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

Abstract

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.

Global optimization of clusters using electronic structure methods

“…On the other hand, EP-GOs for similar systems can treat nanoparticles with up to hundreds or thousands of atoms. [217][218][219] Structural refinement of many candidate (EP-)isomers of this size is possible at the DFT level of theory. [220] The drawback of this approach, as has been made clear throughout the article, is that for small clusters EPs may introduce errors due to the simplified description of the bonding.…”

Efficient moves for global geometry optimization methods and their application to binary systems

“…We compare the performance of the LB method to that of the standard molecular dynamics (MD) version and to that of the saddle point based lowest mode (LM) method which will be discussed in section II B. As usual 22 we start our molecular dynamics trajectory in a soft direction, i.e. in a direction with low curvature in order to overcome a low barrier with a small number of molecular dynamics steps.…”

Crystal structure prediction using the minima hopping method

“…37 For the crystal structure prediction MH the velocity vector consists not only of atomic velocities, but also of the cell velocities. First, a random velocity direction with Gaussian distributed magnitudes is chosen.…”

“…30,31,37 In Table I the performance of the MH method with and without softening is compared for a benchmark system, a BLJ mixture with type A and B atoms in a small cell, A 8 B 4 . It can be clearly seen that the curvature of the configurational enthalpy along the velocity direction is reduced by roughly one order of magnitude when softening is used.…”