Fast all-electron density functional theory calculations in solids using orthogonalized enriched finite elements

We present a computationally efficient approach to perform real-space all-electron Kohn-Sham DFT calculations for bulk solids using an enriched finite element (FE) basis, wherein the classical FE basis are augmented with atom-centered numerical basis functions constructed from atomic solutions to the Kohn-Sham problem. We term these atom-centered numerical basis functions as enrichment functions. Notably, to improve the conditioning we orthogonalize the enrichment function with respect to the classical FE basis, without compromising on 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 acceleration technique to efficiently compute the occupied eigenspace in each self-consistent iteration. We demonstrate the accuracy and efficiency for periodic unit-cells and supercells, ranging up to 5000 electrons (containing as many as 500 atoms). We observe a staggering 50-100x speedup over the classical FE basis. We also benchmark with (L)APW(+lo) basis for accuracy and performance. Finally, we demonstrate parallel scalability for a system with ~216 Si and C atoms.