Global geometry optimization of silicon clusters described by three empirical potentials

Abstract

The ''basic-hopping'' global optimization technique developed by Wales and Doye is employed to study the global minima of silicon clusters Si n (3рnр30) with three empirical potentials: the Stillinger-Weber ͑SW͒, the modified Stillinger-Weber ͑MSW͒, and the Gong potentials. For the small-sized SW and Gong clusters (3рnр15), it is found that the global minima obtained based on the basin-hopping method are identical to those reported by using the genetic algorithm ͓Iwamatsu, J. Chem. Phys. 112, 10976 ͑2000͔͒, as well as with those by using molecular dynamics and the steepest-descent quench ͑SDQ͒ method ͓Feuston, Kalia, and Vashishta, Phys. Rev. B 37, 6297 ͑1988͔͒. However, for the mid-sized SW clusters (16рnр20), the global minima obtained differ from those based on the SDQ method, e.g., the appearance of the endohedral atom with fivefold coordination starting at nϭ17, as opposed to nϭ19. For larger SW clusters (20рn р30), it is found that the ''bulklike'' endohedral atom with tetrahedral coordination starts at n ϭ20. In particular, the overall structural features of SW Si 21 , Si 23 , Si 25 , and Si 28 are nearly identical to the MSW counterparts. With the SW Si 21 as the starting structure, a geometric optimization at the B3LYP/6-31G͑d͒ level of density-functional theory yields an isomer similar to the ground-stateisomer of Si 21 reported by Pederson et al. ͓Phys. Rev. B 54, 2863 ͑1996͔͒.

Structural and energetic analysis of copper clusters: MD study of Cu n (n = 2-45)

“…with the parameters 25 21 = 0.436092895, and D 22 = 0.245082238 for copper. In these parameters, the energy is in eV and the distance is in Å. Erkoç has reviewed various potentials used in atomistic simulations.…”

“…For example, Genetic Algorithms (GA) 16,17 and basin hopping (BH) [18][19][20] have shown to be reasonably accurate and are widely used for inspecting the global minimum of various empirical PEFs. 21 As alternative methods, minima hopping (MH) for complex molecular systems 22 39 used embedded-atom method to obtain a detailed description of copper clusters. Erkoç 44 has investigated the effect of radiation damage on copper clusters by performing MD simulation using empirical PEF.…”

Atomistic Modelling of Si Nanoparticles Synthesis

“…The FF parameters have been optimized in order to reproduce a training-set (t-set) of properties (i.e., energies and geometries) derived from quantum chemical (QC) calculations on selected model systems. Few experimental measurements of dissociation/ionization energies and mobilities of the ionized structures are available in the literature [21][22][23][24], whereas geometries and electronic structures of small silicon clusters have been studied extensively by QC approaches over the last few years [25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”

Reexamine structures and relative stability of medium-sized silicon clusters: Low-lying endohedral fullerene-like clusters Si30–Si38

“…Structures of medium-sized silicon clusters have been investigated by many researchers over the last five years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] using various global optimization methods [21][22][23][24][25][26]. Numerous theoretical studies of medium-sized neutral clusters Si N in the size range N = 25-40 have shown that beyond N = 29, compact and spherical-like structures are more stable than elongated structures [4,8,11,12,15] and that carbon fullerene cages tend to be generic cage motifs for low-lying spherical-like clusters [4,9,[11][12][13][15][16][17][18][19][20].…”

“…To date, a large population of low-energy clusters of Si N (N = 25-40) have been obtained from independent global-minimum searches by several research groups: (1) an unbiased search [4] using genetic algorithm [21] combined with the non-orthogonal tightbinding method [27]. (2) an unbiased search [11,12] using minima-hopping method [25] combined with the density-functional based tight-binding (DFTB) model [28], and (3) various biased searches (based on a large number of pre-constructed endohedral fullerene structures) using a compression method [20] combined with a tight-binding model of silicon [29], or a relaxation method combined with quantum molecular dynamics simulation [16], or a basin-hopping method combined with density-functional theory (DFT) geometry optimization [4,8,26]. Although for each size there are many candidates to compete for the lowest-energy structure, the homologue carbon cage motifs (carbon fullerenes [30]) and the number of core atoms inside the cages for most low-lying clusters are reasonably established [11,13,16,20].…”