Unbiased fuzzy global optimization of Morse clusters with short-range potential for N ≤ 400

Abstract

Global optimization of Morse clusters with shortrange potential is a great challenge. Here, we apply our recently developed unbiased fuzzy global optimization method to systematically study Morse clusters with the potential range ρ = 14 and the number of atoms N up to 400. All the putative global minima reported in the literature have been successfully reproduced with relatively high success ratios. Compared to the available results for N ≤ 240 and several larger Morse clusters, new global minima (and local minima) with lower energies have been found out for N = 164, 175, 188, 193, 194, 197, 239, 246, 260, 318, and 389. Clusters with magic numbers are figured out through fitting the size-dependent global minimum energies. The cluster structures tend to be close-packed for short-range potential with large N.

Growth Pattern of Large Morse Clusters with Medium-Range Potentials

“…To the best of our knowledge, the GM structures and energies have been systematically studied only for N values of ≤240 with different potential ranges in the literature. , Recently, we have successfully investigated Morse clusters with short-range potential ρ = 14 and N values of up to 400 . Compared with the available results, new GM (and local minimum) structures with lower energies have been found for N values of 164, 175, 188, 193, 194, 197, 239, 246, 260, 318, and 389 with ρ = 14.…”

“…Clusters described by the Lennard-Jones (LJ) potential are termed LJ clusters and have been extensively investigated. ,,− ,,,,,,, While LJ clusters with up to 1610 atoms have been studied on the basis of the construction of different motifs, LJ clusters with up to 1000 atoms have been investigated by our unbiased FGO method and new GM structures with 894, 974, and 991 atoms have been reported . In comparison, due to the higher degree of difficulty, relatively fewer studies have been conducted on Morse clusters, ,,− which are characterized by the Morse potential V normalM ( r ) = ε normale ρ ( 1 − r / r 0 ) [ e ρ false( 1 − r / r 0 false) − 2 ] where ε is the well depth, r 0 is the equilibrium distance, r is the interatomic distance, and ρ describes the range of the Morse potential. Reduced units for which ε = r 0 = 1 are generally used for the sake of simplicity.…”

“…Therefore, the distance-dependent energy in eq can be precomputed, stored in an array, and read out without recalculation when needed. To this end, the FGO algorithm is mainly carried out in discrete space and has been described in detail in refs and . Only a brief description is given below.…”

“…The success ratio is defined as the proportion of the hit number of the GM structure in all of the FGO runs. Note that all of the parameters in DMC and SMC used for ρ = 6 and 10 here are the same as those in our previous study for Morse clusters with ρ = 14 …”

Structural Evolution of Cadmium Selenide Clusters: An Unbiased Global Optimization Study of (CdSe)N for 5 ≤ N ≤ 80

“…Recently, we proposed an unbiased fuzzy global optimization (FGO) method. Its effectiveness has been demonstrated in obtaining the GM structures of large Lennard-Jones (LJ) clusters with ≤1000 atoms, 39 Morse clusters with short-range potentials with ≤400 atoms, 40 and Morse clusters with medium-range potentials with ≤700 atoms. 41 In addition to reproducing previously reported GM structures, FGO also identified a series of new GM structures with lower energies and revealed the detailed growth pattern, magic sizes, and central vacancies.…”