  This work presents a dynamic parallel distribution scheme for the
Hartree-Fock exchange~(HFX) calculations based on the real-space NAO2GTO
framework. The most time-consuming electron repulsion integrals~(ERIs)
calculation is perfectly load-balanced with 2-level master-worker dynamic
parallel scheme, the density matrix and the HFX matrix are both stored in the
sparse format, the network communication time is minimized via only
communicating the index of the batched ERIs and the final sparse matrix form of
the HFX matrix. The performance of this dynamic scalable distributed algorithm
has been demonstrated by several examples of large scale hybrid
density-functional calculations on Tianhe-2 supercomputers, including both
molecular and solid states systems with multiple dimensions, and illustrates
good scalability.
