2.1 Crystal Structure Prediction

The evolutionary algorithm USPEX 4; 23, used here for predicting new stable structures, searches for the structure with the lowest free energy at the given pressure-temperature conditions and is capable of predicting the stable structure of a compound knowing just the chemical composition. Details of the method are described elsewhere 4; 23 and a number of applications 4; 12 illustrate its power. All structure prediction runs discussed here were done with the USPEX code, with structure relaxations done using DFT within GGA in the framework of PAW method in the VASP. We used the plane wave kinetic energy cutoff of 520 eV and the Brillouin zone was sampled with the resolution of 2$\pi $ $\times $ 0.08 $^{-1}$, which showed excellent convergences of the energy differences, stress tensors and structural parameters. We studied systems containing up to 36 atoms per unit cell. The first generation of structures was created randomly. All structures were relaxed at constant pressure and the enthalpy was used as fitness. The energetically worst structures (40$\% $) were discarded and a new generation was created from the remaining structures through heredity, lattice mutation and permutation of atoms. Additionally, the best structure of a generation was carried over into the next generation. We terminated the runs generally after 50 generations, and all runs had found the minimum enthalpy structures much earlier. The population size was set to at least twice the number of atoms in the cell. Results obtained with and without the vdW functional 54 (as implemented in the VASP code) are very similar, and here we show the results that include this functional.