1
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Rahrt R, Hein-Janke B, Amarasinghe KN, Shafique M, Feldt M, Guo L, Harvey JN, Pollice R, Koszinowski K, Mata RA. The Fe-MAN Challenge: Ferrates-Microkinetic Assessment of Numerical Quantum Chemistry. J Phys Chem A 2024; 128:4663-4673. [PMID: 38832568 PMCID: PMC11182345 DOI: 10.1021/acs.jpca.4c01361] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/05/2024]
Abstract
Organometallic species, such as organoferrate ions, are prototypical nucleophiles prone to reacting with a wide range of electrophiles, including proton donors. In solution, the operation of dynamic equilibria and the simultaneous presence of several organometallic species severely complicate the analysis of these fundamentally important reactions. This can be overcome by gas-phase experiments on mass-selected ions, which allow for the determination of the microscopic reactivity of the target species. In this contribution, we focus on the reactivity of a series of trisarylferrate complexes toward 2,2,2-trifluoroethanol and 2,2-difluoroethanol. By means of mass-spectrometric measurements, we determined the experimental bimolecular rate constants kexp of the gas-phase protolysis reactions of the trisarylferrate anions FePh3- and FeMes3- with the aforementioned acids. Based on these experiments, we carried out a dual blind challenge, inviting theoretical groups to submit their best predictions for the activation barriers and/or theoretical rate constants ktheo. This provides a unique opportunity to evaluate different computational protocols under minimal bias and sets the stage for further benchmarking of quantum chemical methods and data-driven approaches in the future.
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Affiliation(s)
- Rene Rahrt
- Institut
für Organische und Biomolekulare Chemie, Universität Göttingen, Tammannstr. 2, Göttingen 37077, Germany
| | - Björn Hein-Janke
- Institut
für Physikalische Chemie, Universität
Göttingen, Tammannstr.
6, Göttingen 37077, Germany
| | - Kosala N. Amarasinghe
- Leibniz
Institute for Catalysis (LIKAT), Albert-Einstein-Str. 29A, Rostock 18059, Germany
| | - Muhammad Shafique
- Leibniz
Institute for Catalysis (LIKAT), Albert-Einstein-Str. 29A, Rostock 18059, Germany
| | - Milica Feldt
- Leibniz
Institute for Catalysis (LIKAT), Albert-Einstein-Str. 29A, Rostock 18059, Germany
| | - Luxuan Guo
- Department
of Chemistry, KU Leuven, Celestijnenlaan 200F, Leuven B-3001, Belgium
| | - Jeremy N. Harvey
- Department
of Chemistry, KU Leuven, Celestijnenlaan 200F, Leuven B-3001, Belgium
| | - Robert Pollice
- Stratingh
Institute for Chemistry, University of Groningen, Nijenborgh 4, Groningen 9747 AG, The
Netherlands
| | - Konrad Koszinowski
- Institut
für Organische und Biomolekulare Chemie, Universität Göttingen, Tammannstr. 2, Göttingen 37077, Germany
| | - Ricardo A. Mata
- Institut
für Physikalische Chemie, Universität
Göttingen, Tammannstr.
6, Göttingen 37077, Germany
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2
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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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3
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Gasevic T, Bursch M, Ma Q, Grimme S, Werner HJ, Hansen A. The p-block challenge: assessing quantum chemistry methods for inorganic heterocycle dimerizations. Phys Chem Chem Phys 2024; 26:13884-13908. [PMID: 38661329 DOI: 10.1039/d3cp06217a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/26/2024]
Abstract
The elements of the p-block of the periodic table are of high interest in various chemical and technical applications like frustrated Lewis-pairs (FLP) or opto-electronics. However, high-quality benchmark data to assess approximate density functional theory (DFT) for their theoretical description are sparse. In this work, we present a benchmark set of 604 dimerization energies of 302 "inorganic benzenes" composed of all non-carbon p-block elements of main groups III to VI up to polonium. This so-called IHD302 test set comprises two classes of structures formed by covalent bonding and by weaker donor-acceptor (WDA) interactions, respectively. Generating reliable reference data with ab initio methods is challenging due to large electron correlation contributions, core-valence correlation effects, and especially the slow basis set convergence. To compute reference values for these dimerization reactions, after thorough testing, we applied a computational protocol using state-of-the-art explicitly correlated local coupled cluster theory termed PNO-LCCSD(T)-F12/cc-VTZ-PP-F12(corr.). It includes a basis set correction at the PNO-LMP2-F12/aug-cc-pwCVTZ level. Based on these reference data, we assess 26 DFT methods in combination with three different dispersion corrections and the def2-QZVPP basis set, five composite DFT approaches, and five semi-empirical quantum mechanical methods. For the covalent dimerizations, the r2SCAN-D4 meta-GGA, the r2SCAN0-D4 and ωB97M-V hybrids, and the revDSD-PBEP86-D4 double-hybrid functional are found to be the best-performing methods among the evaluated functionals of the respective class. However, since def2 basis sets for the 4th period are not associated to relativistic pseudo-potentials, we obtained significant errors in the covalent dimerization energies (up to 6 kcal mol-1) for molecules containing p-block elements of the 4th period. Significant improvements were achieved for systems containing 4th row elements by using ECP10MDF pseudopotentials along with re-contracted aug-cc-pVQZ-PP-KS basis sets introduced in this work with the contraction coefficients taken from atomic DFT (PBE0) calculations. Overall, the IHD302 set represents a challenge to contemporary quantum chemical methods. This is due to a large number of spatially close p-element bonds which are underrepresented in other benchmark sets, and the partial covalent bonding character for the WDA interactions. The IHD302 set may be helpful to develop more robust and transferable approximate quantum chemical methods in the future.
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Affiliation(s)
- Thomas Gasevic
- Mulliken Center for Theoretical Chemistry, Rheinische Friedrich-Wilhelms-Universität Bonn, Beringstr. 4, 53115 Bonn, Germany.
| | - Markus Bursch
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany.
- FACCTs GmbH, 50677, Koeln, Germany
| | - Qianli Ma
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany.
| | - Stefan Grimme
- Mulliken Center for Theoretical Chemistry, Rheinische Friedrich-Wilhelms-Universität Bonn, Beringstr. 4, 53115 Bonn, Germany.
| | - Hans-Joachim Werner
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany.
| | - Andreas Hansen
- Mulliken Center for Theoretical Chemistry, Rheinische Friedrich-Wilhelms-Universität Bonn, Beringstr. 4, 53115 Bonn, Germany.
