Abstract 抽象的
The structures and electronic states of alkyl-radical-functionalized C20 fullerenes (denoted by C20–R) have been investigated using density functional theory (DFT). The different alkyl radicals investigated were methyl, ethyl, propyl, and butyl radicals. The DFT calculation indicated that the alkyl radical binds to the carbon atom of C20 in the on-top site, thus forming a strong C–C single bond. The binding energies of the alkyl radicals to C20 were calculated to be 83.9–86.6 kcal/mol at the CAM-B3LYP/6-311G(d,p) level. The electronic states of the C20–R complex are discussed on the basis of the theoretical results.
使用密度泛函理论（DFT）研究了烷基自由基官能化的C 20富勒烯（用C 20 –R表示）的结构和电子态。研究的不同烷基是甲基、乙基、丙基和丁基。 DFT计算表明烷基与顶部位点的C 20碳原子结合，从而形成强的C-C单键。在 CAM-B3LYP/6-311G(d,p) 水平上，烷基自由基与 C 20的结合能为 83.9–86.6 kcal/mol。在理论结果的基础上讨论了C 20 -R配合物的电子态。
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1. Introduction 一、简介
Carbon materials have a potential to interact with a variety of chemical species at both the surface and the edge regions of carbon sheets.1–7) In particular, the interaction of fullerene with radicals and radical ions is very important for electronic devices and hydrogen storage materials. The electronic states of fullerene are modified by the interaction with several radical species. Modified graphene is known as a functionalized fullerene.8) C20 is the smallest fullerene and has been experimentally produced by gas-phase debromination.9) Also, the C20 cage can be regarded as a potential candidate for superconductors.10,11) Prinzbach et al. measured photo-electron spectra of the mass selected C20 cluster using electron-impact ionization in a time-of-flight mass spectrometer. They showed that the C20 fullerene is stable and has an electron affinity of 2.25 ± 0.03 eV.12
碳材料有可能与碳片表面和边缘区域的各种化学物质相互作用。 1 – 7特别是，富勒烯与自由基和自由基离子的相互作用对于电子器件和储氢材料非常重要。富勒烯的电子态通过与几种自由基物质的相互作用而改变。改性石墨烯被称为功能化富勒烯。 8 C 20是最小的富勒烯，已通过气相脱溴实验生产。 9此外，C 20笼可被视为超导体的潜在候选者。 10 11普林茨巴赫等人。在飞行时间质谱仪中使用电子轰击电离测量了质量选择的 C 20簇的光电子光谱。他们表明C 20富勒烯是稳定的并且具有2.25±0.03 eV的电子亲和力。 12)
An alkyl radical (CnH2n+1) is the simplest organic radical and is sometimes utilized in the surface modification of carbon materials such as diamond,13) graphene and fullerene.14) The radical strongly influences the electronic conductivity and band gap in a semiconductor. However, the interactions between organic radicals and C20 are not clearly understood. Specifically, the addition process of alkyl radicals to the C20 surface is barely known. In the present study, the structures and electronic states of alkyl radicals (R, CnH2n+1, n = 1–4) added to C20 fullerenes were investigated by means of density functional theory (DFT) method. Also, the potential energy curve of the alkyl radical approaching to the surface of C20 was investigated.
