Geometry Optimisation of Aluminium Clusters Using a Genetic Algorithm

Abstract

The application of a Genetic Algorithm, for optimising the geometry of aluminium clusters with 21–55 atoms bound by the many‐body Murrell–Mottram potential, is described. In this size regime, a number of different structural motifs are identified—face‐centred cubic, hexagonal close packed, decahedral and icosahedral structures. The larger clusters consist of hollow icosahedral geometric shells, with Al55 having a centred icosahedral structure. Evolutionary Progress Plots for Al19 and Al38 reveal how the best structure evolves from generation to generation upon operation of the Genetic Algorithm.

Global minima of AlN, AuNand PtN,N⩽ 80, clusters described by the Voter–Chen version of embedded-atom potentials

“…It goes back to the middle of the 1980s that a number of theoretical studies of Al clusters have been carried out by different groups [20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39]. These studies range from the simple jellium model [20] where the cluster geometry is ignored, to a number of models where the geometry explicitly enters into the picture including semiempirical molecular orbital calculations [21], quantum molecular dynamics [26,27,28,29,31], quantum-mechanical calculations based on quantumchemical [22,23,24] and density-functional [25,26,27,28,29,30,31,32,33] theories (DFT) within local density or local spin-density approximations, molecular dynamics and Monte Carlo simulations based on empirical model potentials [34,35,36,37,38,39]...…”

“…On the other hand, while the empirical model potential studies [34,35,36,37,38,39] cannot calculate the electronic properties of the clusters, it is possible to search PES of higher sized clusters with them since they are computationally much less demanding than ab initio calculations. In these model potential studies carried out by random search, simulated annealing or genetic algorithms, Al clusters are described by an empirical many-body potential [34], two-plus-three body Murrell-Mottram potential [35,36,37], Gupta [38] or Sutton-Chen [39] potentials. Similarly, the experimental studies on Al clusters [40,41,42,43,44,45,46,47,48,49,50,51] go back to the middle of the 1980s.…”

Theoretical study of the melting of aluminum clusters

“…19,20,21,22,23,24,25 However, the results show a strong dependence on the model potential used. The Murrell-Mottram potential 26 predicts a competition between fcc and icosahedral structures in the size regime N = 2-55, with strong magic numbers for the 38-atom truncated octahedron and the 54-atom uncentered Mackay icosahedron.…”

“…However, in spite of the experimental 6,7 and theoretical 8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25 effort, a consensus has not yet been achieved about the structure of many of the experimentally observed magic numbers. Only for large sizes (N > 250) the structure of Al clusters seems to have been rationalized.…”

Structures and stabilities of Aln+, Aln, and Aln− (n=13–34) clusters

“…A controversy has arisen regarding the correct global minimum ͑GM͒ for Al 13 : the optimizations based on parametrized potential models 32,34,35,41,42,46,52 invariably predict an icosahedral structure, but these methods do not contain an explicit description of the electronic degrees of freedom and their accuracy is questionable. A majority of the ab initio calculations ͓mostly based on density functional theory ͑DFT͒ and differing in the election of exchangecorrelation functional, aluminum pseudopotential, and basis set͔ predict an icosahedron as the most stable structure, [22][23][24][25]27,28,30,33,37,39,45 but a small number of calculations 26,31,38,48,49 predict a decahedron to be more stable.…”