1
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Zheng Y, Ni Z, Wang Y, Li W, Li S. Analytical Gradient Using Cluster-in-Molecule RI-MP2 Method for the Geometry Optimizations of Large Systems. J Chem Theory Comput 2024; 20:3626-3636. [PMID: 38626287 DOI: 10.1021/acs.jctc.4c00087] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/18/2024]
Abstract
We present an efficient analytical energy gradient algorithm for the cluster-in-molecule resolution-of-identity second-order Møller-Plesset perturbation (CIM-RI-MP2) method based on the Lagrange multiplier method. Our algorithm independently constructs the Lagrangian formalism within each cluster, avoiding the solution of the coupled-perturbed Hartree-Fock (CPHF) equation for the whole system. Due to this feature, the computational cost of the CIM-RI-MP2 gradients is much lower than that of other local MP2 algorithms. Benchmark calculations of several molecules containing up to 312 atoms demonstrate the general applicability of our CIM-RI-MP2 gradient algorithm. The optimized structure of a 244-atom molecule using the CIM-RI-MP2 method with the cc-pVDZ basis set is in good agreement with the corresponding crystal structure. A single-point gradient calculation conducted for a molecular cage containing 972 atoms and 9612 basis functions takes 48 h on 25 nodes, utilizing a total of 600 CPU cores. The present CIM-RI-MP2 gradient program is applicable for obtaining the optimized geometries of large systems with hundreds of atoms.
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Affiliation(s)
- Yang Zheng
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, New Cornerstone Science Laboratory, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, Jiangsu 210023, P. R. China
| | - Zhigang Ni
- College of Material, Chemistry and Chemical Engineering, Key Laboratory of Organosilicon Chemistry and Material Technology of Ministry of Education, Hangzhou Normal University, Hangzhou 311121, P. R. China
| | - Yuqi Wang
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, New Cornerstone Science Laboratory, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, Jiangsu 210023, P. R. China
| | - Wei Li
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, New Cornerstone Science Laboratory, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, Jiangsu 210023, P. R. China
| | - Shuhua Li
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, New Cornerstone Science Laboratory, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, Jiangsu 210023, P. R. China
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2
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Werner HJ, Hansen A. Accurate Calculation of Isomerization and Conformational Energies of Larger Molecules Using Explicitly Correlated Local Coupled Cluster Methods in Molpro and ORCA. J Chem Theory Comput 2023; 19:7007-7030. [PMID: 37486154 DOI: 10.1021/acs.jctc.3c00270] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/25/2023]
Abstract
An overview of the approximations in the explicitly correlated local coupled cluster methods PNO-LCCSD(T)-F12 in Molpro and DLPNO-CCSD(T)F12 in ORCA is given. Options to select the domains of projected atomic orbitals (PAOs), pair natural orbitals (PNOs), and triples natural orbitals (TNOs) in both programs are described and compared in detail. The two programs are applied to compute isomerization and conformational energies of the ISOL24 and ACONFL test sets, where the former is part of the GMTKN55 benchmark suite. Thorough studies of basis set effects are presented for selected systems. These revealed large intramolecular basis set superposition effects that make it practically impossible to reliably determine the complete basis set (CBS) limits without including explicitly correlated terms. The latter strongly reduce the basis set dependence and at the same time also errors caused by the local domain approximations. On the basis of these studies, the PNO-LCCSD(T)-F12 method is applied to determine new reference energies for the above-mentioned benchmark sets. We are confident that our results should agree within a few tenths of a kcal mol-1 with the (unknown) CCSD(T)/CBS values, which therefore allowed us to define computational settings for accurate explicitly correlated local coupled cluster methods with moderate computational effort. With these protocols, especially PNO-LCCSD(T)-F12b/AVTZ', reliable reference values for comprehensive benchmark sets can be generated efficiently. This can significantly advance the development and evaluation of the performance of approximate electronic structure methods, especially improved density functional approximations or machine learning approaches.
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Affiliation(s)
- Hans-Joachim Werner
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
| | - Andreas Hansen
- Mulliken Center for Theoretical Chemistry, Universität Bonn, Beringstrasse 4, D-53115 Bonn, Germany
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3
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Corzo HH, Hillers-Bendtsen AE, Barnes A, Zamani AY, Pawłowski F, Olsen J, Jørgensen P, Mikkelsen KV, Bykov D. Corrigendum: Coupled cluster theory on modern heterogeneous supercomputers. Front Chem 2023; 11:1256510. [PMID: 37654900 PMCID: PMC10466216 DOI: 10.3389/fchem.2023.1256510] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2023] [Accepted: 07/11/2023] [Indexed: 09/02/2023] Open
Abstract
[This corrects the article DOI: 10.3389/fchem.2023.1154526.].
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Affiliation(s)
| | | | | | - Abdulrahman Y. Zamani
- Department of Chemistry and Biochemistry and Center for Chemical Computation and Theory, University of California, Merced, CA, United States
| | - Filip Pawłowski
- Department of Chemistry and Biochemistry, Auburn University, Auburn, AL, United States
| | - Jeppe Olsen
- Department of Chemistry, Aarhus University, Aarhus, Denmark
| | - Poul Jørgensen
- Department of Chemistry, Aarhus University, Aarhus, Denmark
| | - Kurt V. Mikkelsen
- Department of Chemistry, University of Copenhagen, Copenhagen, Denmark
| | - Dmytro Bykov
- Oak Ridge National Laboratory, Oak Ridge, TN, United States
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4
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Corzo HH, Hillers-Bendtsen AE, Barnes A, Zamani AY, Pawłowski F, Olsen J, Jørgensen P, Mikkelsen KV, Bykov D. Coupled cluster theory on modern heterogeneous supercomputers. Front Chem 2023; 11:1154526. [PMID: 37388945 PMCID: PMC10303140 DOI: 10.3389/fchem.2023.1154526] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Accepted: 05/11/2023] [Indexed: 07/01/2023] Open
Abstract
This study examines the computational challenges in elucidating intricate chemical systems, particularly through ab-initio methodologies. This work highlights the Divide-Expand-Consolidate (DEC) approach for coupled cluster (CC) theory-a linear-scaling, massively parallel framework-as a viable solution. Detailed scrutiny of the DEC framework reveals its extensive applicability for large chemical systems, yet it also acknowledges inherent limitations. To mitigate these constraints, the cluster perturbation theory is presented as an effective remedy. Attention is then directed towards the CPS (D-3) model, explicitly derived from a CC singles parent and a doubles auxiliary excitation space, for computing excitation energies. The reviewed new algorithms for the CPS (D-3) method efficiently capitalize on multiple nodes and graphical processing units, expediting heavy tensor contractions. As a result, CPS (D-3) emerges as a scalable, rapid, and precise solution for computing molecular properties in large molecular systems, marking it an efficient contender to conventional CC models.
