# Theoretical Studies of the Stone-Wales Defect in C36 Fullerene Embedded inside Zigzag Carbon Nanotube

Authors: Konstantin S. Grishakov; Konstantin P. Katin; Mikhail M. Maslov
Journal: Advances in Physical Chemistry
 (2016)

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## Abstract

We apply density functional theory at PBE/6-311G(d) level as well as nonorthogonal tight-binding model to study the Stone-Wales transformation in C36 fullerene embedded inside the (14,0) zigzag carbon nanotube. We optimize geometries of two different isomers with the D2d and the D6h symmetries and the transition state dividing them. The mechanism of Stone-Wales transformation from D2d to D6h symmetry for the encapsulated C36 is calculated to be the same as for the isolated one. It is found that the outer carbon wall significantly stabilizes the D6h isomer. However, carbon nanotube reduces the activation barrier of Stone-Wales rearrangement by 0.4 eV compared with the corresponding value for the isolated C36.


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## Body

## 1. Introduction

Carbon peapods are the host-guest compounds (endohedral complexes) that consist of fullerenes encapsulated inside the single-walled carbon nanotubes. Original peapods containing only C60 fullerenes were synthesized in 1998 through the catalytic pulsed laser vaporization of graphite [1]. At present peapods are of special interest as they are forming the basis for future nanoelectronic devices, since the fullerenes encapsulated have strong effect on the electronic properties of the outer nanotube [2]. Raman spectroscopy and electronic transport measurements on individual peapod confirm this significant doping impact produced by the encapsulated C60s [3]. In addition,ab initio calculations clearly predict the dependence of charge transfer in the carbon peapod on the mutual orientation of the fullerenes [4] and their distribution [5].The Stone-Wales (SW) defects [6] in the cages of encapsulated fullerenes are the subject of special interest, because they can lead to the significant changes in the electronic structure of peapod [3]. The SW defects occur during the peapods synthesis or as a result of their thermal and ultraviolet treatment [7]. This type of defects can be regarded as a rotation of single C–C bond around its center through an angle of 90° [6]. It should be noted that SW defects are characterized by the lowest activation energy barrier compared with the other possible atomic rearrangements, but they considerably influence on the physicochemical characteristics of fullerenes and othersp2-hybridized carbon systems [8–12]. Furthermore, they play a crucial role in the processes of fullerenes isomerization [13] and coalescence [7]. For example, it is possible to transform peapod to the double-walled carbon nanotube by means of the partial or complete coalescence of the encapsulated fullerenes into the nanotube with smaller diameter under the high temperatures (~3600°C) through the SW mechanism [14, 15]. Recent experiments confirmed that such transformation resulted in the drastic reduction of the conductivity of the whole system [3]. Thus, the introduction of isolated SW defect as well as the initiation of series of SW mechanisms can be regarded as an effective method for the tuning of peapod electronic characteristics.Here we present a theoretical study of the SW defect formation in the C36 fullerene cage embedded inside the zigzag carbon nanotube. It should be noted that C36 possesses a number of distinctive features compared with C60. It has more strained cage and higher reactivity [16]. In addition, its smaller effective diameter allows one to introduce it inside the thinner carbon nanotubes for peapod formation. The SW activation energy barrier in the isolated C36 is equal to 6.23 eV [17], which is lower than the corresponding value 7.16 eV for C60 [18]. Therefore, the C36 isomerization process can be initiated more easily. Various C36 isomers possess different physicochemical properties; for example, they may vary in electronic characteristics (their HOMO-LUMO gaps lie in the range of 0.20–0.83 eV [19]) and in thermodynamic stability. One of the most stable isomers of C36 has D6h symmetry; thus, this fullerene is stretched along its symmetry axis. Therefore, it can be expected that the encapsulated D6h-C36s are arranged inside the carbon nanotube so that their symmetry axes are parallel to the main axis of the nanotube. Thus, the inner side of the carbon nanotube wall is able to stabilize the D6h-C36 fullerene and to prevent its isomerization. Charge transfer between the tube and the fullerene can also effect on the SW defect formation in C36. Note that for the neutral and positively charged C36 the most energetically favorable isomer has D2d symmetry, whereas for the negatively charged C36 the D6h isomer is more thermodynamically stable [17]. On the other hand, it was demonstrated that both positive and negative charges changed weakly the SW activation barrier of isolated C36 [17]. So, the main purpose of this work is to study the influence of the host zigzag carbon nanotube on the formation of SW defect in the encapsulated C36 guest fullerene.


