1
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Mester D, Nagy PR, Kállay M. Basis-Set Limit CCSD(T) Energies for Large Molecules with Local Natural Orbitals and Reduced-Scaling Basis-Set Corrections. J Chem Theory Comput 2024; 20:7453-7468. [PMID: 39207805 DOI: 10.1021/acs.jctc.4c00777] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/04/2024]
Abstract
The calculation of density-based basis-set correction (DBBSC), which remedies the basis-set incompleteness (BSI) error of the correlation energy, is combined with local approximations. Aiming at large-scale applications, the procedure is implemented in our efficient local natural orbital-based coupled-cluster singles and doubles with perturbative triples [LNO-CCSD(T)] scheme. To this end, the range-separation function, which characterizes the one-electron BSI in space, is decomposed into the sum of contributions from individual localized molecular orbitals (LMOs). A compact domain is constructed around each LMO, and the corresponding contributions are evaluated only within these restricted domains. Furthermore, for the calculation of the complementary auxiliary basis set (CABS) correction, which significantly improves the Hartree-Fock (HF) energy, the local density fitting approximation is utilized. The errors arising from the local approximations are examined in detail, efficient prescreening techniques are introduced to compress the numerical quadrature used for DBBSC, and conservative default thresholds are selected for the truncation parameters. The efficiency of the DBBSC-LNO-CCSD(T) method is demonstrated through representative examples of up to 1000 atoms. Based on the numerical results, we conclude that the corrections drastically reduce the BSI error using double-ζ basis sets, often to below 1 kcal/mol compared to the reliable LNO-CCSD(T) complete basis set references, while significant improvements are also achieved with triple-ζ basis sets. Considering that the calculation of the DBBSC and CABS corrections only moderately increases the wall-clock time required for the post-HF steps in practical applications, the proposed DBBSC-LNO-CCSD(T) method offers a highly efficient and robust tool for large-scale calculations.
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Affiliation(s)
- Dávid Mester
- Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics, Muegyetem rkp. 3, H-1111 Budapest, Hungary
- HUN-REN-BME Quantum Chemistry Research Group, Muegyetem rkp. 3, H-1111 Budapest, Hungary
- MTA-BME Lendület Quantum Chemistry Research Group, Muegyetem rkp. 3, H-1111 Budapest, Hungary
| | - Péter R Nagy
- Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics, Muegyetem rkp. 3, H-1111 Budapest, Hungary
- HUN-REN-BME Quantum Chemistry Research Group, Muegyetem rkp. 3, H-1111 Budapest, Hungary
- MTA-BME Lendület Quantum Chemistry Research Group, Muegyetem rkp. 3, H-1111 Budapest, Hungary
| | - Mihály Kállay
- Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics, Muegyetem rkp. 3, H-1111 Budapest, Hungary
- HUN-REN-BME Quantum Chemistry Research Group, Muegyetem rkp. 3, H-1111 Budapest, Hungary
- MTA-BME Lendület Quantum Chemistry Research Group, Muegyetem rkp. 3, H-1111 Budapest, Hungary
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2
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Kats D, Christlmaier EMC, Schraivogel T, Alavi A. Orbital optimisation in xTC transcorrelated methods. Faraday Discuss 2024. [PMID: 39072553 DOI: 10.1039/d4fd00036f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/30/2024]
Abstract
We present a combination of the bi-orthogonal orbital optimisation framework with the recently introduced xTC version of transcorrelation. This allows us to implement non-iterative perturbation based methods on top of the transcorrelated Hamiltonian. Additionally, the orbital optimisation influences results of other truncated methods, such as the distinguishable cluster with singles and doubles. The accuracy of these methods in comparison to standard xTC methods is demonstrated, and the advantages and disadvantages of the orbital optimisation are discussed.
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Affiliation(s)
- Daniel Kats
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany.
| | | | - Thomas Schraivogel
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany.
| | - Ali Alavi
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany.
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3
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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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4
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Mester D, Kállay M. Basis Set Limit of CCSD(T) Energies: Explicit Correlation Versus Density-Based Basis-Set Correction. J Chem Theory Comput 2023; 19:8210-8222. [PMID: 37950703 PMCID: PMC10688194 DOI: 10.1021/acs.jctc.3c00979] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2023] [Revised: 10/21/2023] [Accepted: 10/23/2023] [Indexed: 11/13/2023]
Abstract
A thorough comparison is carried out for explicitly correlated and density-based basis-set correction approaches, which were primarily developed to mitigate the basis-set incompleteness error of wave function methods. An efficient implementation of the density-based scheme is also presented, utilizing the density-fitting approximation. The performance of these approaches is comprehensively tested for the second-order Møller-Plesset (MP2), coupled-cluster singles and doubles (CCSD), and CCSD with perturbative triples [CCSD(T)] methods with respect to the corresponding complete basis set references. It is demonstrated that the density-based correction together with complementary auxiliary basis set (CABS)-corrected Hartree-Fock energies is highly robust and effectively reduces the error of the standard approaches; however, it does not outperform the corresponding explicitly correlated methods. Nevertheless, what still makes the density-corrected CCSD and CCSD(T) methods competitive is that their computational costs are roughly half of those of the corresponding explicitly correlated variants. Additionally, an incremental approach for standard CCSD and CCSD(T) is introduced. In this simple scheme, the total energies are corrected with the CABS correction and explicitly correlated MP2 contributions. As demonstrated, the resulting methods yield surprisingly good results, below 1 kcal/mol for thermochemical properties even with a double-ζ basis, while their computational expenses are practically identical to those of the density-based basis-set correction approaches.
