Increased computational resources now make it possible to generate large data sets solely from first principles. Such “high-throughput” screening is employed to create a database of embedding enthalpies for extrinsic point defects and their vacancy complexes in Si and Ge for 73 impurities from H to Rn. Calculations are performed both at the PBE and HSE06 levels of theory. The data set is verified by comparison of the predicted lowest-enthalpy positions with experimental observations. The effect of temperature on the relative occupation of defect sites is estimated through configurational entropy. Potential applications are demonstrated by selecting optimal vacancy traps, directly relevant to industrial processes such as Czochralski growth as a means to suppress void formation.