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Affiliation(s)
| | | | | | - Abdulrahman Y. Zamani
- Department of Chemistry and Biochemistry and Center for Chemical Computation and Theory, University of California, Merced, CA, United States
| | - Filip Pawłowski
- Department of Chemistry and Biochemistry, Auburn University, Auburn, AL, United States
| | - Jeppe Olsen
- Department of Chemistry, Aarhus University, Aarhus, Denmark
| | - Poul Jørgensen
- Department of Chemistry, Aarhus University, Aarhus, Denmark
| | - Kurt V. Mikkelsen
- Department of Chemistry, University of Copenhagen, Copenhagen, Denmark
| | - Dmytro Bykov
- Oak Ridge National Laboratory, Oak Ridge, TN, United States
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5
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Bangerter F, Glasbrenner M, Ochsenfeld C. Tensor-Hypercontracted MP2 First Derivatives: Runtime and Memory Efficient Computation of Hyperfine Coupling Constants. J Chem Theory Comput 2022; 18:5233-5245. [PMID: 35943450 PMCID: PMC9476664 DOI: 10.1021/acs.jctc.2c00118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
We employ our recently introduced tensor-hypercontracted (THC) second-order Møller-Plesset perturbation theory (MP2) method [Bangerter, F. H., Glasbrenner, M., Ochsenfeld, C. J. Chem. Theory Comput. 2021, 17, 211-221] for the computation of hyperfine coupling constants (HFCCs). The implementation leverages the tensor structure of the THC factorized electron repulsion integrals for an efficient formation of the integral-based intermediates. The computational complexity of the most expensive and formally quintic scaling exchange-like contribution is reduced to effectively subquadratic, by making use of the intrinsic, exponentially decaying coupling between tensor indices through screening based on natural blocking. Overall, this yields an effective subquadratic scaling with a low prefactor for the presented THC-based AO-MP2 method for the computation of isotropic HFCCs on DNA fragments with up to 500 atoms and 5000 basis functions. Furthermore, the implementation achieves considerable speedups with up to a factor of roughly 600-1000 compared to previous implementations [Vogler, S., Ludwig, M., Maurer, M., Ochsenfeld, C. J. Chem. Phys. 2017, 147, 024101] for medium-sized organic radicals, while also significantly reducing storage requirements.
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Affiliation(s)
- Felix
H. Bangerter
- Chair
of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
| | - Michael Glasbrenner
- Chair
of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair
of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany,Max
Planck Institute for Solid State Research, D-70569 Stuttgart, Germany,
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6
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Liang Q, Yang J. Third-Order Many-Body Expansion of OSV-MP2 Wave Function for Low-Order Scaling Analytical Gradient Computation. J Chem Theory Comput 2021; 17:6841-6860. [PMID: 34704757 DOI: 10.1021/acs.jctc.1c00581] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
We present a many-body expansion (MBE) formulation and implementation for efficient computation of analytical energy gradients from the orbital-specific-virtual second-order Møllet-Plesset perturbation theory (OSV-MP2) based on our earlier work (Zhou et al. J. Chem. Theory Comput. 2020, 16, 196-210). The third-order MBE(3) expansion of OSV-MP2 amplitudes and density matrices was developed to adopt the orbital-specific clustering and long-range termination schemes, which avoids term-by-term differentiations of the MBE energy bodies. We achieve better efficiency by exploiting the algorithmic sparsity that allows us to prune out insignificant fitting integrals and OSV relaxations. With these approximations, the present implementation is benchmarked on a range of molecules that show an economic scaling in the linear and quadratic regimes for computing MBE(3)-OSV-MP2 amplitude and gradient equations, respectively, and yields normal accuracy comparable to the original OSV-MP2 results. The MPI-3-based parallelism through shared memory one-sided communication is further developed for improving parallel scalability and memory accessibility by sorting the MBE(3) orbital clusters into independent tasks that are distributed on multiple processes across many nodes, supporting both global and local data locations in which selected MBE(3)-OSV-MP2 intermediates of different sizes are distinguished and accordingly placed. The accuracy and efficiency level of our MBE(3)-OSV-MP2 analytical gradient implementation is finally illustrated in two applications: we show that the subtle coordination structure differences of mechanically interlocked Cu-catenane complexes can be distinguished when tuning ligand lengths; and the porphycene molecular dynamics reveals the emergence of the vibrational signature arising from softened N-H stretching associated with hydrogen transfer, using an MP2 level of electron correlation and classical nuclei for the first time.
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Affiliation(s)
- Qiujiang Liang
- Department of Chemistry, The University of Hong Kong, Hong Kong SAR, P. R. China
| | - Jun Yang
- Department of Chemistry, The University of Hong Kong, Hong Kong SAR, P. R. China
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7
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Hansen AS, Aurbakken E, Pedersen TB. Smooth potential-energy surfaces in fragmentation-based local correlation methods for periodic systems. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1896046] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- A. S. Hansen
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, Oslo, Norway
| | - E. Aurbakken
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, Oslo, Norway
| | - T. B. Pedersen
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, Oslo, Norway
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8
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Ma Q, Werner HJ. Scalable Electron Correlation Methods. 8. Explicitly Correlated Open-Shell Coupled-Cluster with Pair Natural Orbitals PNO-RCCSD(T)-F12 and PNO-UCCSD(T)-F12. J Chem Theory Comput 2021; 17:902-926. [PMID: 33405921 DOI: 10.1021/acs.jctc.0c01129] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Abstract
We present explicitly correlated open-shell pair natural orbital local coupled-cluster methods, PNO-RCCSD(T)-F12 and PNO-UCCSD(T)-F12. The methods are extensions of our previously reported PNO-R/UCCSD methods (J. Chem. Theory Comput., 2020, 16, 3135-3151, https://pubs.acs.org/doi/10.1021/acs.jctc.0c00192) with additions of explicit correlation and perturbative triples corrections. The explicit correlation treatment follows the spin-orbital CCSD-F12b theory using Ansatz 3*A, which is found to yield comparable or better basis set convergence than the more rigorous Ansatz 3C in computed ionization potentials and reaction energies using double- to quaduple-ζ basis sets. The perturbative triples correction is adapted from the spin-orbital (T) theory to use triples natural orbitals (TNOs). To address the coupling due to off-diagonal Fock matrix elements, the local triples amplitudes are iteratively solved using small domains of TNOs, and a semicanonical (T0) domain correction with larger domains is applied to reduce the domain errors. The performance of the methods is demonstrated through benchmark calculations on ionization potentials, radical stabilization energies, reaction energies of fragmentations and rearrangements in radical cations, and spin-state energy differences of iron complexes. For a few test sets where canonical calculations are feasible, PNO-RCCSD(T)-F12 results agree with the canonical ones to within 0.4 kcal mol-1, and this maximum error is reduced to below 0.2 kcal mol-1 when large local domains are used. For larger systems, results using different thresholds for the local approximations are compared to demonstrate that 1 kcal mol-1 level of accuracy can be achieved using our default settings. For a couple of difficult cases, it is demonstrated that the errors from individual approximations are only a fraction of 1 kcal mol-1, and the overall accuracy of the method does not rely on error compensations. In contrast to canonical calculations, the use of spin-orbitals does not lead to a significant increase of computational time and memory usage in the most expensive steps of PNO-R/UCCSD(T)-F12 calculations. The only exception is the iterative solution of the (T) amplitudes, which can be avoided without significant errors by using a perturbative treatment of the off-diagonal coupling, known as (T1) approximation. For most systems, even the semicanonical approximation (T0) leads only to small errors in relative energies. Our program is well parallelized and capable of computing accurate correlation energies for molecules with 100-200 atoms using augmented triple-ζ basis sets in less than a day of elapsed time on a small computer cluster.
