We present recent developments of the NTChem program for performing large scale hybrid density functional theory calculations on the supercomputer Fugaku. We combine these developments with our recently proposed complexity reduction framework to assess the impact of basis set and functional choice on its measures of fragment quality and interaction. We further exploit the all electron representation to study system fragmentation in various energy envelopes. Building off this analysis, we propose two algorithms for computing the orbital energies of the Kohn–Sham Hamiltonian. We demonstrate that these algorithms can efficiently be applied to systems composed of thousands of atoms and as an analysis tool that reveals the origin of spectral properties.
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