1 Introduction

In general, there are two types of strategies for predicting crystal structures. One is to directly scan the whole energy landscape, and find the most stable crystal structures using random sampling ⁹ or generally more efficient evolutionary algorithms ⁴. Alternatively, one could also use some known structures as the starting point, and predict the new structures by crossing the energy barriers, until the lowest energy structure is found ^{5; 7; 8; 10}. The latter group of methods can be described as neighborhood search methods and some of them - in particular, metadynamics ^{7; 219}, can be very efficient, but rely on availability of a good starting structure.

Metadynamics explores the properties of the multidimensional free energy surface (FES) of complex many-body systems by means of a coarse-grained non-Markovian dynamics in the space defined by a few collective coordinates. By introducing a history-dependent potential term, it fills the minima in the FES and allows efficient exploration of the FES as a function of the collective coordinates ²¹⁹. The technique is usually applied as an extension of the molecular dynamics (MD) simulation technique. Martonak et al. used the edges of the simulation cell as collective variables for the study of pressure-induced structural transformations ⁷. The method proved to be much more powerful in predicting crystal structure transformations ^{77; 171; 220}, compared with the normal MD approach. However, at each metastep it uses MD for equilibrating the system and MD is not always an efficient method for equilibration, which leads to trapping in metastable states and often amorphization rather than transition to a stable crystal structure. This motivated us to develop an alternative strategy.

In this chapter, we present a method combining the features of both strategies for predicting crystal structures, basically a metadynamics-like method driven not by local MD sampling, but by efficient global optimization moves ^{4; 79}. Following Martonak et al. ⁷, we adopt the cell edges as collective variables, and equilibrate the system at each value of the collective variables using moves inspired by the evolutionary variation operators ⁷⁹, rather than previously used MD simulation. We find that this approach is very efficient for predicting stable and low-energy metastable states and avoids amorphization.