碳簇结构及其光谱性质的理论研究
摘要
碳簇，从几个原子的团簇到C_(60)、C_(70)的微粒以及碳纳米管等，有许多的存在形式，是一类非常重要的体系。近年来，碳簇的实验与理论研究引起了人们的极大兴趣，并在碳簇的制备、表征和性能研究等领域取得了很大的进展。随着研究的深入，涉及碳簇科学的一些基本问题：如C_(60)和碳纳米管的形成机理，碳簇幻数特征峰的内在原因，星际空间中DIBs谱带与碳簇的关联等开始受到关注，期待着人们的解答。
本文通过量子化学计算对碳簇的结构、稳定性和光谱性质进行了理论探讨，研究工作主要包括三个方面：
1．直链碳簇的理论研究
实验上关于线性碳链HC_nH，C_(2n)H和C_(2n-1)N光谱性质的研究比较完整，但缺乏相应的理论研究。我们应用密度泛函理论(DFT)优化了HC_(2n)H(n=1-13)和HC_(2n+1)H(n=2-12)的基态平衡几何构型，计算了它们的振动频率。用含时密度泛函理论方法(TD-DFT)和ab initio CASPT2方法对HC_(2n)H(n=1-5)的X~1∑_g~+→1~1∑_u~+和HC_(2n+1)H(n=2-5)X~3∑_g~-→1~3∑_u~-的垂直激发能进行了计算。计算结果表明：(1)奇数碳链HC_(2n+1)H的激发能所对应的波长与链长n成线性关系，即λ_0=A+Bn；(2)偶数碳链HC_(2n)H的激发能所对应的波长与链长n成非线性关系，即
这些解析的λ-n关系式可以定量地预测这两类碳链体系的电子光谱。进一步的分析表明，由于这两类碳链体系基态与激发态成键性质上的差异，导
摘要
导致了不同的无n光谱行为。类似的计算研究拓展到了线性碳链CZnH和
CZn.IN，并获得了对应的补n解析关系式。
在DFT和ab initio水平上，应用有限场计算方法对HCZnH和HCZ。、，H
的静态极化率进行了计算。基于HF计算结果，建议了HCZnH和HCZn+IH
经向静态极化率与n的对数解析关系式和纬向静态极化率对n的线性解
析关系式。我们给出的对数解析关系式A(n)二anIn(b才+c)优于其它
理论计算结果所得到的指数关系式A(n)=an”.
为了了解碳链光异构化行为，应用DFT和ab initio电子相关方法对
CSHZ三态和单态势能面上的异构化过程进行了理论计算研究。计算表明，
C尹:的异构化过程容易在三态势能面进行，在单态势能面上直接的l，3
氢迁移非常困难。
2.遗传算法对碳簇几何结构的优化
利用遗传算法(GA)在B~r势能面上对C。(n二2一30)进行了结构
优化和平均结合能计算。模拟计算表明:当n<6时，C。是直线型的结构;
当6立<13时，C。是平面单环结构;n=13，14时，C。是平面双环结构;
当n>14时，开始出现多环结构，其中C加为碗状结构，C28.是唯一的fuuerene
结构，与量子Monte Carl。和abl’nitio预测的结果完全一致。
3.C6。和碳纳米管生长机理研究
依据共振论，假定Kekule结构数对碳簇稳定性起重要作用，体系Kekule
结构数越多，体系越稳定。应用这一Kekule结构数与共辘体系稳定性关
系的假定，以及对石墨碎片、碳纳米粒子、碳纳米管、戴帽碳纳米管等
体系Kekule结构数的计算，合理地解释了石墨碎片在高温下的卷曲、可
能的卷曲方式及封闭碳纳米管和类洋葱碳纳米粒子形成的实验现象;建
摘要
议了C6。和碳纳米管的可能形成方式;解释了(n，n)纳米管形成的可能原
因。对于具有相似Kekule结构数的笼状构型，其结构的表面曲率(近似
用体积与表面积比表示)对其结构稳定性的影响不能忽略，结合量子化
学计算，合理地解释了C60最稳定的笼状结构具有I。对称性。
Carbon clusters, comprising aggregates up to several carbon atoms,
and C70 particles, and carbon nanotubes, have diverse interests in astrophysics and in material science. Recently, experimental and theoretical studies on carbon clusters have attracted a considerable attention, and significant progresses have been made in synthesis and characterization of carbon clusters and in investigation of their physical and chemical performances. With research deepening, fundamental questions concerning carbon clusters, such as formation mechanism of C60 and carbon nanotubes and identification of DIBs carriers, etc, become increasing important.
