Robust mixing in self-consistent linearized augmented planewave calculations

Abstract

We devise a mixing algorithm for full-potential (FP) all-electron calculations in the linearized augmented planewave (LAPW) method. Pulay’s direct inversion in the iterative subspace is complemented with the Kerker preconditioner and further improvements to achieve smooth convergence, avoiding charge sloshing and noise in the exchange–correlation potential. As the Kerker preconditioner was originally designed for the planewave basis, we have adapted it to the FP-LAPW method and implemented in the exciting code. Applications to the 2 × 2 Au(111) surface with a vacancy and to the Pd(111) surface demonstrate that this approach and our implementation work reliably with both density and potential mixing.

Solution to the Modified Helmholtz Equation for Arbitrary Periodic Charge Densities

“…In the previous Section 2.2 the interstitial Yukawa potential is used as boundary values for the Yukawa potential in the atomic spheres. This subsection is concerned with the construction of the Fourier transformable pseudo-charge density ρ α that replaces the true local charge density ρ α [see (11)] inside the muffin-tin sphere such that the Yukawa potential in the interstitial region,…”

“…By solving Eq. 1 for general periodic densities, the Kerker preconditioner [9] can be extended to density functional methods of general densities [10,11].…”

Resta-like preconditioning for self-consistent field iterations in the linearized augmented planewave method

“…They were originally devised for planewave based methods. Recent theoretical studies have shown a formulation of the Kerker preconditioner as well as its implementation in full-potential (FP) calculations with the linearized augmented planewave (LAPW) basis set [26,27]. The Resta preconditioner, however, is not yet reformulated to implement in the FP-LAPW method.…”

“…In practice, strong fluctuations in ρ out i caused by a small change of ρ in i prevent the convergence during the self-consistency iteration. This phenomenon is well-known as charge sloshing [17][18][19][20][21][22][23][24][25][26][27], which is more severe in metals with large supercells. To avoid this problem, one can add an effective preconditioner in Eq.…”

“…Based on this method, thus, the Hartree potential can be evaluated. Several studies have shown that it is still available for solving the screened Poisson equation [26,27,41]. Tran et al used this method for the implementation of screened hybrid functionals [41].…”