1
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Urban L, Laqua H, Thompson TH, Ochsenfeld C. Efficient Exploitation of Numerical Quadrature with Distance-Dependent Integral Screening in Explicitly Correlated F12 Theory: Linear Scaling Evaluation of the Most Expensive RI-MP2-F12 Term. J Chem Theory Comput 2024; 20:3706-3718. [PMID: 38626443 PMCID: PMC11099969 DOI: 10.1021/acs.jctc.4c00193] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2024] [Revised: 03/23/2024] [Accepted: 03/25/2024] [Indexed: 04/18/2024]
Abstract
We present a linear scaling atomic orbital based algorithm for the computation of the most expensive exchange-type RI-MP2-F12 term by employing numerical quadrature in combination with CABS-RI to avoid six-center-three-electron integrals. Furthermore, a robust distance-dependent integral screening scheme, based on integral partition bounds [Thompson, T. H.; Ochsenfeld, C. J. Chem. Phys. 2019, 150, 044101], is used to drastically reduce the number of the required three-center-one-electron integrals substantially. The accuracy of our numerical quadrature/CABS-RI approach and the corresponding integral screening is thoroughly assessed for interaction and isomerization energies across a variety of numerical integration grids. Our method outperforms the standard density fitting/CABS-RI approach with errors below 1 μEh even for small grid sizes and moderate screening thresholds. The choice of the grid size and screening threshold allows us to tailor our ansatz to a desired accuracy and computational efficiency. We showcase the approach's effectiveness for the chemically relevant system valinomycin, employing a triple-ζ F12 basis set combination (C54H90N6O18, 5757 AO basis functions, 10,266 CABS basis functions, 735,783 grid points). In this context, our ansatz achieves higher accuracy combined with a 135× speedup compared to the classical density fitting based variant, requiring notably less computation time than the corresponding RI-MP2 calculation. Additionally, we demonstrate near-linear scaling through calculations on linear alkanes. We achieved an 817-fold acceleration for C80H162 and an extrapolated 28,765-fold acceleration for C200H402, resulting in a substantially reduced computational time for the latter─from 229 days to just 11.5 min. Our ansatz may also be adapted to the remaining MP2-F12 terms, which will be the subject of future work.
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Affiliation(s)
- Lars Urban
- 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
| | - Henryk Laqua
- Chair
of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
| | - Travis H. Thompson
- 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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2
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Ten-No SL. Nonunitary projective transcorrelation theory inspired by the F12 ansatz. J Chem Phys 2023; 159:171103. [PMID: 37921247 DOI: 10.1063/5.0175337] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2023] [Accepted: 10/16/2023] [Indexed: 11/04/2023] Open
Abstract
An alternative nonunitary transcorrelation, inspired by the F12 ansatz, is investigated. In contrast to the Jastrow transcorrelation of Boys-Handy, the effective Hamiltonian of this projective transcorrelation features: 1. a series terminating formally at four-body interactions. 2. no spin-contamination within the non-relativistic framework. 3. simultaneous satisfaction of the singlet and triplet first-order cusp conditions. 4. arbitrary choices of pairs for correlation including frozen-core approximations. We discuss the connection between the projective transcorrelation and F12 theory with applications to small molecules, to show that the cusp conditions play an important role to reduce the uncertainty arising from the nonunitary transformation.
