Fast and robust all-electron density functional theory calculations in solids using orthogonalized enriched finite elements
Nelson D. Rufus, Bikash Kanungo, Vikram Gavini
Abstract
We present a computationally efficient approach to perform systematically convergent real-space all-electron Kohn-Sham density functional theory calculations for solids using an enriched finite element (FE) basis. The enriched FE basis is constructed by augmenting the classical FE basis with atom-centered numerical basis functions, comprising of atomic solutions to the Kohn-Sham problem. Notably, to improve the conditioning, we orthogonalize the enrichment functions with respect to the classical FE basis, without sacrificing the locality of the resultant basis. In addition to improved conditioning, this orthogonalization procedure also renders the overlap matrix block diagonal, greatly simplifying its inversion. Subsequently, we use a Chebyshev polynomial based filtering technique to efficiently compute the occupied eigenspace in each self-consistent field iteration. We demonstrate the accuracy and efficiency of the proposed approach on periodic unit cells and supercells. The benchmark studies show a staggering $130\ifmmode\times\else\texttimes\fi{}$ speedup of the orthogonalized enriched FE basis over the classical FE basis. We also present a comparison of the orthogonalized enriched FE basis with the linearized augmented plane-wave $+$ local orbitals basis, both in terms of accuracy and efficiency. Notably, we demonstrate that the orthogonalized enriched FE basis can handle large system sizes of $\ensuremath{\sim}10\phantom{\rule{0.16em}{0ex}}000$ electrons. Finally, we observe good parallel scalability of our implementation with $92%$ efficiency at $22\ifmmode\times\else\texttimes\fi{}$ speedup for a system with 620 electrons.