀₂。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C₁₁₆-C₁₂₀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C₁₁₆-C₁₂₀，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C₁₆₀，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C₁₃₂-C₁₆₀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C₁₃₂-C₁₆₀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C₁₅₀和C₁₅₂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C₁₃₂-C₁₆₀最低能量异构体的电离能和电子亲和势。结果显示，C₁₃₂-C₁₆₀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，C₁₃₂和C₁₅₀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C₁₆₀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C₆₀-C₁₆₀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C₁₂₂-C₁₃₀和C₁₆₂-C₁₈₀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C₁₂₂-C₁₃₀和C₁₆₂-C₁₈₀的热力学稳定异构体。研究结果表明，C₁₇₄和C₁₈₀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C₁₂₂-C₁₃₀和C₁₆₂-C₁₈₀，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。更多还原

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