Hybrid Distributed/Shared Memory Model for the RI-MP2 Method in the Fragment Molecular Orbital Framework

Abstract

The general distributed data interface (GDDI) that was developed for the fragment molecular orbital (FMO) method is combined with the shared memory OpenMP parallel middleware to support a threading multilevel parallelism. First, GDDI partitions [logical] compute nodes into groups, which are statically or dynamically assigned to different fragments. A small number of processes are created on each compute node. Each process subsequently spawns multiple threads for the actual computation. The performance of the hybrid GDDI/OpenMP approach relative to the pure GDDI model was examined in terms of the FMO/RI-MP2 method; that is, the second-order Moller−Plesset (MP2) correlation energy was evaluated using the resolution-of-the-identity (RI) and the FMO approximations. The GDDI and OpenMP workload balances are handled by an arithmetic progression and a loop fusion, respectively. Other OpenMP properties, such as threadprivate or shared memory, are combined with the low memory demand of the RI two-electron integrals to enhance the performance. Benchmark calculations demonstrate that because the hybrid parallel model can make use of multiprocessor resources more efficiently than the regular distributed memory-based GDDI model, calculations for small to large water clusters containing 139−2165 molecules and an ionic liquid cluster exhibit node linear scaling and speedups of a factor of 10×.

PDG: A Composite Method Based on the Resolution of the Identity

“…Bottlenecks in the RI-G3 method, including the HF/6-31G­(d) gradient, RI-MP2/6-31G­(d) gradient, RI-CCSD­(T)/6-31G­(d), and RI-MP2/G3L single point energy calculations have been parallelized using the hybrid distributed/shared memory models based on MPI and OpenMP API. In practice, one MPI rank is created on each compute node or socket, which then spawns a team of threads for the actual computation.…”

“…This subsequently minimizes the memory footprint compared with the distributed model that needs to replicate most data structures. The performance of MPI/OpenMP for the RI-MP2 energy and gradient and the RI-CCSD­(T) energy have been implemented and demonstrated previously. − These methods are interfaced with the G3 driver for the MPI/OpenMP RI-G3 method, whose accuracy and performance are discussed in the next sections.…”

“…One approach to reduce the computational effort as well as the memory footprint of correlated electronic structure methods is to apply the resolution of the identity (RI) approximation. − In the RI approximation one employs an auxiliary basis set to reduce time-consuming and memory-demanding 4-index 2-electron integrals to 3-index 2-electron integrals. Recently, the authors have derived and implemented in GAMESS computationally efficient second-order perturbation theory (MP2) energies and gradients and coupled cluster with singles, doubles, and noniterative triples [CCSD­(T)] energies within the RI ansatz . In this work, the RI-MP2 and RI-CCSD­(T) methods in GAMESS are used in a reformulation of the Gaussian-3 (G3) method. − The accuracy of this new RI-G3 method, also called the PDG method, is essentially the same as that of the original method, while the computational efficiency and memory footprint are greatly improved.…”

“…They might even get slower due to the limitation of the memory resource per compute process and/or reduction of the CPU frequency of individual processing units. Therefore, employing a hybrid programming model, which uses shared memory for on-node parallelism and distributed memory for internode communication, is a natural approach to boost application performance. , In combination with the reduction of the memory footprint, enabling node shared memory using lightweight threading processes can potentially maximize local computation and speed up calculations.…”

“…Recently, the MPI/OpenMP hybrid distributed/shared memory parallel programming model has been applied to the RI-MP2 energy and gradient and RI-CCSD­(T) energy and implemented in the GAMESS suite of electronic structure programs. These new algorithms have been demonstrated to significantly increase the performance and the applicability domain of these electron correlation methods.…”