51
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Nagy PR, Kállay M. Optimization of the linear-scaling local natural orbital CCSD(T) method: Redundancy-free triples correction using Laplace transform. J Chem Phys 2017; 146:214106. [PMID: 28576082 PMCID: PMC5453808 DOI: 10.1063/1.4984322] [Citation(s) in RCA: 66] [Impact Index Per Article: 9.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2017] [Accepted: 05/05/2017] [Indexed: 01/30/2023] Open
Abstract
An improved algorithm is presented for the evaluation of the (T) correction as a part of our local natural orbital (LNO) coupled-cluster singles and doubles with perturbative triples [LNO-CCSD(T)] scheme [Z. Rolik et al., J. Chem. Phys. 139, 094105 (2013)]. The new algorithm is an order of magnitude faster than our previous one and removes the bottleneck related to the calculation of the (T) contribution. First, a numerical Laplace transformed expression for the (T) fragment energy is introduced, which requires on average 3 to 4 times fewer floating point operations with negligible compromise in accuracy eliminating the redundancy among the evaluated triples amplitudes. Second, an additional speedup factor of 3 is achieved by the optimization of our canonical (T) algorithm, which is also executed in the local case. These developments can also be integrated into canonical as well as alternative fragmentation-based local CCSD(T) approaches with minor modifications. As it is demonstrated by our benchmark calculations, the evaluation of the new Laplace transformed (T) correction can always be performed if the preceding CCSD iterations are feasible, and the new scheme enables the computation of LNO-CCSD(T) correlation energies with at least triple-zeta quality basis sets for realistic three-dimensional molecules with more than 600 atoms and 12 000 basis functions in a matter of days on a single processor.
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Affiliation(s)
- Péter R Nagy
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Mihály Kállay
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
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52
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Kjærgaard T, Baudin P, Bykov D, Kristensen K, Jørgensen P. The divide–expand–consolidate coupled cluster scheme. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2017. [DOI: 10.1002/wcms.1319] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
| | - Pablo Baudin
- Department of ChemistryAarhus UniversityAarhusDenmark
| | - Dmytro Bykov
- Department of ChemistryAarhus UniversityAarhusDenmark
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53
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Schmitz G, Hättig C. Accuracy of Explicitly Correlated Local PNO-CCSD(T). J Chem Theory Comput 2017; 13:2623-2633. [DOI: 10.1021/acs.jctc.7b00180] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Gunnar Schmitz
- Department
of Chemistry, Aarhus Universitet, Aarhus 8000, Denmark
| | - Christof Hättig
- Arbeitsgruppe
Quantenchemie, Ruhr-Universität, Bochum 44780, Germany
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54
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Pavošević F, Peng C, Pinski P, Riplinger C, Neese F, Valeev EF. SparseMaps—A systematic infrastructure for reduced scaling electronic structure methods. V. Linear scaling explicitly correlated coupled-cluster method with pair natural orbitals. J Chem Phys 2017; 146:174108. [DOI: 10.1063/1.4979993] [Citation(s) in RCA: 93] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Fabijan Pavošević
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Chong Peng
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Peter Pinski
- Max Planck Institute for Chemical Energy Conversion, Stiftstr. 34-36, 45470 Mülheim an der Ruhr, Germany
| | - Christoph Riplinger
- Max Planck Institute for Chemical Energy Conversion, Stiftstr. 34-36, 45470 Mülheim an der Ruhr, Germany
| | - Frank Neese
- Max Planck Institute for Chemical Energy Conversion, Stiftstr. 34-36, 45470 Mülheim an der Ruhr, Germany
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
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55
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56
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Grüneis A, Hirata S, Ohnishi YY, Ten-no S. Perspective: Explicitly correlated electronic structure theory for complex systems. J Chem Phys 2017; 146:080901. [DOI: 10.1063/1.4976974] [Citation(s) in RCA: 47] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Andreas Grüneis