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Affiliation(s)
- Qianli Ma
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
| | - Hans-Joachim Werner
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
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9
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Olsen JMH, Reine S, Vahtras O, Kjellgren E, Reinholdt P, Hjorth Dundas KO, Li X, Cukras J, Ringholm M, Hedegård ED, Di Remigio R, List NH, Faber R, Cabral Tenorio BN, Bast R, Pedersen TB, Rinkevicius Z, Sauer SPA, Mikkelsen KV, Kongsted J, Coriani S, Ruud K, Helgaker T, Jensen HJA, Norman P. Dalton Project: A Python platform for molecular- and electronic-structure simulations of complex systems. J Chem Phys 2020; 152:214115. [PMID: 32505165 DOI: 10.1063/1.5144298] [Citation(s) in RCA: 40] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Abstract
The Dalton Project provides a uniform platform access to the underlying full-fledged quantum chemistry codes Dalton and LSDalton as well as the PyFraME package for automatized fragmentation and parameterization of complex molecular environments. The platform is written in Python and defines a means for library communication and interaction. Intermediate data such as integrals are exposed to the platform and made accessible to the user in the form of NumPy arrays, and the resulting data are extracted, analyzed, and visualized. Complex computational protocols that may, for instance, arise due to a need for environment fragmentation and configuration-space sampling of biochemical systems are readily assisted by the platform. The platform is designed to host additional software libraries and will serve as a hub for future modular software development efforts in the distributed Dalton community.
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Affiliation(s)
- Jógvan Magnus Haugaard Olsen
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Simen Reine
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, N-0315 Oslo, Norway
| | - Olav Vahtras
- Department of Theoretical Chemistry and Biology, School of Engineering Sciences in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, SE-106 91 Stockholm, Sweden
| | - Erik Kjellgren
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark
| | - Peter Reinholdt
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark
| | - Karen Oda Hjorth Dundas
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Xin Li
- Department of Theoretical Chemistry and Biology, School of Engineering Sciences in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, SE-106 91 Stockholm, Sweden
| | - Janusz Cukras
- Department of Chemistry, University of Warsaw, 02-093 Warsaw, Poland
| | - Magnus Ringholm
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Erik D Hedegård
- Division of Theoretical Chemistry, Lund University, SE-223 62 Lund, Sweden
| | - Roberto Di Remigio
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Nanna H List
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA and SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Rasmus Faber
- DTU Chemistry, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
| | | | - Radovan Bast
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Thomas Bondo Pedersen
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, N-0315 Oslo, Norway
| | - Zilvinas Rinkevicius
- Department of Theoretical Chemistry and Biology, School of Engineering Sciences in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, SE-106 91 Stockholm, Sweden
| | - Stephan P A Sauer
- Department of Chemistry, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
| | - Kurt V Mikkelsen
- Department of Chemistry, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
| | - Jacob Kongsted
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark
| | - Sonia Coriani
- DTU Chemistry, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
| | - Kenneth Ruud
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Trygve Helgaker
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, N-0315 Oslo, Norway
| | - Hans Jørgen Aa Jensen
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark
| | - Patrick Norman
- Department of Theoretical Chemistry and Biology, School of Engineering Sciences in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, SE-106 91 Stockholm, Sweden
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10
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Schmitz G, Elm J. Assessment of the DLPNO Binding Energies of Strongly Noncovalent Bonded Atmospheric Molecular Clusters. ACS OMEGA 2020; 5:7601-7612. [PMID: 32280904 PMCID: PMC7144154 DOI: 10.1021/acsomega.0c00436] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2020] [Accepted: 03/11/2020] [Indexed: 05/03/2023]
Abstract
This work assesses the performance of DLPNO-CCSD(T0), DLPNO-MP2, and density functional theory methods in calculating the binding energies of a representative test set of 45 atmospheric acid-acid, acid-base, and acid-water dimer clusters. The performance of the approximate methods is compared to high level explicitly correlated CCSD(F12*)(T)/complete basis set (CBS) reference calculations. Out of the tested density functionals, ωB97X-D3(BJ) shows the best performance with a mean deviation of 0.09 kcal/mol and a maximum deviation of 0.83 kcal/mol. The RI-CC2/aug-cc-pV(T+d)Z level of theory severely overpredicts the cluster binding energies with a mean deviation of -1.31 kcal/mol and a maximum deviation up to -3.00 kcal/mol. Hence, RI-CC2/aug-cc-pV(T+d)Z should not be utilized for studying atmospheric molecular clusters. The DLPNO variants are tested both with and without the inclusion of explicit correlation (F12) in the wavefunction, with different pair natural orbital (PNO) settings (loosePNO, normalPNO, and tightPNO) and using both double and triple zeta basis sets. The performance of the DLPNO-MP2 methods is found to be independent of PNO settings and yield low mean deviations of -0.84 kcal/mol or below. However, DLPNO-MP2 requires explicitly correlated wavefunctions to yield maximum deviations below 1.40 kcal/mol. For obtaining high accuracy, with maximum deviation below ∼1.0 kcal/mol, either DLPNO-CCSD(T0)/aug-cc-pVTZ (normalPNO) calculations or DLPNO-CCSD(T0)-F12/cc-pVTZ-F12 (normalPNO) calculations are required. The most accurate level of theory is found to be DLPNO-CCSD(T0)-F12/cc-pVTZ-F12 using a tightPNO criterion which yields a mean deviation of 0.10 kcal/mol, with a maximum deviation of 0.20 kcal/mol, compared to the CCSD(F12*)(T)/CBS reference.
