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The crystal structure of tungsten monocarbide (WC) is researched from 0 to 650 GPa through first principles calculations. The results verify that the experimental structure (hP2-WC) with the space group P 6 ¯ m2 is the most stable phase in a wide range of pressure. Above 231 GPa, a new stable structure (space group P63/mmc, hP4-WC) is found to be the most stable phase, and it will transform to a CsCl-type phase (cF8-WC) around 582 GPa. Phonon calculations reveal that the hP4-WC phase is dynamically stable and may be a metastable structure at ambient conditions. The cF8-WC phase possesses dynamical stability above 20 GPa. The hP4-WC phase is a low compressible material with a large bulk modulus of 377 GPa at zero pressure. The hardness values of hP2-WC and hP4-WC at zero pressure are 32 and 21 GPa, respectively, while the cF8-WC phase possesses a hardness of 21 GPa at 20 GPa, implying that these phases are potential hard materials. The temperature–pressure phase boundary of WC is obtained by means of the quasi-harmonic approximation method. As the temperature increases, the transition pressure from hP2-WC to hP4-WC remained nearly unchanged. The transition pressure between hP4-WC and cF8-WC decreases with the increasing temperature. [ABSTRACT FROM AUTHOR]