Linear-response theory within the density-functional formalism: Application to atomic polarizabilities

The linear response of an arbitrary electronic system is considered within the framework of the density-functional theory. An integral equation determining the density induced by an external perturbation is derived. The independent-particle response function for an inhomogeneous system appearing in this equation is obtained in a form convenient for numerical calculations. The equation is applied to the calculation of dipole polarizabilities of spherically symmetric atoms and ions. Results for the rare-gas atoms obtained by means of the local-density approximation are in good agreement with experimental values, except for the case of He. Polarizabilities are also evaluated for the alkali-metal ions, the alkaline-earth and other closed-shell metallic atoms.