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Wang Y, Guo Y, Neese F, Valeev EF, Li W, Li S. Cluster-in-Molecule Approach with Explicitly Correlated Methods for Large Molecules. J Chem Theory Comput 2023; 19:8076-8089. [PMID: 37920973 DOI: 10.1021/acs.jctc.3c00627] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2023]
Abstract
In this article, we present a series of explicitly correlated local correlation methods developed under the cluster-in-molecule (CIM) framework, including explicitly correlated second-order Møller-Plesset perturbation (MP2), coupled-cluster singles and doubles (CCSD), domain-based local pair natural orbital CCSD (DLPNO-CCSD), and DLPNO-CCSD with perturbative triples (DLPNO-CCSD(T)). In these methods, F12 correction is decomposed into contributions from each occupied local molecular orbital and then evaluated independently in a given cluster, which consists of a subset of localized orbitals. These newly developed methods allow F12 calculations of large molecules (up to 145 atoms for quasi-one-dimensional systems) on a single node. We use these methods to investigate the relative stability between extended and folded alkane C30H62, the relative stability of four secondary structures of a polyglycine Ace(Gly)10NH2, and the binding energies of two host-guest complexes. The results demonstrate that the combination of CIM with F12 methods is a promising way to investigate large molecules with small basis set errors.
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Affiliation(s)
- Yuqi Wang
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of MOE, New Cornerstone Science Laboratory, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210023, P. R. China
| | - Yang Guo
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, Shandong 266237, P. R. China
| | - Frank Neese
- Max Planck Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
| | - Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Wei Li
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of MOE, New Cornerstone Science Laboratory, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210023, P. R. China
| | - Shuhua Li
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of MOE, New Cornerstone Science Laboratory, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210023, P. R. China
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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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Kodrycka M, Patkowski K. Efficient Density-Fitted Explicitly Correlated Dispersion and Exchange Dispersion Energies. J Chem Theory Comput 2021; 17:1435-1456. [PMID: 33606539 DOI: 10.1021/acs.jctc.0c01158] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The leading-order dispersion and exchange-dispersion terms in symmetry-adapted perturbation theory (SAPT), Edisp(20) and Eexch-disp(20), suffer from slow convergence to the complete basis set limit. To alleviate this problem, explicitly correlated variants of these corrections, Edisp(20)-F12 and Eexch-disp(20)-F12, have been proposed recently. However, the original formalism (M., Kodrycka , J. Chem. Theory Comput. 2019, 15, 5965-5986), while highly successful in terms of improving convergence, was not competitive to conventional orbital-based SAPT in terms of computational efficiency due to the need to manipulate several kinds of two-electron integrals. In this work, we eliminate this need by decomposing all types of two-electron integrals using robust density fitting. We demonstrate that the error of the density fitting approximation is negligible when standard auxiliary bases such as aug-cc-pVXZ/MP2FIT are employed. The new implementation allowed us to study all complexes in the A24 database in basis sets up to aug-cc-pV5Z, and the Edisp(20)-F12 and Eexch-disp(20)-F12 values exhibit vastly improved basis set convergence over their conventional counterparts. The well-converged Edisp(20)-F12 and Eexch-disp(20)-F12 numbers can be substituted for conventional Edisp(20) and Eexch-disp(20) ones in a calculation of the total SAPT interaction energy at any level (SAPT0, SAPT2+3, ...). We show that the addition of F12 terms does not improve the accuracy of low-level SAPT treatments. However, when the theory errors are minimized in high-level SAPT approaches such as SAPT2+3(CCD)δMP2, the reduction of basis set incompleteness errors thanks to the F12 treatment substantially improves the accuracy of small-basis calculations.
