Fullerene Genetic Code: Inheritable Stability and Regioselective C2

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Fullerene Genetic Code: Inheritable Stability and Regioselective C2 Assembly Jing-Shuang Dang, Wei-Wei Wang, Jia-Jia Zheng, Xiang Zhao, Eiji Osawa, and Shigeru Nagase J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp302881u • Publication Date (Web): 28 Jun 2012 Downloaded from http://pubs.acs.org on July 19, 2012

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The Journal of Physical Chemistry

Fullerene Genetic Code: Inheritable Stability and Regioselective C2 Assembly Jing-Shuang Dang,† Wei-Wei Wang,† Jia-Jia Zheng,† Xiang Zhao,*† Eiji Ōsawa,‡ and Shigeru Nagase # † Institute for Chemical Physics & Department of Chemistry, State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, Xi’an 710049, China ‡ NanoCarbon Research Institute, AREC, Shinshu University, Ueda, Nagano 386-8567, Japan

# Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan E-mail: [email protected] Received March 26, 2012, revised June 21, 2012

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ABSTRACT A bottom-up topological pathway was established to elucidate the growth of small fullerenes and the generation of Ih-symmetric C60. In contrast to countless growth mechanisms, the model described herein has two distinctive features. First, each fullerene on the route possesses the lowest potential energy or exhibits a predominant molar fraction at elevated temperatures in the corresponding series. Second, a C2 insertion without any high-barrier rearrangement process (such as Stone–Wales transformation) can connect two adjacent molecules on the route directly. These two characteristics imply that the fullerene stability can be inherited through continuous insertion of a C2 cluster during carbon-cage enlargement. Various adducts can be generated from different active sites on the parent fullerene surface. Therefore, an investigation of the regioselectivity of C2 addition using density functional theory is reported herein for the first time. A systematic simulation demonstrates that the reaction to the most stable product exhibits the highest chemical reactivity, indicating that the proposed growth route is favorable both thermodynamically and kinetically.

KEYWORDS density functional calculations, fullerene, formation mechanism, thermodynamics, kinetics


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Introduction Ever since the discovery and macroscopic scale synthesis of Ih-symmetric buckminsterfullerene C60,1, 2 several hypothetical models have been established to elucidate the formation process of fullerenes from graphite or amorphous carbon. Based on mass spectrometry information elicited from previous experiments, fullerenes are believed to derive from atomic carbon or small clusters. Such a growth model is defined as a bottom-up mechanism. A heptagon-corporation chlorinated C68 species was captured and isolated recently from carbon arc plasma in situ,3 which provides important evidence for the rationality of the formation modeling. During the past two decades, many distinct bottom-up models, such as the fullerene road, 4 the pentagon road,5, 6 ring-stacking,7 the cycloaddition mechanism,8 and the shrinking hot giant (SHG) road ,9 have been proposed to describe the formation of the closed, highly symmetric buckminsterfullerene C60. Among those theoretical predictions, the size-up fullerene road and the size-down shrinking hot giant road are two widely accepted mechanisms because of support from experimental findings.10,

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Recently, quantum chemical molecular dynamics (QM/MD) simulations

suggest that the carbon cage size can both increase and decrease at elevated temperatures,12 meaning that different, even conflicting, formation mechanisms might coexist under similar experimental conditions. In comparison with the SHG road, the fullerene road exhibits greater performance to explain the formation of fullerenes smaller than C60, but its salient disadvantage is that a series of intermediates is too unstable to be identified. Therefore, uncovering each adduct is the most important step to clarifying the growth of small fullerenes and the high yield of C60. In the fullerene road, each closed carbon cage (Cn) is the product of a smaller fullerene (Cn-2) as well as the reagent of a larger one (Cn+2). The fullerenes in the growth pathway are connected by specific chemical reactions including the increase in quantities of atoms and the rearrangement between species. Theoretically, the enlargement of carbon cages can be accomplished using the adsorption and assemblage between fullerenes and atomic carbon groups such as C1, C2, and C3.13 In addition, the C2 cluster has been confirmed to play the most important role in fullerene growth because of support from both experimental and theoretical information.7, 10, 14 However, without altering the quantity of atoms, ACS Paragon Plus Environment