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Affiliation(s)
- Gunnar Schmitz
- Department
of Chemistry, Aarhus University, Langelandsgade 140, 8000 Aarhus C, Denmark
| | - Jonas Elm
- Department
of Chemistry and iClimate, Aarhus University, Langelandsgade 140, 8000 Aarhus C, Denmark
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11
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Förster A, Franchini M, van Lenthe E, Visscher L. A Quadratic Pair Atomic Resolution of the Identity Based SOS-AO-MP2 Algorithm Using Slater Type Orbitals. J Chem Theory Comput 2020; 16:875-891. [PMID: 31930915 PMCID: PMC7027358 DOI: 10.1021/acs.jctc.9b00854] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2019] [Indexed: 01/04/2023]
Abstract
We report a production level implementation of pair atomic resolution of the identity (PARI) based second-order Møller-Plesset perturbation theory (MP2) in the Slater type orbital (STO) based Amsterdam Density Functional (ADF) code. As demonstrated by systematic benchmarks, dimerization and isomerization energies obtained with our code using STO basis sets of triple-ζ-quality show mean absolute deviations from Gaussian type orbital, canonical, basis set limit extrapolated, global density fitting (DF)-MP2 results of less than 1 kcal/mol. Furthermore, we introduce a quadratic scaling atomic orbital based spin-opposite-scaled (SOS)-MP2 approach with a very small prefactor. Due to a worst-case scaling of [Formula: see text], our implementation is very fast already for small systems and shows an exceptionally early crossover to canonical SOS-PARI-MP2. We report computational wall time results for linear as well as for realistic three-dimensional molecules and show that triple-ζ quality calculations on molecules of several hundreds of atoms are only a matter of a few hours on a single compute node, the bottleneck of the computations being the SCF rather than the post-SCF energy correction.
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Affiliation(s)
- Arno Förster
- Theoretical Chemistry, Vrije
Universiteit, De Boelelaan 1083, NL-1081 HV Amsterdam, The
Netherlands
| | - Mirko Franchini
- Theoretical Chemistry, Vrije
Universiteit, De Boelelaan 1083, NL-1081 HV Amsterdam, The
Netherlands
- Scientific Computing & Modelling
NV, De Boelelaan 1083, NL-1081 HV Amsterdam, The
Netherlands
| | - Erik van Lenthe
- Scientific Computing & Modelling
NV, De Boelelaan 1083, NL-1081 HV Amsterdam, The
Netherlands
| | - Lucas Visscher
- Theoretical Chemistry, Vrije
Universiteit, De Boelelaan 1083, NL-1081 HV Amsterdam, The
Netherlands
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12
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Zhou R, Liang Q, Yang J. Complete OSV-MP2 Analytical Gradient Theory for Molecular Structure and Dynamics Simulations. J Chem Theory Comput 2019; 16:196-210. [DOI: 10.1021/acs.jctc.9b00806] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- Ruiyi Zhou
- Department of Chemistry, The University of Hong Kong, Hong Kong SAR, P. R. China
| | - Qiujiang Liang
- Department of Chemistry, The University of Hong Kong, Hong Kong SAR, P. R. China
| | - Jun Yang
- Department of Chemistry, The University of Hong Kong, Hong Kong SAR, P. R. China
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13
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Ni Z, Wang Y, Li W, Pulay P, Li S. Analytical Energy Gradients for the Cluster-in-Molecule MP2 Method and Its Application to Geometry Optimizations of Large Systems. J Chem Theory Comput 2019; 15:3623-3634. [PMID: 31091102 DOI: 10.1021/acs.jctc.9b00259] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
An efficient analytical energy gradient algorithm for the cluster-in-molecule (CIM) second order Møller-Plesset perturbation theory (MP2) method is presented. In our algorithm, the gradient contributions from the nonseparable term of the two-body density matrix on a given atom is extracted from calculations on a cluster constructed for this atom. The other terms in the CIM-MP2 energy gradient expression are evaluated by constructing the density matrices of the whole system with the contributions from all clusters constructed. For basis sets with diffuse functions, tight CIM parameters are necessary to obtain accurate gradients. Benchmark calculations show that the CIM-MP2 method can accurately reproduce the conventional MP2 gradients and geometries for larger systems. The optimized structure of a 174-atom oligopeptide using the CIM-MP2 method with the cc-pVDZ basis set is in good agreement with the corresponding crystal structure. The present CIM-MP2 gradient program can be used for optimizing the geometries of large systems with hundreds of atoms on ordinary workstations.
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Affiliation(s)
- Zhigang Ni
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry , Nanjing University , Nanjing 210023 , P. R. China.,Department of Chemistry and Biochemistry , University of Arkansas , Fayetteville , Arkansas 72701 , United States
| | - Yuqi Wang
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry , Nanjing University , Nanjing 210023 , P. R. China
| | - Wei Li
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry , Nanjing University , Nanjing 210023 , P. R. China
| | - Peter Pulay
- Department of Chemistry and Biochemistry , University of Arkansas , Fayetteville , Arkansas 72701 , United States
| | - Shuhua Li
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry , Nanjing University , Nanjing 210023 , P. R. China
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14
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Pinski P, Neese F. Analytical gradient for the domain-based local pair natural orbital second order Møller-Plesset perturbation theory method (DLPNO-MP2). J Chem Phys 2019; 150:164102. [DOI: 10.1063/1.5086544] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Affiliation(s)
- Peter Pinski
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
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15
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Krause C, Werner HJ. Scalable Electron Correlation Methods. 6. Local Spin-Restricted Open-Shell Second-Order Møller-Plesset Perturbation Theory Using Pair Natural Orbitals: PNO-RMP2. J Chem Theory Comput 2019; 15:987-1005. [PMID: 30571916 DOI: 10.1021/acs.jctc.8b01012] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present a (near) linear scaling implementation of high-spin open-shell Møller-Plesset perturbation theory using pair natural orbitals (PNO-RMP2). The theory is based on a new variant of open-shell MP2 which is fully spin-adapted and uses a single set of spin-free amplitudes, as in closed-shell MP2. This method, denoted SROMP2, is invariant to unitary orbital transformations within the closed, open, and virtual orbital subspaces. Accordingly, only a single set of PNOs per spatial orbital pair is needed, and the efficiency is similar to closed-shell calculations. The PNOs are obtained using a semicanonical approximation with large domains of projected atomic orbitals (PAOs). Linear scaling is achieved provided that the open-shell orbitals are local, and distant pairs are treated by multipole approximations. The method is efficiently parallelized. The convergence of ionization and reaction energies as a function of the PAO and PNO domain sizes is demonstrated and found to be very similar as for closed-shell calculations. The suitability of the PNOs for explicitly correlated PNO-RCCSD-F12 calculations is also tested. So far, this method is only simulated using a conventional program with appropriate projections to the PAO and PNO subspaces. It is demonstrated for radical stabilization energies as well as ionization potentials that the errors caused by the local domain approximations with our default thresholds are negligible.