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4
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Türkmen I, Dolg M. Linear Scaling Incremental Scheme for Correlation Energies with Embedding Generated Virtuals. J Chem Theory Comput 2024; 20:3154-3168. [PMID: 38588492 DOI: 10.1021/acs.jctc.3c01377] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/10/2024]
Abstract
A novel incremental scheme is presented including an incremental expansion of the virtual space for the calculation of electron correlation energies, which is compatible with any size-extensive correlation method and scales asymptotically linear for large molecules. The performance is studied for organic molecules, water clusters, and a La(III)-water complex, where the compatibility with pseudopotentials is also examined. The computational requirements are already reduced tremendously for medium-sized water clusters and hydrocarbons with respect to the canonical CCSD as well as the ordinary incremental scheme references. Correlation energies within chemical accuracy have been observed for all studied systems. The novelty of the method is that relatively small virtual spaces are used in combination with tuples of localized occupied spaces. The corresponding orthonormal occupied and virtual orbitals are obtained from QM/QM embedding calculations and can thus be used with standard quantum chemistry codes for correlation calculations. It is presented how relevant virtual spaces are selected and the correlation energies are linked in the new virtual space expansion.
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Affiliation(s)
- Ilyas Türkmen
- Institute for Theoretical Chemistry, University of Cologne, Greinstr. 4, D-50939 Cologne, Germany
| | - Michael Dolg
- Institute for Theoretical Chemistry, University of Cologne, Greinstr. 4, D-50939 Cologne, Germany
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5
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Sorathia K, Frantzov D, Tew DP. Improved CPS and CBS Extrapolation of PNO-CCSD(T) Energies: The MOBH35 and ISOL24 Data Sets. J Chem Theory Comput 2024; 20:2740-2750. [PMID: 38513261 PMCID: PMC11008106 DOI: 10.1021/acs.jctc.3c00974] [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] [Revised: 03/06/2024] [Accepted: 03/08/2024] [Indexed: 03/23/2024]
Abstract
Computation of heats of reaction of large molecules is now feasible using the domain-based pair natural orbital (PNO)-coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] theory. However, to obtain agreement within 1 kcal/mol of experiment, it is necessary to eliminate basis set incompleteness error, which comprises both the AO basis set error and the PNO truncation error. Our investigation into the convergence to the canonical limit of PNO-CCSD(T) energies with the PNO truncation threshold T shows that errors follow the model E ( T ) = E + A T 1 / 2 . Therefore, PNO truncation errors can be eliminated using a simple two-point CPS extrapolation to the canonical limit so that subsequent CBS extrapolation is not limited by the residual PNO truncation error. Using the ISOL24 and MOBH35 data sets, we find that PNO truncation errors are larger for molecules with significant static correlation and that it is necessary to use very tight thresholds of T = 10 - 8 to ensure that errors do not exceed 1 kcal/mol. We present a lower-cost extrapolation scheme that uses information from small basis sets to estimate the PNO truncation errors for larger basis sets. In this way, the canonical limit of CCSD(T) calculations on sizable molecules with large basis sets can be reliably estimated in a practical way. Using this approach, we report near complete basis set (CBS)-CCSD(T) reaction energies for the full ISOL24 and MOBH35 data sets.
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Affiliation(s)
- Kesha Sorathia
- University of Oxford, South Parks Road, Oxford OX1 3QZ, U.K.
| | - Damyan Frantzov
- University of Oxford, South Parks Road, Oxford OX1 3QZ, U.K.
| | - David P. Tew
- University of Oxford, South Parks Road, Oxford OX1 3QZ, U.K.
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6
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Kurian JS, Ye HZ, Mahajan A, Berkelbach TC, Sharma S. Toward Linear Scaling Auxiliary-Field Quantum Monte Carlo with Local Natural Orbitals. J Chem Theory Comput 2024; 20:134-142. [PMID: 38113195 DOI: 10.1021/acs.jctc.3c01122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2023]
Abstract
We develop a local correlation variant of auxiliary-field quantum Monte Carlo (AFQMC) based on local natural orbitals (LNO-AFQMC). In LNO-AFQMC, independent AFQMC calculations are performed for each localized occupied orbital using a truncated set of tailored orbitals. Because the size of this space does not grow with the system size for a target accuracy, the method has linear scaling. Applying LNO-AFQMC to molecular problems containing a few hundred to a thousand orbitals, we demonstrate convergence of total energies with significantly reduced costs. The savings are more significant for larger systems and larger basis sets. However, even for our smallest system studied, we find that LNO-AFQMC is cheaper than canonical AFQMC, in contrast with many other reduced-scaling methods. Perhaps most significantly, we show that energy differences converge much more quickly than total energies, making the method ideal for applications in chemistry and material science. Our work paves the way for linear scaling AFQMC calculations of strongly correlated systems, which would have a transformative effect on ab initio quantum chemistry.
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Affiliation(s)
- Jo S Kurian
- Department of Chemistry, University of Colorado, Boulder, Colorado 80302, United States
| | - Hong-Zhou Ye
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Ankit Mahajan
- Department of Chemistry, University of Colorado, Boulder, Colorado 80302, United States
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Timothy C Berkelbach
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Sandeep Sharma
- Department of Chemistry, University of Colorado, Boulder, Colorado 80302, United States
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7
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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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8
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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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9
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Semidalas E, Martin JML. Correlation Consistent Basis Sets for Explicitly Correlated Theory: The Transition Metals. J Chem Theory Comput 2023; 19:5806-5820. [PMID: 37540641 PMCID: PMC10500978 DOI: 10.1021/acs.jctc.3c00506] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Indexed: 08/06/2023]
Abstract
We present correlation consistent basis sets for explicitly correlated (F12) calculations, denoted VnZ(-PP)-F12-wis (n = D,T), for the d-block elements. The cc-pVDZ-F12-wis basis set is contracted to [8s7p5d2f] for the 3d-block, while its ECP counterpart for the 4d and 5d-blocks, cc-pVDZ-PP-F12-wis, is contracted to [6s6p5d2f]. The corresponding contracted sizes for cc-pVTZ(-PP)-F12-wis are [9s8p6d3f2g] for the 3d-block elements and [7s7p6d3f2g] for the 4d and 5d-block elements. Our VnZ(-PP)-F12-wis basis sets are evaluated on challenging test sets for metal-organic barrier heights (MOBH35) and group-11 metal clusters (CUAGAU-2). In F12 calculations, they are found to be about as close to the complete basis set limit as the combination of standard cc-pVnZ-F12 on main-group elements with the standard aug-cc-pV(n+1)Z(-PP) basis sets on the transition metal(s). While our basis sets are somewhat more compact than aug-cc-pV(n+1)Z(-PP), the CPU time benefit is negligible for catalytic complexes that contain only one or two transition metals among dozens of main-group elements; however, it is somewhat more significant for metal clusters.
