Structure prediction for novel materials requires computationally inexpensive lattice relaxation methods. Prediction of the band gap and excited state properties depends on the accuracy of the relaxations and the sensitivity of the band edges to structural parameters. We examine the relaxation performance of common relaxation methods for several members of the type IB3-V-VI4 copper chalcogenide semiconductors, which have become of recent interest for potential photovoltaic and thermoelectric applications. These materials are members of a larger family of materials, composed of type IB and type VI elements and additional elements acting as cations, which contains structures as complex as Cu12Sb4S13 (tetrahedrite) and may benefit from materials prediction studies. Examining Cu3PS4, Cu3PSe4, Cu3AsS4, and Cu3AsSe4, we find that relaxation induced structural errors cause subsequently calculated band gap values E
to deviate by as much as 0.6 eV from values obtained using experimentally determined structures. Using the HSE06 hybrid functional we find that the complex V/VI* anti-bonding character of the conduction band minimum creates a band gap sensitivity of order 10 eV/Å to the mean V-VI distance 〈V-VI〉. A weaker correlation between E
and 〈IB-VI〉 exists due to the Cu-d/Ch-p* character of the valence band maximum (Ch = S, Se). Type IB-III-VI2 materials are known to have similar properties and we include CuInSe2, CuAlS2, and CuAlSe2. Regarding structural relaxation accuracy, we find that GGA+U and meta-GGA functional MS2 typically perform better than GGA (PBE) or PBEsol, but not as well as the much more expensive HSE functional.