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Stone–Wales (SW) rearrangement is another popular measure to link two species. In 1986, Stone and Wales proposed that by rotating a 6-6 bond by 90°, isomers can be transformed reciprocally.15 Since then, SW reconstruction has been widely accepted as explaining the isomerization of fullerenes, carbon nanotubes, graphenes, and other sp2 carbon nanostructures.16–18 However, the transformation has a high energy barrier of about 7.0 eV, which makes it difficult to test experimentally. 19 To clarify the growth process from a small cage to C60 and to ascertain all feasible intermediates along the path, the first and the fundamental question is: Is the growth random or directional? That is to say, is there an optimal growth pathway that is more consummate compared with that of any other model? Although the fullerene road has been proposed for years, no previous investigation has revealed an optimal route that can explain the growth of small fullerenes and C60 formation. The reason probably lies in the fact that the fullerene road is fundamentally a cage-to-cage process. For that reason, the addition or reconstruction reaction on any site of an isomer will create an entirely new growth route, thereby rendering it difficult to infer an ideal channel among those countless paths. Regarding the perspectives of thermodynamic and kinetic controls for fullerenes generation, the optimal growth pathway should fulfill the following requirements: (1) No SW rearrangement participates. Because of the high activation barrier of SW reconstruction,19, 20 any route to yield the target product via Stone–Wales transformation seems unreasonable. As for an optimal growth pathway, we consider that only a simple and direct C2 addition reaction is allowed. (2) Regarded thermodynamically, each fullerene on the route is expected to possess high relative stabilities of corresponding series to warrant the continuity of the growth. As a result, for random 'n', a stable Cn can change directly into a stable Cn+2 by one step of C2 addition without any isomerization process. The fullerene stability inherited through successive addition reactions might be valuable for elucidating the self-assembly process from carbon vapor into closed cage-like molecules. (3) Because each fullerene Cn has plenty of potential addition sites on the carbon cage surface, even if a stable Cn+2 can be produced by a certain site, it does not mean that the corresponding reaction barrier is the lowest among all possible reactions. We must confirm whether the


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reaction toward the most stable product is the process with the lowest activation energy to demonstrate the unity of thermodynamic and kinetic selectivity. Using density functional theory (DFT) calculations to find an optimal pathway for fullerene growth, the inheritance of fullerene stabilities and the regioselectivity of C2 insertion reaction on both thermodynamic and kinetic arguments will be examined for the first time ever reported. The discovery of this novel growth pathway through experimentation is expected to provide strong theoretical support for the preparation of undiscovered small fullerenes. Computational Methods

All calculations were performed using the Gaussian03 program package.21 Full geometry optimizations from C24 to C60 were carried out by using Becke’s three-parameter exchange functional with the correlation functional of Lee, Yang, and Parr22 (B3LYP) and the standard 6-31G(d)23 basis set. In this report, Cn_Xy_Z respectively denote fullerenes, where n signifies the number of carbon atoms and Xy represents the point group symmetry. Z is a unique label for each species according to the spiral codes.24 The symmetries, number of pentagon pairs, relative energies and HOMO–LUMO gaps for lowlying isomers of C24–C60 are given in the supporting information (Table S1). In addition, while studying the reaction mechanism of C2 insertion, the reactants, products, intermediates and transition states are optimized at the B3LYP/6-31G(d) level of theory. Vibrational frequency analysis is conducted at the same level to verify the stationary point to be a minimum or saddle point. For each reaction, intrinsic reaction coordinates (IRC) are ascertained to confirm the correctness of the pathway on the potential energy surface (PES). Results and Discussion Although plenty of predictions on the C2 insertion process have been proposed in theory,25–28 the model presented in Scheme 1(A), which was advanced by Endo and Kroto in 1992,26 is regarded as the most reasonable one for the weight of experimental evidence.10,


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mechanism, the growth process is the transformation from one hexagonal ring into two fused pentagonal rings (a pentalene unit) by digesting a dimeric carbon cluster. The limitation of this model lies in the inevitable pentagon pair of product, which violates the well-recognized isolated pentagon rule (IPR).29 However, classical fullerenes below C60 are well known to comprise fused pentagons ineluctably, which means that any small fullerene formed by less than 60 atoms can be obtained by C2 insertion according to model (A). Therefore, this study examines the growth of small fullerenes following this addition model. To explain the yield of fullerenes of other types, such as IPR isomers or non-classical structures including tetragonal or heptagonal rings, the addition mode must be generalized. Scheme 1 shows that the reactant of model (B) contains a heptagon. After assembling a C2 unit, the heptagon will transform into a pentagon–hexagon pair without production of extra fused pentagons. This is the only way to generate an IPR fullerene by inserting a carbon dimer directly. For example, the only parent of C60_Ih has been proved as a stable non-classical fullerene with one heptagonal ring (C58_Cs_7mr).30–33 Furthermore, to interpret the formation of heptagon, which is served as the addition site of model (B), reaction (C) can be treated as the prelude to reaction (B). For instance, it is expected that there is a C56 isomer with fragment 5-6-6, as exhibited in Scheme 1(C), which can be transformed into C58_Cs_7mr. Consequently, the growth process from classical C56 to non-classical C58, and finally to IPR C60 has been accomplished. Additionally, model (D) is used to describe the tetragonal ring formation. Once the addition site is located at the meta-position of a hexagon, the product is not a pentagon pair but a square–hexagon adjacency. This addition mode is widely accepted as the way to use C60_Ih to generate the C62 with a four-membered ring, which is the one and only non-classical fullerene with squares verified experimentally.34, 35 Scheme 1 Overall, based on those models discussed above, any fullerene, no matter what type it is (classical or non classical, IPR or non-IPR), can be obtained through C2 addition without any configuration reconstruction. In the following, our aim is to ascertain a more specialized growth route that includes stable fullerenes only, thereby proving that the fullerene stability can be inherited by an insertion ACS Paragon Plus Environment

