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

The 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 calculations. However, a question still remains regarding its applicability to the inhomogeneous systems. We develop a modified Kerker preconditioning scheme which captures the long-range screening behavior of inhomogeneous systems and thus improves 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.

Figure 1

The preconditioning models as a function of reciprocal vector $\mathbf{q}$. A threshold parameter can be added to the Kerker preconditioner to simulate the small-$\mathbf{q}$ behavior of the insulating systems.

Figure 2

(a) The DOS of the 96-atom Si slab. The vertical blue line indicates the Fermi level. The states right below the Fermi level are the surface states, as shown by the partial charge density plot. The bottom surface is identical to the top surface, thus only one is shown. (b) The DOS of the Si slab with H passivation (96 layers of Si with 2 H-passivation layers on the top and the bottom Si surfaces). The added H layers remove the surface states: a clear band gap now occurs right above the Fermi level.

Figure 3

The (a) a posteriori indicator and (b) energy convergence vs SCF iteration step under $a_0=0.01$, and two self-adaptive schemes. The arrows on the axis indicate that we launch the self-adaptive configuration at the eighth step and 67th step.

Figure 4

Indicators under different $k$-point sampling grids for a 22-layer ${\mathrm{MoS}}_2$ slab and 54-layer Au slab.

Figure 5

Indicators under different $k$-point sampling grids and smearing width for a 5-layer Au + 20-layer ${\mathrm{MoS}}_2$ slab.

Figure 6

DOS plot for $11\times 11\times 1$ and $12\times 12\times 1$ grid calculations. The Fermi level is at $E=0$, indicated by the vertical blue line.