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Affiliation(s)
- Dávid Mester
- Department
of Physical Chemistry and Materials Science, Faculty of Chemical Technology
and Biotechnology, Budapest University of
Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- HUN-REN-BME
Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- MTA-BME
Lendület Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
| | - Mihály Kállay
- Department
of Physical Chemistry and Materials Science, Faculty of Chemical Technology
and Biotechnology, Budapest University of
Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- HUN-REN-BME
Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- MTA-BME
Lendület Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
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5
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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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6
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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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7
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Gill WA, Janjua MRSA. Ab Initio Calculations of the Interaction Potential of the N 2O-N 2O Dimer: Strength of the Intermolecular Interactions and Physical Insights. J Phys Chem A 2023. [PMID: 37478471 DOI: 10.1021/acs.jpca.3c02634] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/23/2023]
Abstract
N2O, or nitrous oxide, is an important greenhouse gas with a significant impact on global warming and climate change. To accurately model the behavior of N2O in the atmosphere, precise representations of its intermolecular force fields are required. First principles quantum mechanical calculations followed by appropriate fitting are commonly used to establish such force fields. However, fitting such force fields is challenging due to the complex mathematical functions that describe the molecular interactions of N2O. As such, ongoing research is focused on improving our understanding of N2O and developing more accurate models for use in climate modeling and other applications. In this study, we investigated the strength of the intermolecular interactions in the N2O-N2O dimer using the coupled-cluster theory with single, double, and perturbative triple excitation [CCSD(T)] method with the def2-QZVPP basis set. Our calculations provided a detailed understanding of the intermolecular forces that govern the stability and structure of the N2O dimer. We found that the N2O-N2O dimer is stabilized by a combination of van der Waals forces and dipole-dipole interactions. The calculated interaction energy between the two N2O molecules in the dimer was found to be -5.09 kcal/mol, which is in good agreement with previous theoretical and experimental results. Additionally, we analyzed the molecular properties of the N2O-N2O dimer, including its geometry and charge distribution. Our calculations provide a comprehensive understanding of the intermolecular interactions in the N2O-N2O dimer using the CCSD(T) method with the def2-QZVPP basis set by using the improved Lennard-Jones interaction potential method. These results can be used to improve our understanding of atmospheric chemistry and climate modeling, as well as to aid in the interpretation of experimental data.
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Affiliation(s)
- Waqas Amber Gill
- Departamento de Química Física, Universidad de Valencia, Avda Dr. Moliner, 50, Burjassot E-46100, Valencia, Spain
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8
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Aðalsteinsson HM, Bjornsson R. Ionization energies of metallocenes: a coupled cluster study of cobaltocene. Phys Chem Chem Phys 2023; 25:4570-4587. [PMID: 36723003 DOI: 10.1039/d2cp04715b] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Abstract
Open-shell transition metal chemistry presents challenges to contemporary electronic structure methods, based on either density functional or wavefunction theory. While CCSD(T) is the well-trusted gold standard for maingroup thermochemistry, the accuracy and robustness of the method is less clear for open-shell transition metal chemistry, requiring benchmarking of CCSD(T)-based protocols against either higher-level theory or experiment. Ionization energies (IEs) of metallocenes provide an interesting test case with metallocenes being common redox reagents as well as playing roles as redox mediators and cocatalysts in redox catalysis. Using highly accurate ZEKE-MATI experimental measurements of gas phase adiabatic (5.3275 ± 0.0006 eV) and vertical (5.4424 ± 0.0006 eV) ionization energies of cobaltocene, we systematically assessed the accuracy of the local coupled-cluster method DLPNO-CCSD(T) with respect to geometry, reference determinant, basis set size and extrapolation schemes, PNO cut-off and extrapolation, local triples approximation, relativistic effects and core-valence correlation. We show that PNO errors are controllable via the recently introduced PNO extrapolation schemes and that the expensive iterative triples (T1) contribution can be made more manageable by calculating it as a smaller-basis/smaller PNO-cutoff correction. The reference determinant turns out to be a critical aspect in these calculations with the HF determinant resulting in large DLPNO-CCSD(T) errors, likely due to the qualitatively flawed molecular orbital spectrum. The BP86 functional on the other hand was found to provide reference orbitals giving small DLPNO-CCSD(T) errors, likely due to more realistic orbitals as suggested by the more consistent MO spectrum compared to HF. A protocol including complete basis set extrapolations with correlation-consistent basis sets, complete PNO space extrapolations, iterative triples- and core-valence correlation corrections was found to give errors of -0.07 eV and -0.03 eV for adiabatic- and vertical-IE of cobaltocene, respectively, giving close to chemical accuracy for both properties. A computationally efficient DLPNO-CCSD(T) protocol was devised and tested against adiabatic ionization energies of 6 different metallocenes (V, Cr, Mn, Fe, Co, Ni). For the other metallocenes, the iterative triples (T1) and PNO extrapolation contributions turn out to be even more important. The results give errors close to the experimental uncertainty, similar to recent auxiliary-field quantum Monte Carlo results. The quality of the reference determinant orbitals is identified as the main source of uncertainty in CCSD(T) calculations of metallocenes.
