It is well known that Professor H.F. Schaefer III played a very important role in the early days of parallel electronic structure theory. Therefore, it is appropriate to discuss modern highly parallel computing in the exscale era. The Hartree-Fock method, as a useful qualitative metric and building block for higher-accuracy quantum chemistry methods, is one of the fundamental computational methods in quantum chemistry. For this reason, an optimized Hartree-Fock algorithm is highly desirable for any quantum chemistry program. While numerous algorithms for the execution of the Hartree-Fock algorithm already exist, modern algorithms must be designed to optimally exploit the capabilities of modern supercomputers, which are at the verge of reaching exascale compute speeds. To that end, a new Hartree-Fock algorithm is proposed to achieve high scalability on modern supercomputers. Shell quartets are constructed via shell pairs combined from a binned shell pair container, allowing construction of exclusively the significant shell quartets and thus improving load balancing. Shell quartets are distributed across two layers of parallelism, with shell quartet batches being distributed across MPI ranks and individual shell quartets being distributed across individual threads within a rank. Quartets within a batch share a common bra shell pair and unique ket shell pairs. By distributing batches of shell quartets in such a manner, the Fock contraction step can be implemented with reduced thread synchronization compared to previous Hartree-Fock algorithms. In combining these aspects, the new Hartree-Fock algorithm achieves higher scalability compared to previous Hartree-Fock algorithms, a desirable trait for use on exascale supercomputers.

New, scalable Hartree-Fock algorithm for the exascale computing era

2019 Fall National Meeting

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