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reaction. Fortunately, based on the DFT optimization results of small fullerenes in Table S1, an amazing growth pathway is discovered by analyzing the topological relations between the low-lying isomers of every series. As shown in Scheme 2, from C24 to C60, each of two adjacent molecules is connected by one step of C2 addition (the added C2 dimer is denoted in red) and therefore the Stone-Wales rearrangement reaction can be avoided in this growth channel. All points on the route are lowest in potential energy except four molecules (C48_C2_199, C50_C2_263, C56_C2_843 and C58_Cs_7mr). Furthermore, although C50_C2_263 and C58_Cs_7mr are not the lowest energy isomer in a respective series, they predominate in molar fractions of the respective series over a large range at high temperatures (>1000 K), which can demonstrate their high thermodynamic stabilities.36–37 Fullerene formation is well known to occur at high temperatures. Therefore, those two isomers are actually suitable parent molecules of C2 insertion reaction toward C60. Additionally, although C48 and C56 are not lowest in energy, they are both one of the four isomers with the smallest number of pentagon pairs in respective series, within an energy gap of 4.0 kcal mol-1 with the ground state on potential energy surface, which can illuminate the high relative stabilities of the two isomers. Moreover, topologically, C48_C2_199 serves as the one and only structure that connects with C46_C2_109 and C50_C2_263. In a similar case, C56 is the unique addition parent for C58_Cs_7mr. Accordingly, those fullerenes are unique and irreplaceable for the growth route. Scheme 2 This report is the first to describe the optimal growth pathway that connects the most stable, or an extremely stable isomer of each series. This growth route is sequential, exclusive, and thermodynamically favorable. Hereinafter, each structure of the route is indicated as Cn*. However, from the kinetic point of view, the chemical reactivity of the route is still uncertain. In order to demonstrate the rationality of the proposed growth mechanism, we must prove that the addition reaction toward the most stable product holds the lowest energy barrier. In other words, the consistency between kinetic and thermodynamic controls of this route should be taken into account. Selectivity also must be treated


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because it is believed to be the only suitable route from C56 to C58 and then to C60. Consequently, only enlargement from C24 to C56 based on model (A) is discussed in this article. Among various addition fragments in one reactant, which site gives the most stable product? The number of pentagon pairs (N55) is known to be the most important factor influencing the stability of small fullerenes.29 Therefore, we sort the insertion reaction into different patterns according to the change in N55 after addition. Figure 1 shows that one step of C2 insertion will cause one more pentagon adjacency added to the structure, but the two pentagons bonding with the hexagon will change into two hexagons. Therefore, the total change of N55 correlates with the yellow areas (a, b, c, and d) in Figure 1. Assuming that the area x (a, b, c, or d) represents the pentagon, one 5-5 bond will be lost and one 5-6 bond will be added to the structure after the C2 insertion. In contrast, although the area x is hexagonal, there will be one 5-6 bond lost and one 6-6 bond added, which will engender no change to N55 in the yellow areas. Here, Px=1 (x=a, b, c, d) shows that area x is pentagonal, and Px=0 shows that area x is hexagonal. The change of N55 (∆N55) for the structure is expressed as ∆N55 = N55(product) - N55(reactant) = 1 (Pa+ Pb+ Pc+ Pd) = 1 -∑Px. Figure 1 Consequently, based on the quantity and location of pentagons on the four areas of a, b, c, and d, seven diverse addition patterns are shown in Figure 2, which correspond to the range of ∆N55 from -3 to 1. Thermodynamically, the C2 insertion more tends to locate on pattern (1), which will reduce N55 by three. According to the seven addition types, we make a refinement of the optimal growth pathway that we discovered. As exhibited in Scheme 3, C24* is set as the start point, and the each reaction of fragment type is labeled concretely. The optimal route composed by Cn* is emphasized in bold, whereas all the other possible products (Cn+2) of the C2 addition on each Cn* are listed next to Cn+2*. It is noteworthy that, among those products, Cn+2* is gained from addition on site that causes N55 to decrease by maximum degree, which indicates that the number of adjacent pentagons is used as a reasonable representation for the stabilities of products. Figure 2 ACS Paragon Plus Environment

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Scheme 3 We sorted the C2 insertion reaction into different types according to their ∆N55 values. Next, the kinetic process of each reaction will be described in detail. All intermediates and transition states are optimized to calculate the activation energy of each reaction. To compare the reactivity of various addition patterns, we sought to find one fullerene cage that contains all seven segments. However, according to our observation on all classic fullerenes Cn (n

Fullerene Genetic Code: Inheritable Stability and Regioselective C2

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