An efficient MPI/OpenMP parallelization of the Hartree–Fock–Roothaan method for the first generation of Intel® Xeon Phi™ processor architecture

Abstract

The Hartree-Fock method in the General Atomic and Molecular Structure System (GAMESS) quantum chemistry package represents one of the most irregular algorithms in computation today. Major steps in the calculation are the irregular computation of electron repulsion integrals and the building of the Fock matrix. These are the central components of the main self consistent field (SCF) loop, the key hot spot in electronic structure codes. By threading the Message Passing Interface (MPI) ranks in the official release of the GAMESS code, we not only speed up the main SCF loop (43 to 63 for large systems) but also achieve a significant (.23) reduction in the overall memory footprint. These improvements are a direct consequence of memory access optimizations within the MPI ranks. We benchmark our implementation against the official release of the GAMESS code on the Intel â Xeon Phiä supercomputer. Scaling numbers are reported on up to 7680 cores on Intel Xeon Phi coprocessors.

Multithreaded parallelization of the energy and analytic gradient in the fragment molecular orbital method

“…It also eliminates intranode MPI communications. This hybrid MPI+OpenMP parallelization has been recently implemented in GAMESS …”

“…This matrix (Equation ) is composed of the internal contribution and ESP. The former is the usual Fock matrix as in non‐FMO calculations, and its parallelization is described elsewhere . Therefore, the description below (Sections 2.2.1 and 2.2.2) focuses on ESP, which is FMO specific, and according to Equation consists from one‐electron and two‐electron contributions.…”

“…The scheme in Algorithm 2 is a modification of the Fock matrix calculation . It contains nested loops over shells of fragment X (indices k and l ) and monomer L (indices i and j ).…”

“…This model executes multiple copies of GAMESS program per node, which is not very efficient on CPUs with a very large number of cores (eg, on Intel Xeon Phi processors 128 MPI processes per node are executed). To improve the memory usage and increase the computational efficiency, an OpenMP version of GAMESS has been developed independent of the two older OpenMP codes of GAMESS on the K computer and Cray XT5…”

Novel Computer Architectures and Quantum Chemistry

“…Hybrid MPI + OpenMP programming has found significant use in multiple modern electronic structure theory programs. Restricted Hartree−Fock (RHF) codes, such as GTFock, 148 the LibCChem RHF code, 89 and the OpenMP implementation of the GAMESS RHF code, 149 all use hybrid programming to improve code parallelism. These codes typically parallelize the Fock build by distributing the two electron integral shell quartets across different MPI ranks and then use multiple OpenMP threads within each MPI process to calculate its assigned shell quartet(s).…”