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Affiliation(s)
- Seiichiro L Ten-No
- Graduate School of System Informatics, Kobe University, Nada-ku, Kobe 657-8501, Japan
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3
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Urban L, Laqua H, Ochsenfeld C. Highly Efficient and Accurate Computation of Multiple Orbital Spaces Spanning Fock Matrix Elements on Central and Graphics Processing Units for Application in F12 Theory. J Chem Theory Comput 2022; 18:4218-4228. [PMID: 35674337 DOI: 10.1021/acs.jctc.2c00215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We employ our recently published highly efficient seminumerical exchange (sn-LinK) [Laqua, H.; Thompson, T. H.; Kussmann, J.; Ochsenfeld, C. J. Chem. Theory Comput. 2020, 16, 1456-1468] and integral-direct resolution of the identity Coulomb (RI-J) [Kussmann, J.; Laqua, H.; Ochsenfeld, C. J. Chem. Theory Comput. 2021, 17, 1512-1521] methods to significantly accelerate the computation of the demanding multiple orbital spaces spanning Fock matrix elements present in R12/F12 theory on central and graphics processing units. The errors introduced by RI-J and sn-LinK into the RI-MP2-F12 energy are thoroughly assessed for a variety of basis sets and integration grids. We find that these numerical errors are always below "chemical accuracy" (∼1 mH) even for the coarsest settings and can easily be reduced below 1 μH by employing only moderately large integration grids and RI-J basis sets. Since the number of basis functions of the multiple orbital spaces is notably larger compared with conventional Hartree-Fock theory, the efficiency gains from the superior basis scaling of RI-J and sn-LinK (O(Nbas2) instead of O(Nbas4) for both) are even more significant, with maximum speedup factors of 37 000 for RI-J and 4500 for sn-LinK. In total, the multiple orbital spaces spanning Fock matrix evaluation of the largest tested structure using a triple-ζ F12 basis set (5058 AO basis functions, 9267 CABS basis functions) is accelerated over 1575× using CPUs and over 4155× employing GPUs.
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Affiliation(s)
- Lars Urban
- 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
| | - Henryk Laqua
- 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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4
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Schleich P, Kottmann JS, Aspuru-Guzik A. Improving the accuracy of the variational quantum eigensolver for molecular systems by the explicitly-correlated perturbative [2] R12-correction. Phys Chem Chem Phys 2022; 24:13550-13564. [PMID: 35638435 DOI: 10.1039/d2cp00247g] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
We provide an integration of the universal, perturbative explicitly correlated [2]R12-correction in the context of the Variational Quantum Eigensolver (VQE). This approach is able to increase the accuracy of the underlying reference method significantly while requiring no additional quantum resources. The proposed approach only requires knowledge of the one- and two-particle reduced density matrices (RDMs) of the reference wavefunction; these can be measured after having reached convergence in the VQE. This computation comes at a cost that scales as the sixth power of the number of electrons. We explore the performance of the VQE + [2]R12 approach using both conventional Gaussian basis sets and our recently proposed directly determined pair-natural orbitals obtained by multiresolution analysis (MRA-PNOs). Both Gaussian orbital and PNOs are investigated as a potential set of complementary basis functions in the computation of [2]R12. In particular the combination of MRA-PNOs with [2]R12 has turned out to be very promising - persistently throughout our data, this allowed very accurate simulations at a quantum cost of a minimal basis set. Additionally, we found that the deployment of PNOs as complementary basis can greatly reduce the number of complementary basis functions that enter the computation of the correction at a complexity.
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Affiliation(s)
- Philipp Schleich
- Department of Computer Science, University of Toronto, Canada. .,Applied and Computational Mathematics, Department of Mathematics, RWTH Aachen University, Aachen, Germany.,Vector Institute for Artificial Intelligence, Toronto, Canada
| | - Jakob S Kottmann
- Department of Computer Science, University of Toronto, Canada. .,Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Canada
| | - Alán Aspuru-Guzik
- Department of Computer Science, University of Toronto, Canada. .,Vector Institute for Artificial Intelligence, Toronto, Canada.,Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Canada.,Canadian Institute for Advanced Research (CIFAR) Lebovic Fellow, Toronto, Canada
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5
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Chattopadhyay S. Single-Root Multireference Brillouin-Wigner Perturbative Approach to Excitation Energies. ACS OMEGA 2021; 6:1668-1686. [PMID: 33490826 PMCID: PMC7818614 DOI: 10.1021/acsomega.0c05714] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/24/2020] [Accepted: 12/28/2020] [Indexed: 06/12/2023]
Abstract
The state-specific Brillouin-Wigner multireference perturbation theory [which employs Jeziorski-Monkhorst parametrization of the wave function] using improved virtual orbitals, denoted as IVO-BWMRPT, is applied to calculate excitation energies (EEs) for methylene, ethylene, trimethylenemethane, and benzyne systems exhibiting various degrees of diradical character. In IVO-BWMRPT, all of the parameters appearing in the wave function ansatz are optimized for a specific electronic state. For these systems, the IVO-BWMRPT method provides EEs that are in close agreement with the benchmark results and experiments, where available, indicating that the method does not introduce imbalance in the target-specific treatment of closed- and open-shell states involved. The good performance of the present methodology is primarily related to structural compactness of the formalism. Overall, present findings are encouraging for both further development of the approach and chemical applications on the energy differences of strongly correlated systems.