In the present work, structures, stabilities, and spectroscopic features of carbon clusters have been investigated by quantum chemistry calculations. Our work will focus in three aspects:
1. Theoretical study on linear carbon chains
New developments in matrix isolation spectroscopy have led to spectroscopic characterization of mass-selected carbon clusters HCnH, C2nH and C2n-1N in the gas phase. Among the numerous observed bands, only a few bands of specific species were assigned, both experimentally and theoretically. A precise understanding of these electronic spectra remains open. Using DFT calculations, we optimized geometries of carbon chains in their ground states, and calculated their vibrational frequencies. Vertical excitation energies for the
transition of HC2nH (n=l-5) and for the
transition of HC2n+1H (n=2-5) have been calculated by the time-dependent density functional theory and ab initio second order multiconfiguration perturbation method. On the basis of present calculations, explicit size-dependent expressions for the wavelength of excitation energies in linear polyynes are suggested. Present calculations show that the odd-numbered polyynes has a linear dependence as =A + Bn, while there is a nonlinear size dependence for the even-numbered polyynes:
Such analytical -n relationships work very well for prediction of electronic excitation energies in linear polyynes. Further analyses reveal that such significant difference in spectroscopic feature of both series can be ascribed to distinct bonding features between the ground and excited states in the odd- and even-numbered polyynes.
Similar theoretical treatments are extended to C2nH and C2n-1N, the size dependence of vertical excitation energies for transitions of C2nH and C2n-1N have been discussed.
Static longitudinal polarizabilities of HC2nH and HC2n+1H have been calculated by ab initio Hartree-Fock and B3LYP methods with several basis sets. On the basis of HF calculations, simple exponential and logarithmic expressions are proposed for the size dependences of longitudinal polarizabilities of polyynes HC2nH and HC2n+iH. The logarithmic expression is A(n) = anln(bn2+c). In comparison with other theoretical treatments, it is found that the logarithmic expression has better extrapolation behavior than the exponential one A{n) = anb.
Density functional theory calculations with the B3LYP functional are used to study the structure and stabilities of C5H2 isomers and possible isomerization mechanisms on the triplet and singlet potential energy surfaces. Calculated results show that isomerization of C5H2 is likely to occur on the triplet potential energy surface while direct conversions of the singlet C5H2 isomers via 1,3-hydrogen migration transition states are extremely difficult dynamically.
2. The optimization of carbon clusters with genetic algorithm (GA)
Geometrical optimization of Cn (n=2-30) has been performed with a GA method. A modified Brenner's potential energy surface (PES) of carbon species, which omits the conjugate-compensation term F(ij,k) in the original form, is employed in the present study. Our results show that Cn is a linear chain for n<5, and a single ring from C6 to C12. Multi-ring structure starts to form at C13. In particular, we find the most stable forms of C20 and C28 are bowl-like structure and fullerene, respectively, in good agreement with the results
本文通过量子化学计算对碳簇的结构、稳定性和光谱性质进行了理论探讨，研究工作主要包括三个方面：
1．直链碳簇的理论研究
实验上关于线性碳链HC_nH，C_(2n)H和C_(2n-1)N光谱性质的研究比较完整，但缺乏相应的理论研究。我们应用密度泛函理论(DFT)优化了HC_(2n)H(n=1-13)和HC_(2n+1)H(n=2-12)的基态平衡几何构型，计算了它们的振动频率。用含时密度泛函理论方法(TD-DFT)和ab initio CASPT2方法对HC_(2n)H(n=1-5)的X~1∑_g~+→1~1∑_u~+和HC_(2n+1)H(n=2-5)X~3∑_g~-→1~3∑_u~-的垂直激发能进行了计算。计算结果表明：(1)奇数碳链HC_(2n+1)H的激发能所对应的波长与链长n成线性关系，即λ_0=A+Bn；(2)偶数碳链HC_(2n)H的激发能所对应的波长与链长n成非线性关系，即
这些解析的λ-n关系式可以定量地预测这两类碳链体系的电子光谱。进一步的分析表明，由于这两类碳链体系基态与激发态成键性质上的差异，导
摘要
导致了不同的无n光谱行为。类似的计算研究拓展到了线性碳链CZnH和
CZn.IN，并获得了对应的补n解析关系式。
在DFT和ab initio水平上，应用有限场计算方法对HCZnH和HCZ。、，H
的静态极化率进行了计算。基于HF计算结果，建议了HCZnH和HCZn+IH
经向静态极化率与n的对数解析关系式和纬向静态极化率对n的线性解
析关系式。我们给出的对数解析关系式A(n)二anIn(b才+c)优于其它
理论计算结果所得到的指数关系式A(n)=an”.
