© 2015 American Physical Society. We study the physical properties of ZnX (X = O, S, Se, Te) and CdX (X = O, S, Se, Te) in the zinc-blende, rock-salt, and wurtzite structures using the recently developed fully ab initio pseudohybrid Hubbard density functional ACBN0. We find that both the electronic and vibrational properties of these wide band-gap semiconductors are systematically improved over the PBE values and reproduce closely the experimental measurements. Similar accuracy is found for the structural parameters, especially the bulk modulus. ACBN0 results compare well with hybrid functional calculations at a fraction of the computational cost.