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Affiliation(s)
- Sudip Chattopadhyay
- Department of Chemistry, Indian Institute of Engineering Science and Technology,
Shibpur, Howrah 711103, India
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6
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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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7
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Manna S, Chaudhuri RK, Chattopadhyay S. Taming the excited states of butadiene, hexatriene, and octatetraene using state specific multireference perturbation theory with density functional theory orbitals. J Chem Phys 2020; 152:244105. [DOI: 10.1063/5.0007198] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Shovan Manna
- Department of Chemistry, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India
| | | | - Sudip Chattopadhyay
- Department of Chemistry, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India
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8
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Giner E, Scemama A, Loos PF, Toulouse J. A basis-set error correction based on density-functional theory for strongly correlated molecular systems. J Chem Phys 2020; 152:174104. [DOI: 10.1063/5.0002892] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Emmanuel Giner
- Laboratoire de Chimie Théorique (UMR 7616), Sorbonne Université, CNRS, Paris, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique (UMR 7616), Sorbonne Université, CNRS, Paris, France
- Institut Universitaire de France, Paris, France
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9
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Chattopadhyay S. Simplified Treatment of Electronic Structures of the Lowest Singlet and Triplet States of Didehydropyrazines. J Phys Chem A 2019; 123:5980-5994. [DOI: 10.1021/acs.jpca.9b03998] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Sudip Chattopadhyay
- Department of Chemistry, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India
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10
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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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11
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Győrffy W, Werner HJ. Analytical energy gradients for explicitly correlated wave functions. II. Explicitly correlated coupled cluster singles and doubles with perturbative triples corrections: CCSD(T)-F12. J Chem Phys 2018; 148:114104. [DOI: 10.1063/1.5020436] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Affiliation(s)
- Werner Győrffy
- 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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12
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Ma Q, Werner HJ. Scalable Electron Correlation Methods. 5. Parallel Perturbative Triples Correction for Explicitly Correlated Local Coupled Cluster with Pair Natural Orbitals. J Chem Theory Comput 2017; 14:198-215. [DOI: 10.1021/acs.jctc.7b01141] [Citation(s) in RCA: 59] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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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13
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Győrffy W, Knizia G, Werner HJ. Analytical energy gradients for explicitly correlated wave functions. I. Explicitly correlated second-order Møller-Plesset perturbation theory. J Chem Phys 2017; 147:214101. [DOI: 10.1063/1.5003065] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Affiliation(s)
- Werner Győrffy
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
| | - Gerald Knizia
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
- Department of Chemistry, Pennsylvania State University, 401A Chemistry Building, University Park, Pennsylvania 16802, USA
| | - Hans-Joachim Werner
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
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14
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Ma Q, Schwilk M, Köppl C, Werner HJ. Scalable Electron Correlation Methods. 4. Parallel Explicitly Correlated Local Coupled Cluster with Pair Natural Orbitals (PNO-LCCSD-F12). J Chem Theory Comput 2017; 13:4871-4896. [DOI: 10.1021/acs.jctc.7b00799] [Citation(s) in RCA: 65] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Qianli Ma
- Institut für Theoretische
Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
| | - Max Schwilk
- 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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15
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Guo Y, Sivalingam K, Valeev EF, Neese F. Explicitly correlated N-electron valence state perturbation theory (NEVPT2-F12). J Chem Phys 2017; 147:064110. [DOI: 10.1063/1.4996560] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yang Guo
- Max Planck Institut für Chemische Energiekonversion, Stiftstr. 34-36, D-45470 Mülheim an der Ruhr, Germany
| | - Kantharuban Sivalingam
- Max Planck Institut für Chemische Energiekonversion, Stiftstr. 34-36, D-45470 Mülheim an der Ruhr, Germany
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Frank Neese
- Max Planck Institut für Chemische Energiekonversion, Stiftstr. 34-36, D-45470 Mülheim an der Ruhr, Germany
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16
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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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17