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Affiliation(s)
| | - Ragnar Bjornsson
- Science Institute, University of Iceland, 107 Reykjavik, Iceland.,Univ Grenoble Alpes, CNRS, CEA, IRIG, Laboratoire de Chimie et Biologie des Métaux, 17 Rue des Martyrs, F-38054 Grenoble Cedex, France.
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9
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Kállay M, Horváth RA, Gyevi-Nagy L, Nagy PR. Basis Set Limit CCSD(T) Energies for Extended Molecules via a Reduced-Cost Explicitly Correlated Approach. J Chem Theory Comput 2022; 19:174-189. [PMID: 36576419 PMCID: PMC9835832 DOI: 10.1021/acs.jctc.2c01031] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
Several approximations are introduced and tested to reduce the computational expenses of the explicitly correlated coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method for both closed and open-shell species. First, the well-established frozen natural orbital (FNO) technique is adapted to explicitly correlated CC approaches. Second, our natural auxiliary function (NAF) scheme is employed to reduce the size of the auxiliary basis required for the density fitting approximation regularly used in explicitly correlated calculations. Third, a new approach, termed the natural auxiliary basis (NAB) approximation, is proposed to decrease the size of the auxiliary basis needed for the expansion of the explicitly correlated geminals. The performance of the above approximations and that of the combined FNO-NAF-NAB approach are tested for atomization and reaction energies. Our results show that overall speedups of 7-, 5-, and 3-times can be achieved with double-, triple-, and quadruple-ζ basis sets, respectively, without any loss in accuracy. The new method can provide, e.g., reaction energies and barrier heights well within chemical accuracy for molecules with more than 40 atoms within a few days using a few dozen processor cores, and calculations with 50+ atoms are still feasible. These routinely affordable computations considerably extend the reach of explicitly correlated CCSD(T).
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Affiliation(s)
- Mihály Kállay
- Department
of Physical Chemistry and Materials Science, Faculty of Chemical Technology
and Biotechnology, Budapest University of
Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary,ELKH-BME
Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary,MTA-BME
Lendület Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary,
| | - Réka A. Horváth
- Department
of Physical Chemistry and Materials Science, Faculty of Chemical Technology
and Biotechnology, Budapest University of
Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary,ELKH-BME
Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary,MTA-BME
Lendület Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
| | - László Gyevi-Nagy
- Department
of Physical Chemistry and Materials Science, Faculty of Chemical Technology
and Biotechnology, Budapest University of
Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary,ELKH-BME
Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary,MTA-BME
Lendület Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
| | - Péter R. Nagy
- Department
of Physical Chemistry and Materials Science, Faculty of Chemical Technology
and Biotechnology, Budapest University of
Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary,ELKH-BME
Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary,MTA-BME
Lendület Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
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10
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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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Affiliation(s)
- Nisha Mehta
- Department of Molecular Chemistry and
Materials Science, Weizmann Institute of
Science, Reḥovot7610001, Israel
| | - Jan M. L. Martin
- Department of Molecular Chemistry and
Materials Science, Weizmann Institute of
Science, Reḥovot7610001, Israel
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11
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Nagy PR, Gyevi-Nagy L, Lőrincz BD, Kállay M. Pursuing the basis set limit of CCSD(T) non-covalent interaction energies for medium-sized complexes: case study on the S66 compilation. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2109526] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/15/2022]
Affiliation(s)
- Péter R. Nagy
- Faculty of Chemical Technology and Biotechnology, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, Budapest, Hungary
- ELKH-BME Quantum Chemistry Research Group, Budapest, Hungary
| | - László Gyevi-Nagy
- Faculty of Chemical Technology and Biotechnology, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, Budapest, Hungary
- ELKH-BME Quantum Chemistry Research Group, Budapest, Hungary
| | - Balázs D. Lőrincz
- Faculty of Chemical Technology and Biotechnology, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, Budapest, Hungary
- ELKH-BME Quantum Chemistry Research Group, Budapest, Hungary
| | - Mihály Kállay
- Faculty of Chemical Technology and Biotechnology, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, Budapest, Hungary
- ELKH-BME Quantum Chemistry Research Group, Budapest, Hungary
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12
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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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13
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Mehta N, Martin JML. MP2-F12 Basis Set Convergence near the Complete Basis Set Limit: Are h Functions Sufficient? J Phys Chem A 2022; 126:3964-3971. [PMID: 35687124 PMCID: PMC9234959 DOI: 10.1021/acs.jpca.2c02494] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
We have investigated
the title question for the W4-08 thermochemical
benchmark using l-saturated truncations of a large
reference (REF) basis set, as well as for standard F12-optimized basis
sets. With the REF basis set, the root-mean-square (RMS) contribution
of i functions to the MP2-F12 total atomization energies
(TAEs) is about 0.01 kcal/mol, the largest individual contributions
being 0.04 kcal/mol for P2 and P4. However,
even for these cases, basis set extrapolation from {g,h} basis sets adequately addresses the problem.
