Computation of two-electron repulsion integrals is the critical and the most time-consuming step in a typical parallel quantum chemistry simulation. Such calculations have massive computing and storage requirements, which scale as O(N^4) with the size of a chemical system. Compressing the integral's data and storing it on disk can avoid costly recalculation, significantly speeding the overall quantum chemistry calculations; but it requires a fast compression algorithm. To this end, we developed PaSTRI (Pattern Scaling for Two-electron Repulsion Integrals) and implemented the algorithm in the data compression package SZ. PaSTRI leverages the latent pattern features in the integral dataset and optimizes the calculation of the appropriate number of bits required for the storage of the integral. We have evaluated PaSTRI using integral datasets generated by the quantum chemistry program GAMESS. The results show an excellent 16.8 compression ratio with low overhead, while maintaining 10-10absolute precision based on user's requirement.

Modern OpenMP threading techniques are used to convert the MPI-only Hartree-Fock code in the GAMESS program to a hybrid MPI/OpenMP algorithm. Two separate implementations that differ by the sharing or replication of key data structures among threads are considered, density and Fock matrices. All implementations are benchmarked on a super-computer of 3,000 Intel® Xeon Phi™ processors. With 64 cores per processor, scaling numbers are reported on up to 192,000 cores. The hybrid MPI/OpenMP implementation reduces the memory footprint by approximately 200 times compared to the legacy code. The MPI/OpenMP code was shown to run up to six times faster than the original for a range of molecular system sizes.