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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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18
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Sharma S, Knizia G, Guo S, Alavi A. Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory. J Chem Theory Comput 2017; 13:488-498. [DOI: 10.1021/acs.jctc.6b00898] [Citation(s) in RCA: 46] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Affiliation(s)
- Sandeep Sharma
- Max Planck Institute
for Solid State Research, Heisenbergstraße
1, 70569 Stuttgart, Germany
- Department
of Chemistry and Biochemistry, University of Colorado Boulder, Boulder, Colorado 80302, United States
| | - Gerald Knizia
- Department
of Chemistry, Pennsylvania State University, 401A Chemistry Building, University Park, Pennsylvania 16802, United States
| | - Sheng Guo
- Department
of Chemistry, Princeton University, Princeton, New Jersey 08544, United States
| | - Ali Alavi
- Max Planck Institute
for Solid State Research, Heisenbergstraße
1, 70569 Stuttgart, Germany
- Department
of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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19
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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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20
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Tew DP. Explicitly correlated coupled-cluster theory with Brueckner orbitals. J Chem Phys 2016; 145:074103. [DOI: 10.1063/1.4960655] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- David P. Tew
- School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
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21
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Kersten JAF, Booth GH, Alavi A. Assessment of multireference approaches to explicitly correlated full configuration interaction quantum Monte Carlo. J Chem Phys 2016; 145:054117. [DOI: 10.1063/1.4959245] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- J. A. F. Kersten
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - George H. Booth
- Department of Physics, King’s College London, Strand, London WC2R 2LS, United Kingdom
| | - Ali Alavi
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
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22
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Chattopadhyay S, Chaudhuri RK, Mahapatra US, Ghosh A, Ray SS. State-specific multireference perturbation theory: development and present status. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2016. [DOI: 10.1002/wcms.1248] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Sudip Chattopadhyay
- Department of Chemistry; Indian Institute of Engineering Science and Technology; Shibpur, Howrah India
| | | | | | - Anirban Ghosh
- Department of Chemistry; Indian Institute of Engineering Science and Technology; Shibpur, Howrah India
| | - Suvonil Sinha Ray
- Department of Chemistry; Indian Institute of Engineering Science and Technology; Shibpur, Howrah India
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23
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Silkowski M, Lesiuk M, Moszynski R. Calculation of the molecular integrals with the range-separated correlation factor. J Chem Phys 2015; 142:124102. [DOI: 10.1063/1.4915272] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Affiliation(s)
- Michał Silkowski
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Michał Lesiuk
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Robert Moszynski
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
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24
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Wallace AJ, Crittenden DL. Optimal composition of atomic orbital basis sets for recovering static correlation energies. J Phys Chem A 2014; 118:2138-48. [PMID: 24552569 DOI: 10.1021/jp500686m] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Static correlation energies (Estat) are calculated in a range of basis sets for a chemically diverse collection of atoms and molecules. The reliability of a basis set in capturing Estat is assessed according to the following: mean and maximum absolute deviations from near-exact Estat estimates, monotonic convergence to the complete basis set limit, and ability to capture Estat accurately independent of changes in geometry, molecular size, and electronic configuration. Within the polarization and correlation-consistent basis set series, triple-ζ basis sets are the smallest that can reliably capture Estat. The cc-pVTZ basis set performs particularly well, recovering Estat to chemical accuracy for all atoms and molecules in our data set. A series of customized basis sets are constructed by stripping polarization functions from, and swapping polarization functions among, existing basis sets. Basis sets without polarization functions are incapable of accurately recovering Estat. Basis sets with a near-complete set of s, p, and d functions can approach chemical accuracy in maximum absolute error. However, this may be achieved at lower computational cost by using a well balanced triple-ζ basis set including f functions, along with a smaller number of s, p, and d functions. Recommended basis sets for calculating Estat with increasing accuracy at increasing computational cost are 6-311G(2d,2p), cc-pVTZ, and cc-pVQZ stripped of g functions.