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Affiliation(s)
- Monika Kodrycka
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849, United States
| | - Konrad Patkowski
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849, United States
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Kodrycka M, Holzer C, Klopper W, Patkowski K. Explicitly Correlated Dispersion and Exchange Dispersion Energies in Symmetry-Adapted Perturbation Theory. J Chem Theory Comput 2019; 15:5965-5986. [PMID: 31503481 DOI: 10.1021/acs.jctc.9b00547] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The individual interaction energy terms in symmetry-adapted perturbation theory (SAPT) not only have different physical interpretations but also converge to their complete basis set (CBS) limit values at quite different rates. Dispersion energy is notoriously the slowest converging interaction energy contribution, and exchange dispersion energy, while smaller in absolute value, converges just as poorly in relative terms. To speed up the basis set convergence of the lowest-order SAPT dispersion and exchange dispersion energies, we borrow the techniques from explicitly correlated (F12) electronic structure theory and develop practical expressions for the closed-shell Edisp(20)-F12 and Eexch-disp(20)-F12 contributions. While the latter term has been derived and implemented for the first time, the former correction was recently proposed by Przybytek [ J. Chem. Theory Comput. 2018 , 14 , 5105 - 5117 ] using an Ansatz with a full optimization of the explicitly correlated amplitudes. In addition to reimplementing the fully optimized variant of Edisp(20)-F12, we propose three approximate Ansätze that substantially improve the scaling of the method and at the same time avoid the numerical instabilities of the unrestricted optimization. The performance of all four resulting flavors of Edisp(20)-F12 and Eexch-disp(20)-F12 is first tested on helium, neon, argon, water, and methane dimers, with orbital and auxiliary basis sets up to aug-cc-pV5Z and aug-cc-pV5Z-RI, respectively. The double- and triple-ζ basis set calculations are then extended to the entire A24 database of noncovalent interaction energies and compared with CBS estimates for Edisp(20) and Eexch-disp(20) computed using conventional SAPT with basis sets up to aug-cc-pV6Z with midbond functions. It is shown that the F12 treatment is highly successful in improving the basis set convergence of the SAPT terms, with the F12 calculations in an X-tuple ζ basis about as accurate as conventional calculations in bases with cardinal numbers (X + 2) for Edisp(20) and either (X + 1) or (X + 2) for Eexch-disp(20). While the full amplitude optimization affords the highest accuracy for both corrections, the much simpler and numerically stable optimized diagonal Ansatz is a very close second. We have also tested the performance of the simple F12 correction based on the second-order Møller-Plesset perturbation theory, SAPT-F12(MP2) [ Frey , J. A. ; Chem. Rev. 2016 , 116 , 5614 - 5641 ] and observed that it is also quite successful in speeding up the basis set convergence of conventional Edisp(20) + Eexch-disp(20), albeit with some outliers.
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Affiliation(s)
- Monika Kodrycka
- Department of Chemistry and Biochemistry , Auburn University , Auburn , Alabama 36849 , United States
| | - Christof Holzer
- Theoretical Chemistry Group, Institute of Physical Chemistry , Karlsruhe Institute of Technology (KIT) , KIT Campus South , P.O. Box 6980, D-76049 Karlsruhe , Germany
| | - Wim Klopper
- Theoretical Chemistry Group, Institute of Physical Chemistry , Karlsruhe Institute of Technology (KIT) , KIT Campus South , P.O. Box 6980, D-76049 Karlsruhe , Germany
| | - Konrad Patkowski
- Department of Chemistry and Biochemistry , Auburn University , Auburn , Alabama 36849 , United States
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Tew DP, Kats D. Relaxing Constrained Amplitudes: Improved F12 Treatments of Orbital Optimization and Core–Valence Correlation Energies. J Chem Theory Comput 2018; 14:5435-5440. [DOI: 10.1021/acs.jctc.8b00792] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- David P. Tew
- Max Planck Institute for Solid State
Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Daniel Kats
- Max Planck Institute for Solid State
Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
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6
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Laude G, Calderini D, Tew DP, Richardson JO. Ab initio instanton rate theory made efficient using Gaussian process regression. Faraday Discuss 2018; 212:237-258. [PMID: 30230495 DOI: 10.1039/c8fd00085a] [Citation(s) in RCA: 38] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
Ab initio instanton rate theory is a computational method for rigorously including tunnelling effects into the calculations of chemical reaction rates based on a potential-energy surface computed on the fly from electronic-structure theory. This approach is necessary to extend conventional transition-state theory into the deep-tunnelling regime, but it is also more computationally expensive as it requires many more ab initio calculations. We propose an approach which uses Gaussian process regression to fit the potential-energy surface locally around the dominant tunnelling pathway. The method can be converged to give the same result as from an on-the-fly ab initio instanton calculation but it requires far fewer electronic-structure calculations. This makes it a practical approach for obtaining accurate rate constants based on high-level electronic-structure methods. We show fast convergence to reproduce benchmark H + CH4 results and evaluate new low-temperature rates of H + C2H6 in full dimensionality at a UCCSD(T)-F12b/cc-pVTZ-F12 level.
