Kerker mixing scheme for self-consistent muffin-tin based all-electron electronic structure calculations

We propose a computationally efficient Kerker mixing scheme for robust and rapidly converging self-consistent-field calculations using all-electron first-principles electronic structure methods based on the muffin-tin partitioning of space. The mixing scheme is composed of the Kerker preconditioner in combination with quasi-Newton methods. We construct the Kerker preconditioner in the muffin-tin sphere by determining the screened Coulomb potential in real space, solving a modified Helmholtz equation by adopting Weinert's pseudocharge method for calculating the Poisson equation for periodic charge densities without shape approximation to the solution of the modified Helmholtz equation. Implemented in a full-potential linearized augmented plane-wave (FLAPW) method, we found that the Kerker preconditioning scheme (i) leads to a convergence to self-consistency that is independent of system size, (ii) is extremely robust in the choice of the mixing and preconditioning parameters, (iii) scales linearly with system size in computational cost, and (iv) conserves the total charge. We have related the preconditioning parameter to the density of states of the delocalized electrons at the Fermi energy and developed a model to choose the preconditioning parameter either prior to the calculation or on the fly. Our computationally validated model supports the hypothesis that, in the absence of Kerker preconditioning, the delocalized s and p electrons of simple and transition metals are the primary cause for the slowing of the convergence speed and that the stronger, localized d and f electrons account for only a small fraction of the charge sloshing problem. The presented formulation of the Kerker preconditioning scheme establishes an efficient methodology for the simulation of magnetic and nonmagnetic metallic large-scale material systems by means of muffin-tin-based all-electron methods.