Authors: Dipayan Datta | Mark S. Gordon
Source: Journal of Chemical Theory and Computation (article, 2021-07-19)
Field: Chemistry — Spectroscopy

A Massively Parallel Implementation of the CCSD(T) Method Using the Resolution-of-the-Identity Approximation and a Hybrid Distributed/Shared Memory Parallelization Model A parallel algorithm is described for the coupled-cluster singles and doubles method augmented with a perturbative correction for triple excitations [CCSD(T)] using the resolution-of-the-identity (RI) approximation for two-electron repulsion integrals (ERIs). The algorithm bypasses the storage of four-center ERIs by adopting an integral-direct strategy. The CCSD amplitude equations are given in a compact quasi-linear form by factorizing them in terms of amplitude-dressed three-center intermediates. A hybrid MPI/OpenMP parallelization scheme is employed, which uses the OpenMP-based shared memory model for intranode parallelization and the MPI-based distributed memory model for internode parallelization. Parallel efficiency has been optimized for all terms in the CCSD amplitude equations. Two different algorithms have been implemented for the rate-limiting terms in the CCSD amplitude equations that entail <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>O</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:msubsup><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>O</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msubsup><mml:msubsup><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:math>-scaling computational costs, where <i>N</i><sub><i>O</i></sub> and <i>N</i><sub><i>V</i></sub> denote the number of correlated occupied and virtual orbitals, respectively. One of the algorithms assembles the four-center ERIs requiring <i>N</i><sub><i>V</i></sub><sup>4</sup> and <i>N</i><sub><i>O</i></sub><sup>2</sup><i>N</i><sub><i>V</i></sub><sup>2</sup>-scaling memory costs in a distributed manner on a number of MPI ranks, while the other algorithm completely bypasses the assembling of quartic memory-scaling ERIs and thus largely reduces the memory demand. It is demonstrated that the former memory-expensive algorithm is faster on a few hundred cores, while the latter memory-economic algorithm shows a better strong scaling in the limit of a few thousand cores. The program is shown to exhibit a near-linear scaling, in particular for the compute-intensive triples correction step, on up to 8000 cores. The performance of the program is demonstrated via calculations involving molecules with 24-51 atoms and up to 1624 atomic basis functions. As the first application, the complete basis set (CBS) limit for the interaction energy of the π-stacked uracil dimer from the S66 data set has been investigated. This work reports the first calculation of the interaction energy at the CCSD(T)/aug-cc-pVQZ level without local orbital approximation. The CBS limit for the CCSD correlation contribution to the interaction energy was found to be -8.01 kcal/mol, which agrees very well with the value -7.99 kcal/mol reported by Schmitz, Hättig, and Tew [ <i>Phys. Chem. Chem. Phys.</i> 2014, 16, 22167-22178]. The CBS limit for the total interaction energy was estimated to be -9.64 kcal/mol. Scaling ; Computer science ; Parallel computing ; Shared memory ; Massively parallel ; Linear scale ; Distributed memory ; Parallel algorithm ; Mathematics ; Geometry Advanced NMR Techniques and Applications ; Advanced Chemical Physics Studies ; Lanthanide and Transition Metal Complexes