Combined Topological and Kinetic Approach to Modeling Fullerene Formation

A combined topological and kinetic approach to modeling abundant fullerene isomer formation is proposed. This approach considers a fullerene isomer formation event as a time trajectory of topological changes in the fullerene structure, represented as a sequence of bond rearrangement reactions (or transitions between fullerene isomers). Each reaction in the sequence is chosen on the basis of its calculated reaction rate from the complete list of all possible reactions for the current isomer and the reaction types corresponding to the atomistic formation mechanism under consideration. A detailed description of the proposed approach is provided, including the program structure and workflow. The result of the performed calculation is the yield of an abundant isomer for the considered atomistic mechanism as a function of synthesis conditions (for example, temperature and carbon vapor pressure). Algorithms for generating a complete list of reactions for a given isomer are developed based on topological description in the dual space for a set of possible reaction types, and methods for calculating the corresponding reaction rates are described. The sensitivity of the modeling results to the accuracy of the description of reaction rates is tested using the example of sp-atom migration in C₅₈-C_2v fullerene, which is a precursor for the most abundant C₆₀-I_h fullerene isomer. Possible applications of the proposed approach and auxiliary tasks required for its development are discussed.