5 Conclusions

We have developed a novel method crystal structure prediction, based on the ideas of metadynamics and evolutionary global optimization. We use the cell shape (6 degrees of freedom) as the collective variable, sampling which we find and cross the energy barrier, and point out the direction where the phase transition might occur. At each value of the collective variable h, we equilibrate the system using evolutionary variation operators (in the example given here - softmutation), which efficiently explores the remaining 3N-3 internal degrees of freedom. The success of tests on carbon and Al$_2$SiO$_5$ proves the power of this method. Going beyond crystal structure prediction, this method also could produce transformation trajectories between phases, and is thus useful for understanding the transition mechanisms. The method marries ideas from the standard MD-metadynamics 224 and evolutionary algorithm USPEX 4. Like standard metadynamics and unlike USPEX, present technique does require a reasonable starting structure and has the ability to find transition pathways (due to the use of finite displacements along the lowest-frequency mode eigenvectors) and low-energy metastable structures. Yet, unlike MD-metadynamics, our method has a more efficient equilibration and at each metastep produces a set of structures (rather than a single structure), i.e. gives richer chemical information. It avoids amorphization during the simulation - a common problem for MD-metadynamics. For large systems, it can in some cases be more efficient than USPEX, provided a good initial structure. Present technique has a very different philosophy from the USPEX method and in many ways is complementary to it.