Using basis sets insufficiently saturated in the spdfgh angular momenta may lead to exaggerated i function
contributions. For extrapolation from spdfg and spdfgh basis sets, basis set convergence appears to be quite
close to the theoretical asymptotic ∝ L–7 behavior. We hence conclude that h functions are sufficient even for highly demanding F12 applications.
With one-parameter extrapolation, spdf and spdfg basis sets are adequate, aug-cc-pV{T,Q}Z-F12 yielding
a RMSD = 0.03 kcal/mol. A limited exploration of CCSD(F12*) and CCSD-F12b
suggests our conclusions are applicable to higher-level F12 methods
as well.
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Affiliation(s)
- Nisha Mehta
- Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Reḥovot, 7610001, Israel
| | - Jan M L Martin
- Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Reḥovot, 7610001, Israel
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14
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Schraivogel T, Cohen AJ, Alavi A, Kats D. Transcorrelated coupled cluster methods. J Chem Phys 2021; 155:191101. [PMID: 34800963 DOI: 10.1063/5.0072495] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Transcorrelated coupled cluster and distinguishable cluster methods are presented. The Hamiltonian is similarity transformed with a Jastrow factor in the first quantization, which results in up to three-body integrals. The coupled cluster with singles and doubles equations on this transformed Hamiltonian are formulated and implemented. It is demonstrated that the resulting methods have a superior basis set convergence and accuracy to the corresponding conventional and explicitly correlated methods. Additionally, approximations for three-body integrals are suggested and tested.
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Affiliation(s)
- Thomas Schraivogel
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Aron J Cohen
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Ali Alavi
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Daniel Kats
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
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15
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Kállay M, Horváth RA, Gyevi-Nagy L, Nagy PR. Size-consistent explicitly correlated triple excitation correction. J Chem Phys 2021; 155:034107. [PMID: 34293884 DOI: 10.1063/5.0057426] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
A new approach is proposed to reduce the basis set incompleteness error of the triple excitation correction in explicitly correlated coupled-cluster singles and doubles with perturbative triples calculations. Our method is similar to the intuitive triples correction approach of Knizia et al. [J. Chem. Phys. 130, 054104 (2009)] but, in contrast to the latter, is size-consistent. The new approximation is easy to implement, and its overhead is negligible with respect to the conventional (T) correction. The performance of the approach is assessed for atomization, reaction, and interaction energies as well as for bond lengths and harmonic vibrational frequencies. The advantages of its size consistency are also demonstrated.
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Affiliation(s)
- Mihály Kállay
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, Budapest H-1521, Hungary
| | - Réka A Horváth
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, Budapest H-1521, Hungary
| | - László Gyevi-Nagy
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, Budapest H-1521, Hungary
| | - Péter R Nagy
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, Budapest H-1521, Hungary
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16
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Lee TJ, Fortenberry RC. The unsolved issue with out-of-plane bending frequencies for CC multiply bonded systems. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2021; 248:119148. [PMID: 33293227 DOI: 10.1016/j.saa.2020.119148] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2020] [Accepted: 10/26/2020] [Indexed: 06/12/2023]
Abstract
More than 30 years ago two groups independently identified a problem in the calculation of the out-of-plane bending (OPB) vibrational frequencies for the ethylene molecule using correlated electronic structure methods. Several studies have been done in the meantime to try and understand and resolve this issue. In so doing this problem has been found to be far more insidious than previously realized for acetylene-like and benzene-like molecules, which can become non-linear and non-planar, respectively. The one common feature that all molecules with this problem have is that they contain CC multiple bonds, and so this has been called the "CC multiple bond OPB frequency issue" or "the CC OPB problem." Various explanations for this problem have been advanced such as basis set superposition error, basis set incompleteness error, linear dependences in the basis set, proper balancing of the basis set between saturation and inclusion of higher angular momentum functions, etc. and possible solutions have arisen from these suggestions. All of these proposed solutions, however, amount to one main point connecting them all: modifying the one-particle basis set in some way. None of the explanations that have been advanced, however, really fit all of the data for all of the molecules where this problem has been identified, and importantly, none of these diagnostic tests have been applied to similar molecules where this issue does not appear. In this review, the studies over the last 30 plus years are discussed and relevant data from each of these is compared and contrasted. It is hoped that by collecting and analyzing the data from these studies a path forward to understanding and resolving this issue will become evident.
