  We have developed a method for prediction of the hardest crystal structures
in a given chemical system. It is based on the evolutionary algorithm USPEX
(Universal Structure Prediction: Evolutionary Xtallography) and
electronegativity-based hardness model that we have augmented with bond-valence
model and graph theory. These extensions enable correct description of the
hardness of layered, molecular, and low-symmetry crystal structures. Applying
this method to C and TiO2, we have (i) obtained a number of low-energy carbon
structures with hardness slightly lower than diamond and (ii) proved that TiO2
in any of its possible polymorphs cannot be the hardest oxide, its hardness
being below 17 GPa.
