“…The first method involved “searching for existing structures.” The 11 existing structures reported from the experimental and theoretical studies of AlB 2 -type metal borides were as follows: the tetragonal structures α-TiB 2 type (SG, I 4 1 / amd ) and β-TiB 2 type (SG, P 4 2 / mmc ); the orthorhombic structures KHg 2 type (SG, Imma ), oP12 (SG, Pnma ), and oP6 (SG, Pmmn ); the hexagonal structures AlB 2 type (SG, P 6/ mmm ), hP12(SG, P 6 3 / mmc ), and hP6 (SG, P 6 3 / mmc ); the monoclinic structure C2/m (SG, C2/m ); the rhombohedral structures hR18 (SG, R -3 m ) and hR9 (SG, R -3 m ) . The second method used the recently developed evolutionary and particle-swarm optimization algorithms for crystal-structure prediction, and the most stable structures were predicted using the CALYPSO codes. , Details of the search algorithms and their applications are described in previous reports. − …”