为了了解碳链光异构化行为，应用DFT和ab initio电子相关方法对
CSHZ三态和单态势能面上的异构化过程进行了理论计算研究。计算表明，
C尹:的异构化过程容易在三态势能面进行，在单态势能面上直接的l，3
氢迁移非常困难。
2.遗传算法对碳簇几何结构的优化
利用遗传算法(GA)在B~r势能面上对C。(n二2一30)进行了结构
优化和平均结合能计算。模拟计算表明:当n<6时，C。是直线型的结构;
当6立<13时，C。是平面单环结构;n=13，14时，C。是平面双环结构;
当n>14时，开始出现多环结构，其中C加为碗状结构，C28.是唯一的fuuerene
结构，与量子Monte Carl。和abl’nitio预测的结果完全一致。
3.C6。和碳纳米管生长机理研究
依据共振论，假定Kekule结构数对碳簇稳定性起重要作用，体系Kekule
结构数越多，体系越稳定。应用这一Kekule结构数与共辘体系稳定性关
系的假定，以及对石墨碎片、碳纳米粒子、碳纳米管、戴帽碳纳米管等
体系Kekule结构数的计算，合理地解释了石墨碎片在高温下的卷曲、可
能的卷曲方式及封闭碳纳米管和类洋葱碳纳米粒子形成的实验现象;建
摘要
议了C6。和碳纳米管的可能形成方式;解释了(n，n)纳米管形成的可能原
因。对于具有相似Kekule结构数的笼状构型，其结构的表面曲率(近似
用体积与表面积比表示)对其结构稳定性的影响不能忽略，结合量子化
学计算，合理地解释了C60最稳定的笼状结构具有I。对称性。
Carbon clusters, comprising aggregates up to several carbon atoms,
and C70 particles, and carbon nanotubes, have diverse interests in astrophysics and in material science. Recently, experimental and theoretical studies on carbon clusters have attracted a considerable attention, and significant progresses have been made in synthesis and characterization of carbon clusters and in investigation of their physical and chemical performances. With research deepening, fundamental questions concerning carbon clusters, such as formation mechanism of C60 and carbon nanotubes and identification of DIBs carriers, etc, become increasing important.
In the present work, structures, stabilities, and spectroscopic features of carbon clusters have been investigated by quantum chemistry calculations. Our work will focus in three aspects:
1. Theoretical study on linear carbon chains
New developments in matrix isolation spectroscopy have led to spectroscopic characterization of mass-selected carbon clusters HCnH, C2nH and C2n-1N in the gas phase. Among the numerous observed bands, only a few bands of specific species were assigned, both experimentally and theoretically. A precise understanding of these electronic spectra remains open. Using DFT calculations, we optimized geometries of carbon chains in their ground states, and calculated their vibrational frequencies. Vertical excitation energies for the
transition of HC2nH (n=l-5) and for the
transition of HC2n+1H (n=2-5) have been calculated by the time-dependent density functional theory and ab initio second order multiconfiguration perturbation method. On the basis of present calculations, explicit size-dependent expressions for the wavelength of excitation energies in linear polyynes are suggested. Present calculations show that the odd-numbered polyynes has a linear dependence as =A + Bn, while there is a nonlinear size dependence for the even-numbered polyynes:
Such analytical -n relationships work very well for prediction of electronic excitation energies in linear polyynes. Further analyses reveal that such significant difference in spectroscopic feature of both series can be ascribed to distinct bonding features between the ground and excited states in the odd- and even-numbered polyynes.
Similar theoretical treatments are extended to C2nH and C2n-1N, the size dependence of vertical excitation energies for transitions of C2nH and C2n-1N have been discussed.
Static longitudinal polarizabilities of HC2nH and HC2n+1H have been calculated by ab initio Hartree-Fock and B3LYP methods with several basis sets. On the basis of HF calculations, simple exponential and logarithmic expressions are proposed for the size dependences of longitudinal polarizabilities of polyynes HC2nH and HC2n+iH. The logarithmic expression is A(n) = anln(bn2+c). In comparison with other theoretical treatments, it is found that the logarithmic expression has better extrapolation behavior than the exponential one A{n) = anb.
Density functional theory calculations with the B3LYP functional are used to study the structure and stabilities of C5H2 isomers and possible isomerization mechanisms on the triplet and singlet potential energy surfaces. Calculated results show that isomerization of C5H2 is likely to occur on the triplet potential energy surface while direct conversions of the singlet C5H2 isomers via 1,3-hydrogen migration transition states are extremely difficult dynamically.
2. The optimization of carbon clusters with genetic algorithm (GA)
Geometrical optimization of Cn (n=2-30) has been performed with a GA method. A modified Brenner's potential energy surface (PES) of carbon species, which omits the conjugate-compensation term F(ij,k) in the original form, is employed in the present study. Our results show that Cn is a linear chain for n<5, and a single ring from C6 to C12. Multi-ring structure starts to form at C13. In particular, we find the most stable forms of C20 and C28 are bowl-like structure and fullerene, respectively, in good agreement with the results
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