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Affiliation(s)
- Andrew J Wallace
- Department of Chemistry, University of Canterbury , Christchurch, New Zealand
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25
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Roskop LB, Kong L, Valeev EF, Gordon MS, Windus TL. Assessment of Perturbative Explicitly Correlated Methods for Prototypes of Multiconfiguration Electronic Structure. J Chem Theory Comput 2013; 10:90-101. [PMID: 26579894 DOI: 10.1021/ct4006773] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Luke B Roskop
- Department of Chemistry, Iowa State University , Ames, Iowa 50010, United States
| | - Liguo Kong
- Department of Chemistry, Virginia Tech , Blacksburg, Virginia 24061, United States
| | - Edward F Valeev
- Department of Chemistry, Virginia Tech , Blacksburg, Virginia 24061, 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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26
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Usvyat D. Linear-scaling explicitly correlated treatment of solids: Periodic local MP2-F12 method. J Chem Phys 2013; 139:194101. [DOI: 10.1063/1.4829898] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.6] [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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Olszówka M, Musiał M. Coupled cluster calculations in the (0,2) and (2,0) sectors of the Fock space for the lowest electronic states of the O2molecule. Mol Phys 2013. [DOI: 10.1080/00268976.2013.847215] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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28
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Lesiuk M, Jeziorski B, Moszynski R. On the large interelectronic distance behavior of the correlation factor for explicitly correlated wave functions. J Chem Phys 2013; 139:134102. [DOI: 10.1063/1.4822045] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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29
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Demel O, Kedžuch S, Noga J, Pittner J. Perturbative triples correction for explicitly correlated Mukherjee’s state-specific coupled cluster method. Mol Phys 2013. [DOI: 10.1080/00268976.2013.809488] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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30
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Ohnishi YY, Ten-no S. Alternative formulation of explicitly correlated third-order Møller–Plesset perturbation theory. Mol Phys 2013. [DOI: 10.1080/00268976.2013.793846] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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31
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Grüneis A, Shepherd JJ, Alavi A, Tew DP, Booth GH. Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions. J Chem Phys 2013; 139:084112. [DOI: 10.1063/1.4818753] [Citation(s) in RCA: 56] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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32
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Haunschild R, Cheng L, Mukherjee D, Klopper W. Communication: Extension of a universal explicit electron correlation correction to general complete active spaces. J Chem Phys 2013; 138:211101. [DOI: 10.1063/1.4810748] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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33
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Patkowski K. Basis set converged weak interaction energies from conventional and explicitly correlated coupled-cluster approach. J Chem Phys 2013; 138:154101. [DOI: 10.1063/1.4800981] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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34
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Explicitly correlated internally contracted multireference coupled-cluster singles and doubles theory: ic-MRCCSD(F12∗). Chem Phys Lett 2013. [DOI: 10.1016/j.cplett.2012.12.052] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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35
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Győrffy W, Shiozaki T, Knizia G, Werner HJ. Analytical energy gradients for second-order multireference perturbation theory using density fitting. J Chem Phys 2013; 138:104104. [DOI: 10.1063/1.4793737] [Citation(s) in RCA: 86] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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36
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37
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Shiozaki T, Woywod C, Werner HJ. Pyrazine excited states revisited using the extended multi-state complete active space second-order perturbation method. Phys Chem Chem Phys 2013; 15:262-9. [DOI: 10.1039/c2cp43381h] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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38
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Booth GH, Cleland D, Alavi A, Tew DP. An explicitly correlated approach to basis set incompleteness in full configuration interaction quantum Monte Carlo. J Chem Phys 2012; 137:164112. [DOI: 10.1063/1.4762445] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
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39
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Cleland D, Booth GH, Overy C, Alavi A. Taming the First-Row Diatomics: A Full Configuration Interaction Quantum Monte Carlo Study. J Chem Theory Comput 2012; 8:4138-52. [DOI: 10.1021/ct300504f] [Citation(s) in RCA: 71] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Deidre Cleland
- Department
of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K
| | - George H. Booth
- Department
of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K
| | - Catherine Overy
- Department
of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K
| | - Ali Alavi
- Department
of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K
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40
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Zhang J, Valeev EF. Prediction of Reaction Barriers and Thermochemical Properties with Explicitly Correlated Coupled-Cluster Methods: A Basis Set Assessment. J Chem Theory Comput 2012; 8:3175-86. [DOI: 10.1021/ct3005547] [Citation(s) in RCA: 62] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- 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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41
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State specific multireference Møller–Plesset perturbation theory: A few applications to ground, excited and ionized states. Chem Phys 2012. [DOI: 10.1016/j.chemphys.2011.04.011] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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42
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Bokhan D, Trubnikov DN. Explicitly correlated second-order Møller-Plesset perturbation theory employing pseudospectral numerical quadratures. J Chem Phys 2012; 136:204110. [PMID: 22667543 DOI: 10.1063/1.4719037] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
We implemented explicitly correlated second-order Møller-Plesset perturbation theory with numerical quadratures using pseudospectral construction of grids. Introduction of pseudospectral approach for the calculation of many-electron integrals gives a possibility to use coarse grids without significant loss of precision in correlation energies, while the number of points in the grid is reduced about nine times. The use of complementary auxiliary basis sets as the sets of dealiasing functions is justified at both theoretical and computational levels. Benchmark calculations for a set of 16 molecules have shown the possibility to keep an error of second-order correlation energies within 1 milihartree (mH) with respect to MP2-F12 method with dense grids. Numerical tests for a set of 13 isogyric reactions are also performed.
