  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. 
Applicability of Kerker preconditioning scheme to the self-consistent   density functional theory calculations of inhomogeneous systems