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Affiliation(s)
- Gabriel Laude
- Laboratory of Physical Chemistry, ETH Zurich, Switzerland. and On exchange from School of Chemistry, University of Edinburgh, UK
| | | | - David P Tew
- Max-Planck-Institut für Festkörperforschung, Heisenbergstraße 1, 70569 Stuttgart, Germany
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Barca GMJ, Loos PF. Three- and four-electron integrals involving Gaussian geminals: Fundamental integrals, upper bounds, and recurrence relations. J Chem Phys 2017; 147:024103. [DOI: 10.1063/1.4991733] [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)
- Giuseppe M. J. Barca
- Research School of Chemistry, Australian National University, Canberra, ACT 2601, Australia
| | - Pierre-François Loos
- Research School of Chemistry, Australian National University, Canberra, ACT 2601, Australia
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
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8
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Lasar C, Klüner T. Explicitly Correlated Orbital Optimized Contracted Pair Correlation Methods: A Short Overview. J Phys Chem A 2017; 121:4707-4711. [PMID: 28570077 DOI: 10.1021/acs.jpca.7b03960] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Designing efficient algorithms to apply highly accurate pair correlation methods to large molecules of scientific interest has remained an important field of research for a long period of time. We present a new approach toward fast algorithms, which represents an interesting alternative and extension to currently existing methods. The presented new contraction scheme saves a significant amount of memory and can be easily combined with efficient linear scaling algorithms. Additionally, the extension to orbital optimization and explicitly correlated f12-theory is demonstrated to further improve accuracy and applicablility.
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Affiliation(s)
- Christian Lasar
- Department of Chemistry, Carl von Ossietzky University Oldenburg , 26111 Oldenburg, Germany
| | - Thorsten Klüner
- Department of Chemistry, Carl von Ossietzky University Oldenburg , 26111 Oldenburg, Germany
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9
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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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10
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Yang B, Wang XH, Stancil PC, Bowman JM, Balakrishnan N, Forrey RC. Full-dimensional quantum dynamics of rovibrationally inelastic scattering between CN and H2. J Chem Phys 2016; 145:224307. [DOI: 10.1063/1.4971322] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Benhui Yang
- Department of Physics and Astronomy and the Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
| | - X. H. Wang
- Department of Chemistry, Emory University, Atlanta, Georgia 30322, USA
| | - P. C. Stancil
- Department of Physics and Astronomy and the Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
| | - J. M. Bowman
- Department of Chemistry, Emory University, Atlanta, Georgia 30322, USA
| | - N. Balakrishnan
- Department of Chemistry, University of Nevada, Las Vegas, Nevada 89154, USA
| | - R. C. Forrey
- Department of Physics, Penn State University, Berks Campus, Reading, Pennsylvania 19610, USA
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11
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Friedrich J. Efficient Calculation of Accurate Reaction Energies—Assessment of Different Models in Electronic Structure Theory. J Chem Theory Comput 2015; 11:3596-609. [DOI: 10.1021/acs.jctc.5b00087] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Joachim Friedrich
- Institute for Chemistry, Chemnitz University of Technology, Straße der Nationen
62, 09111 Chemnitz, Germany
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12
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Hehn AS, Tew DP, Klopper W. Explicitly correlated ring-coupled-cluster-doubles theory. J Chem Phys 2015; 142:194106. [DOI: 10.1063/1.4921256] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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13
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Blunt NS, Smart SD, Kersten JAF, Spencer JS, Booth GH, Alavi A. Semi-stochastic full configuration interaction quantum Monte Carlo: Developments and application. J Chem Phys 2015; 142:184107. [DOI: 10.1063/1.4920975] [Citation(s) in RCA: 75] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- N. S. Blunt
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Simon D. Smart
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - J. A. F. Kersten
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - J. S. Spencer
- Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom
- Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom
| | - George H. Booth
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- 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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14