## 2. Materials and Methods

In our study we consider C36 fullerenes with the D2d and the D6h symmetries both isolated and encapsulated inside the center of the (14,0) zigzag carbon nanotube. Previousab initio calculations confirmed that such type of nanotubes with the encapsulated C36s demonstrated the highest binding energy among all zigzag [20] and armchair [21] tubes. In our simulations carbon nanotube is constructed from 224 carbon atoms. To avoid the dangling bonds hydrogen passivation of the tube edges is performed. So, carbon nanotube considered is 11 Å in diameter with the length of 16 Å. Note that the same representation was used in [20]. Finally, our atomistic model of peapod has the chemical view C36@C224H28 as it is shown in Figure 1.Figure 1
Atomistic model of carbon peapod C36@C224H28: side view (a) and front view (b).
(a) (b)The geometries of minima and transition states of C36 and C36@C224H28 molecular systems are obtained within the nonorthogonal tight-binding model (NTBM) [22]. Previously, we successfully used this model to simulate the C60s coalescence in peapods [3], to determine the SW mechanism in isolated C36 [23, 24] and other fullerenes [23–25], and so forth. Initial molecular structures are relaxed without any symmetry constrains until the residual forces acting on atoms are less than 10−3eV/Å. For each configuration obtained the Hessian matrix and normal frequencies are also calculated in the framework of NTBM model to confirm the energy minima (imaginary frequencies are absent) or transition state (the frequency spectrum has only one imaginary frequency). Next, using the geometries found at NTBM level the total energies of various C36 configurations (both minima and transition state) are computed by means of the density functional theory (DFT) approach via the single-point energy calculation procedure. All the quantum-chemical DFT calculations are performed in the frame of GAMESS software package [26]. The hybrid Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional [27] is used along with the 6-311G(d) basis set [28]. It was shown that this basis set was good enough to provide an adequate description of SW defect formation in isolated C36 [17]. Finally, the peapod total energy is calculated according to the following formula [29]:(1)EC36@C224H28=ENTBMC36@C224H28-ENTBMC36+EDFTC36,where ENTBMC36@C224H28, ENTBMC36, and EDFTC36 are the total energies of the peapod sample and encapsulated C36 obtained at the corresponding level of theory (NTBM or DFT, resp.). Grimme empirical dispersion corrections [30] are taken into account for all energies. GAMESS program package is used for their calculation. Note that formula (1) is applicable both to reactant/product configurations and to transition state.