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Affiliation(s)
- Christine Krause
- Institut für Theoretische Chemie , Universität Stuttgart , Pfaffenwaldring 55 , D-70569 Stuttgart , Germany
| | - Hans-Joachim Werner
- Institut für Theoretische Chemie , Universität Stuttgart , Pfaffenwaldring 55 , D-70569 Stuttgart , Germany
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16
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Dornbach M, Werner HJ. Analytical energy gradients for local second-order Møller-Plesset perturbation theory using intrinsic bond orbitals. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1537529] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Mark Dornbach
- Institut für Theoretische Chemie, Universität Stuttgart, Stuttgart, Germany
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17
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Ma Q, Werner H. Explicitly correlated local coupled‐cluster methods using pair natural orbitals. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2018. [DOI: 10.1002/wcms.1371] [Citation(s) in RCA: 100] [Impact Index Per Article: 16.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Qianli Ma
- Institute for Theoretical ChemistryUniversity of StuttgartStuttgartGermany
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18
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Vogler S, Ludwig M, Maurer M, Ochsenfeld C. Low-scaling first-order properties within second-order Møller-Plesset perturbation theory using Cholesky decomposed density matrices. J Chem Phys 2018; 147:024101. [PMID: 28711065 DOI: 10.1063/1.4990413] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An efficient implementation of energy gradients and of hyperfine coupling constants in second-order Møller-Plesset perturbation theory (MP2) is presented based on our fully atomic orbital (AO)-based approach. For the latter, an unrestricted AO-based MP2 formulation is introduced. A reduction in the dependency of the computational efficiency on the size of the basis set is achieved by a Cholesky decomposition and the prefactor is reduced by the resolution-of-the-identity approximation. Significant integral contributions are selected based on distance-including integral estimates (denoted as QQR-screening) and its reliability as a fully controlled screening procedure is demonstrated. The rate-determining steps are shown via model computations to scale cubically in the computation of energy gradients and quadratically in the case of hyperfine coupling constants. Furthermore, a significant speed-up of the computational time with respect to the canonical formulation is demonstrated.
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Affiliation(s)
- Sigurd Vogler
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, 81377 Munich, Germany
| | - Martin Ludwig
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, 81377 Munich, Germany
| | - Marina Maurer
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, 81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, 81377 Munich, Germany
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19
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Rebolini E, Baardsen G, Hansen AS, Leikanger KR, Pedersen TB. Divide-Expand-Consolidate Second-Order Møller-Plesset Theory with Periodic Boundary Conditions. J Chem Theory Comput 2018; 14:2427-2438. [PMID: 29554431 DOI: 10.1021/acs.jctc.8b00021] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present a generalization of the divide-expand-consolidate (DEC) framework for local coupled-cluster calculations to periodic systems and test it at the second-order Møller-Plesset (MP2) level of theory. For simple model systems with periodicity in one, two, and three dimensions, comparisons with extrapolated molecular calculations and the local MP2 implementation in the Cryscor program show that the correlation energy errors of the extended DEC (X-DEC) algorithm can be controlled through a single parameter, the fragment optimization threshold. Two computational bottlenecks are identified: the size of the virtual orbital spaces and the number of pair fragments required to achieve a given accuracy of the correlation energy. For the latter, we propose an affordable algorithm based on cubic splines interpolation of a limited number of pair-fragment interaction energies to determine a pair cutoff distance in accordance with the specified fragment optimization threshold.
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Affiliation(s)
- Elisa Rebolini
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry , University of Oslo , P.O. Box 1033 Blindern, N-0315 Oslo , Norway
| | - Gustav Baardsen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry , University of Oslo , P.O. Box 1033 Blindern, N-0315 Oslo , Norway
| | - Audun Skau Hansen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry , University of Oslo , P.O. Box 1033 Blindern, N-0315 Oslo , Norway
| | - Karl R Leikanger
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry , University of Oslo , P.O. Box 1033 Blindern, N-0315 Oslo , Norway
| | - Thomas Bondo Pedersen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry , University of Oslo , P.O. Box 1033 Blindern, N-0315 Oslo , Norway
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20
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Guo Y, Becker U, Neese F. Comparison and combination of “direct” and fragment based local correlation methods: Cluster in molecules and domain based local pair natural orbital perturbation and coupled cluster theories. J Chem Phys 2018; 148:124117. [DOI: 10.1063/1.5021898] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Affiliation(s)
- Yang Guo
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
| | - Ute Becker
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
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21
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Song C, Martínez TJ. Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units. J Chem Phys 2017; 147:161723. [DOI: 10.1063/1.4997997] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Chenchen Song
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA and SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Todd J. Martínez
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA and SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
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22
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Schwilk M, Ma Q, Köppl C, Werner HJ. Scalable Electron Correlation Methods. 3. Efficient and Accurate Parallel Local Coupled Cluster with Pair Natural Orbitals (PNO-LCCSD). J Chem Theory Comput 2017; 13:3650-3675. [DOI: 10.1021/acs.jctc.7b00554] [Citation(s) in RCA: 100] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Affiliation(s)
- Max Schwilk
- Institut für Theoretische
Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
| | - Qianli Ma
- Institut für Theoretische
Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
| | - Christoph Köppl
- Institut für Theoretische
Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
| | - Hans-Joachim Werner
- Institut für Theoretische
Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
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23
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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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24
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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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25
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Bykov D, Kjaergaard T. The GPU-enabled divide-expand-consolidate RI-MP2 method (DEC-RI-MP2). J Comput Chem 2016; 38:228-237. [DOI: 10.1002/jcc.24678] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2016] [Revised: 10/27/2016] [Accepted: 11/01/2016] [Indexed: 01/16/2023]
Affiliation(s)
- Dmytro Bykov
- Department of Chemistry; qLeap Center for Theoretical Chemistry, University of Aarhus; DK-8000 Århus C Denmark
| | - Thomas Kjaergaard
- Department of Chemistry; qLeap Center for Theoretical Chemistry, University of Aarhus; DK-8000 Århus C Denmark
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26
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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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27
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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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28
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Bykov D, Kristensen K, Kjærgaard T. The molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory: The DEC-RI-MP2 gradient. J Chem Phys 2016; 145:024106. [DOI: 10.1063/1.4956454] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Dmytro Bykov
- Department of Chemistry, qLeap Center for Theoretical Chemistry, University of Aarhus, DK-8000 Århus C, Denmark
| | - Kasper Kristensen
- Department of Chemistry, qLeap Center for Theoretical Chemistry, University of Aarhus, DK-8000 Århus C, Denmark
| | - Thomas Kjærgaard
- Department of Chemistry, qLeap Center for Theoretical Chemistry, University of Aarhus, DK-8000 Århus C, Denmark
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29
