  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. The population analysis is accomplished by projecting either the
self-consistently converged FE discretized Kohn-Sham orbitals, or the FE
discretized Hamiltonian onto a subspace spanned by a localized atom-centred
basis set. The proposed methods are implemented in a unified framework within
DFT-FE code where the ground-state DFT calculations and the population analysis
are performed on the same FE 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
quantitative chemical bonding information of hydrogen chemisorbed in large
silicon nanoparticles alloyed with carbon, a candidate material for hydrogen
storage.
