  Linear scaling density functional theory approaches to electronic structure
are often based on the tendency of electrons to localize even in large atomic
and molecular systems. However, in many cases of actual interest, for example
in semiconductor nanocrystals, system sizes can reach very large extension
before significant electron localization sets in and the scaling of the
numerical methods may deviate strongly from linear. Here, we address this class
of systems, by developing a massively parallel density functional theory (DFT)
approach which doesn't rely on electron localizationa and is formally quadratic
scaling, yet enables highly efficient linear wall-time complexity in the weak
scalability regime. The approach extends from the stochastic DFT method
described in Fabian et. al. WIRES: Comp. Mol. Science, e1412 2019 but is fully
deterministic. It uses standard quantum chemical atom-centered Gaussian basis
sets for representing the electronic wave functions combined with Cartesian
real space grids for some of the operators and for enabling a fast solver for
the Poisson equation. Our main conclusion is, that when a processor-abundant
high performance computing (HPC) infrastructure is available, this type of
approach has the potential to allow the study of large systems in regimes where
quantum confinement or electron delocalization prevents linear-scaling.