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Yang B, Zhang P, Wang X, Stancil P, Bowman J, Balakrishnan N, Forrey R. Quantum dynamics of CO–H2 in full dimensionality. Nat Commun 2015; 6:6629. [PMID: 25800802 DOI: 10.1038/ncomms7629] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2014] [Accepted: 02/12/2015] [Indexed: 11/09/2022] Open
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15
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Belikov VV, Bokhan DA, Trubnikov DN. Estimating the basis set superposition error in the CCSD(T)(F12) explicitly correlated method using the example of a water dimer. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A 2014. [DOI: 10.1134/s0036024414040037] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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16
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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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17
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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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18
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Vogiatzis KD, Klopper W. Accurate non-covalent interactions with basis-set corrections from interference-corrected perturbation theory: comparison with the S22B database. Mol Phys 2013. [DOI: 10.1080/00268976.2013.805888] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Konstantinos D. Vogiatzis
- Center for Functional Nanostructures (CFN) and Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), , P. O. Box 6980, Karlsruhe, D-76049, Germany
| | - Wim Klopper
- Center for Functional Nanostructures (CFN) and Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), , P. O. Box 6980, Karlsruhe, D-76049, Germany
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19
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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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21
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Affiliation(s)
- Joseph R. Lane
- Department
of Chemistry, University of Waikato, Private Bag 3105, Hamilton, New Zealand
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22
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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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23
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Patkowski K. On the accuracy of explicitly correlated coupled-cluster interaction energies — have orbital results been beaten yet? J Chem Phys 2012; 137:034103. [DOI: 10.1063/1.4734597] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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24
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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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25
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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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26
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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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27
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McMahon JD, Lane JR. Explicit correlation and basis set superposition error: The structure and energy of carbon dioxide dimer. J Chem Phys 2011; 135:154309. [DOI: 10.1063/1.3653230] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
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28
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Peterson KA, Krause C, Stoll H, Hill JG, Werner HJ. Application of explicitly correlated coupled-cluster methods to molecules containing post-3d main group elements. Mol Phys 2011. [DOI: 10.1080/00268976.2011.624129] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
Affiliation(s)
- Kirk A. Peterson
- a Department of Chemistry , Washington State University , Pullman , Washington 99164-4630 , USA
| | - Christine Krause
- b Institut für Theoretische Chemie, Universität Stuttgart , Pfaffenwaldring 55, D-70569 Stuttgart , Germany
| | - Hermann Stoll
- b Institut für Theoretische Chemie, Universität Stuttgart , Pfaffenwaldring 55, D-70569 Stuttgart , Germany
| | - J. Grant Hill
- a Department of Chemistry , Washington State University , Pullman , Washington 99164-4630 , USA
| | - Hans-Joachim Werner
- b Institut für Theoretische Chemie, Universität Stuttgart , Pfaffenwaldring 55, D-70569 Stuttgart , Germany
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29
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de Lange KM, Lane JR. Quantifying cooperative intermolecular interactions for improved carbon dioxide capture materials. J Chem Phys 2011; 135:064304. [DOI: 10.1063/1.3624363] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
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30
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Wilke JJ, Schaefer HF. Spin-Restriction in Explicitly Correlated Coupled Cluster Theory: The Z-Averaged CCSD(2)R12 Approach. J Chem Theory Comput 2011; 7:2416-26. [DOI: 10.1021/ct200292z] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Affiliation(s)
