The performance of minima hopping and evolutionary algorithms for cluster structure prediction.

We compare evolutionary algorithms with minima hopping for global optimization in the field of cluster structure prediction. We introduce a new average offspring recombination operator and compare it with previously used operators. Minima hopping is improved with a softening method and a stronger feedback mechanism. Test systems are atomic clusters with Lennard-Jones interaction as well as silicon and gold clusters described by force fields. The improved minima hopping is found to be well-suited to all these homoatomic problems. The evolutionary algorithm is more efficient for systems with compact and symmetric ground states, including LJ(150), but it fails for systems with very complex energy landscapes and asymmetric ground states, such as LJ(75) and silicon clusters with more than 30 atoms. Both successes and failures of the evolutionary algorithm suggest ways for its improvement.

[1]  Stefan Goedecker.  Optimization and parallelization of a force field for silicon using OpenMP ? ? This program can be d , 2002 .

[2]  H. Scheraga,et al.  Monte Carlo-minimization approach to the multiple-minima problem in protein folding. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Ho,et al.  Molecular geometry optimization with a genetic algorithm. , 1995, Physical review letters.

[4]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

[5]  Kaxiras,et al.  Modeling of Covalent Bonding in Solids by Inversion of Cohesive Energy Curves. , 1996, Physical review letters.

[6]  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 .

[7]  S. Goedecker,et al.  Ubiquitous mechanisms of energy dissipation in noncontact atomic force microscopy. , 2008, Physical review letters.

[8]  C. V. Ciobanu,et al.  Evolutionary approach for finding the atomic structure of steps on stable crystal surfaces , 2007 .

[9]  S. Goedecker.  Minima hopping: an efficient search method for the global minimum of the potential energy surface of complex molecular systems. , 2004, The Journal of chemical physics.

[10]  A. Oganov,et al.  Crystal structure prediction using ab initio evolutionary techniques: principles and applications. , 2006, The Journal of chemical physics.

[11]  Wayne Pullan,et al.  Genetic operators for the atomic cluster problem , 1997 .

[12]  Bernd Hartke,et al.  Larger water clusters with edges and corners on their way to ice: structural trends elucidated with an improved parallel evolutionary algorithm. , 2006, The journal of physical chemistry. A.

[13]  Nikolaus Hansen,et al.  USPEX - Evolutionary crystal structure prediction , 2006, Comput. Phys. Commun..

[14]  Ralf Gehrke,et al.  Assessing the efficiency of first-principles basin-hopping sampling , 2009 .

[15]  Structure of Si(1 1 4) determined by global optimization methods , 2005, cond-mat/0411569.

[16]  A. Oganov,et al.  High-pressure phases of CaCO3: Crystal structure prediction and experiment , 2006 .

[17]  U. Landman,et al.  Genetic Algorithms for Structural Cluster Optimization , 1998 .

[18]  Robert H. Leary,et al.  Global Optima of Lennard-Jones Clusters , 1997, J. Glob. Optim..

[19]  K. Ho,et al.  Structural optimization of Lennard-Jones clusters by a genetic algorithm , 1996 .

[20]  E. Kaxiras,et al.  INTERATOMIC POTENTIAL FOR SILICON DEFECTS AND DISORDERED PHASES , 1997, cond-mat/9712058.

[21]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[22]  E. Kaxiras,et al.  Environment-dependent interatomic potential for bulk silicon , 1997, cond-mat/9704137.

[23]  Yanming Ma,et al.  Novel high-pressure structures of MgCO3, CaCO3 and CO2 and their role in Earth's lower mantle , 2008 .

[24]  Yanming Ma,et al.  Structure of the metallic ζ-phase of oxygen and isosymmetric nature of the ε-ζ phase transition : Ab initio simulations , 2007 .

[25]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[26]  Yanming Ma,et al.  Superconducting high pressure phase of germane. , 2008, Physical review letters.

[27]  G. Henkelman,et al.  A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives , 1999 .

[28]  Michael R. Shirts,et al.  Mathematical analysis of coupled parallel simulations. , 2001, Physical review letters.

[29]  Stefan Goedecker,et al.  Structure of large gold clusters obtained by global optimization using the minima hopping method , 2009 .

[30]  Stefan Goedecker,et al.  Bell-Evans-Polanyi principle for molecular dynamics trajectories and its implications for global optimization. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Riccardo Ferrando,et al.  Crossover among structural motifs in transition and noble-metal clusters , 2002 .