Reactivity, stability, and formation of fullerenes

Finding Reaction Pathways with Optimal Atomic Index Mappings

Finding complex reaction and transformation pathways involving many intermediate states is, in general, not possible on the density-functional theory level with existing simulation methods, due to the very large number of required energy and force evaluations. For complex reactions, it is not possible to determine which atom in the reactant is mapped onto which atom in the product. Trying out all possible atomic index mappings is not feasible because of the factorial increase in the number of possible mappings. We use a penalty function that is invariant under index permutations to bias the potential energy surface in such a way that it obtains the characteristics of a structure seeker, whose global minimum is the reaction product. By performing a minima-hopping-based global optimization on this biased potential energy surface, we rapidly find intermediate states that lead into the global minimum and allow us to then extract entire reaction pathways. We first demonstrate for a benchmark system, namely, the Lennard-Jones cluster LJ_{38}, that our method finds intermediate states relevant to the lowest energy reaction pathway, and hence we need to consider much fewer intermediate states than previous methods to find the lowest energy reaction pathway. Finally, we apply the method to two real systems, C_{60} and C_{20}H_{20}, and show that the reaction pathways found contain valuable information on how these molecules can be synthesized.

Top-down formation of fullerenes in the interstellar medium

Fullerenes have been recently detected in various circumstellar and interstellar environments, raising the question of their formation pathway. It has been proposed that they can form at the low densities found in the interstellar medium by the photo-chemical processing of large polycyclic aromatic hydrocarbons (PAHs). Following our previous work on the evolution of PAHs in the NGC 7023 reflection nebula, we evaluate, using photochemical modeling, the possibility that the PAH C66H20 (i.e. circumovalene) can lead to the formation of C60 upon irradiation by ultraviolet photons. The chemical pathway involves full dehydrogenation of C66H20, folding into a floppy closed cage and shrinking of the cage by loss of C2 units until it reaches the symmetric C60 molecule. At 10" from the illuminating star and with realistic molecular parameters, the model predicts that 100% of C66H20 is converted into C60 in ~ 105 years, a timescale comparable to the age of the nebula. Shrinking appears to be the kinetically limiting step of the whole process. Hence, PAHs larger than C66H20 are unlikely to contribute significantly to the formation of C60, while PAHs containing between 60 and 66 C atoms should contribute to the formation of C60 with shorter timescales, and PAHs containing less than 60 C atoms will be destroyed. Assuming a classical size distribution for the PAH precursors, our model predicts absolute abundances of C60 are up to several 10-4 of the elemental carbon, i.e. less than a percent of the typical interstellar PAH abundance, which is consistent with observational studies. According to our model, once formed, C60 can survive much longer (> 107 years for radiation fields below G0 = 104) than other fullerenes because of the remarkable stability of the C60 molecule at high internal energies. Hence, a natural consequence is that C60 is more abundant than other fullerenes in highly irradiated environments.

Global optimization method for cluster structures

A time-going-backward quasidynamics method is developed for global optimization of cluster structures, and its merits are examined by a simple classical mechanics model, indicating that the probability for the system to jump over high potential barriers by this method is much higher than that by common annealing methods. The method is then used to investigate the isomers of a Lennard-Jones cluster containing 38 atoms and the C60 cluster with the Brenner potential, and can easily give the most stable structures, which are difficult to obtain by common annealing methods. In addition, for small carbon clusters C_{n} (n=21-30) , most of the potential energies optimized by this method are much lower than those obtained by a genetic algorithm.