Theoretical Investigation of the Key Roles in Fullerene-Formation Mechanisms: Enantiomer and Enthalpy

Abstract

Fullerenes are important zero-dimensional materials in photoelectric, antioxidant, pharmaceutical, and single-molecular-magnet fields, but the fullereneformation mechanism has been elusive since the discovery of #1812 C 60 _I h in 1985 because of the missing key links and low yield. Therefore, experimental and theoretical research is required to explore some fundamental questions of the fullerene-formation mechanism. Considering the temperature, here we carried out two fullerene-formation models, bottom-up and top-down, for C 2n (50 ≤ 2n ≤ 70) containing optical enantiomers, heptagons, and tetragons via density functional and transition-state theories. The thermodynamically and kinetically preferred pathway for C 2n (50 ≤ 2n ≤ 70) was the bottom-up model instead of the top-down model. Furthermore, this is the first time revealing that the enantiomer and enthalpy play key roles in forming fullerenes C 2n (50 ≤ 2n ≤ 70). Especially, the effect of the enantiomer on the fullerene-formation mechanism had been neglected in previous research. KEYWORDS: density functional theory, thermodynamic and kinetic fullerene-formation mechanisms, competitive relationship between the top-down and bottom-up models, key roles in the top-down model, enantiomer and enthalpy

Multiscale modeling strategy to solve fullerene formation mystery

“…According to DFT calculations, SW reactions of bond rearrangements in even fullerenes have a huge activation barrier: 4.7eV [44 ' 45] , 5.7eV [55] for the transition from C 60 -C 2v to the C 60 -ifc fullerene, 6.2eV [44] , 7.0-7.3 eV [65] and 7.0-7.3 eV [66] for the back transition from C 60 -I h to the C 60 -C 2v fullerene, 6.07eV [51] for the transition between two isomers of the C 66 fullerene, 6.0eV [47>51] for the transition from C 70 -C s to the C 70 -D 5h fullerene, 7.5eV [56] for the transition from C 70 with one heptagon in the sp 2 structure to the C 70 -D 5h fullerene. This makes these reactions unlikely under conditions of selection of abundant fullerene isomers (see, for example, calculations of the rate constant of the SW reaction [47] ). Note that no reactions of bond rearrangements were observed during 0.5-1 us at temperature 2500 K in classical MD simulations for eight different even fullerenes even when they had heptagons in the sp 2 structure or a one-coordinated atom attached.…”

“…First, a C 2 molecule attaches to the sp 2 structure without an activation barrier and then the attached molecule gets inserted into the sp 2 structure with an activation barrier. [47] The values of this barrier for different fullerenes range from 0.5 to 5eV according to DFT calculations. showed that all emission events occur at the defects of the sp 2 structure.…”

“…The rate constants for reactions of C 2 molecule insertion into the sp 2 structure of about ten fullerene isomers have been evaluated recently through DFT calculations of the activation barriers. [47] None of the described methods of atomistic modeling is capable of dealing simultaneously with all four difficulties related to the inherent features of the process of abundant fullerene selection listed in the beginning of the section within a limited computing time.…”

“…[72] The reaction probabilities as functions of temperature can be estimated using the activation barriers obtained in the framework of the transition state theory. [47] The fourth research line within the discussed strategy is application of kinetic models to study of selection of abundant fullerene isomers. We believe that sets of isomer pairs related by bond-rearrangement reactions for the same fullerene (such as SW reactions, changes of the sp 2 structure promoted by an sp atom, and annihilation of pairs of sp atoms) as well as isomer pairs related by insertion and emission of carbon atoms and C 2 molecules for different fullerenes can be obtained by numerical methods using graph theoretical techniques.…”

Molecular Dynamics Study of sp-Defect Migration in Odd Fullerene: Possible Role in Synthesis of Abundant Isomers of Fullerenes

“…The reactions observed here are divided into three types based on their relation to the annealing of sp 2 defects (such as annealing of 7-rings or separation of 5-rings). The reactions of type I are those that change the number of atoms in the rings of the sp 2 structure and can lead to annealing or formation of sp 2 defects (such as the SW reaction facilitated by the nearby sp atom ,,, ). An example of such a reaction is shown in Figure a.…”