- Jeremiah J. Wilke
- Center for Computational Chemistry, University of Georgia, Athens, Georgia, United States
| | - Henry F. Schaefer
- Center for Computational Chemistry, University of Georgia, Athens, Georgia, United States
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Bachorz RA, Bischoff FA, Glöss A, Hättig C, Höfener S, Klopper W, Tew DP. The MP2-F12 method in the Turbomole program package. J Comput Chem 2011; 32:2492-513. [PMID: 21590779 DOI: 10.1002/jcc.21825] [Citation(s) in RCA: 91] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2010] [Revised: 03/25/2011] [Accepted: 03/27/2011] [Indexed: 01/21/2023]
Abstract
A detailed description of the explicitly correlated second-order Møller-Plesset perturbation theory (MP2-F12) method, as implemented in the TURBOMOLE program package, is presented. The TURBOMOLE implementation makes use of density fitting, which greatly reduces the prefactor for integral evaluation. Methods are available for the treatment of ground states of open- and closed-shell species, using unrestricted as well as restricted (open-shell) Hartree-Fock reference determinants. Various methodological choices and approximations are discussed. The performance of the TURBOMOLE implementation is illustrated by example calculations of the molecules leflunomide, prednisone, methotrexate, ethylenedioxytetrafulvalene, and a cluster model for the adsorption of methanol on the zeolite H-ZSM-5. Various basis sets are used, including the correlation-consistent basis sets specially optimized for explicitly correlated calculations (cc-pVXZ-F12).
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Affiliation(s)
- Rafał A Bachorz
- Center for Functional Nanostructures (CFN, Karlsruhe Institute of Technology, Karlsruhe, Germany
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de Lange KM, Lane JR. Explicit correlation and intermolecular interactions: Investigating carbon dioxide complexes with the CCSD(T)-F12 method. J Chem Phys 2011; 134:034301. [DOI: 10.1063/1.3526956] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Koput J. The ground-state potential energy function of a beryllium dimer determined using the single-reference coupled-cluster approach. Phys Chem Chem Phys 2011; 13:20311-7. [DOI: 10.1039/c1cp22417d] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
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Boese AD, Jansen G, Torheyden M, Höfener S, Klopper W. Effects of counterpoise correction and basis set extrapolation on the MP2 geometries of hydrogen bonded dimers of ammonia, water, and hydrogen fluoride. Phys Chem Chem Phys 2011; 13:1230-8. [DOI: 10.1039/c0cp01493a] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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35
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Bokhan D, Ten-no S. Explicitly correlated equation-of-motion coupled-cluster methods for excited and electron-attached states. J Chem Phys 2010; 133:204103. [DOI: 10.1063/1.3505637] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
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Höfener S, Klopper W. Analytical nuclear gradients of the explicitly correlated Møller–Plesset second-order energy. Mol Phys 2010. [DOI: 10.1080/00268976.2010.490795] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Sebastian Höfener
- a Institute of Physical Chemistry, Karlsruhe Institute of Technology , KIT Campus South, Kaiserstraße 12, D-76131 Karlsruhe, Germany
| | - Wim Klopper
- a Institute of Physical Chemistry, Karlsruhe Institute of Technology , KIT Campus South, Kaiserstraße 12, D-76131 Karlsruhe, Germany
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Werner HJ, Knizia G, Adler TB, Marchetti O. Benchmark Studies for Explicitly Correlated Perturbation- and Coupled Cluster Theories. javascript:filterformular(´3´). ACTA ACUST UNITED AC 2010. [DOI: 10.1524/zpch.2010.6120] [Citation(s) in RCA: 60] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
Abstract
The recently developed explicitly correlated MP2-F12 and CCSD(T)-F12x (x = a,b) methods are reviewed. The explicit correlation treatment leads to a dramatic improvement of the basis set convergence. Extensive benchmarks for reaction energies, atomization energies, electron affinities, ionization potentials, equilibrium structures, vibrational frequencies, and intermolecular interaction energies are presented which show that for many molecular properties the intrinsic accuracy of the CCSD(T) method is already reached with double-zeta (VDZ-F12) basis sets, while triple-zeta (VTZ-F12) basis sets yield results that are very close to the complete basis set limit. The steep scaling of the MP2-F12 method with molecular size can be reduced by local approximations. This has made it possible to carry out MP2-F12 calculations for molecules with up to 100 atoms. The errors caused bjavascript:filterformular(´3´)y the local domain approximation are largely removed by the explicitly correlated terms, which account for the neglected configurations in an approximate way. Extensions to LCCSD(T)-F12 are discussed and preliminary results for LCCSD-F12 are presented.
