  Kerker preconditioner, based on the dielectric function of homogeneous
electron gas, is designed to accelerate the self-consistent field (SCF)
iteration in the density functional theory (DFT) calculations. However,
question still remains regarding its applicability to the inhomogeneous
systems. In this paper, we develop a modified Kerker preconditioning scheme
which captures the long-range screening behavior of inhomogeneous systems thus
improve the SCF convergence. The effectiveness and efficiency is shown by the
tests on long-z slabs of metals, insulators and metal-insulator contacts. For
situations without a priori knowledge of the system, we design the a posteriori
indicator to monitor if the preconditioner has suppressed charge sloshing
during the iterations. Based on the a posteriori indicator, we demonstrate two
schemes of the self-adaptive configuration for the SCF iteration.
