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International Journal of Quantum Chemistry

Efficient parallel algorithm of second‐order Møller–Plesset perturbation theory with resolution‐of‐identity approximation (RI‐MP2)

Michio Katouda, Shigeru Nagase

Published Jan 1, 2009• 71 citations
Publisher

Abstract

Abstract An efficient parallel algorithm is developed for second‐order Møller–Plesset perturbation theory with the resolution‐of‐identity approximation of two‐electron repulsion integrals (RI‐MP2) to perform MP2 energy calculations of large molecules on distributed memory processors. Benchmark calculations are carried out for taxol (C47H51NO14), valinomycin (C54H90N6O18), and two‐layer nanographene sheets (C96H24)2, which show the high parallel efficiency of the developed algorithm. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

DOI
10.1002/qua.22068

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Abstract An efficient parallel algorithm is developed for second‐order Møller–Plesset perturbation theory with the resolution‐of‐identity approximation of two‐electron repulsion integrals (RI‐MP2) to perform MP2 energy calculations of large molecules on distributed memory processors. Benchmark calculations are carried out for taxol (C47H51NO14), valinomycin (C54H90N6O18), and two‐layer nanographene sheets (C96H24)2, which show the high parallel efficiency of the developed algorithm. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009
Second-order Møller-Plesset perturbation theory (MP2) using the Resolution of the Identity approximation (RI-MP2) is a widely used method for computing molecular energies beyond the Hartree-Fock mean-field approximation. However, its high computational cost and lack of efficient algorithms for modern supercomputing architectures limit its applicability to large molecules. In this paper, we present the first distributed-memory many-GPU RI-MP2 algorithm explicitly designed to utilize hundreds of GPU accelerators for every step of the computation. Our novel algorithm achieves near-peak performance on GPU-based supercomputers through the development of a distributed memory algorithm for forming RI-MP2 intermediate tensors with zero inter-node communication, except for a single O(N^2) asynchronous broadcast, and a distributed memory algorithm for the O(N^5) energy reduction step, capable of sustaining near-peak performance on clusters with several hundred GPUs. Comparative analysis shows our implementation outperforms state-of-the-art quantum chemistry software by over 3.5 times in speed while achieving an eightfold reduction in computational power consumption. Benchmarking on the Perlmutter supercomputer, our algorithm achieves 11.8 PFLOP/s (83% of peak performance) performing and the RI-MP2 energy calculation on a 314-water cluster with 7,850 primary and 30,144 auxiliary basis functions in 4 minutes on 180 nodes and 720 A100 GPUs. This performance represents a substantial improvement over traditional CPU-based methods, demonstrating significant time-to-solution and power consumption benefits of leveraging modern GPU-accelerated computing environments for quantum chemistry calculations.
A hybrid MPI/OpenMP parallel code of the explicitly correlated second‐order Møller–Plesset perturbation theory (MP2‐F12) is implemented into the GELLAN program for massively parallel computations on the K computer in Japan. Various many‐electron integrals are generated using numerical quadrature techniques. For integral evaluation and transformation, we distribute the grid points to MPI processes to reduce the operation count and memory requirement. Operations over grid points are efficiently performed by the matrix–matrix product library (DGEMM). This numerical MP2‐F12 program achieves more than 30% of the peak performance of the K computer and the calculation of with aug‐cc‐pVTZ basis set finishes in less than 15 min using 8148 nodes (65,184 cores) of the K computer. The implementation enables us to use MP2‐F12/aug‐cc‐pVTZ level of theory routinely for large molecules such as organic photovoltaics and electronic materials. © 2014 Wiley Periodicals, Inc.
A stochastic orbital approach to the resolution of identity (RI) approximation for 4-index 2-electron electron repulsion integrals (ERIs) is presented. The stochastic RI-ERIs are then applied to Møller-Plesset perturbation theory (MP2) utilizing a \textit{multiple stochastic orbital approach}. The introduction of multiple stochastic orbitals results in an N3N^3N3 scaling for both the stochastic RI-ERIs and stochastic RI-MP2. We demonstrate that this method exhibits a small prefactor and an observed scaling of N2.4N^{2.4}N2.4 for a range of water clusters, already outperforming MP2 for clusters with as few as 21 water molecules.
Second-order Møller-Plesset perturbation theory using the Resolution-of-the-Identity approximation (RI-MP2) is a state-of-the-art approach to accurately estimate many-body electronic correlation effects. This is critical for predicting the physicochemical properties of complex molecular systems; however, the scale of these calculations is limited by their extremely high computational cost. In this paper, a novel many-GPU algorithm and implementation of a molecular-fragmentation-based RI-MP2 method are presented that enable correlated calculations on over 180,000 electrons and 45,000 atoms using up to the entire Summit supercomputer in 12 minutes. The implementation demonstrates remarkable speedups with respect to other current GPU and CPU codes, excellent strong scalability on Summit achieving 89.1% parallel efficiency on 4600 nodes, and shows nearly-ideal weak scaling up to 612 nodes. This work makes feasible ab initio correlated quantum chemistry calculations on significantly larger molecular scales than before on both large supercomputing systems and on commodity clusters, with a potential for major impact on progress in chemical, physical, biological and engineering sciences.
The modification of a general purpose code for quantum mechanical calculations of molecular properties (Q-Chem) to use a graphical processing unit (GPU) is reported. A 4.3x speedup of the resolution-of-the-identity second-order Møller-Plesset perturbation theory (RI-MP2) execution time is observed in single point energy calculations of linear alkanes. The code modification is accomplished using the compute unified basic linear algebra subprograms (CUBLAS) library for an NVIDIA Quadro FX 5600 graphics card. Furthermore, speedups of other matrix algebra based electronic structure calculations are anticipated as a result of using a similar approach.
This article presents a novel algorithm for the calculation of analytic energy gradients from second-order Møller-Plesset perturbation theory within the Resolution-of-the-Identity approximation (RI-MP2), which is designed to achieve high performance on clusters with multiple graphical processing units (GPUs). The algorithm uses GPUs for all major steps of the calculation, including integral generation, formation of all required intermediate tensors, solution of the Z-vector equation and gradient accumulation. The implementation in the EXtreme Scale Electronic Structure System (EXESS) software package includes a tailored, highly efficient, multistream scheduling system to hide CPU-GPU data transfer latencies and allows nodes with 8 A100 GPUs to operate at over 80% of theoretical peak floating-point performance. Comparative performance analysis shows a significant reduction in computational time relative to traditional multicore CPU-based methods, with our approach achieving up to a 95-fold speedup over the single-node performance of established software such as Q-Chem and ORCA. Additionally, we demonstrate that pairing our implementation with the molecular fragmentation framework in EXESS can drastically lower the computational scaling of RI-MP2 gradient calculations from quintic to subquadratic, enabling further substantial savings in runtime while retaining high numerical accuracy in the resulting gradients.