A number of Green's-function methods have recently been used to study the electronic structure of point defects and impurities in semiconductors. These methods are based on the same underlying operator formalism. An important factor controlling the efficiency of any of these methods is the basis set used to represent the operators in matrix form. Here we point out that it is the physical character of the perturbation potential that should suggest the nature of suitable basis sets. For point defects, the perturbation potential has recently been demonstrated by self-consistent calculations to have a predominantly single-center character. A single-center basis set, therefore, appears to be more suitable than multicenter basis sets. We present formal arguments and calculations that indicate that a set of harmonic-oscillator eigenfunctions centered at the point-defect site is particularly suitable, largely because such functions concentrate their variational flexibility in a small volume. © 1979.