We present nonlinear self-consistent calculations of the charge density induced by isolated ${\mathrm{Li}}^{+}$, ${\mathrm{K}}^{+}$, ${\mathrm{Mg}}^{++}$, ${\mathrm{Al}}^{+++}$, and ${\mathrm{Ca}}^{++}$ ions when placed in an electron gas of the appropriate metallic density. By comparison with linear-response theory we show that in the first four metals nonlinear effects in the response of the conduction electrons to the ionic perturbations play an important role in determining the charge density and the interionic potential. However as in the case of Na studied in the previous paper these nonlinear effects can be simulated by using a suitably adjusted model potential. The calculated phonon dispersion curves for Li, K, and Al agree very well with experiment. Nonlinear effects are also very likely to be important in Ca but further work is necessary before conclusions can be drawn.

• Received 24 June 1974

DOI:https://doi.org/10.1103/PhysRevB.11.2726