Real-space Kerker method for self-consistent calculation using non-orthogonal basis functions

摘要

We have proposed the real-space Kerker method for fast self-consistent-field calculations in real-space approaches using non-orthogonal basis functions. In large-scale systems with many atoms, the Kerker method is a very efficient way to prevent charge sloshing, which induces numerical instability during the self-consistent iterations. We construct the Kerker preconditioning matrix with non-orthogonal basis functions and the preconditioning is performed by solving linear equations. The proposed real-space Kerker method is identical to the method in reciprocal space, with the following two advantages: (i) the method is suitable for massively parallel computation since it does not use the fast Fourier transform. (ii) The preconditioning is performed in an acceptable computational time since time-consuming integration, including the exponential kernel, need not be performed, unlike the method used by Manninen et al (1975 Phys. Rev. B 12 4012).