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Affiliation(s)
- Timothy J Lee
- MS245-3, Planetary Systems Branch, Space Science and Astrobiology Division, NASA Ames Research Center, Moffett Field, CA 94035, USA.
| | - Ryan C Fortenberry
- Department of Chemistry & Biochemistry, University of Mississippi, University, MS 38677-1848, USA
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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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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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19
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Dargelos A, Pouchan C. CCSD(T)-F12 calculations of the IR spectrum of cyanoacetylene HC3N beyond the harmonic approximation. Chem Phys Lett 2020. [DOI: 10.1016/j.cplett.2020.137746] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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20
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Peng C, Lewis CA, Wang X, Clement MC, Pierce K, Rishi V, Pavošević F, Slattery S, Zhang J, Teke N, Kumar A, Masteran C, Asadchev A, Calvin JA, Valeev EF. Massively Parallel Quantum Chemistry: A high-performance research platform for electronic structure. J Chem Phys 2020; 153:044120. [DOI: 10.1063/5.0005889] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Chong Peng
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Cannada A. Lewis
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Xiao Wang
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | | | - Karl Pierce
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Varun Rishi
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Fabijan Pavošević
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Samuel Slattery
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Jinmei Zhang
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Nakul Teke
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Ashutosh Kumar
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Conner Masteran
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Andrey Asadchev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Justus A. Calvin
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
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21
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Peels M, Knizia G. Fast Evaluation of Two-Center Integrals over Gaussian Charge Distributions and Gaussian Orbitals with General Interaction Kernels. J Chem Theory Comput 2020; 16:2570-2583. [PMID: 32040326 DOI: 10.1021/acs.jctc.9b01296] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
We present efficient algorithms for computing two-center integrals and integral derivatives, with general interaction kernels K(r12), over Gaussian charge distributions of general angular momenta l. While formulated in terms of traditional ab initio integration techniques, full derivations and required secondary information, as well as a reference implementation, are provided to make the content accessible to other fields. Concretely, the presented algorithms are based on an adaption of the McMurchie-Davidson Recurrence Relation (MDRR) combined with analytical properties of the solid harmonic transformation; this obviates all intermediate recurrences except the adapted MDRR itself, and allows it to be applied to fully contracted auxiliary kernel integrals. The technique is particularly well-suited for semiempirical molecular orbital methods, where it can serve as a more general and efficient replacement of Slater-Koster tables, and for first-principles quantum chemistry methods employing density fitting. But the formalism's high efficiency and ability of handling general interaction kernels K(r12) and multipolar Gaussian charge distributions may also be of interest for modeling electrostatic interactions and short-range exchange and charge penetration effects in classical force fields and model potentials. With the presented technique, a 4894 × 4894 univ-JKFIT Coulomb matrix JAB = (A|1/r12|B) (183 MiB) can be computed in 50 ms on a Q2'2018 notebook CPU, without any screening or approximations.
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Affiliation(s)
- Mieke Peels
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Gerald Knizia
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
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22
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Patel P, Wang J, Wilson AK. Prediction of pK a s of Late Transition-Metal Hydrides via a QM/QM Approach. J Comput Chem 2020; 41:171-183. [PMID: 31495951 DOI: 10.1002/jcc.26057] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2019] [Accepted: 08/04/2019] [Indexed: 11/09/2022]
Abstract
Three implicit solvation models, the conductor-like polarizable continuum model (C-PCM), the conductor-like screening model (COSMO), and universal implicit solvent model (SMD), combined with a hybrid two layer QM/QM approach (ONIOM), were utilized to calculate the pKa values, using a direct thermodynamic scheme, of a set of Group 10 transition metal (TM) hydrides in acetonitrile. To obtain the optimal combination of quantum methods for ONIOM calculations with implicit solvation models, the influence of factors, such as the choice of density functional and basis set, the atomic radii used to build a cavity in the solvent, and the size of the model system in an ONIOM scheme, was examined. Additionally, the impact of Grimme's empirical dispersion correction and exact exchange was also investigated. The results were calibrated by experimental data. This investigation provides insight about effective models for the prediction of thermodynamic properties of TM-containing complexes with bulky ligands. © 2019 Wiley Periodicals, Inc.
