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Title: A Massively Parallel Implementation of the CCSD(T) Method Using the Resolution-of-the-Identity Approximation and a Hybrid Distributed/Shared Memory Parallelization Model

Journal Article · · Journal of Chemical Theory and Computation
ORCiD logo [1]; ORCiD logo [1]
  1. Ames Lab., and Iowa State Univ., Ames, IA (United States)
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In this work, 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 and -scaling computational costs, where NO and NV denote the number of correlated occupied and virtual orbitals, respectively. One of the algorithms assembles the four-center ERIs requiring NV4 and NO2NV2-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 [ Phys. Chem. Chem. Phys. 2014, 16, 22167-22178]. The CBS limit for the total interaction energy was estimated to be -9.64 kcal/mol.

Research Organization:
Ames Lab., Ames, IA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division; National Science Foundation (NSF)
Grant/Contract Number:
AC02-07CH11338; OCI-1047772
OSTI ID:
1817656
Report Number(s):
IS-J 10,553
Journal Information:
Journal of Chemical Theory and Computation, Vol. 17, Issue 8; ISSN 1549-9618
Publisher:
American Chemical SocietyCopyright Statement
Country of Publication:
United States
Language:
English

References (95)

Conformers of Gaseous Cysteine journal May 2009
Reduced scaling in electronic structure calculations using Cholesky decompositions journal June 2003
Approaching the Basis Set Limit of CCSD(T) Energies for Large Molecules with Local Natural Orbital Coupled-Cluster Methods journal August 2019
An efficient reformulation of the closed‐shell coupled cluster single and double excitation (CCSD) equations journal December 1988
Toward a W4-F12 approach: Can explicitly correlated and orbital-based ab initio CCSD(T) limits be reconciled? journal June 2016
Optimization of the Coupled Cluster Implementation in NWChem on Petascale Parallel Architectures journal September 2014
The MRCC program system: Accurate quantum chemistry from water to proteins journal February 2020
Tensor decomposition in post-Hartree–Fock methods. II. CCD implementation journal December 2013
A direct coupled cluster algorithm for massively parallel computers journal January 1997
Singular value decomposition approach for the approximate coupled-cluster method journal October 2003
Advances, Applications and Performance of the Global Arrays Shared Memory Programming Toolkit journal May 2006
Linear scaling density fitting journal November 2006
General implementation of the resolution-of-the-identity and Cholesky representations of electron repulsion integrals within coupled-cluster and equation-of-motion methods: Theory and benchmarks journal October 2013
Linear scaling coupled cluster and perturbation theories in the atomic orbital basis journal November 1999
Array files for computational chemistry: MP2 energies journal January 2007
Accuracy and Efficiency of Coupled-Cluster Theory Using Density Fitting/Cholesky Decomposition, Frozen Natural Orbitals, and a t 1 -Transformed Hamiltonian journal May 2013
Combined Fragment Molecular Orbital Cluster in Molecule Approach to Massively Parallel Electron Correlation Calculations for Large Systems. journal April 2015
Carboxylate-Assisted Transition-Metal-Catalyzed C−H Bond Functionalizations: Mechanism and Scope journal March 2011
Recent developments in the general atomic and molecular electronic structure system journal April 2020
Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations journal February 2002
Non-iterative fifth-order triple and quadruple excitation energy corrections in correlated methods journal February 1990
Parallel Calculation of Coupled Cluster Singles and Doubles Wave Functions Using Array Files journal May 2007
Coupled‐cluster singles, doubles and perturbative triples with density fitting approximation for massively parallel heterogeneous platforms journal January 2019
S66: A Well-balanced Database of Benchmark Interaction Energies Relevant to Biomolecular Structures journal July 2011
A fully direct RI-HF algorithm: Implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency journal August 2002
Localizability of dynamic electron correlation journal September 1983
Combined Experimental and Computational Investigations of Rhodium- and Ruthenium-Catalyzed C–H Functionalization of Pyrazoles with Alkynes journal February 2014
The fragment molecular orbital method: theoretical development, implementation in GAMESS, and applications: Fragment molecular orbital method in GAMESS journal June 2017
Optimized accurate auxiliary basis sets for RI-MP2 and RI-CC2 calculations for the atoms Rb to Rn journal January 2007
RI-MP2: optimized auxiliary basis sets and demonstration of efficiency journal September 1998
Extensions of the S66 Data Set: More Accurate Interaction Energies and Angular-Displaced Nonequilibrium Geometries journal October 2011
Massively Parallel Implementation of Explicitly Correlated Coupled-Cluster Singles and Doubles Using TiledArray Framework journal December 2016
A new hierarchical parallelization scheme: Generalized distributed data interface (GDDI), and an application to the fragment molecular orbital method (FMO) journal January 2004
Ab initio molecular simulations with numeric atom-centered orbitals journal November 2009
Density fitting with auxiliary basis sets from Cholesky decompositions journal July 2009
Tensor-structured coupled cluster theory journal November 2017
Fragmentation Methods: A Route to Accurate Calculations on Large Systems journal August 2011
A Non-antisymmetric Tensor Contraction Engine for the Automated Implementation of Spin-Adapted Coupled Cluster Approaches journal May 2013
Efficient Parallel Implementation of the CCSD External Exchange Operator and the Perturbative Triples (T) Energy Calculation journal September 2008
A massively parallel tensor contraction framework for coupled-cluster computations journal December 2014
Tensor decomposition in post-Hartree–Fock methods. I. Two-electron integrals and MP2 journal February 2011
Activation of C−H Bonds by Metal Complexes journal December 1997