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Affiliation(s)
- Denis Bokhan
- Laboratory of Molecular Beams, Physical Chemistry Division, Department of Chemistry, Moscow Lomonosov State University, Moscow 119991, Russian Federation.
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43
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Haunschild R, Mao S, Mukherjee D, Klopper W. A universal explicit electron correlation correction applied to Mukherjee’s multi-reference perturbation theory. Chem Phys Lett 2012. [DOI: 10.1016/j.cplett.2012.02.020] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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44
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Yanai T, Shiozaki T. Canonical transcorrelated theory with projected Slater-type geminals. J Chem Phys 2012; 136:084107. [DOI: 10.1063/1.3688225] [Citation(s) in RCA: 48] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
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45
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46
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Demel O, Kedžuch S, Švaňa M, Ten-no S, Pittner J, Noga J. An explicitly correlated Mukherjee's state specific coupled cluster method: development and pilot applications. Phys Chem Chem Phys 2012; 14:4753-62. [DOI: 10.1039/c2cp23198k] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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47
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Yanai T, Kurashige Y, Neuscamman E, Chan GKL. Extended implementation of canonical transformation theory: parallelization and a new level-shifted condition. Phys Chem Chem Phys 2012; 14:7809-20. [DOI: 10.1039/c2cp23767a] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
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48
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Hättig C, Klopper W, Köhn A, Tew DP. Explicitly Correlated Electrons in Molecules. Chem Rev 2011; 112:4-74. [DOI: 10.1021/cr200168z] [Citation(s) in RCA: 401] [Impact Index Per Article: 30.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Christof Hättig
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum, Germany
| | - Wim Klopper
- Abteilung für Theoretische Chemie, Institut für Physikalische Chemie, Karlsruher Institut für Technologie, KIT-Campus Süd, Postfach 6980, D-76049 Karlsruhe, Germany
| | - Andreas Köhn
- Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany
| | - David P. Tew
- School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
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49
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Szalay PG, Müller T, Gidofalvi G, Lischka H, Shepard R. Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications. Chem Rev 2011; 112:108-81. [DOI: 10.1021/cr200137a] [Citation(s) in RCA: 470] [Impact Index Per Article: 36.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Péter G. Szalay
- Laboratory for Theoretical Chemistry, Institute of Chemistry, Eötvös Loránd University, P. O. Box 32, H-1518 Budapest, Hungary
| | - Thomas Müller
- Jülich Supercomputer Centre, Institute of Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Gergely Gidofalvi
- Department of Chemistry and Biochemistry, Gonzaga University, 502 East Boone Avenue, Spokane, Washington 99258-0102, United States
| | - Hans Lischka
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, United States
- Institute for Theoretical Chemistry, University of Vienna, Waehringerstrasse 17, A-1090 Vienna, Austria
| | - Ron Shepard
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
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50
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Kong L, Bischoff FA, Valeev EF. Explicitly Correlated R12/F12 Methods for Electronic Structure. Chem Rev 2011; 112:75-107. [DOI: 10.1021/cr200204r] [Citation(s) in RCA: 353] [Impact Index Per Article: 27.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Liguo Kong
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Florian A. Bischoff
- 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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