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Affiliation(s)
- Prajay Patel
- Department of Chemistry and Center for Advanced Scientific Computing and Modeling (CASCaM), University of North Texas, Denton, Texas, 76203-5017.,Department of Chemistry, Michigan State University, East Lansing, Michigan, 48824-1322
| | - Jiaqi Wang
- Department of Chemistry and Center for Advanced Scientific Computing and Modeling (CASCaM), University of North Texas, Denton, Texas, 76203-5017.,Department of Chemistry, Beijing Forestry University, Beijing, China, 100083
| | - Angela K Wilson
- Department of Chemistry and Center for Advanced Scientific Computing and Modeling (CASCaM), University of North Texas, Denton, Texas, 76203-5017.,Department of Chemistry, Michigan State University, East Lansing, Michigan, 48824-1322
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23
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Teke NK, Pavošević F, Peng C, Valeev EF. Explicitly correlated renormalized second-order Green’s function for accurate ionization potentials of closed-shell molecules. J Chem Phys 2019; 150:214103. [DOI: 10.1063/1.5090983] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Nakul K. Teke
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Fabijan Pavošević
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Chong Peng
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
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24
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Höfener S, Schieschke N, Klopper W, Köhn A. The extended explicitly-correlated second-order approximate coupled-cluster singles and doubles ansatz suitable for response theory. J Chem Phys 2019; 150:184110. [DOI: 10.1063/1.5094434] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Affiliation(s)
- Sebastian Höfener
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), P.O. Box 6980, D-76049 Karlsruhe, Germany
| | - Nils Schieschke
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), P.O. Box 6980, D-76049 Karlsruhe, Germany
| | - Wim Klopper
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), P.O. Box 6980, D-76049 Karlsruhe, Germany
| | - Andreas Köhn
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
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25
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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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26
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Al-Hamdani YS, Tkatchenko A. Understanding non-covalent interactions in larger molecular complexes from first principles. J Chem Phys 2019; 150:010901. [PMID: 30621423 PMCID: PMC6910608 DOI: 10.1063/1.5075487] [Citation(s) in RCA: 38] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2018] [Accepted: 12/05/2018] [Indexed: 01/02/2023] Open
Abstract
Non-covalent interactions pervade all matter and play a fundamental role in layered materials, biological systems, and large molecular complexes. Despite this, our accumulated understanding of non-covalent interactions to date has been mainly developed in the tens-of-atoms molecular regime. This falls considerably short of the scales at which we would like to understand energy trends, structural properties, and temperature dependencies in materials where non-covalent interactions have an appreciable role. However, as more reference information is obtained beyond moderately sized molecular systems, our understanding is improving and we stand to gain pertinent insights by tackling more complex systems, such as supramolecular complexes, molecular crystals, and other soft materials. In addition, accurate reference information is needed to provide the drive for extending the predictive power of more efficient workhorse methods, such as density functional approximations that also approximate van der Waals dispersion interactions. In this perspective, we discuss the first-principles approaches that have been used to obtain reference interaction energies for beyond modestly sized molecular complexes. The methods include quantum Monte Carlo, symmetry-adapted perturbation theory, non-canonical coupled cluster theory, and approaches based on the random-phase approximation. By considering the approximations that underpin each method, the most accurate theoretical references for supramolecular complexes and molecular crystals to date are ascertained. With these, we also assess a handful of widely used exchange-correlation functionals in density functional theory. The discussion culminates in a framework for putting into perspective the accuracy of high-level wavefunction-based methods and identifying future challenges.
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Affiliation(s)
- Yasmine S Al-Hamdani
- Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Alexandre Tkatchenko
- Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
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27
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Kats D, Tew DP. Orbital-Optimized Distinguishable Cluster Theory with Explicit Correlation. J Chem Theory Comput 2018; 15:13-17. [DOI: 10.1021/acs.jctc.8b01047] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Daniel Kats
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - David P. Tew
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
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28
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Li MW, Zimmerman PM. Stepwise basis set selection. J Comput Chem 2018; 39:2153-2162. [DOI: 10.1002/jcc.25363] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2018] [Accepted: 05/01/2018] [Indexed: 11/08/2022]
Affiliation(s)
- M. W. Li
- Department of ChemistryUniversity of Michigan930 N. University Ave, Ann Arbor MI48109
| | - P. M. Zimmerman
- Department of ChemistryUniversity of Michigan930 N. University Ave, Ann Arbor MI48109
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29
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Tew DP, Kats D. Relaxing Constrained Amplitudes: Improved F12 Treatments of Orbital Optimization and Core–Valence Correlation Energies. J Chem Theory Comput 2018; 14:5435-5440. [DOI: 10.1021/acs.jctc.8b00792] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- David P. Tew
- Max Planck Institute for Solid State
Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Daniel Kats
- Max Planck Institute for Solid State
Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
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30
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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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31
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Győrffy W, Werner HJ. Analytical energy gradients for explicitly correlated wave functions. II. Explicitly correlated coupled cluster singles and doubles with perturbative triples corrections: CCSD(T)-F12. J Chem Phys 2018; 148:114104. [DOI: 10.1063/1.5020436] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Affiliation(s)
- Werner Győrffy
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
| | - Hans-Joachim Werner
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
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32
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Kesharwani MK, Karton A, Sylvetsky N, Martin JML. The S66 Non-Covalent Interactions Benchmark Reconsidered Using Explicitly Correlated Methods Near the Basis Set Limit. Aust J Chem 2018. [DOI: 10.1071/ch17588] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
The S66 benchmark for non-covalent interactions has been re-evaluated using explicitly correlated methods with basis sets near the one-particle basis set limit. It is found that post-MP2 ‘high-level corrections’ are treated adequately well using a combination of CCSD(F12*) with (aug-)cc-pVTZ-F12 basis sets on the one hand, and (T) extrapolated from conventional CCSD(T)/heavy-aug-cc-pV{D,T}Z on the other hand. Implications for earlier benchmarks on the larger S66×8 problem set in particular, and for accurate calculations on non-covalent interactions in general, are discussed. At a slight cost in accuracy, (T) can be considerably accelerated by using sano-V{D,T}Z+ basis sets, whereas half-counterpoise CCSD(F12*)(T)/cc-pVDZ-F12 offers the best compromise between accuracy and computational cost.
