A method of estimating the energy of an impurity in a host electronic system using density-functional theory is presented. The impurity ion plus its electronic screening cloud is treated as a unit and is used to define a quasiatom. The energy of the quasiatom is a functional of the host electron density in which it is immersed. In the simplest approximation it is given by the energy of the impurity in a uniform electron gas having a density equal to that of the host at the position of the impurity nucleus. This uniform-density approximation (UDA) is tested for light atoms in a variety of model and realistic situations and is found to be successful in reproducing qualitative trends. By developing a perturbation expansion for a weakly inhomogeneous host the UDA is shown to be the leading term in a rigorous expansion of the quasiatom energy in gradients of the host electron density, and corrections to second order in gradients are determined. As an example, these corrections are used in the calculation of the binding energy of a helium atom to a vacancy and excellent agreement with exact results is achieved. The perturbation expansion also suggests an ansatz for the quasiatom energy in which the host electron density is sampled by the quasiatom electrostatic potential. Tests of this ansatz are equally successful.

• Received 20 December 1979

DOI:https://doi.org/10.1103/PhysRevB.22.1564