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart,
Germany
- Department Chemie, Technische Universität München (TUM), Lichtenbergstrasse 4, D-85747 Garching,
Germany
- Graduate School of Science, Technology, and Innovation,
Kobe University, Nada-ku, Kobe 657-8501,
Japan
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Yu-ya Ohnishi
- Graduate School of System Informatics, Kobe University, Nada-ku, Kobe 657-8501, Japan
| | - Seiichiro Ten-no
- Graduate School of Science, Technology, and Innovation,
Kobe University, Nada-ku, Kobe 657-8501,
Japan
- Graduate School of System Informatics, Kobe University, Nada-ku, Kobe 657-8501, Japan
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57
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Frank MS, Schmitz G, Hättig C. The PNO–MP2 gradient and its application to molecular geometry optimisations. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1263762] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Marius S. Frank
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, Bochum, Germany
| | - Gunnar Schmitz
- Deparment of Chemistry, Aarhus University, Aarhus C, Denmark
| | - Christof Hättig
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, Bochum, Germany
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58
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Peng C, Calvin JA, Pavošević F, Zhang J, Valeev EF. Massively Parallel Implementation of Explicitly Correlated Coupled-Cluster Singles and Doubles Using TiledArray Framework. J Phys Chem A 2016; 120:10231-10244. [DOI: 10.1021/acs.jpca.6b10150] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Chong Peng
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Justus A. Calvin
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Fabijan Pavošević
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Jinmei Zhang
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
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59
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Werner HJ. Communication: Multipole approximations of distant pair energies in local correlation methods with pair natural orbitals. J Chem Phys 2016; 145:201101. [DOI: 10.1063/1.4968595] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Affiliation(s)
- Hans-Joachim Werner
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
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60
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Menezes F, Kats D, Werner HJ. Local complete active space second-order perturbation theory using pair natural orbitals (PNO-CASPT2). J Chem Phys 2016; 145:124115. [DOI: 10.1063/1.4963019] [Citation(s) in RCA: 68] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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61
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Nagy PR, Samu G, Kállay M. An Integral-Direct Linear-Scaling Second-Order Møller-Plesset Approach. J Chem Theory Comput 2016; 12:4897-4914. [PMID: 27618512 DOI: 10.1021/acs.jctc.6b00732] [Citation(s) in RCA: 68] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
An integral-direct, iteration-free, linear-scaling, local second-order Møller-Plesset (MP2) approach is presented, which is also useful for spin-scaled MP2 calculations as well as for the efficient evaluation of the perturbative terms of double-hybrid density functionals. The method is based on a fragmentation approximation: the correlation contributions of the individual electron pairs are evaluated in domains constructed for the corresponding localized orbitals, and the correlation energies of distant electron pairs are computed with multipole expansions. The required electron repulsion integrals are calculated directly invoking the density fitting approximation; the storage of integrals and intermediates is avoided. The approach also utilizes natural auxiliary functions to reduce the size of the auxiliary basis of the domains and thereby the operation count and memory requirement. Our test calculations show that the approach recovers 99.9% of the canonical MP2 correlation energy and reproduces reaction energies with an average (maximum) error below 1 kJ/mol (4 kJ/mol). Our benchmark calculations demonstrate that the new method enables MP2 calculations for molecules with more than 2300 atoms and 26000 basis functions on a single processor.