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33
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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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34
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Győrffy W, Knizia G, Werner HJ. Analytical energy gradients for explicitly correlated wave functions. I. Explicitly correlated second-order Møller-Plesset perturbation theory. J Chem Phys 2017; 147:214101. [DOI: 10.1063/1.5003065] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Affiliation(s)
- Werner Győrffy
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
| | - Gerald Knizia
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
- Department of Chemistry, Pennsylvania State University, 401A Chemistry Building, University Park, Pennsylvania 16802, USA
| | - Hans-Joachim Werner
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
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35
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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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36
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Klippenstein SJ, Harding LB, Ruscic B. Ab Initio Computations and Active Thermochemical Tables Hand in Hand: Heats of Formation of Core Combustion Species. J Phys Chem A 2017; 121:6580-6602. [DOI: 10.1021/acs.jpca.7b05945] [Citation(s) in RCA: 106] [Impact Index Per Article: 15.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Stephen J. Klippenstein
- Chemical Sciences and Engineering
Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Lawrence B. Harding
- Chemical Sciences and Engineering
Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Branko Ruscic
- Chemical Sciences and Engineering
Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
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37
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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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38
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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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39
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Pavošević F, Peng C, Pinski P, Riplinger C, Neese F, Valeev EF. SparseMaps—A systematic infrastructure for reduced scaling electronic structure methods. V. Linear scaling explicitly correlated coupled-cluster method with pair natural orbitals. J Chem Phys 2017; 146:174108. [DOI: 10.1063/1.4979993] [Citation(s) in RCA: 93] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Fabijan Pavošević
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Chong Peng
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Peter Pinski
- Max Planck Institute for Chemical Energy Conversion, Stiftstr. 34-36, 45470 Mülheim an der Ruhr, Germany
| | - Christoph Riplinger
- Max Planck Institute for Chemical Energy Conversion, Stiftstr. 34-36, 45470 Mülheim an der Ruhr, Germany
| | - Frank Neese
- Max Planck Institute for Chemical Energy Conversion, Stiftstr. 34-36, 45470 Mülheim an der Ruhr, Germany
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
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40
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Tew DP. Explicitly correlated coupled-cluster theory with Brueckner orbitals. J Chem Phys 2016; 145:074103. [DOI: 10.1063/1.4960655] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- David P. Tew
- School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
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41
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Xu X, Zhang W, Tang M, Truhlar DG. Do Practical Standard Coupled Cluster Calculations Agree Better than Kohn–Sham Calculations with Currently Available Functionals When Compared to the Best Available Experimental Data for Dissociation Energies of Bonds to 3d Transition Metals? J Chem Theory Comput 2015; 11:2036-52. [DOI: 10.1021/acs.jctc.5b00081] [Citation(s) in RCA: 94] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xuefei Xu
- Department
of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Wenjing Zhang
- Department
of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
- College
of Chemistry and Molecular Engineering, Zhengzhou University, Zhengzhou, Henan Province 450001, People’s Republic of China
| | - Mingsheng Tang
- College
of Chemistry and Molecular Engineering, Zhengzhou University, Zhengzhou, Henan Province 450001, People’s Republic of China
| | - Donald G. Truhlar
- Department
of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
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42
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Kats D, Kreplin D, Werner HJ, Manby FR. Accurate thermochemistry from explicitly correlated distinguishable cluster approximation. J Chem Phys 2015; 142:064111. [DOI: 10.1063/1.4907591] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Affiliation(s)
- Daniel Kats
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
| | - David Kreplin
- 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
| | - Frederick R. Manby
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS,United Kingdom
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43
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Werner HJ, Knizia G, Krause C, Schwilk M, Dornbach M. Scalable Electron Correlation Methods I.: PNO-LMP2 with Linear Scaling in the Molecular Size and Near-Inverse-Linear Scaling in the Number of Processors. J Chem Theory Comput 2015; 11:484-507. [DOI: 10.1021/ct500725e] [Citation(s) in RCA: 103] [Impact Index Per Article: 11.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Affiliation(s)
- Hans-Joachim Werner
- Institut für Theoretische
Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Gerald Knizia
- Institut für Theoretische
Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Christine Krause
- Institut für Theoretische
Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Max Schwilk
- Institut für Theoretische
Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Mark Dornbach
- Institut für Theoretische
Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
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44
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Howard JC, Tschumper GS. Wavefunction methods for the accurate characterization of water clusters. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2013. [DOI: 10.1002/wcms.1168] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
| | - Gregory S. Tschumper
- Department of Chemistry and Biochemistry University of Mississippi, University Mississippi USA
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45
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Riplinger C, Neese F. An efficient and near linear scaling pair natural orbital based local coupled cluster method. J Chem Phys 2013; 138:034106. [PMID: 23343267 DOI: 10.1063/1.4773581] [Citation(s) in RCA: 1110] [Impact Index Per Article: 100.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In previous publications, it was shown that an efficient local coupled cluster method with single- and double excitations can be based on the concept of pair natural orbitals (PNOs) [F. Neese, A. Hansen, and D. G. Liakos, J. Chem. Phys. 131, 064103 (2009)]. The resulting local pair natural orbital-coupled-cluster single double (LPNO-CCSD) method has since been proven to be highly reliable and efficient. For large molecules, the number of amplitudes to be determined is reduced by a factor of 10(5)-10(6) relative to a canonical CCSD calculation on the same system with the same basis set. In the original method, the PNOs were expanded in the set of canonical virtual orbitals and single excitations were not truncated. This led to a number of fifth order scaling steps that eventually rendered the method computationally expensive for large molecules (e.g., >100 atoms). In the present work, these limitations are overcome by a complete redesign of the LPNO-CCSD method. The new method is based on the combination of the concepts of PNOs and projected atomic orbitals (PAOs). Thus, each PNO is expanded in a set of PAOs that in turn belong to a given electron pair specific domain. In this way, it is possible to fully exploit locality while maintaining the extremely high compactness of the original LPNO-CCSD wavefunction. No terms are dropped from the CCSD equations and domains are chosen conservatively. The correlation energy loss due to the domains remains below <0.05%, which implies typically 15-20 but occasionally up to 30 atoms per domain on average. The new method has been given the acronym DLPNO-CCSD ("domain based LPNO-CCSD"). The method is nearly linear scaling with respect to system size. The original LPNO-CCSD method had three adjustable truncation thresholds that were chosen conservatively and do not need to be changed for actual applications. In the present treatment, no additional truncation parameters have been introduced. Any additional truncation is performed on the basis of the three original thresholds. There are no real-space cutoffs. Single excitations are truncated using singles-specific natural orbitals. Pairs are prescreened according to a multipole expansion of a pair correlation energy estimate based on local orbital specific virtual orbitals (LOSVs). Like its LPNO-CCSD predecessor, the method is completely of black box character and does not require any user adjustments. It is shown here that DLPNO-CCSD is as accurate as LPNO-CCSD while leading to computational savings exceeding one order of magnitude for larger systems. The largest calculations reported here featured >8800 basis functions and >450 atoms. In all larger test calculations done so far, the LPNO-CCSD step took less time than the preceding Hartree-Fock calculation, provided no approximations have been introduced in the latter. Thus, based on the present development reliable CCSD calculations on large molecules with unprecedented efficiency and accuracy are realized.
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Affiliation(s)
- Christoph Riplinger
- Max Planck Institut für Chemische Energiekonversion, Stiftstr. 34-36, D-45470 Mülheim an der Ruhr, Germany
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46
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47
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Hollman DS, Wilke JJ, Schaefer HF. Explicitly correlated atomic orbital basis second order Møller–Plesset theory. J Chem Phys 2013; 138:064107. [DOI: 10.1063/1.4790582] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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49
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Zhang J, Valeev EF. Prediction of Reaction Barriers and Thermochemical Properties with Explicitly Correlated Coupled-Cluster Methods: A Basis Set Assessment. J Chem Theory Comput 2012; 8:3175-86. [DOI: 10.1021/ct3005547] [Citation(s) in RCA: 62] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Jinmei Zhang
- Department of Chemistry, Virginia Tech, Blacksburg,
Virginia 24061, United States
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg,
Virginia 24061, United States
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50
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Patkowski K. On the accuracy of explicitly correlated coupled-cluster interaction energies — have orbital results been beaten yet? J Chem Phys 2012; 137:034103. [DOI: 10.1063/1.4734597] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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