Communication: A new paradigm for structure prediction in multicomponent systems

Abstract

We analyse the combinatorial aspect of global optimisation for multicomponent systems, which involves searching for the optimal chemical ordering by permuting particles corresponding to different species. The overall composition is presumed fixed, and the geometry is relaxed after each permutation in order to relieve local strain. From ideas used to solve graph partitioning problems we devise a deterministic search scheme that outperforms (by orders of magnitude) conventional and self-guided basin-hopping global optimisation. The search is guided by the energy gain from either swapping particles i and j (ΔEij) or changing the identity of particles i (ΔEi). These quantities are derived from the underlying (arbitrary) energy function, hence not constituting external bias, and for site-separable force fields each ΔEi can be approximated simply and efficiently. In our self-guided variant of basin-hopping, particles are weighted by an approximate ΔEi when randomly selected for an exchange, yielding a significant improvement for segregated multicomponent systems with modest particle size mismatch.

Structure diagram of binary Lennard-Jones clusters

“…To find an optimal permutation we use another deterministic scheme based on an iterated local search where a sequence of identity swaps is performed until a termination criterion is met. This is similar to a graph partitioning heuristic of Kernighan and Lin with the difference that only swaps that produce lower energy are accepted and the next swap is determined by a sequence of approximated flip gains while the iteration terminates if no swap producing a lower energy is found 22 . Every swap of particle identities is followed by a geometrical local optimization which converges to special points in the configuration space called biminima -the lo- cal minima in both coordinate and permutation space 23 .…”

Fast optimization of binary clusters using a novel dynamic lattice searching method

“…Recently, Lai et al 36 proposed an iterated local search (ILS) method to search the optimal homotop, which has been proved to be an efficient metaheuristic for solving a large number of combinatorial optimization problems. More recently, Schebarchov et al 37 devised a deterministic algorithm based on Kernighan and Lin's (KL) 38 ideas used to solve graph partitioning problems.…”

Extending DFT-based genetic algorithms by atom-to-place re-assignment via perturbation theory: A systematic and unbiased approach to structures of mixed-metallic clusters

“…If the composition is known, the number is somewhat smaller, but nevertheless usually too large for the explicit treatment of all isomers, in particular for 1:1 mixtures. For GAs basing on empirical potentials, several (similar) strategies for the efficient search of the best occupation have been proposed, 5 starting always from an initial distribution and improving it step by step by swapping that pair of A and B atoms with the largest energy gain upon that swap. This procedure has to be carried out for all atoms of the minority compound.…”

“…Explicit calculation of all swaps (in order to find the best) a) E-mail: florian.weigend@kit.edu would require n · (N − n) energy calculations, thus the total effort of a straightforward implementation would be min(n, N − n) · n · (N − n) energy calculations, see, for example, the algorithm sketched in Ref. 5. The effort for finding the best pair of atoms to be swapped can be reduced from n · (N − n) to N calculations by considering single-site flips instead, i.e., comparing the energy changes when exchanging an A atom by a B atom (or vice versa) for every single site, in this way identifying the most preferred sites for A and for B, and thus the pair to be swapped, see Ref.…”