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Efficient Explicitly Correlated Coupled-Cluster Approximations. CHALLENGES AND ADVANCES IN COMPUTATIONAL CHEMISTRY AND PHYSICS 2010. [DOI: 10.1007/978-90-481-2885-3_21] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
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Hill JG, Peterson KA. Correlation consistent basis sets for explicitly correlated wavefunctions: valence and core–valence basis sets for Li, Be, Na, and Mg. Phys Chem Chem Phys 2010; 12:10460-8. [DOI: 10.1039/c0cp00020e] [Citation(s) in RCA: 78] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
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Tew DP, Hättig C, Bachorz RA, Klopper W. Explicitly Correlated Coupled-Cluster Theory. CHALLENGES AND ADVANCES IN COMPUTATIONAL CHEMISTRY AND PHYSICS 2010. [DOI: 10.1007/978-90-481-2885-3_20] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
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Wilke JJ, Schaefer HF. The subtleties of explicitly correlated Z-averaged perturbation theory: Choosing an R12 method for high-spin open-shell molecules. J Chem Phys 2009; 131:244116. [DOI: 10.1063/1.3269031] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
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Optimized complementary auxiliary basis sets for explicitly correlated methods: aug-cc-pVnZ orbital basis sets. Chem Phys Lett 2009. [DOI: 10.1016/j.cplett.2009.06.003] [Citation(s) in RCA: 174] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Köhn A. Explicitly correlated connected triple excitations in coupled-cluster theory. J Chem Phys 2009; 130:131101. [DOI: 10.1063/1.3116792] [Citation(s) in RCA: 73] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
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Knizia G, Adler TB, Werner HJ. Simplified CCSD(T)-F12 methods: theory and benchmarks. J Chem Phys 2009; 130:054104. [PMID: 19206955 DOI: 10.1063/1.3054300] [Citation(s) in RCA: 1286] [Impact Index Per Article: 85.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The simple and efficient CCSD(T)-F12x approximations (x = a,b) we proposed in a recent communication [T. B. Adler, G. Knizia, and H.-J. Werner, J. Chem. Phys. 127, 221106 (2007)] are explained in more detail and extended to open-shell systems. Extensive benchmark calculations are presented, which demonstrate great improvements in basis set convergence for a wide variety of applications. These include reaction energies of both open- and closed-shell reactions, atomization energies, electron affinities, ionization potentials, equilibrium geometries, and harmonic vibrational frequencies. For all these quantities, results better than the AV5Z quality are obtained already with AVTZ basis sets, and usually AVDZ treatments reach at least the conventional AVQZ quality. For larger molecules, the additional cost for these improvements is only a few percent of the time for a standard CCSD(T) calculation. For the first time ever, total reaction energies with chemical accuracy are obtained using valence-double-zeta basis sets.
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Affiliation(s)
- Gerald Knizia
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
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47
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Köhn A. A modified ansatz for explicitly correlated coupled-cluster wave functions that is suitable for response theory. J Chem Phys 2009; 130:104104. [DOI: 10.1063/1.3079543] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Monari A, Vetere V, Bendazzoli GL, Evangelisti S, Paulus B. End states and singlet–triplet degeneracy in linear atomic chains. Chem Phys Lett 2008. [DOI: 10.1016/j.cplett.2008.09.059] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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