A novel algorithm has been proposed for simulating thermal decomposition of atomic clusters at such low temperatures that the corresponding lifetimes are macroscopic and, hence, standard molecular dynamics algorithms are inapplicable. The proposed algorithm is based on a combination of the molecular dynamics and Monte Carlo techniques. It is used to calculate the temperature dependence of the lifetime of the thermalized C20 fullerene until it decomposes at T = 1300-4000 K. The frequency factor and activation energy of the decomposition are determined. It is demonstrate that the temperature dependences of the lifetimes of the heat-isolated and thermalized fullerenes differ significantly.
compared to the molecular dynamics method, which eliminates the problem of time scaling of dynamic processes, and makes it possible to observe the evolution of the cluster over macroscopic time spans [11]. This approach, however, is only applicable to a rather narrow class of problems, in which the many-particle potential of the system in the generalized atomic coordinate space of the cluster has a set of minima (with the known residence times of the system), and the evolution of the system is determined by transitions between these minima. This class includes, in particular, the problems of island formation by atoms adsorbed onto the surface of a crystalline adsorbent, the diffusion and coagulation of interacting defects in solids, and so on; however, the problem of decomposition of an isolated cluster doesn⥪t belong to this class. For example, moving along the reaction coordinate from a perfect (defect-free) C 20 fullerene towards the products of its decomposition, only four or five metastable configurations can be detected [12], which is insufficient for the efficient use of the Monte Carlo + transition state theory approach.
The combined Monte Carlo + molecular dynamics algorithm has been proposed for simulations of atomic clusters on prolonged time scales [13]. The evolution of the system is described by the stochastic motion of atoms according to the Metropolis Monte Carlo algorithm [14]. Each step of this algorithm corresponds to a certain time interval. The correspondence between one step of the Metropolis algorithm and the real (“physical”) time interval is determined from matching the atomic diffusion mobilities computed using the molecular dynamics method and the Monte Carlo approach. However, the performance of the algorithm [13] offers only a fourfold to sixfold advantage with respect to the molecular dynamics method, which obviously is not sufficient. Apart from the relatively low performance, another shortcoming of the combined algorithm [13] is that it is applicable only to some dynamical problems, since the Metropolis algorithm (the most commonly used among the Monte Carlo methods) has been developed for calculations of the characteristics of stationary statistical equilibrium systems. The fundamental justification of this algorithm in [14] is based on the detailed equilibrium principle, which, strictly speaking, is not valid for the irreversible process of the cluster decomposition (when the statistics is accumulated for these problems, only the probability flow for the transition of the system from the initial cluster to the products of its decomposition is taken into consideration, while the reverse process of “regeneration” of the cluster is ignored, which violates the detailed equilibrium principle). The algorithm proposed in the present work is based on the idea of the sequential application of the molecular dynamics and Monte Carlo methods [13], but it is modified so as to remediate the principal shortcomings of the technique [13].
In our approach, the region in the configuration space, where the potential energy of the cluster deviates weakly from its average value, and the detailed equilibrium condition is satisfied well enough, is simulated using the Monte Carlo technique (the Metropolis algorithm [14]). The regions with a higher potential energy (exceeding a certain threshold value U ) are termed fluctuation regions in the following. The dynamics of the system in these regions is simulated using the molecular dynamics method. The magnitude of the threshold potential energy U is an important parameter in the proposed scheme. The correct choice of the value of the threshold potential energy makes it possible to eliminate the systematic error of the Metropolis algorithm caused by the violation of the detailed equilibrium principle. In our algorithm, the Monte Carlo step does not correspond to a fixed time interval, as in [13]. The time scale matching is done basing on the average time interval between two sequential fluctuations, which is determined in advance using the molecular dynamics method. The proposed algorithm is multistep. During the simulation of the system with a lower fluctuation threshold of the potential energy U , the average time interval between fluctuations with a threshold U 1 > U is determined, and, when the accumulated statistics is sufficient, the simulation is repeated with a new, larger threshold value U 1 . The increase of the threshold value U is repeated up to the decomposition of the cluster. Owing to its multistep structure, our algorithm outperforms the molecular dynamics method by many orders of magnitude, and is comparable to the Monte Carlo + transition state theory approach, while at the same time being free of the limitations that the transition state theory imposes on the potential energy landscape of the cluster.
In our simulations of the decomposition of the C 20 fullerene, we used the tight-binding potential [6] which performs adequately
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