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

Abstract

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.

On preconditioning the self-consistent field iteration in real-space Density Functional Theory

“…We now verify the accuracy and efficiency of the proposed real-space formulation for isotropic Fourier-space preconditioners used to accelerate the SCF iteration in Kohn-Sham DFT. As representative schemes, we consider the truncated-Kerker (t-Kerker) [16,24] and Resta [25,24] preconditioners:…”

“…Specifically, convergence can be slow to non-existent due to charge sloshing effects, particularly as the size of the system is increased for metallic as well as inhomogeneous systems [15,16,17,18]. In order to mitigate this behavior, there have been a number of efforts to develop preconditioners that can be employed in conjunction with mixing schemes to further accelerate the convergence of the underlying fixed-point iteration [17,19,20,9,21,22,23,24].…”

“…Indeed, this prefactor can be substantially reduced using the extrapolar method [23], however the quartic scaling still represents a serious bottleneck. In view of this, there have been efforts directed towards the development of simpler models of the dielectric matrix, resulting in preconditioners that are efficient to compute and apply [19,21,17,24]. Among these, isotropic Fourier-space preconditioners are perhaps the most popular in Kohn-Sham DFT, with origins in the work of Kerker [19], who employed a model dielectric function suitable for simple metallic systems.…”

Robust mixing in self-consistent linearized augmented planewave calculations

“…The latter method contains also the screening parameter λ, which strongly influences the convergence properties of the method. Previous studies [31,32] have suggested to use the wavevector of the Thomas-Fermi screening, k T F . Following Ref.…”

Mathematical Analysis and Numerical Approximations of Density Functional Theory Models for Metallic Systems

“…It is not difficult to apply the SCF iteration approach for the classical Kohn-Sham DFT model to the ensemble Kohn-Sham DFT model. We understand that some preconditioners have been also constructed to accelerate the SCF iterations [19,22,24,42]. Unfortunately, the convergence of the SCF iterations for the ensemble Kohn-Sham DFT is not guaranteed yet.…”