A technique for an accurate and efficient calculation of point-defect-induced changes in the electronic structure of an otherwise perfect crystal is described. It is based on the Green's-function method introduced by Koster and Slater and developed further by Callaway and coworkers, and achieves its efficiency and convenience by avoiding the use of Wannier functions. The efficiency and accuracy of the method is exhibited by calculating the states of a widely studied model system, namely, the ideal vacancy in covalent solids, using semiempirical, but realistic, host energy-band structures. Results for the vacancy in Si, Ge, and GaAs compare favorably with those obtained previously. In addition, a wealth of new information is obtained. It is argued that the present method is the most efficient technique available for the study of deep-level impurities and defects in semiconductorsthe efficiency stemming from an exploitation of both the short-range nature of the defect potential and the translational symmetry of the host crystal. © 1978 The American Physical Society.