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Baudin P, Ettenhuber P, Reine S, Kristensen K, Kjærgaard T. Efficient linear-scaling second-order Møller-Plesset perturbation theory: The divide-expand-consolidate RI-MP2 model. J Chem Phys 2016; 144:054102. [PMID: 26851903 DOI: 10.1063/1.4940732] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Resolution of the Identity second-order Møller-Plesset perturbation theory (RI-MP2) method is implemented within the linear-scaling Divide-Expand-Consolidate (DEC) framework. In a DEC calculation, the full molecular correlated calculation is replaced by a set of independent fragment calculations each using a subset of the total orbital space. The number of independent fragment calculations scales linearly with the system size, rendering the method linear-scaling and massively parallel. The DEC-RI-MP2 method can be viewed as an approximation to the DEC-MP2 method where the RI approximation is utilized in each fragment calculation. The individual fragment calculations scale with the fifth power of the fragment size for both methods. However, the DEC-RI-MP2 method has a reduced prefactor compared to DEC-MP2 and is well-suited for implementation on massively parallel supercomputers, as demonstrated by test calculations on a set of medium-sized molecules. The DEC error control ensures that the standard RI-MP2 energy can be obtained to the predefined precision. The errors associated with the RI and DEC approximations are compared, and it is shown that the DEC-RI-MP2 method can be applied to systems far beyond the ones that can be treated with a conventional RI-MP2 implementation.
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Affiliation(s)
- Pablo Baudin
- qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Patrick Ettenhuber
- qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Simen Reine
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033, N-1315 Blindern, Norway
| | - Kasper Kristensen
- qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Thomas Kjærgaard
- qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
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30
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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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31
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Ettenhuber P, Baudin P, Kjærgaard T, Jørgensen P, Kristensen K. Orbital spaces in the divide-expand-consolidate coupled cluster method. J Chem Phys 2016; 144:164116. [DOI: 10.1063/1.4947019] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Patrick Ettenhuber
- qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Pablo Baudin
- qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Thomas Kjærgaard
- qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Poul Jørgensen
- 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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32
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Anacker T, Tew DP, Friedrich J. First UHF Implementation of the Incremental Scheme for Open-Shell Systems. J Chem Theory Comput 2015; 12:65-78. [PMID: 26605975 DOI: 10.1021/acs.jctc.5b00933] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
The incremental scheme makes it possible to compute CCSD(T) correlation energies to high accuracy for large systems. We present the first extension of this fully automated black-box approach to open-shell systems using an Unrestricted Hartree-Fock (UHF) wave function, extending the efficient domain-specific basis set approach to handle open-shell references. We test our approach on a set of organic and metal organic structures and molecular clusters and demonstrate standard deviations from canonical CCSD(T) values of only 1.35 kJ/mol using a triple ζ basis set. We find that the incremental scheme is significantly more cost-effective than the canonical implementation even for relatively small systems and that the ease of parallelization makes it possible to perform high-level calculations on large systems in a few hours on inexpensive computers. We show that the approximations that make our approach widely applicable are significantly smaller than both the basis set incompleteness error and the intrinsic error of the CCSD(T) method, and we further demonstrate that incremental energies can be reliably used in extrapolation schemes to obtain near complete basis set limit CCSD(T) reaction energies for large systems.
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Affiliation(s)
- Tony Anacker
- Institute for Chemistry, Chemnitz University of Technology , Straße der Nationen 62, D-09111 Chemnitz, Sachsen, Germany
| | - David P Tew
- School of Chemistry, University of Bristol , Bristol BS8 1TS, United Kingdom
| | - Joachim Friedrich
- Institute for Chemistry, Chemnitz University of Technology , Straße der Nationen 62, D-09111 Chemnitz, Sachsen, Germany
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33
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Ma Q, Werner HJ. Scalable Electron Correlation Methods. 2. Parallel PNO-LMP2-F12 with Near Linear Scaling in the Molecular Size. J Chem Theory Comput 2015; 11:5291-304. [DOI: 10.1021/acs.jctc.5b00843] [Citation(s) in RCA: 57] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Qianli Ma
- Institut für Theoretische
Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Baden-Württemberg, Germany
| | - Hans-Joachim Werner
- Institut für Theoretische
Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Baden-Württemberg, Germany
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34
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Eriksen JJ, Baudin P, Ettenhuber P, Kristensen K, Kjærgaard T, Jørgensen P. Linear-Scaling Coupled Cluster with Perturbative Triple Excitations: The Divide–Expand–Consolidate CCSD(T) Model. J Chem Theory Comput 2015; 11:2984-93. [DOI: 10.1021/acs.jctc.5b00086] [Citation(s) in RCA: 67] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Janus J. Eriksen
- qLEAP Center for Theoretical
Chemistry, Department of Chemistry, Aarhus University, Langelandsgade
140, DK-8000 Aarhus
C, Denmark
| | - Pablo Baudin
- qLEAP Center for Theoretical
Chemistry, Department of Chemistry, Aarhus University, Langelandsgade
140, DK-8000 Aarhus
C, Denmark
| | - Patrick Ettenhuber
- 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
| | - Thomas Kjærgaard
- qLEAP Center for Theoretical
Chemistry, Department of Chemistry, Aarhus University, Langelandsgade
140, DK-8000 Aarhus
C, Denmark
| | - Poul Jørgensen
- qLEAP Center for Theoretical
Chemistry, Department of Chemistry, Aarhus University, Langelandsgade
140, DK-8000 Aarhus
C, Denmark
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35
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Schwilk M, Usvyat D, Werner HJ. Communication: Improved pair approximations in local coupled-cluster methods. J Chem Phys 2015; 142:121102. [DOI: 10.1063/1.4916316] [Citation(s) in RCA: 64] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Affiliation(s)
- Max Schwilk
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
| | - Denis Usvyat
- Institute for Physical and Theoretical Chemistry, Universität Regensburg, Universitätsstrasse 31, D-93040 Regensburg, Germany
| | - Hans-Joachim Werner
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
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36
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Werner HJ, Knizia G, Krause C, Schwilk M, Dornbach M. Scalable Electron Correlation Methods I.: PNO-LMP2 with Linear Scaling in the Molecular Size and Near-Inverse-Linear Scaling in the Number of Processors. J Chem Theory Comput 2015; 11:484-507. [DOI: 10.1021/ct500725e] [Citation(s) in RCA: 103] [Impact Index Per Article: 11.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Affiliation(s)
- Hans-Joachim Werner
- Institut für Theoretische
Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Gerald Knizia
- Institut für Theoretische
Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Christine Krause
- Institut für Theoretische
Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Max Schwilk
- Institut für Theoretische
Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Mark Dornbach
- Institut für Theoretische
Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
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37
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Guo Y, Li W, Li S. Improved cluster-in-molecule local correlation approach for electron correlation calculation of large systems. J Phys Chem A 2014; 118:8996-9004. [PMID: 24963784 DOI: 10.1021/jp501976x] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
An improved cluster-in-molecule (CIM) local correlation approach is developed to allow electron correlation calculations of large systems more accurate and faster. We have proposed a refined strategy of constructing virtual LMOs of various clusters, which is suitable for basis sets of various types. To recover medium-range electron correlation, which is important for quantitative descriptions of large systems, we find that a larger distance threshold (ξ) is necessary for highly accurate results. Our illustrative calculations show that the present CIM-MP2 (second-order Møller-Plesser perturbation theory, MP2) or CIM-CCSD (coupled cluster singles and doubles, CCSD) scheme with a suitable ξ value is capable of recovering more than 99.8% correlation energies for a wide range of systems at different basis sets. Furthermore, the present CIM-MP2 scheme can provide reliable relative energy differences as the conventional MP2 method for secondary structures of polypeptides.
