  Hafnium carbides are studied by a systematic search for possible stable
stoichiometric compounds in the Hf-C system at ambient pressure using
variable-composition ab initio evolutionary algorithm implemented in the USPEX
code. In addition to well-known HfC, we predicted two additional compounds
Hf3C2 and Hf6C5. The structure of Hf6C5 with space group C2/m contains 11 atoms
in the primitive cell and this prediction revives the earlier proposal by A. I.
Gusev. The stable structure of Hf3C2 also has space group C2/m, and is more
energetically favorable than the Immm, P-3m1, P2 and C2221 structures put
forward by A. I. Gusev. Dynamical and mechanical stability of the newly
predicted structures have been verified by calculations of their phonons and
elastic constants. The bulk and shear moduli of Hf3C2 are 195.8 GPa and 143.1
GPa, respectively, while for Hf6C5 they are 227.9 GPa and 187.2 GPa,
respectively. Their mechanical properties are inferior to those of HfC due to
the presence of structural vacancies. Chemical bonding, band structure, and
Bader charge are presented and discussed.
