  Hybrid density functional approximations (DFAs) offer compelling accuracy for
ab initio electronic-structure simulations of molecules, nanosystems, and bulk
materials, addressing some deficiencies of computationally cheaper, frequently
used semilocal DFAs. However, the computational bottleneck of hybrid DFAs is
the evaluation of the non-local exact exchange contribution, which is the
limiting factor for the application of the method for large-scale simulations.
In this work, we present a drastically optimized resolution-of-identity-based
real-space implementation of the exact exchange evaluation for both
non-periodic and periodic boundary conditions in the all-electron code
FHI-aims, targeting high-performance CPU compute clusters. The introduction of
several new refined Message Passing Interface (MPI) parallelization layers and
shared memory arrays according to the MPI-3 standard were the key components of
the optimization. We demonstrate significant improvements of memory and
performance efficiency, scalability, and workload distribution, extending the
reach of hybrid DFAs to simulation sizes beyond ten thousand atoms. As a
necessary byproduct of this work, other code parts in FHI-aims have been
optimized as well, e.g., the computation of the Hartree potential and the
evaluation of the force and stress components. We benchmark the performance and
scaling of the hybrid DFA based simulations for a broad range of chemical
systems, including hybrid organic-inorganic perovskites, organic crystals and
ice crystals with up to 30,576 atoms (101,920 electrons described by 244,608
basis functions).
