Scalable computational approach to extract chemical bonding from real-space density functional theory calculations using finite-element basis: A projected orbital and Hamiltonian population analysis

Abstract

We present an efficient and scalable computational approach for conducting projected population analysis from real-space finite-element (FE) based Kohn-Sham density functional theory calculations (DFT-FE). This work provides an important direction towards extracting chemical bonding information from large-scale DFT calculations on materials systems involving thousands of atoms while accommodating periodic, semi-periodic or fully non-periodic boundary conditions. Towards this, we derive the relevant mathematical expressions and develop efficient numerical implementation procedures that are scalable on multi-node CPU architectures to compute the projected overlap and Hamilton populations. This is accomplished by projecting either the self-consistently converged FE discretized Kohn-Sham eigenstates, or the FE discretized Hamiltonian onto a subspace spanned by localized atom-centered basis set. The proposed method is implemented in a unified framework within DFT-FE where the ground-state DFT calculations and the population analysis are performed on the same finite-element grid. We further benchmark the accuracy and performance of this approach on representative material systems involving periodic and non-periodic DFT calculations with LOBSTER, a widely used projected population analysis code. Finally, we discuss a case study demonstrating the advantages of our scalable approach to extract the chemical bonding information from increasingly large silicon nanoparticles up to a few thousand atoms.Comment: 9 Figures, 5 Tables, 53 pages with references and supplementary informatio