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Affiliation(s)
- Emmanouil Semidalas
- Department of Molecular Chemistry
and Materials Science, Weizmann Institute
of Science, 7610001 Reḥovot, Israel
| | - Jan M. L. Martin
- Department of Molecular Chemistry
and Materials Science, Weizmann Institute
of Science, 7610001 Reḥovot, Israel
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10
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Spadetto E, Philipsen PHT, Förster A, Visscher L. Toward Pair Atomic Density Fitting for Correlation Energies with Benchmark Accuracy. J Chem Theory Comput 2023; 19:1499-1516. [PMID: 36787494 PMCID: PMC10018742 DOI: 10.1021/acs.jctc.2c01201] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/16/2023]
Abstract
Pair atomic density fitting (PADF) has been identified as a promising strategy to reduce the scaling with system size of quantum chemical methods for the calculation of the correlation energy like the direct random-phase approximation (RPA) or second-order Møller-Plesset perturbation theory (MP2). PADF can however introduce large errors in correlation energies as the two-electron interaction energy is not guaranteed to be bounded from below. This issue can be partially alleviated by using very large fit sets, but this comes at the price of reduced efficiency and having to deal with near-linear dependencies in the fit set. One posibility is to use global density fitting (DF), but in this work, we introduce an alternative methodology to overcome this problem that preserves the intrinsically favorable scaling of PADF. We first regularize the Fock matrix by projecting out parts of the basis set which gives rise to orbital products that are hard to describe by PADF. After having thus obtained a reliable self-consistent field solution, we then also apply this projector to the orbital coefficient matrix to improve the precision of PADF-MP2 and PADF-RPA. We systematically assess the accuracy of this new approach in a numerical atomic orbital framework using Slater type orbitals (STO) and correlation consistent Gaussian type basis sets up to quintuple-ζ quality for systems with more than 200 atoms. For the small and medium systems in the S66 database we show the maximum deviation of PADF-MP2 and PADF-RPA relative correlation energies to DF-MP2 and DF-RPA reference results to be 0.07 and 0.14 kcal/mol, respectively. When the new projector method is used, the errors only slightly increase for large molecules and also when moderately sized fit sets are used the resulting errors are well under control. Finally, we demonstrate the computational efficiency of our algorithm by calculating the interaction energies of large, non-covalently bound complexes with more than 1000 atoms and 20000 atomic orbitals at the RPA@PBE/CC-pVTZ level of theory.
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Affiliation(s)
- Edoardo Spadetto
- Software for Chemistry and Materials NV, NL-1081HV Amsterdam, The Netherlands
| | | | - Arno Förster
- Software for Chemistry and Materials NV, NL-1081HV Amsterdam, The Netherlands.,Theoretical Chemistry, Vrije Universiteit, 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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11
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Wang Y, Ni Z, Neese F, Li W, Guo Y, Li S. Cluster-in-Molecule Method Combined with the Domain-Based Local Pair Natural Orbital Approach for Electron Correlation Calculations of Periodic Systems. J Chem Theory Comput 2022; 18:6510-6521. [PMID: 36240189 DOI: 10.1021/acs.jctc.2c00412] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The cluster-in-molecule (CIM) method was extended to systems with periodic boundary conditions (PBCs) in a previous work (PBC-CIM) [J. Chem. Theory Comput.2019, 15, 2933], which is able to compute the electronic structures of periodic systems at second-order Møller-Plesset perturbation theory (MP2) and coupled cluster singles and doubles (CCSD) levels. However, the high computational costs of CCSD with respect to the size of clusters limit the usage of PBC-CIM to crystals with small or medium unit cells. In this work, we further develop the PBC-CIM method by employing the domain-based local pair natural orbital (DLPNO) methods for the electron correlation calculations of clusters to reduce the computational costs. The combined approach allows CCSD with perturbative triples, denoted as CCSD(T), to be computationally available for accurate descriptions of periodic systems. The distant-pair correction is also implemented to improve the accuracy of PBC-CIM. As in the molecular cases, the distant pair correction significantly improves the accuracy of various PBC-CIM methods with few additional costs. The PBC-CIM-DLPNO-CCSD(T) approach has been applied to investigate the optimized lattice parameter of the cubic LiCl crystal and two adsorption problems (CO on the NaCl(100) surface and H2O on the h-BN surface). The results show that the CIM-DLPNO-CCSD(T) method offers accurate and efficient descriptions for the studied systems. Another application to the cohesive energy of the acetic acid crystal reveals that large basis sets are necessary for reliable calculations on the cohesive energies of molecular crystals.
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Affiliation(s)
- Yuqi Wang
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of MOE, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing210023, 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, Hangzhou311121, P. R. China
| | - Frank Neese
- Max Planck Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, Mülheim an der RuhrD-45470, Germany
| | - Wei Li
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of MOE, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing210023, P. R. China
| | - Yang Guo
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, Shandong266237, P. R. China
| | - Shuhua Li
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of MOE, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing210023, P. R. China
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12
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Mehta N, Martin JML. Reduced-Scaling Double Hybrid Density Functional Theory with Rapid Basis Set Convergence through Localized Pair Natural Orbital F12. J Phys Chem Lett 2022; 13:9332-9338. [PMID: 36178852 PMCID: PMC9575149 DOI: 10.1021/acs.jpclett.2c02620] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2022] [Accepted: 09/26/2022] [Indexed: 06/16/2023]
Abstract
Following earlier work [Mehta, N.; Martin, J. M. L. J. Chem. Theory Comput.2022, 10.1021/acs.jctc.2c00426] that showed how the slow basis set convergence of the double hybrid density functional theory can be obviated by the use of F12 explicit correlation in the GLPT2 step (second order Görling-Levy perturbation theory), we demonstrate here for the very large and chemically diverse GMTKN55 benchmark suite that the CPU time scaling of this step can be reduced (asymptotically linearized) using the localized pair natural orbital (PNO-L) approximation at negligible cost in accuracy.