烷基(C n H 2 n +1 )是最简单的有机基团，有时用于碳材料如金刚石、 13石墨烯和富勒烯的表面改性。 14自由基强烈影响半导体中的电子电导率和带隙。然而，有机自由基和C 20之间的相互作用尚不清楚。具体而言，烷基自由基向C 20表面的加成过程几乎不为人所知。本研究采用密度泛函理论(DFT)方法研究了C 20富勒烯上添加的烷基(R, C n H 2 n +1 , n = 1–4)的结构和电子态。另外，研究了接近C 20表面的烷基的势能曲线。
2. Method of calculation 2、计算方法
The geometries of C20 complexes with alkyl radicals (R) (expressed by C20–R) were fully optimized at the CAM-B3LYP/6-31G(d) and 6-311G(d,p) levels of theory. As demonstrated in our previous works, these levels of theory gave reasonable electronic structures of graphene and fullerene systems.7,15–23) To confirm their molecular stability at stationary points along the reaction coordinate, harmonic vibrational frequencies were calculated at the CAM-B3LYP/6-31G(d) level. Potential energy curves representing the interaction of alkyl radicals with C20 were calculated at the CAM-B3LYP/6-31G(d) level. The electronic states of C20–R were obtained by natural population analysis (NPA) method at the CAM-B3LYP/6-311G(d,p) level. The simulated absorption spectra were calculated and fifty electronic states were solved using time dependent DFT (TDDFT). All DFT calculations were performed using the Gaussian 09 program package.24
具有烷基(R)的C 20配合物(用C 20 –R表示)的几何形状在CAM-B3LYP/6-31G(d)和6-311G(d,p)的理论水平上得到了充分优化。正如我们之前的工作所证明的，这些理论水平给出了石墨烯和富勒烯系统的合理电子结构。 7 15 – 23为了确认它们在沿反应坐标的固定点处的分子稳定性，在 CAM-B3LYP/6-31G(d) 水平上计算了谐波振动频率。在CAM-B3LYP/6-31G(d)水平上计算代表烷基自由基与C 20相互作用的势能曲线。通过自然群体分析(NPA)方法在CAM-B3LYP/6-311G(d,p)水平上获得了C 20 –R的电子态。计算了模拟吸收光谱，并使用时间相关 DFT (TDDFT) 求解了 50 个电子态。所有 DFT 计算均使用 Gaussian 09 程序包进行。 24)
3. Results 3. 结果
3.1. Structures of C20–R
3.1. C 20 –R 的结构
The optimized structure of the C20 molecule is given in Fig. 1. D2h symmetry was assumed in the geometry optimization. The C–C bond lengths were 1.388, 1.412, 1.436, and 1.479 Å. The calculated structure of the C20–R system is given in Fig. 2. Here, electronic states and structures of C20–R are discussed using the results of CAM-B3LYP/6-311G(d,p) calculations. For n = 1, the methyl radical was added to the C20 fullerene with a bond distance of R1 = 1.514 Å. The planar structure of the free methyl radical was changed to the bent form; the H–C–H angles changed from 120.0 to 108.3° by the addition. The bond lengths for n = 2, 3, and 4 were R1 = 1.519, 1.518, and 1.518 Å, respectively. All alkyl radicals were found to bind to the on-top site of C20. The binding energies of R for n = 1, 2, 3, and 4 were calculated to be 86.6, 83.9, 84.3, and 84.1 kcal/mol, respectively, indicating that the binding energy is independent of the alkyl radical (n) size.
C 20分子的优化结构如图1所示。在几何优化中假设D 2 h对称。 C-C 键长分别为 1.388、1.412、1.436 和 1.479 Å。 C 20 –R系统的计算结构如图2所示。在此，使用 CAM-B3LYP/6-311G(d,p) 计算结果讨论了 C 20 –R 的电子态和结构。对于n = 1，甲基自由基被添加到C 20富勒烯上，键距为R 1 = 1.514 Å。自由基甲基的平面结构变为弯曲形式；通过添加，H-C-H 角从 120.0 变为 108.3°。 n = 2、3 和 4 时的键长分别为R 1 = 1.519、1.518 和 1.518 Å。发现所有烷基均结合至 C 20的顶部位点。 n = 1、2、3 和 4 时 R 的结合能经计算分别为 86.6、83.9、84.3 和 84.1 kcal/mol，表明结合能与烷基 ( n ) 大小无关。
Fig. 1. Optimized structure of C20 molecule obtained at the CAM-B3LYP/6-311G(d,p) level. Bond lengths and angles are given in Å and degrees, respectively.
图1.在CAM-B3LYP/6-311G(d,p)水平上获得的C 20分子的优化结构。键长和键角分别以 Å 和度数给出。
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Fig. 2. Optimized structure of the C20–R complexes at the CAM-B3LYP/6-311G(d,p) level. Bond lengths are in Å.
