Global optimization of binary Lennard–Jones clusters

In this paper we present our experience with the optimization of atomic clusters under the binary Lennard–Jones potential. This is a generalization of the single atom type Lennard–Jones model to the case in which atoms of two different types (and ‘sizes’) interact within the same cluster. This problem has a combinatorial structure which increases complexity and requires strategies to be revised in order to take into account such new aspects. Our approach has been a very effective one: we have been able not only to confirm most putative optima listed in the Cambridge Cluster Database, but also to find 95 improved solutions.

[1]  Andrea Grosso,et al.  A Population-based Approach for Hard Global Optimization Problems based on Dissimilarity Measures , 2007, Math. Program..

[2]  Marco Locatelli,et al.  On the Multilevel Structure of Global Optimization Problems , 2005, Comput. Optim. Appl..

[3]  J. Doye,et al.  Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms , 1997, cond-mat/9803344.

[4]  Jorge Nocedal,et al.  On the limited memory BFGS method for large scale optimization , 1989, Math. Program..

[5]  Bernd Hartke,et al.  Global cluster geometry optimization by a phenotype algorithm with Niches: Location of elusive minima, and low-order scaling with cluster size , 1999, J. Comput. Chem..

[6]  Andrea Grosso,et al.  An experimental analysis of a population based approach for global optimization , 2007, Comput. Optim. Appl..

[7]  J. Doye.  Physical Perspectives on the Global Optimization of Atomic Clusters , 2000, cond-mat/0007338.

[8]  Robert H. Leary,et al.  Global Optimization on Funneling Landscapes , 2000, J. Glob. Optim..

[9]  Fabio Schoen,et al.  Global Optimization of Morse Clusters by Potential Energy Transformations , 2004, INFORMS J. Comput..

[10]  Julian Lee,et al.  Unbiased global optimization of Lennard-Jones clusters for N < or =201 using the conformational space annealing method. , 2003, Physical review letters.

[11]  Giulia Rossi,et al.  Global optimization of bimetallic cluster structures. I. Size-mismatched Ag-Cu, Ag-Ni, and Au-Cu systems. , 2005, The Journal of chemical physics.

[12]  Lars Meyer,et al.  Mapping the magic numbers in binary Lennard-Jones clusters. , 2005, Physical review letters.

[13]  Arnold N. Tharrington,et al.  Global optimization and finite temperature simulations of atomic clusters: Use of XenArm clusters as test systems , 2002 .

[14]  Wayne J. Pullan,et al.  An unbiased population‐based search for the geometry optimization of Lennard–Jones clusters: 2 ≤ N ≤ 372 , 2005, J. Comput. Chem..

[15]  Fabio Schoen,et al.  Efficient Algorithms for Large Scale Global Optimization: Lennard-Jones Clusters , 2003, Comput. Optim. Appl..