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13
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Saitow M, Uemura K, Yanai T. A local pair-natural orbital-based complete-active space perturbation theory using orthogonal localized virtual molecular orbitals. J Chem Phys 2022; 157:084101. [DOI: 10.1063/5.0094777] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The multireference second-order perturbation theory (CASPT2) is known to deliver a quantitative description of various complex electronic states. Despite its near-size-consistent nature, the applicability of the CASPT2 method to large, real-life systems is mostly hindered by large computational and storage costs for the two-external tensors, such as two-electron integrals, amplitudes, and residuum. To this end, Menezes and co-workers developed a reduced-scaling CASPT2 scheme by incorporating the local pair-natural orbital (PNO) representation of the many-body wave functions using non-orthonormal projected atomic orbitals (PAOs) into the CASPT theory [F. Menezes et al., J. Chem. Phys. 145, 124115 (2016)]. Alternatively, in this paper, we develop a new PNO-based CASPT2 scheme using the orthonormal localized virtual molecular orbitals (LVMOs) and assess its performance and accuracy in comparison with the conventional PAO-based counterpart. Albeit the compactness, the LVMOs were considered to perform somewhat poorly compared to PAOs in the local correlation framework because they caused enormously large orbital domains. In this work, we show that the size of LVMO domains can be rendered comparable to or even smaller than that of PAOs by the use of the differential overlap integrals for domain construction. Optimality of the MOs from the CASSCF treatment is a key to reducing the LVMO domain size for the multireference case. Due to the augmented Hessian-based localization algorithm, an additional computational cost for obtaining the LVMOs is relatively minor. We demonstrate that the LVMO-based PNO-CASPT2 method is routinely applicable to large, real-life molecules such as Menshutkin SN2 reaction in a single-walled carbon nanotube reaction field.
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Affiliation(s)
- Masaaki Saitow
- Department of Chemistry, Graduate School of Science, Nagoya University, Furocho, Chikusa Ward, Nagoya, Aichi 464-8601, Japan
| | - Kazuma Uemura
- Department of Chemistry, Graduate School of Science, Nagoya University, Furocho, Chikusa Ward, Nagoya, Aichi 464-8601, Japan
| | - Takeshi Yanai
- Department of Chemistry, Graduate School of Science, Nagoya University, Furocho, Chikusa Ward, Nagoya, Aichi 464-8601, Japan
- Institute of Transformative Bio-Molecules (WPI-ITbM), Nagoya University, Furocho, Chikusa Ward, Nagoya, Aichi 464-8601, Japan
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14
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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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15
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Haldar S, Dutta AK. An efficient Fock space multi-reference coupled cluster method based on natural orbitals: Theory, implementation, and benchmark. J Chem Phys 2021; 155:014105. [PMID: 34241374 DOI: 10.1063/5.0054171] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a natural orbital-based implementation of the intermediate Hamiltonian Fock space coupled-cluster method for the (1, 1) sector of Fock space. The use of natural orbitals significantly reduces the computational cost and can automatically choose an appropriate set of active orbitals. The new method retains the charge transfer separability of the original intermediate Hamiltonian Fock space coupled-cluster method and gives excellent performance for valence, Rydberg, and charge-transfer excited states. It offers significant computational advantages over the popular equation of motion coupled cluster method for excited states dominated by single excitations.
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Affiliation(s)
- Soumi Haldar
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Achintya Kumar Dutta
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
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16
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Fujimori T, Kobayashi M, Taketsugu T. Energy-based automatic determination of buffer region in the divide-and-conquer second-order Møller-Plesset perturbation theory. J Comput Chem 2021; 42:620-629. [PMID: 33534916 PMCID: PMC7986104 DOI: 10.1002/jcc.26486] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2020] [Revised: 12/19/2020] [Accepted: 01/15/2021] [Indexed: 11/21/2022]
Abstract
In the linear‐scaling divide‐and‐conquer (DC) electronic structure method, each subsystem is calculated together with the neighboring buffer region, the size of which affects the energy error introduced by the fragmentation in the DC method. The DC self‐consistent field calculation utilizes a scheme to automatically determine the appropriate buffer region that is as compact as possible for reducing the computational time while maintaining acceptable accuracy (J. Comput. Chem. 2018, 39, 909). To extend the automatic determination scheme of the buffer region to the DC second‐order Møller–Plesset perturbation (MP2) calculation, a scheme for estimating the subsystem MP2 correlation energy contribution from each atom in the buffer region is proposed. The estimation is based on the atomic orbital Laplace MP2 formalism. Based on this, an automatic buffer determination scheme for the DC‐MP2 calculation is constructed and its performance for several types of systems is assessed.
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Affiliation(s)
- Toshikazu Fujimori
- Graduate School of Chemical Sciences and EngineeringHokkaido UniversitySapporoJapan
| | - Masato Kobayashi
- Department of Chemistry, Faculty of ScienceHokkaido UniversitySapporoJapan
- WPI‐ICReDDHokkaido UniversitySapporoJapan
- ESICB, Kyoto UniversityKyotoJapan
| | - Tetsuya Taketsugu
- Department of Chemistry, Faculty of ScienceHokkaido UniversitySapporoJapan
- WPI‐ICReDDHokkaido UniversitySapporoJapan
- ESICB, Kyoto UniversityKyotoJapan
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17
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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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18
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Tew DP. Principal domains in F12 explicitly correlated theory. ADVANCES IN QUANTUM CHEMISTRY 2021. [DOI: 10.1016/bs.aiq.2021.06.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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19
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Mukherjee M, Tripathi D, Brehm M, Riplinger C, Dutta AK. Efficient EOM-CC-based Protocol for the Calculation of Electron Affinity of Solvated Nucleobases: Uracil as a Case Study. J Chem Theory Comput 2020; 17:105-116. [DOI: 10.1021/acs.jctc.0c00655] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
| | - Divya Tripathi
- Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Martin Brehm
- Institute of Chemistry, Martin Luther University Halle-Wittenberg, Von-Danckelmann-Platz 4, 06120 Halle (Saale), Germany
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20
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Calvin JA, Peng C, Rishi V, Kumar A, Valeev EF. Many-Body Quantum Chemistry on Massively Parallel Computers. Chem Rev 2020; 121:1203-1231. [DOI: 10.1021/acs.chemrev.0c00006] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- Justus A. Calvin
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Chong Peng
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Varun Rishi
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Ashutosh Kumar
- 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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21
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Kumar A, Neese F, Valeev EF. Explicitly correlated coupled cluster method for accurate treatment of open-shell molecules with hundreds of atoms. J Chem Phys 2020; 153:094105. [PMID: 32891102 DOI: 10.1063/5.0012753] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a near-linear scaling formulation of the explicitly correlated coupled-cluster singles and doubles with the perturbative triples method [CCSD(T)F12¯] for high-spin states of open-shell species. The approach is based on the conventional open-shell CCSD formalism [M. Saitow et al., J. Chem. Phys. 146, 164105 (2017)] utilizing the domain local pair-natural orbitals (DLPNO) framework. The use of spin-independent set of pair-natural orbitals ensures exact agreement with the closed-shell formalism reported previously, with only marginally impact on the cost (e.g., the open-shell formalism is only 1.5 times slower than the closed-shell counterpart for the C160H322 n-alkane, with the measured size complexity of ≈1.2). Evaluation of coupled-cluster energies near the complete-basis-set (CBS) limit for open-shell systems with more than 550 atoms and 5000 basis functions is feasible on a single multi-core computer in less than 3 days. The aug-cc-pVTZ DLPNO-CCSD(T)F12¯ contribution to the heat of formation for the 50 largest molecules among the 348 core combustion species benchmark set [J. Klippenstein et al., J. Phys. Chem. A 121, 6580-6602 (2017)] had root-mean-square deviation (RMSD) from the extrapolated CBS CCSD(T) reference values of 0.3 kcal/mol. For a more challenging set of 50 reactions involving small closed- and open-shell molecules [G. Knizia et al., J. Chem. Phys. 130, 054104 (2009)], the aug-cc-pVQ(+d)Z DLPNO-CCSD(T)F12¯ yielded a RMSD of ∼0.4 kcal/mol with respect to the CBS CCSD(T) estimate.
