Evolutionary construction of a formation-energy convex hull: Practical scheme and application to a carbon-hydrogen binary system

We present an evolutionary construction technique of formation-energy convex hull to search for thermodynamically stable compounds. In this technique, candidates with a wide variety of chemical compositions and crystal structures are created by systematically applying evolutionary operators, ``mating,'' ``mutation,'' and ``adaptive mutation,'' to two target compounds, and the convex hull is directly updated through the evolution. We applied the technique to carbon-hydrogen binary system at 10 GPa and obtained 15 hydrocarbons within the convex hull distance less than 0.5 mRy/atom: graphane, polybutadiene, polyethylene, butane, ethane, methane, three molecular compounds of ethane and methane, and six molecular compounds of methane and hydrogen. These results suggest that our evolutionary construction technique is useful for the exploration of stable phases under extreme conditions and the synthesis of new compounds.