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Affiliation(s)
- Péter R Nagy
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics , P.O. Box 91, Budapest H-1521, Hungary
| | - Gyula Samu
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics , P.O. Box 91, Budapest H-1521, Hungary
| | - Mihály Kállay
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics , P.O. Box 91, Budapest H-1521, Hungary
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62
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Pavošević F, Pinski P, Riplinger C, Neese F, Valeev EF. SparseMaps--A systematic infrastructure for reduced-scaling electronic structure methods. IV. Linear-scaling second-order explicitly correlated energy with pair natural orbitals. J Chem Phys 2016; 144:144109. [PMID: 27083710 DOI: 10.1063/1.4945444] [Citation(s) in RCA: 78] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a formulation of the explicitly correlated second-order Møller-Plesset (MP2-F12) energy in which all nontrivial post-mean-field steps are formulated with linear computational complexity in system size. The two key ideas are the use of pair-natural orbitals for compact representation of wave function amplitudes and the use of domain approximation to impose the block sparsity. This development utilizes the concepts for sparse representation of tensors described in the context of the domain based local pair-natural orbital-MP2 (DLPNO-MP2) method by us recently [Pinski et al., J. Chem. Phys. 143, 034108 (2015)]. Novel developments reported here include the use of domains not only for the projected atomic orbitals, but also for the complementary auxiliary basis set (CABS) used to approximate the three- and four-electron integrals of the F12 theory, and a simplification of the standard B intermediate of the F12 theory that avoids computation of four-index two-electron integrals that involve two CABS indices. For quasi-1-dimensional systems (n-alkanes), the ON DLPNO-MP2-F12 method becomes less expensive than the conventional ON(5) MP2-F12 for n between 10 and 15, for double- and triple-zeta basis sets; for the largest alkane, C200H402, in def2-TZVP basis, the observed computational complexity is N(∼1.6), largely due to the cubic cost of computing the mean-field operators. The method reproduces the canonical MP2-F12 energy with high precision: 99.9% of the canonical correlation energy is recovered with the default truncation parameters. Although its cost is significantly higher than that of DLPNO-MP2 method, the cost increase is compensated by the great reduction of the basis set error due to explicit correlation.
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Affiliation(s)
- Fabijan Pavošević
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Peter Pinski
- Max Planch Institute for Chemical Energy Conversion, Stiftstr. 34-36, D-45470 Mülheim an der Ruhr, Germany
| | - Christoph Riplinger
- Max Planch Institute for Chemical Energy Conversion, Stiftstr. 34-36, D-45470 Mülheim an der Ruhr, Germany
| | - Frank Neese
- Max Planch Institute for Chemical Energy Conversion, Stiftstr. 34-36, D-45470 Mülheim an der Ruhr, Germany
| | - Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
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63
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Kats D. Speeding up local correlation methods: System-inherent domains. J Chem Phys 2016; 145:014103. [DOI: 10.1063/1.4954963] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Daniel Kats
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
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64
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Roskop LB, Valeev EF, Carter EA, Gordon MS, Windus TL. Spin-Free [2]R12 Basis Set Incompleteness Correction to the Local Multireference Configuration Interaction and the Local Multireference Average Coupled Pair Functional Methods. J Chem Theory Comput 2016; 12:3176-84. [DOI: 10.1021/acs.jctc.6b00315] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Luke B. Roskop
- Department
of Chemistry, Iowa State University, Ames, Iowa 50010, United States
| | - Edward F. Valeev
- Department
of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Emily A. Carter
- Department
of Mechanical and Aerospace Engineering, Program in Applied and Computational
Mathematics, and Andlinger Center for Energy and the Environment, Princeton University, Princeton, New Jersey 08544, United States
| | - Mark S. Gordon
- Department
of Chemistry, Iowa State University, Ames, Iowa 50010, United States
| | - Theresa L. Windus
- Department
of Chemistry, Iowa State University, Ames, Iowa 50010, United States
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65
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Köppl C, Werner HJ. Parallel and Low-Order Scaling Implementation of Hartree–Fock Exchange Using Local Density Fitting. J Chem Theory Comput 2016; 12:3122-34. [DOI: 10.1021/acs.jctc.6b00251] [Citation(s) in RCA: 43] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Christoph Köppl
- Institut
für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring
55, 70569 Stuttgart, Germany
| | - Hans-Joachim Werner
- Institut
für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring
55, 70569 Stuttgart, Germany
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66
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Wang YM, Hättig C, Reine S, Valeev E, Kjærgaard T, Kristensen K. Explicitly correlated second-order Møller-Plesset perturbation theory in a Divide-Expand-Consolidate (DEC) context. J Chem Phys 2016; 144:204112. [DOI: 10.1063/1.4951696] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yang Min Wang
- qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Christof Hättig
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum, Germany
| | - Simen Reine
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033, N-1315 Blindern, Norway
| | - Edward Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Thomas Kjærgaard
- qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Kasper Kristensen
- qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
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