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Affiliation(s)
- Ashutosh Kumar
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - 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, USA
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22
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Paiva P, Ramos MJ, Fernandes PA. Assessing the validity of DLPNO-CCSD(T) in the calculation of activation and reaction energies of ubiquitous enzymatic reactions. J Comput Chem 2020; 41:2459-2468. [PMID: 32882060 DOI: 10.1002/jcc.26401] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2020] [Revised: 07/27/2020] [Accepted: 07/27/2020] [Indexed: 12/31/2022]
Abstract
The domain-based local pair natural orbital coupled-cluster with single, double, and perturbative triples excitation (DLPNO-CCSD(T)) method was employed to portray the activation and reaction energies of four ubiquitous enzymatic reactions, and its performance was confronted to CCSD(T)/complete basis set (CBS) to assess its accuracy and robustness in this specific field. The DLPNO-CCSD(T) results were also confronted to those of a set of density functionals (DFs) to understand the benefit of implementing this technique in enzymatic quantum mechanics/molecular mechanics (QM/MM) calculations as a second QM component, which is often treated with DF theory (DFT). On average, the DLPNO-CCSD(T)/aug-cc-pVTZ results were 0.51 kcal·mol-1 apart from the canonic CCSD(T)/CBS, without noticeable biases toward any of the reactions under study. All DFs fell short to the DLPNO-CCSD(T), both in terms of accuracy and robustness, which suggests that this method is advantageous to characterize enzymatic reactions and that its use in QM/MM calculations, either alone or in conjugation with DFT, in a two-region QM layer (DLPNO-CCSD(T):DFT), should enhance the quality and faithfulness of the results.
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Affiliation(s)
- Pedro Paiva
- LAQV@REQUIMTE, Departamento de Química e Bioquímica, Faculdade de Ciências, Universidade do Porto, Porto, Portugal
| | - Maria J Ramos
- LAQV@REQUIMTE, Departamento de Química e Bioquímica, Faculdade de Ciências, Universidade do Porto, Porto, Portugal
| | - Pedro A Fernandes
- LAQV@REQUIMTE, Departamento de Química e Bioquímica, Faculdade de Ciências, Universidade do Porto, Porto, Portugal
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23
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Sylvetsky N, Banerjee A, Alonso M, Martin JML. Performance of Localized Coupled Cluster Methods in a Moderately Strong Correlation Regime: Hückel-Möbius Interconversions in Expanded Porphyrins. J Chem Theory Comput 2020; 16:3641-3653. [PMID: 32338891 PMCID: PMC7304861 DOI: 10.1021/acs.jctc.0c00297] [Citation(s) in RCA: 36] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
![]()
Localized
orbital coupled cluster theory has recently emerged as
a nonempirical alternative to DFT for large systems. Intuitively,
one might expect such methods to perform less well for highly delocalized
systems. In the present work, we apply both canonical CCSD(T) approximations
and a variety of localized approximations to a set of flexible expanded
porphyrins—macrocycles that can switch between Hückel,
figure-eight, and Möbius topologies under external stimuli.
Both minima and isomerization transition states are considered. We
find that Möbius(-like) structures have much stronger static
correlation character than the remaining structures, and that this
causes significant errors in DLPNO-CCSD(T) and even DLPNO-CCSD(T1) approaches, unless TightPNO cutoffs are employed. If sub-kcal
mol–1 accuracy with respect to canonical relative
energies is required even for Möbius-type systems (or other
systems plagued by strong static correlation), then Nagy and Kallay’s
LNO-CCSD(T) method with “tight” settings is the suitable
localized approach. We propose the present POLYPYR21 data set as a
benchmark for localized orbital methods or, more broadly, for the
ability of lower-level methods to handle energetics with strongly
varying degrees of static correlation.
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Affiliation(s)
- Nitai Sylvetsky
- Department of Organic Chemistry, Weizmann Institute of Science, 76100 Reḥovot, Israel
| | - Ambar Banerjee
- Department of Organic Chemistry, Weizmann Institute of Science, 76100 Reḥovot, Israel
| | - Mercedes Alonso
- Department of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, 1050 Brussels, Belgium
| | - Jan M L Martin
- Department of Organic Chemistry, Weizmann Institute of Science, 76100 Reḥovot, Israel
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24
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Ma Q, Werner HJ. Scalable Electron Correlation Methods. 7. Local Open-Shell Coupled-Cluster Methods Using Pair Natural Orbitals: PNO-RCCSD and PNO-UCCSD. J Chem Theory Comput 2020; 16:3135-3151. [PMID: 32275428 DOI: 10.1021/acs.jctc.0c00192] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present well-parallelized local implementations of high-spin open-shell coupled cluster methods with single and double excitations (CCSD) using pair natural orbitals (PNOs). The methods are based on the spin-orbital coupled cluster theory using restricted open-shell Hartree-Fock (ROHF) reference functions. Two variants, namely, PNO-UCCSD and PNO-RCCSD are implemented and compared. In PNO-UCCSD, the coupled cluster amplitudes are spin-unrestricted, while in PNO-RCCSD the linear terms are spin-adapted by a spin-projection approach as described in J. Chem. Phys. 1993, 99, 5219-5227. Near linear scaling of the computational cost with the number of correlated electrons is achieved by applying domain and pair approximations. The PNOs are spin-independent and obtained using a semicanonical spin-restricted MP2 approximation with large domains of projected atomic orbitals (PAOs). The pair approximations of our previously described closed-shell PNO-LCCSD method are carefully revised so that they are compatible to the UCCSD theory, and PNO-UCCSD or PNO-RCCSD calculations for closed-shell molecules yield exactly the same results as corresponding spin-free closed-shell PNO-LCCSD calculations. The convergence of the results with respect to the thresholds and options that control the domain and pair approximations is demonstrated. It is found that large domains are required for the single excitations in open-shell calculations in order to obtain converged results. In general, the errors of relative energies caused by the local approximations can be reduced to below 1 kcal mol-1, even for difficult cases. Presently, PNO-RCCSD and PNO-UCCSD calculations for molecules with 100-200 atoms and augmented triple-ζ basis sets can be carried out in a few hours of elapsed time using ∼100 CPU cores. In addition, the program is also capable of performing distinguishable cluster (PNO-RDCSD and PNO-UDCSC) calculations. The present work is a critical step in developing fully local open-shell PNO-RCCSD(T)-F12 methods.