图2. CAM-B3LYP/6-311G(d,p)水平的C 20 –R复合物的优化结构。键长以 Å 为单位。
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The NPA charges on moieties of C20 and R were −0.1 and +0.1, respectively. These values indicate that the alkyl segment behaves slightly as an electron donor in C20–R. Similar results were obtained from the CAM-B3LYP/6-31G(d) calculations. These results are summarized in Table I.
C 20和R部分上的NPA电荷分别为-0.1和+0.1。这些值表明烷基链段在 C 20 –R 中略微充当电子供体。 CAM-B3LYP/6-31G(d) 计算也得到了类似的结果。这些结果总结于表一中。
Table I. Binding energies (kcal/mol) between the alkyl radicals and C20.
表I.烷基与C 20之间的结合能(kcal/mol)。
| n | 6-31G(d) | 6-311G(d,p) |
|---|---|---|
| 1 | 84.1 | 86.6 |
| 2 | 81.4 | 83.9 |
| 3 | 81.8 | 84.3 |
| 4 | 81.5 | 84.1 |
3.2. Potential energy curve
3.2.势能曲线
The potential energy curve (PEC) for the methyl radical (n = 1) approaching the C20 surface is plotted in Fig. 3 as a function of C0–C1 distance (R1). All geometrical parameters of the C20–R system except for R1 were optimized at each point of R1. The shape of the potential energy curve indicates that the methyl radical approaches and binds to the C20 surface without an activation barrier.
图3绘制了接近 C 20表面的甲基自由基 ( n = 1) 的势能曲线 (PEC)，作为 C 0 –C 1距离 ( R 1 ) 的函数。除R 1外，C 20 –R 系统的所有几何参数均在R 1的每个点进行了优化。势能曲线的形状表明甲基自由基在没有活化势垒的情况下接近并结合到C 20表面。
Fig. 3. Potential energy curve of the methyl radical (CH3) addition to C20.
图3.甲基自由基(CH 3 )加成至C 20的势能曲线。
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3.3. Spin density along the reaction coordinate
3.3.沿反应坐标的自旋密度
The spatial distributions of spin density are given in Fig. 4. The spin density is mainly localized at R1 = 2.50 Å for the alkyl radical and C20. The unpaired electron in the 2p orbital of the carbon atom of the alkyl radical was found to be R1 = 2.50 Å.
自旋密度的空间分布如图4所示。对于烷基和C 20来说，自旋密度主要集中在R 1 = 2.50 Å处。发现烷基碳原子2p轨道上的不成对电子为R 1 = 2.50 Å。
Fig. 4. Spin densities of the C20–CH3 system at R1 = 2.5 Å and the product state (PD).
图 4. R 1 = 2.5 Å 时 C 20 –CH 3体系的自旋密度和产物状态 (PD)。
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At the binding structure, i.e., the optimized structure of the C20–R (n = 4) system, the spin density was widely distributed around the C20 surface, and there was no spin density distribution on the alkyl group surface. This result indicates that the unpaired electron on the alkyl radical (spin density) is fully transferred to the C20 surface by the radical addition.
在结合结构，即C 20 –R（ n = 4）体系的优化结构中，自旋密度广泛分布在C 20表面周围，并且在烷基表面上没有自旋密度分布。该结果表明烷基上的不成对电子（自旋密度）通过自由基加成完全转移到C 20表面。
3.4. Hyperfine coupling constants of C20–R
3.4. C 20 –R 的超精细耦合常数
The hyperfine coupling constant (hfcc) of radical species provides important information on the electronic states and structure of the radical. In the present study, proton-hfccs of the free radical R (n = 4) and C20–R (n = 4) were calculated at the CAM-B3LYP/6-311G(d,p) level. The results are given in Table II. The hfccs of the α- and β-protons of the free radical (denoted by H1 and H2, respectively) were significantly larger than those of the others (−22.13 and 11.28 G). This result indicates that the unpaired electron was localized on the C1 and C2 carbon atoms of the free radical.
