Geometry Optimization and Conformational Analysis of (C₆₀)_N Clusters Using a Dynamic Lattice‐Searching Method

Abstract

A newly developed unbiased global optimization method, named dynamic lattice searching (DLS), is used to locate putative global minima for all (C6O)N clusters with Girifalco potential up to N=150. A simple greedy strategy is adopted for the basic frame, so DLS has a very high convergence speed and may converge at various configurations. As most structures are packed by basic tetrahedra, some sequences are defined by both configurations and the size of the basic tetrahedra. A sequence-based conformational analysis is carried out with the defined sequences by counting the hit number over 10,000 independent DLS runs for all the cases up to N = 5. It was found that the hit rate of a sequence is related to the size of the basic tetrahedra. U.e of this method proved that the Leary tetrahedral sequence is dominant in a certain range of cluster sizes, although the sequence has no potential energy advantage. The calculation results are also consistent with those of annealing experiments at high temperature, both in magic numbers and height of the peaks in the mass spectrum.

A Conformational Analysis Method for Understanding the Energy Landscapes of Clusters

“…The calculated results for (C 60 ) N molecular clusters agree with annealing experiments at high temperature, [36,40] but at low temperature, magic numbers observed in the experiments are different from the results of our calculations. [40] Furthermore, calculated results from DLS are different from those of some other theoretical methods with regard to dominant conformations for some LJ clusters.…”

“…[40] Furthermore, calculated results from DLS are different from those of some other theoretical methods with regard to dominant conformations for some LJ clusters. For example, the Leary tetrahedron is very difficult to locate for most stochastic global optimization methods, [27,28,32] while it is a dominant configuration in the results of DLS calculations.…”

“…[ 40] This may be the reason why I packings of LJ clusters are easy to locate by stochastic optimization methods, while F and D are difficult. [24,45] For (C 60 ) N molecular clusters, conformational distribution as in Figure 4 can also be obtained by using DLS.…”

“…[34] From both Figure 4 and Figure 5, it can be found that, for all the studied clusters, the packing with a small m value corresponds to a large hit number, which completely agrees with the results obtained before. [40] For further investigation of the relationship between hit number and m values, the number of BT and the nearestneighbor contacts [45] of some favored conformations of LJ 98 and (C 60 ) 98 are summarized in Table 1. According to the definition above, for I, D, and F motifs, the numbers of BT are 20, 5, and 1 respectively, and for I + , D+ , F+ , and cp motifs, the antilayers on the {111} faces will increase the number of BT; for example, in the 3I + motif of the 98 cluster, there are 14 antilayer outer {111} faces of the 55-atom Mackay icosahedral core, so the BT number is 34 (20 + 14).…”

“…[38] To combine the advantages of the two kinds of method, that is, fast and stochastic, the dynamic lattice searching (DLS) method was proposed. [39,40] In DLS, a lattice-searching approach is adopted to explore new solutions around a locally minimized starting structure instead of perturbations. Application of the DLS method in the optimization of Lennard-Jones (LJ) clusters and (C 60 ) N clusters showed that it is very efficient compared to methods based on stochastic perturbation.…”