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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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25
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Haldar S, Dutta AK. A Multilayer Approach to the Equation of Motion Coupled-Cluster Method for the Electron Affinity. J Phys Chem A 2020; 124:3947-3962. [DOI: 10.1021/acs.jpca.0c01793] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Affiliation(s)
- Soumi Haldar
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Achintya Kumar Dutta
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
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26
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Werner HJ, Knowles PJ, Manby FR, Black JA, Doll K, Heßelmann A, Kats D, Köhn A, Korona T, Kreplin DA, Ma Q, Miller TF, Mitrushchenkov A, Peterson KA, Polyak I, Rauhut G, Sibaev M. The Molpro quantum chemistry package. J Chem Phys 2020; 152:144107. [PMID: 32295355 DOI: 10.1063/5.0005081] [Citation(s) in RCA: 454] [Impact Index Per Article: 113.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework.
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Affiliation(s)
- Hans-Joachim Werner
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Peter J Knowles
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
| | - Frederick R Manby
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom
| | - Joshua A Black
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Klaus Doll
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Andreas Heßelmann
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Daniel Kats
- Max-Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Andreas Köhn
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Tatiana Korona
- Faculty of Chemistry, University of Warsaw, L. Pasteura 1 St., 02-093 Warsaw, Poland
| | - David A Kreplin
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Qianli Ma
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Thomas F Miller
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | | | - Kirk A Peterson
- Department of Chemistry, Washington State University, Pullman, Washington 99164-4630, USA
| | - Iakov Polyak
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
| | - Guntram Rauhut
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Marat Sibaev
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
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27
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Saitow M, Yanai T. A multireference coupled-electron pair approximation combined with complete-active space perturbation theory in local pair-natural orbital framework. J Chem Phys 2020; 152:114111. [PMID: 32199413 DOI: 10.1063/1.5142622] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Complete-Active Space Second-order Perturbation Theory (CASPT2) has been one of the most widely-used methods for reliably calculating electronic structures of multireference systems. Because of its lowest level treatment of dynamic correlation, it has a high computational feasibility; however, its accuracy in some cases falls short of needs. Here, as a simple yet higher-order alternative, we introduce a hybrid theory of the CASPT2 and a multireference variant of the Coupled-Electron Pair Approximation (CEPA), which is a class of high level correlation theory. A central feature of our theory (CEPT2) is to use the two underlying theories for describing different divisions of correlation components based on the full internal contraction framework. The external components, which usually give a major contribution to the dynamic correlation, are intensively described using the CEPA Ansatz, while the rests are treated at the CASPT2 level. Furthermore, to drastically reduce the computational demands, we have incorporated the pair-natural orbital (PNO) method into our multireference implementations. This development, thus, requires highly complex derivations and coding, while it has been largely facilitated with an automatic expression and code generation technique. To highlight the accuracy of the CEPT2 approach and to assess the errors caused by the PNO truncation, benchmark calculations are shown on small- to medium-size molecules, illustrating the high accuracy of the present CEPT2 model. By tightening the truncation thresholds, the PNO-CEPT2 energy converges toward the canonical counterpart and is more accurate than that of PNO-CASPT2 as long as the same truncation thresholds are used.
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Affiliation(s)
- Masaaki Saitow
- Department of Chemistry, Graduate School of Science, Nagoya University, Furocho, Chikusa Ward, Nagoya, Aichi 464-8601, Japan
| | - Takeshi Yanai
- Department of Chemistry, Graduate School of Science, Nagoya University, Furocho, Chikusa Ward, Nagoya, Aichi 464-8601, Japan
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28
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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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29
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Guo Y, Riplinger C, Liakos DG, Becker U, Saitow M, Neese F. Linear scaling perturbative triples correction approximations for open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory [DLPNO-CCSD(T 0/T)]. J Chem Phys 2020; 152:024116. [PMID: 31941297 DOI: 10.1063/1.5127550] [Citation(s) in RCA: 46] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Abstract
The coupled cluster method with single-, double-, and perturbative triple excitations [CCSD(T)] is considered to be one of the most reliable quantum chemistry theories. However, the steep scaling of CCSD(T) has limited its application to small or medium-sized systems for a long time. In our previous work, the linear scaling domain based local pair natural orbital CCSD variant (DLPNO-CCSD) has been developed for closed-shell and open-shell. However, it is known from extensive benchmark studies that triple-excitation contributions are important to reach chemical accuracy. In the present work, two linear scaling (T) approximations for open-shell DLPNO-CCSD are implemented and compared: (a) an algorithm based on the semicanonical approximation, in which off-diagonal Fock matrix elements in the occupied space are neglected [referred to as DLPNO-(T0)]; and (b) an improved algorithm in which the triples amplitudes are computed iteratively [referred to as DLPNO-(T)]. This work is based on the previous open-shell DLPNO-CCSD algorithm [M. Saitow et al., J. Chem. Phys. 146, 164105 (2017)] as well as the iterative (T) correction for closed-shell systems [Y. Guo et al., J. Chem. Phys. 148, 011101 (2018)]. Our results show that the new open-shell perturbative corrections, DLPNO-(T0/T), can predict accurate absolute and relative correlation energies relative to the canonical reference calculations with the same basis set. The absolute energies from DLPNO-(T) are significantly more accurate than those of DLPNO-(T0). The additional computational effort of DLPNO-(T) relative to DLPNO-(T0) is a factor of 4 on average. We report calculations on systems with more than 4000 basis functions.
