Symmetrisation schemes for global optimisation of atomic clusters

Abstract

Locating the global minima of atomic and molecular clusters can be a difficult optimisation problem. Here we report benchmarks for procedures that exploit approximate symmetry. This strategy was implemented in the GMIN program following a theoretical analysis, which explained why high-symmetry structures are more likely to have particularly high or particularly low energy. The analysis, and the corresponding algorithms, allow for approximate point group symmetry, and can be combined with basin-hopping and genetic algorithms. We report results for 38-, 75-, and 98-atom Lennard-Jones clusters, which are all multiple-funnel systems. Exploiting approximate symmetry reduces the mean time taken to locate the global minimum by up to two orders of magnitude, with smaller improvements in efficiency for LJ(55) and LJ(74), which correspond to simpler single-funnel energy landscapes.

Revised Basin-Hopping Monte Carlo Algorithm for Structure Optimization of Clusters and Nanoparticles

“…Our results are summarized in Table 3, in which we compare them with the most recent BHMC results available for LJ clusters. 48 In all four cases the dynamic scheme of operators proved to be more efficient than the static scheme; however, the differences are only modest, except for LJ 75 . Using the dynamic scheme we were able to obtain lower MFETs than those reported in ref 48 using a traditional BHMC algorithm, with a more pronounced difference for LJ 98 , in which case our implementation using the dynamic scheme was able to locate the global minimum in about 40000 steps less.…”

Global optimization of clusters using electronic structure methods

“…24 This aim will probably be achieved with the help of developments of the GO algorithms. This could include using reasonable initial structures, for example using the CK method, [202] making use of symmetry to speed up the calculations [222] or using available information of previously visited minima (e.g., structural descriptors, energies, frequencies,…) [65,83,87] to assure the exploration of as many funnels of the PES as possible. Most importantly, the GO algorithm itself, not only the electronic structure calculation, must be parallelized to make optimal use of modern computer architectures.…”

Comprehensive genetic algorithm forab initioglobal optimisation of clusters

“…[80] Here we also introduce a method to search for symmetric clusters. For a given point group symmetry, we maintain all populations with this symmetry throughout all GA procedures, including generating the initial structures, crossover and mutation operations, and local DFT optimisations.…”

“…[10] In the SA procedure, the system is first heated up to a high temperature (exceeding the melting point) and then gradually cooled down to room temperature via molecular dynamics (MD) or Monte Carlo simulations, which can be combined with either empirical potentials or first-principles methods. Even though SA procedure combined with first-principles calculations is a robust method and has been successfully employed to a series of clusters, such as Cd n Te n (n = 1-14), [11] Li n (n = 20,30,40,50), [12] P + 2m+1 (m = 1-12), [13] B 28 , [14] B 80 , [15] and B [101][102][103] , [16] it cannot guarantee the global minimum of the PES unless the annealing time is sufficiently long.…”