自由基物种的超精细耦合常数（hfcc）提供了有关自由基的电子态和结构的重要信息。在本研究中，自由基R ( n = 4) 和C 20 –R ( n = 4) 的质子-hfccs 是在CAM-B3LYP/6-311G(d,p) 水平上计算的。结果在表II中给出。自由基的α-和β-质子（分别用H 1和H 2表示）的hfcc 明显大于其他质子（-22.13 和11.28 G）。该结果表明不成对电子位于自由基的C 1和C 2碳原子上。
Table II. Calculated proton-hfccs of the alkyl radical R (n = 4) and alkyl radical moiety in C20–R (n = 4) (hfccs in G). The values are calculated at the CAM-B3LYP/6-311G(d,p) level.
表二.计算出烷基 R ( n = 4) 和 C 20 –R ( n = 4) 中的烷基部分的质子-hfcc（G 中的 hfcc）。这些值是在 CAM-B3LYP/6-311G(d,p) 级别计算的。
| R (n = 4) R ( n = 4) |
C20–R (n = 4) C 20 –R ( n = 4) |
|
|---|---|---|
| H1 | −22.13 | −0.09 |
| H2 | 11.28 | −0.02 |
| H3 | −1.41 | −0.01 |
| H4 | 0.16 | 0.00 |
The H1 and H2 values on C20–R (n = 4) significantly decreased to −0.09 and −0.02 G. This was caused by delocalization of unpaired electrons over the C20 surface. This feature was also found in spatial distribution of spin density (Fig. 3).
C 20 –R ( n = 4) 上的H 1和H 2值显着降低至 -0.09 和 -0.02 G。这是由 C 20表面上不成对电子的离域引起的。自旋密度的空间分布也发现了这一特征（图3 ）。
3.5. Absorption spectra of alkyl functionalized C20 fullerenes
3.5.烷基官能化的C 20富勒烯的吸收光谱
Simulated absorption spectra of C20 and C20–R are given in Fig. 5. The C20 molecule showed three peaks and one shoulder: the absorption maxima were peaked at 226, 322, and 430 nm, and the shoulder was located at 255 nm.
C 20和C 20 -R的模拟吸收光谱如图5所示。 C 20分子显示出三峰一肩：最大吸收峰位于226、322和430 nm处，肩部位于255 nm处。
Fig. 5. Simulated absorption spectra of the C20 and C20–R complexes.
图 5. C 20和 C 20 –R 配合物的模拟吸收光谱。
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After alkyl radical addition, the absorption spectrum of C20 drastically changed because of the interaction with alkyl radicals. The C20–R complexes exhibited only one peak (approximately 300 nm). In addition, the C20–R peak has a long tail in the near-IR region. The long tail is mainly composed of two weak peaks at 470 and 510 nm and several extremely weak peaks around 600–700 nm. This indicates that some small peaks exist at the near-IR region. The peak was hardly independent on the chain length of alkyl radical, although the position of the peak was slightly red-shifted as a function of chain length. The slight red-shifts at 290 nm were caused by the difference in the electro-negativities of the alkyl groups.
添加烷基后，由于与烷基的相互作用，C 20的吸收光谱发生了巨大的变化。 C 20 –R 配合物仅显示一个峰（约300 nm）。此外，C 20 –R 峰在近红外区域有长尾。长尾主要由470和510 nm处的两个弱峰和600-700 nm附近的几个极弱峰组成。这表明在近红外区域存在一些小峰。该峰几乎不依赖于烷基的链长，尽管峰的位置作为链长的函数稍微红移。 290 nm 处的轻微红移是由烷基的电负性差异引起的。
To elucidate the origin of the long tail of the C20–R absorption spectrum, the peaks appeared at 470 and 510 nm were assigned using TDDFT calculation. Figure 6 shows a schematic illustration of the molecular orbitals and energy levels of the highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO), singly occupied molecular orbital (SOMO), and HOMO − 1. The peaks at 470 and 510 nm are the electronic excitations from HOMO − 1 to LUMO and from HOMO − 1 to SOMO, respectively. The spatial distributions of these orbitals were localized on the C20 moiety of C20–R, indicating that the excitations are not a results of charge transfer between the C20 and the alkyl group. In addition, these features indicate that the long tail is local excitation band resulting from the perturbation of the C20 radical by the alkyl group.