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Affiliation(s)
- Yang Guo
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of MOE, Institute of Theoretical and Computational Chemistry, Nanjing University , Nanjing 210093, P. R. China
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38
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Aidas K, Angeli C, Bak KL, Bakken V, Bast R, Boman L, Christiansen O, Cimiraglia R, Coriani S, Dahle P, Dalskov EK, Ekström U, Enevoldsen T, Eriksen JJ, Ettenhuber P, Fernández B, Ferrighi L, Fliegl H, Frediani L, Hald K, Halkier A, Hättig C, Heiberg H, Helgaker T, Hennum AC, Hettema H, Hjertenæs E, Høst S, Høyvik IM, Iozzi MF, Jansík B, Jensen HJA, Jonsson D, Jørgensen P, Kauczor J, Kirpekar S, Kjærgaard T, Klopper W, Knecht S, Kobayashi R, Koch H, Kongsted J, Krapp A, Kristensen K, Ligabue A, Lutnæs OB, Melo JI, Mikkelsen KV, Myhre RH, Neiss C, Nielsen CB, Norman P, Olsen J, Olsen JMH, Osted A, Packer MJ, Pawlowski F, Pedersen TB, Provasi PF, Reine S, Rinkevicius Z, Ruden TA, Ruud K, Rybkin VV, Sałek P, Samson CCM, de Merás AS, Saue T, Sauer SPA, Schimmelpfennig B, Sneskov K, Steindal AH, Sylvester-Hvid KO, Taylor PR, Teale AM, Tellgren EI, Tew DP, Thorvaldsen AJ, Thøgersen L, Vahtras O, Watson MA, Wilson DJD, Ziolkowski M, Agren H. The Dalton quantum chemistry program system. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2013; 4:269-284. [PMID: 25309629 PMCID: PMC4171759 DOI: 10.1002/wcms.1172] [Citation(s) in RCA: 874] [Impact Index Per Article: 79.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree-Fock, Kohn-Sham, multiconfigurational self-consistent-field, Møller-Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms.
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Affiliation(s)
- Kestutis Aidas
- Department of General Physics and Spectroscopy, Faculty of Physics, Vilnius University Vilnius, Lithuania
| | | | - Keld L Bak
- Aarhus University School of Engineering Aarhus, Denmark
| | - Vebjørn Bakken
- Faculty of Mathematics and Natural Sciences, University of Oslo Oslo, Norway
| | - Radovan Bast
- Department of Theoretical Chemistry and Biology, School of Biotechnology, KTH Royal Institute of Technology Stockholm, Sweden
| | | | | | | | - Sonia Coriani
- Department of Chemical and Pharmaceutical Sciences, University of Trieste Trieste, Italy
| | - Pål Dahle
- Norwegian Computing Center Oslo, Norway
| | | | - Ulf Ekström
- CTCC, Department of Chemistry, University of Oslo Oslo, Norway
| | - Thomas Enevoldsen
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark Odense, Denmark
| | | | | | - Berta Fernández
- Department of Physical Chemistry and Center for Research in Biological Chemistry and Molecular Materials (CIQUS), University of Santiago de Compostela Santiago de Compostela, Spain
| | - Lara Ferrighi
- CTCC, Department of Chemistry, UiT The Arctic University of Norway, Tromsø Norway
| | - Heike Fliegl
- CTCC, Department of Chemistry, University of Oslo Oslo, Norway
| | - Luca Frediani
- CTCC, Department of Chemistry, UiT The Arctic University of Norway, Tromsø Norway
| | | | | | - Christof Hättig
- Department of Theoretical Chemistry, Ruhr-University Bochum Bochum, Germany
| | | | - Trygve Helgaker
- CTCC, Department of Chemistry, University of Oslo Oslo, Norway
| | | | - Hinne Hettema
- Department of Philosophy, The University of Auckland Auckland, New Zealand
| | - Eirik Hjertenæs
- Department of Chemistry, Norwegian University of Science and Technology Trondheim, Norway
| | - Stinne Høst
- Department of Geoscience, Aarhus University Aarhus, Denmark
| | | | | | | | - Hans Jørgen Aa Jensen
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark Odense, Denmark
| | - Dan Jonsson
- High-Performance Computing Group, UiT The Arctic University of Norway, Tromsø Norway
| | - Poul Jørgensen
- Department of Chemistry, Aarhus University Aarhus, Denmark
| | - Joanna Kauczor
- Department of Physics, Chemistry and Biology, Linköping University Linköping, Sweden
| | | | | | - Wim Klopper
- Institute of Physical Chemistry, Karlsruhe Institute of Technology Karlsruhe, Germany
| | - Stefan Knecht
- Laboratory of Physical Chemistry, ETH Zürich Zürich, Switzerland
| | - Rika Kobayashi
- Australian National University Supercomputer Facility Canberra, Australia
| | - Henrik Koch
- Department of Chemistry, Norwegian University of Science and Technology Trondheim, Norway
| | - Jacob Kongsted
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark Odense, Denmark
| | | | | | - Andrea Ligabue
- Computer Services: Networks and Systems, University of Modena and Reggio Emilia Modena, Italy
| | | | - Juan I Melo
- Physics Department, FCEyN-UBA and IFIBA-CONICET, Universidad de Buenos Aires Buenos Aires, Argentina
| | - Kurt V Mikkelsen
- Department of Chemistry, University of Copenhagen, Copenhagen Denmark
| | - Rolf H Myhre
- Department of Chemistry, Norwegian University of Science and Technology Trondheim, Norway
| | - Christian Neiss
- Department of Chemistry and Pharmacy, Friedrich-Alexander University Erlangen-Nürnberg Erlangen, Germany
| | | | - Patrick Norman
- Department of Physics, Chemistry and Biology, Linköping University Linköping, Sweden
| | - Jeppe Olsen
- Department of Chemistry, Aarhus University Aarhus, Denmark
| | - Jógvan Magnus H Olsen