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Affiliation(s)
- Yang Guo
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
| | | | - Dimitrios G Liakos
- 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
| | - Masaaki Saitow
- Department of Chemistry, Graduate School of Science, Nagoya University, 1-5 Chikusa-ku, Nagoya, Aichi 464-8602, Japan
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
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30
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Patel P, Wilson AK. Domain-based local pair natural orbital methods within the correlation consistent composite approach. J Comput Chem 2019; 41:800-813. [PMID: 31891196 DOI: 10.1002/jcc.26129] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2019] [Revised: 10/29/2019] [Accepted: 12/01/2019] [Indexed: 01/15/2023]
Abstract
Ab initio composite approaches have been utilized to model and predict main group thermochemistry within 1 kcal mol-1 , on average, from well-established reliable experiments, primarily for molecules with less than 30 atoms. For molecules of increasing size and complexity, such as biomolecular complexes, composite methodologies have been limited in their application. Therefore, the domain-based local pair natural orbital (DLPNO) methods have been implemented within the correlation consistent composite approach (ccCA) framework, namely DLPNO-ccCA, to reduce the computational cost (disk space, CPU (central processing unit) time, memory) and predict energetic properties such as enthalpies of formation, noncovalent interactions, and conformation energies for organic biomolecular complexes including one of the largest molecules examined via composite strategies, within 1 kcal mol-1 , after calibration with 119 molecules and a set of linear alkanes. © 2019 Wiley Periodicals, Inc.
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Affiliation(s)
- Prajay Patel
- Department of Chemistry, Michigan State University, East Lansing, Michigan, 48824
| | - Angela K Wilson
- Department of Chemistry, Michigan State University, East Lansing, Michigan, 48824
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31
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Abstract
The computational efficiency of local correlation methods is strongly dependent on the size of the domain of functions used to expand local correlating orbitals such as orbital specific or pair natural orbitals. Here, we define a principal domain of order m as the subset of m one-particle functions that provides the best support for a given n-electron wave function by maximizing the partial trace of the one-body reduced density matrix. Principal domains maximize the overlap between the wave function and its approximant for two-electron systems and are the domain selection equivalent of Löwdin's natural orbitals. We present an efficient linear scaling greedy algorithm for obtaining principal domains of projected atomic orbitals and demonstrate its utility in the context of the pair natural orbital local correlation theory. We numerically determine thresholds such that the projected atomic orbital domain error is an order of magnitude smaller than the pair natural orbital truncation error.
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Affiliation(s)
- David P Tew
- Max Planck Institute for Solid State Research , Heisenbergstr. 1 , 70569 Stuttgart , Germany
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32
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Kats D, Werner HJ. Multi-state local complete active space second-order perturbation theory using pair natural orbitals (PNO-MS-CASPT2). J Chem Phys 2019; 150:214107. [DOI: 10.1063/1.5097644] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Daniel Kats
- Max-Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Hans-Joachim Werner
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
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33
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Dutta AK, Saitow M, Demoulin B, Neese F, Izsák R. A domain-based local pair natural orbital implementation of the equation of motion coupled cluster method for electron attached states. J Chem Phys 2019; 150:164123. [DOI: 10.1063/1.5089637] [Citation(s) in RCA: 45] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
| | - Masaaki Saitow
- Department of Chemistry, Graduate School of Science, Nagoya University, 1-5 Chikusa-ku, Nagoya, Aichi 464-8602, Japan
| | - Baptiste Demoulin
- 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
| | - Róbert Izsák
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm Platz 1, 45470 Mülheim an der Ruhr, Germany
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34
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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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35
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Wang Y, Ni Z, Li W, Li S. Cluster-in-Molecule Local Correlation Approach for Periodic Systems. J Chem Theory Comput 2019; 15:2933-2943. [DOI: 10.1021/acs.jctc.8b01200] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Yuqi Wang
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of MOE, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210023, People’s Republic of China
| | - Zhigang Ni
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of MOE, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210023, People’s Republic of China
| | - Wei Li
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of MOE, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210023, People’s Republic of China
| | - Shuhua Li
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of MOE, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210023, People’s Republic of China
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36
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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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37
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Kozłowska J, Schwilk M, Roztoczyńska A, Bartkowiak W. Assessment of DFT for endohedral complexes' dipole moment: PNO-LCCSD-F12 as a reference method. Phys Chem Chem Phys 2018; 20:29374-29388. [PMID: 30451255 DOI: 10.1039/c8cp05928d] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present a systematic evaluation of the performance of a wide range of exchange-correlation functionals and related dispersion correction schemes for the computation of dipole moments of endohedral complexes, formed through the encapsulation of an AB molecule (AB = LiF, HCl) inside carbon nanotubes (CNTs) of different diameter. The consistency and accuracy of (i) generalized gradient approximation, (ii) meta GGA, (iii) global hybrid, and (iv) range-separated hybrid density functionals are assessed. In total, 37 density functionals are tested. The results obtained using the highly accurate pair natural orbitals based explicitly correlated local coupled cluster singles doubles (PNO-LCCSD-F12) method of Werner and co-workers [Schwilk et al., J. Chem. Theory Comput., 2017, 13, 3650; Ma et al., J. Chem. Theory Comput., 2017, 13, 4871] with the aug-cc-pVTZ basis set serve as a reference. The static electric dipole moment is computed via the finite field response or, when possible, as the expectation value of the dipole operator. Among others, it is shown that functionals belonging to the class of range-separated hybrids, provide results closest to the coupled cluster reference data. In particular, the ωB97X as well as the M11 functional may be considered as a promising choice for computing electric properties of noncovalent endohedral complexes. On the other hand, the worst performance was found for the functionals which do not include the Hartree-Fock exchange. The analysis of both the coupled cluster and the DFT results indicates a strong coupling of dispersion and polarization that may also explain why lower level DFT methods, as well as Hartree-Fock and MP2, cannot yield dipole moments beyond a qualitative agreement with the higher order reference data. Interestingly, the much smaller and less systematically constructed basis sets of Pople of moderate size provide results of accuracy at least comparable with the extended Dunning's aug-cc-pVTZ basis set.
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Affiliation(s)
- Justyna Kozłowska
- Department of Physical and Quantum Chemistry, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, PL-50370 Wrocław, Poland.
