We reported a developed methodology to design superhard materials for given chemical systems under external conditions (here, pressure). The new approach is based on the CALYPSO algorithm and requires only the chemical compositions to predict the hardness vs. energy map, from which the energetically preferable superhard structures are readily accessible. In contrast to the traditional ground state structure prediction method where the total energy was solely used as the fitness function, here we adopted hardness as the fitness function in combination with the first-principles calculation to construct the hardness vs. energy map by seeking a proper balance between hardness and energy for a better mechanical description of given chemical systems. To allow a universal calculation on the hardness for the predicted structure, we have improved the earlier hardness model based on bond strength by applying the Laplacian matrix to account for the highly anisotropic and molecular systems. We benchmarked our approach in typical superhard systems, such as elemental carbon, binary B-N, and ternary B-C-N compounds. Nearly all the experimentally known and most of the earlier theoretical superhard structures have been successfully reproduced. The results suggested that our approach is reliable and can be widely applied into design of new superhard materials.

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