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark Odense, Denmark
| | | | - Martin J Packer
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark Odense, Denmark
| | - Filip Pawlowski
- Institute of Physics, Kazimierz Wielki University Bydgoszcz, Poland
| | | | - Patricio F Provasi
- Department of Physics, University of Northeastern and IMIT-CONICET Corrientes, Argentina
| | - Simen Reine
- CTCC, Department of Chemistry, University of Oslo Oslo, Norway
| | - Zilvinas Rinkevicius
- Department of Theoretical Chemistry and Biology, School of Biotechnology and Swedish e-Science Research Center (SeRC), KTH Royal Institute of Technology Stockholm, Sweden
| | | | - Kenneth Ruud
- CTCC, Department of Chemistry, UiT The Arctic University of Norway, Tromsø Norway
| | - Vladimir V Rybkin
- Institute of Physical Chemistry, Karlsruhe Institute of Technology Karlsruhe, Germany
| | | | - Claire C M Samson
- Institute of Physical Chemistry, Karlsruhe Institute of Technology Karlsruhe, Germany
| | | | - Trond Saue
- Paul Sabatier University Toulouse, France
| | - Stephan P A Sauer
- Department of Chemistry, University of Copenhagen, Copenhagen Denmark
| | - Bernd Schimmelpfennig
- Institute for Nuclear Waste Disposal, Karlsruhe Institute of Technology Karlsruhe, Germany
| | | | - Arnfinn H Steindal
- CTCC, Department of Chemistry, UiT The Arctic University of Norway, Tromsø Norway
| | | | - Peter R Taylor
- VLSCI and School of Chemistry, University of Melbourne Parkville, Australia
| | - Andrew M Teale
- School of Chemistry, University of Nottingham Nottingham, UK
| | - Erik I Tellgren
- CTCC, Department of Chemistry, University of Oslo Oslo, Norway
| | - David P Tew
- School of Chemistry, University of Bristol Bristol, UK
| | | | | | - Olav Vahtras
- Department of Theoretical Chemistry and Biology, School of Biotechnology, KTH Royal Institute of Technology Stockholm, Sweden
| | - Mark A Watson
- Department of Chemistry, Princeton University Princeton, New Jersey
| | - David J D Wilson
- Department of Chemistry and La Trobe Institute for Molecular Sciences, La Trobe University Melbourne, Australia
| | - Marcin Ziolkowski
- CoE for Next Generation Computing, Clemson University Clemson, South Carolina
| | - Hans Agren
- Department of Theoretical Chemistry and Biology, School of Biotechnology, KTH Royal Institute of Technology Stockholm, Sweden
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39
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Bozkaya U, Sherrill CD. Orbital-optimized coupled-electron pair theory and its analytic gradients: Accurate equilibrium geometries, harmonic vibrational frequencies, and hydrogen transfer reactions. J Chem Phys 2013; 139:054104. [DOI: 10.1063/1.4816628] [Citation(s) in RCA: 47] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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40
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Kristensen K, Kjærgaard T, Høyvik IM, Ettenhuber P, Jørgensen P, Jansik B, Reine S, Jakowski J. The divide–expand–consolidate MP2 scheme goes massively parallel. Mol Phys 2013. [DOI: 10.1080/00268976.2013.783941] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Kasper Kristensen
- a qLEAP – Center for Theoretical Chemistry, Department of Chemistry , Aarhus University , Langelandsgade 140, Aarhus C , 8000 , Denmark
| | - Thomas Kjærgaard
- a qLEAP – Center for Theoretical Chemistry, Department of Chemistry , Aarhus University , Langelandsgade 140, Aarhus C , 8000 , Denmark
| | - Ida-Marie Høyvik
- a qLEAP – Center for Theoretical Chemistry, Department of Chemistry , Aarhus University , Langelandsgade 140, Aarhus C , 8000 , Denmark
| | - Patrick Ettenhuber
- a qLEAP – Center for Theoretical Chemistry, Department of Chemistry , Aarhus University , Langelandsgade 140, Aarhus C , 8000 , Denmark
| | - Poul Jørgensen
- a qLEAP – Center for Theoretical Chemistry, Department of Chemistry , Aarhus University , Langelandsgade 140, Aarhus C , 8000 , Denmark
| | - Branislav Jansik
- b IT4Innovations , VSB – Technical University of Ostrava , 17. listopadu 15/2172, Ostrava , Czech Republic
| | - Simen Reine
- c Centre for Theoretical and Computational Chemistry, Department of Chemistry , Oslo University , Postbox 1033, Blindern, 0315, Oslo , Norway
| | - Jacek Jakowski
- d National Institute for Computational Sciences , JICS-ORNL , One Bethel Valley Road, Bldg. 5100 ms 6173, Oak Ridge , Tennessee , 37831 , USA
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41
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Kobayashi M, Nakai H. An effective energy gradient expression for divide-and-conquer second-order Møller–Plesset perturbation theory. J Chem Phys 2013; 138:044102. [DOI: 10.1063/1.4776228] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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42
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Kristensen K, Høyvik IM, Jansik B, Jørgensen P, Kjærgaard T, Reine S, Jakowski J. MP2 energy and density for large molecular systems with internal error control using the Divide-Expand-Consolidate scheme. Phys Chem Chem Phys 2012; 14:15706-14. [DOI: 10.1039/c2cp41958k] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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