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38
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Peng C, Clement MC, Valeev EF. State-Averaged Pair Natural Orbitals for Excited States: A Route toward Efficient Equation of Motion Coupled-Cluster. J Chem Theory Comput 2018; 14:5597-5607. [DOI: 10.1021/acs.jctc.8b00171] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Chong Peng
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Marjory C. Clement
- 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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39
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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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40
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Dutta AK, Saitow M, Riplinger C, Neese F, Izsák R. A near-linear scaling equation of motion coupled cluster method for ionized states. J Chem Phys 2018; 148:244101. [DOI: 10.1063/1.5029470] [Citation(s) in RCA: 40] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Achintya Kumar Dutta
- Max-Planck-Institut für Chemische Energiekonversion, Stiftstr. 34-36, D-45470 Mülheim an der Ruhr, Germany
| | - Masaaki Saitow
- Max-Planck-Institut für Chemische Energiekonversion, Stiftstr. 34-36, D-45470 Mülheim an der Ruhr, Germany
| | | | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Róbert Izsák
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm Platz 1, 45470 Mülheim an der Ruhr, Germany
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41
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Saitow M, Becker U, Riplinger C, Valeev EF, Neese F. A new near-linear scaling, efficient and accurate, open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory. J Chem Phys 2018; 146:164105. [PMID: 28456208 DOI: 10.1063/1.4981521] [Citation(s) in RCA: 242] [Impact Index Per Article: 40.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023] Open
Abstract
The Coupled-Cluster expansion, truncated after single and double excitations (CCSD), provides accurate and reliable molecular electronic wave functions and energies for many molecular systems around their equilibrium geometries. However, the high computational cost, which is well-known to scale as O(N6) with system size N, has limited its practical application to small systems consisting of not more than approximately 20-30 atoms. To overcome these limitations, low-order scaling approximations to CCSD have been intensively investigated over the past few years. In our previous work, we have shown that by combining the pair natural orbital (PNO) approach and the concept of orbital domains it is possible to achieve fully linear scaling CC implementations (DLPNO-CCSD and DLPNO-CCSD(T)) that recover around 99.9% of the total correlation energy [C. Riplinger et al., J. Chem. Phys. 144, 024109 (2016)]. The production level implementations of the DLPNO-CCSD and DLPNO-CCSD(T) methods were shown to be applicable to realistic systems composed of a few hundred atoms in a routine, black-box fashion on relatively modest hardware. In 2011, a reduced-scaling CCSD approach for high-spin open-shell unrestricted Hartree-Fock reference wave functions was proposed (UHF-LPNO-CCSD) [A. Hansen et al., J. Chem. Phys. 135, 214102 (2011)]. After a few years of experience with this method, a few shortcomings of UHF-LPNO-CCSD were noticed that required a redesign of the method, which is the subject of this paper. To this end, we employ the high-spin open-shell variant of the N-electron valence perturbation theory formalism to define the initial guess wave function, and consequently also the open-shell PNOs. The new PNO ansatz properly converges to the closed-shell limit since all truncations and approximations have been made in strict analogy to the closed-shell case. Furthermore, given the fact that the formalism uses a single set of orbitals, only a single PNO integral transformation is necessary, which offers large computational savings. We show that, with the default PNO truncation parameters, approximately 99.9% of the total CCSD correlation energy is recovered for open-shell species, which is comparable to the performance of the method for closed-shells. UHF-DLPNO-CCSD shows a linear scaling behavior for closed-shell systems, while linear to quadratic scaling is obtained for open-shell systems. The largest systems we have considered contain more than 500 atoms and feature more than 10 000 basis functions with a triple-ζ quality basis set.
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Affiliation(s)
- Masaaki Saitow
- Max-Planck-Institut für Chemische Energiekonversion, Stiftstr. 34-36, D-45470 Mülheim an der Ruhr, Germany
| | - Ute Becker
- Max-Planck-Institut für Chemische Energiekonversion, Stiftstr. 34-36, D-45470 Mülheim an der Ruhr, Germany
| | - Christoph Riplinger
- 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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42
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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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43
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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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44
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Coughtrie DJ, Giereth R, Kats D, Werner HJ, Köhn A. Embedded Multireference Coupled Cluster Theory. J Chem Theory Comput 2018; 14:693-709. [DOI: 10.1021/acs.jctc.7b01144] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- David J. Coughtrie
- Institute for Theoretical
Chemistry, University of Stuttgart, 70569 Stuttgart, Germany
| | - Robin Giereth
- Institute for Theoretical
Chemistry, University of Stuttgart, 70569 Stuttgart, Germany
| | - Daniel Kats
- Institute for Theoretical
Chemistry, University of Stuttgart, 70569 Stuttgart, Germany
| | - Hans-Joachim Werner
- Institute for Theoretical
Chemistry, University of Stuttgart, 70569 Stuttgart, Germany
| | - Andreas Köhn
- Institute for Theoretical
Chemistry, University of Stuttgart, 70569 Stuttgart, Germany
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45
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Usvyat D, Maschio L, Schütz M. Periodic and fragment models based on the local correlation approach. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2018. [DOI: 10.1002/wcms.1357] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Denis Usvyat
- Institut für ChemieHumboldt‐Universität zu BerlinBerlinGermany
| | - Lorenzo Maschio
- Dipartimento di Chimica and NIS (Nanostructured Interfaces and Surfaces) CentreUniversità di TorinoTorinoItaly
| | - Martin Schütz
- Institut für ChemieHumboldt‐Universität zu BerlinBerlinGermany
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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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47
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Fiedler B, Schmitz G, Hättig C, Friedrich J. Combining Accuracy and Efficiency: An Incremental Focal-Point Method Based on Pair Natural Orbitals. J Chem Theory Comput 2017; 13:6023-6042. [PMID: 29045786 DOI: 10.1021/acs.jctc.7b00654] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Abstract
In this work, we present a new pair natural orbitals (PNO)-based incremental scheme to calculate CCSD(T) and CCSD(T0) reaction, interaction, and binding energies. We perform an extensive analysis, which shows small incremental errors similar to previous non-PNO calculations. Furthermore, slight PNO errors are obtained by using TPNO = TTNO with appropriate values of 10-7 to 10-8 for reactions and 10-8 for interaction or binding energies. The combination with the efficient MP2 focal-point approach yields chemical accuracy relative to the complete basis-set (CBS) limit. In this method, small basis sets (cc-pVDZ, def2-TZVP) for the CCSD(T) part are sufficient in case of reactions or interactions, while some larger ones (e.g., (aug)-cc-pVTZ) are necessary for molecular clusters. For these larger basis sets, we show the very high efficiency of our scheme. We obtain not only tremendous decreases of the wall times (i.e., factors >102) due to the parallelization of the increment calculations as well as of the total times due to the application of PNOs (i.e., compared to the normal incremental scheme) but also smaller total times with respect to the standard PNO method. That way, our new method features a perfect applicability by combining an excellent accuracy with a very high efficiency as well as the accessibility to larger systems due to the separation of the full computation into several small increments.
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Affiliation(s)
- Benjamin Fiedler
- Institut für Chemie, Technische Universität Chemnitz , 09111 Chemnitz, Germany
| | - Gunnar Schmitz
- Institut for Kemi, Aarhus Universitet , 8000 Aarhus C, Denmark
| | - Christof Hättig
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum , 44801 Bochum, Germany
| | - Joachim Friedrich
- Institut für Chemie, Technische Universität Chemnitz , 09111 Chemnitz, Germany
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48
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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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49
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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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50
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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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