  Group I/II materials exhibit unexpected structural phase transitions at high
pressures, providing potential insight into the origins of elemental
superconductivity. We present here a computational study of elemental barium
and binary sodium-calcium alloys to identify both known and unknown phases of
barium under pressure, as well as stable high-pressure compounds in the
immiscible Na-Ca system. To predict stability, we performed density functional
theory calculations on randomly generated structures and evolved them using a
genetic algorithm. For barium, we observed all of the expected phases and a
number of new metastable structures, excluding the incommensurate Ba-IV
structure. We also observed a heretofore unreported structure (\alpha-Sm)
predicted to be the ground state from 30-42 GPa. In the Na-Ca system, we
demonstrate feasibility of our search method, but have been unable to predict
any stable compounds. These results have improved the efficacy of the genetic
algorithm, and should provide many promising directions for future work.