## 3. Results and Discussion

First of all, we optimize the geometries of isolated C36 isomers with the D2d and the D6h symmetries and the transition state (TS) dividing them (see Figure 2). The choice of these isomers is caused by their high thermodynamic stability [16] and by their interconversion from one to another through the SW mechanism [17]. We obtain that the length of “rotated” C–C bond (see Figure 2) is equal to 1.455, 1.296, and 1.459 Å for D2d-C36, TS-C36, and D6h-C36 atomic configurations, respectively. These data coincide well with the corresponding values of 1.443, 1.292, and 1.445 Å, calculated in [17] at DFT/B3LYP/6-311G(d) level of theory. Moreover, NTBM model predicts that the energy difference between the D6h-C36 and D2d-C36 neutral isomers is equal to 0.14 eV [23]. This result is in good agreement with the value of 0.11 eV also reported in [17]. Note that the simplified single-point energy calculations also give the small absolute value of energy difference of 0.07 eV, which indicates that D6h-C36 and D2d-C36 states lie very close in energy. Thus, the activation energy barrier obtained for the D2d-C36→D6h-C36 SW transformation of 6.7 eV agrees with the more accurate value of 6.3 eV [17]. So, NTBM model provides adequate geometries of the C36 local minima and transition state.Figure 2
Potential energies ΔE of endohedral complex C36@C224H28 (solid line) and isolated C36 fullerene (dashed line) during the SW transformation D2d-C36→D6h-C36. The insets show the C36 isomers with the D2d and the D6h symmetries and the transition state (TS). Rotation of C–C bond during the SW transformation is indicated in black. The atoms of carbon nanotube are not displayed for clarity.We also calculate the energy and structure of the analogousD6h-C36 and D2d-C36 isomers as well as TS-C36 embedded inside the C224H28 sample nanotube. It is confirmed that there are no intermediate states along the isomerization reaction path as it was earlier established for the isolated neutral and charged C36s [17]. Nevertheless, negligible changes in bond lengths of the encapsulated C36 are identified compared with the isolated one. The “rotated” C–C bond length decreases by only 0.003, 0.001, and 0.002 Å for the D2d-C36, TS-C36, and D6h-C36 atomic configurations, respectively. This slight reduction in bond lengths confirms that the (14,0) carbon nanotube possesses too large diameter for significant compression of the C36 cage. On the other hand, we obtain the carbon nanotube effects on the comparative thermodynamic stability of two C36 isomers considered. For the encapsulated C36 atomic configuration, axially stretched D6h isomer lies lower in energy than the more spherical D2d one by 0.57 eV. Thus, the embedded D6h-C36 is more thermodynamically stable than the D2d-C36.The activation energy barrier for theD2d-C36→D6h-C36 SW transformation inside the carbon nanotube is found to be 6.3 eV. This value is less than the activation energy barrier for the corresponding isomerization reaction for the isolated C36 by ΔE = 0.4 eV. For estimation of the sensitivity of ΔE to the DFT functional used, we recalculate the values of transition barriers for the D2d-C36→D6h-C36 SW transformation (for isolated C36 and embedded one) in the frame of wB97X-D functional, which contains Grimme empirical dispersion corrections by default [31, 32]. The same corrections are applied to NTBM energies as well. As a result, we obtain that the energy barrier for SW transformation in isolated fullerene is equal to 7.8 eV, and the analogous barrier for the encapsulated C36 is equal to 7.5 eV. Although these values are higher than the corresponding ones obtained within the PBE functional, one can see that ΔE depends weakly on the functional choice.The results obtained demonstrate that the activation of SW mechanism in the encapsulated C36 becomes ~exp(ΔE/kBT) times faster compared with the isolated fullerene (here T is the temperature and kB is the Boltzmann constant). For example, the factor exp(ΔE/kBT) is equal to 3.6 at T = 3600 K (this value is typical for the fullerenes coalescence [14]) and achieves ~5·106 at room temperature (300 K).


## 4. Conclusions

In this paper we presented the study of SW defect formation in C36 fullerene placed inside the (14,0) zigzag carbon nanotube. We obtain that the isomerization reaction passes through the in-plane C–C bond rotation without any intermediate steps. The presence of carbon nanotube leads to the negligible changes in the geometry of reactants, products, and transition state. It is found that the most thermodynamically stable C36 isomer in the case of host-guest compound has D6h symmetry whereas the most thermodynamically stable unrelated C36 isomer possesses D2d symmetry. The activation energy barrier for the D2d-C36→D6h-C36 SW transformation inside the nanotube is less than the corresponding value for the isolated C36 isomerization reaction by 0.4 eV. However, the carbon nanotube significantly stabilizes the D6h-C36 isomer. We believe that the data reported in this article will be useful for the further theoretical and experimental studies on the C36s isomerization or their coalescence inside the carbon peapods.



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*Source: 1862959-2016-11-01.xml*