An efficient and near linear scaling pair natural orbital based local coupled cluster method journal January 2013
Local perturbative triples correction (T) with linear cost scaling journal February 2000
Comprehensive Thermochemical Benchmark Set of Realistic Closed-Shell Metal Organic Reactions journal March 2018
Enabling the Efficient Use of SMP Clusters: The GAMESS/DDI Model conference January 2003
Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory journal July 2012
Integral-Direct and Parallel Implementation of the CCSD(T) Method: Algorithmic Developments and Large-Scale Applications journal November 2019
Simplifications in the generation and transformation of two-electron integrals in molecular calculations journal October 1977
The orbital-specific-virtual local coupled cluster singles and doubles method journal April 2012
Density-functional exchange-energy approximation with correct asymptotic behavior journal September 1988
Communication: Acceleration of coupled cluster singles and doubles via orbital-weighted least-squares tensor hypercontraction journal May 2014
Coupled‐cluster theory employing approximate integrals: An approach to avoid the input/output and storage bottlenecks journal July 1994
Optimization of the linear-scaling local natural orbital CCSD(T) method: Redundancy-free triples correction using Laplace transform journal June 2017
Rank reduced coupled cluster theory. I. Ground state energies and wavefunctions journal April 2019
High-Level Ab Initio Electronic Structure Calculations of Water Clusters (H 2 O) 16 and (H 2 O) 17 : A New Global Minimum for (H 2 O) 16 journal October 2010
Higher excitations in coupled-cluster theory journal August 2001
Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen journal January 1989
Effects of London dispersion on the isomerization reactions of large organic molecules: a density functional benchmark study journal January 2010
Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions journal May 1992
A fifth-order perturbation comparison of electron correlation theories journal May 1989
Coulombic potential energy integrals and approximations journal May 1973
Comparison of the boys and Pipek-Mezey localizations in the local correlation approach and automatic virtual basis selection journal June 1993
The Distributed Data Interface in GAMESS journal June 2000
A fully simultaneously optimizing genetic approach to the highly excited coupled-cluster factorization problem journal March 2011
Evaluation of the contribution from triply excited intermediates to the fourth-order perturbation theory energy on Intel distributed memory supercomputers journal January 1993
Basis-set convergence in correlated calculations on Ne, N2, and H2O journal April 1998
CC2 excitation energy calculations on large molecules using the resolution of the identity approximation journal January 2000
Single-reference, size-extensive, non-iterative coupled-cluster approaches to bond breaking and biradicals journal February 2006
Unbiased auxiliary basis sets for accurate two-electron integral approximations journal September 2007
Coupled-cluster theory in quantum chemistry journal February 2007
Linear scaling local correlation approach for solving the coupled cluster equations of large systems journal December 2001
Use of approximate integrals in ab initio theory. An application in MP2 energy calculations journal June 1993
Multilevel Extension of the Cluster-in-Molecule Local Correlation Methodology: Merging Coupled-Cluster and Møller−Plesset Perturbation Theories journal June 2010
Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy journal January 2005
Local configuration interaction: An efficient approach for larger molecules journal January 1985
General atomic and molecular electronic structure system journal November 1993
Communication: An improved linear scaling perturbative triples correction for the domain based local pair-natural orbital based singles and doubles coupled cluster method [DLPNO-CCSD(T)] journal January 2018
Renormalized coupled-cluster methods exploiting left eigenstates of the similarity-transformed Hamiltonian journal December 2005
Scalable Electron Correlation Methods. 3. Efficient and Accurate Parallel Local Coupled Cluster with Pair Natural Orbitals (PNO-LCCSD) journal July 2017
Hybrid Distributed/Shared Memory Model for the RI-MP2 Method in the Fragment Molecular Orbital Framework journal September 2019
A Novel Approach to Parallel Coupled Cluster Calculations:  Combining Distributed and Shared Memory Techniques for Modern Cluster Based Systems journal May 2007
Massive-Parallel Implementation of the Resolution-of-Identity Coupled-Cluster Approaches in the Numeric Atom-Centered Orbital Framework for Molecular Systems journal July 2019
An Introduction to Coupled Cluster Theory for Computational Chemists book January 2000
Agostic interactions in transition metal compounds journal April 2007
Natural triple excitations in local coupled cluster calculations with pair natural orbitals journal October 2013
Accurate local approximations to the triples correlation energy: formulation, implementation and tests of 5th-order scaling models journal January 2005
Energy-adjustedab initio pseudopotentials for the second and third row transition elements journal January 1990
On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell‐Type Expansion Using Quantum‐Field Theoretical Methods journal December 1966
Software design of ACES III with the super instruction architecture: Software design of ACES III
  • Deumens, Erik; Lotrich, Victor F.; Perera, Ajith
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 1, Issue 6 https://doi.org/10.1002/wcms.77
journal June 2011
Local treatment of electron correlation in coupled cluster theory journal April 1996
Reevaluating Amdahl's law journal May 1988
A parallel vectorized implementation of triple excitations in CCSD(T): application to the binding energies of the AlH3, AlH2F, AlHF2 and AlF3 dimers journal April 1991
Integral approximations for LCAO-SCF calculations journal October 1993
Local correlation calculations using standard and renormalized coupled-cluster approaches journal September 2009

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