为了阐明C 20 –R 吸收光谱长尾的起源，使用TDDFT 计算指定出现在470 和510 nm 处的峰。图6显示了最高占据分子轨道 (HOMO)、最低未占据分子轨道 (LUMO)、单占据分子轨道 (SOMO) 和 HOMO − 1 的分子轨道和能级的示意图。峰值位于 470 和 510 nm 分别是从 HOMO - 1 到 LUMO 和从 HOMO - 1 到 SOMO 的电子激发。这些轨道的空间分布位于C 20 –R 的C 20部分，表明激发不是C 20和烷基之间电荷转移的结果。此外，这些特征表明长尾是由烷基对C 20自由基的扰动产生的局部激发带。
Fig. 6. Schematic illustration of the HOMO, LUMO, SOMO, and HOMO − 1 molecular orbitals and energy levels of C20–R (n = 4). Numbers refer to the C20–R orbital number.
图 6. C 20 –R ( n = 4) 的 HOMO、LUMO、SOMO 和 HOMO − 1 分子轨道和能级示意图。数字指的是 C 20 –R 轨道数。
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4. Discussion 4. 讨论
In our previous paper, we investigated methyl-radical-added C60 fullerene at the same theory level.25) The C60–CH3 binding energy was calculated to be 35.1 kcal/mol. This value is 51.5 kcal/mol less than that of C20–CH3. In addition, we found that on activation barrier exists in the addition of CH3 to C60 owing to the change in hybridization of the carbon atom at the binding site, sp2 → sp3.
在我们之前的论文中，我们在相同的理论水平上研究了甲基自由基添加的 C 60富勒烯。 25 C 60 –CH 3结合能为35.1 kcal/mol。该值比C 20 –CH 3低51.5kcal/mol。此外，我们发现由于结合位点sp 2 → sp 3碳原子杂化的变化，CH 3加成到C 60中存在活化势垒。
The orbital of the carbon atom at the binding site (C0) of C20 was close to sp3. Therefore, there is no change in hybridization before and after methyl radical addition. This is the origin of no barrier in the C20–CH3 system. The present study clearly indicates that the lowest electronic states of C20 fullerene are significantly different from those of typical C60 fullerene.
C 20的结合位点(C 0 )处的碳原子轨道接近sp 3 。因此，甲基自由基添加前后杂交没有变化。这就是C 20 –CH 3体系中无势垒的由来。本研究清楚地表明C 20富勒烯的最低电子态与典型C 60富勒烯的最低电子态显着不同。
5. Conclusion 5. 结论
In the present study, the interaction between C20 fullerene and alkyl radicals was investigated based on DFT calculations. The methyl, ethyl, propyl, and butyl radicals (denoted by n = 1–4, where n refer to the number of carbon atoms in the alkyl radical) were applied as alkyl radicals. The DFT calculation revealed that the alkyl radical strongly binds to the carbon atom of C20 in the on-top site. The binding energies between the alkyl radicals and C20 were calculated as 83.9–86.6 kcal/mol at the CAM-B3LYP/6-311G(d,p) level. The absorption spectrum of C20 was red-shifted by the alkyl radical. Furthermore, C20–R has a long tail absorption band at the near-IR region.
在本研究中，基于DFT计算研究了C 20富勒烯和烷基自由基之间的相互作用。甲基、乙基、丙基和丁基（用n = 1-4 表示，其中n指烷基中的碳原子数）用作烷基。 DFT计算表明烷基与顶部位点的C 20碳原子牢固结合。在 CAM-B3LYP/6-311G(d,p) 水平上，烷基自由基和 C 20之间的结合能为 83.9–86.6 kcal/mol。 C 20的吸收光谱因烷基而红移。此外，C 20 –R 在近红外区域具有长尾吸收带。
Acknowledgments 致谢
The author acknowledges partial support from JSPS KAKENHI Grant Number JSPS 15K05371 and MEXT KAKENHI Grant Number 25108004.
作者感谢 JSPS KAKENHI 拨款号 JSPS 15K05371 和 MEXT KAKENHI 拨款号 25108004 的部分支持。