Accelerating the self-consistent field iteration for solving the Kohn-Sham equation





摘要:Solving the Kohn-Sham equation is most computationally demanding in the first-principles calculations of materials. The self-consistent field (SCF) iteration is used to solve such a nonlinear eigenvalue problem. We develop techniques to accelerate the convergence of SCF iteration in static calculations and Born-Oppenheimer molecular dynamics (BOMD) separately. In the static calculation or the first step of BOMD, we modify the Kerker preconditioning scheme to capture the long-range screening behavior of inhomogeneous systems. The effectiveness and efficiency is shown by the tests on long-z slabs of metals, insulators, and metal-insulator contacts. In the following BOMD simulation, the wavefunction extrapolation greatly reduces the number of SCF iterations. Going against the intuition that the higher order of extrapolation possesses a better accuracy, we demonstrate that there exists an optimal extrapolation order in terms of minimal number of SCF iterations. It is illustrated that the optimal extrapolation order covers a broad range when varying the MD time step or the SCF convergence criterion.



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