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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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2
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Hillers-Bendtsen AE, Jensen F, Mikkelsen KV, Olsen J, Jørgensen P. Cluster perturbation theory IX: Perturbation series for the coupled cluster singles and doubles ground state energy. J Chem Phys 2024; 160:104108. [PMID: 38477336 DOI: 10.1063/5.0192388] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2023] [Accepted: 02/17/2024] [Indexed: 03/14/2024] Open
Abstract
In this paper, we develop and analyze a number of perturbation series that target the coupled cluster singles and doubles (CCSD) ground state energy. We show how classical Møller-Plesset perturbation theory series can be restructured to target the CCSD energy based on a reference CCS calculation and how the corresponding cluster perturbation series differs from the classical Møller-Plesset perturbation series. Subsequently, we reformulate these series using the coupled cluster Lagrangian framework to obtain series, where fourth and fifth order energies are determined only using parameters through second order. To test the methods, we perform a series of test calculations on molecular photoswitches of both total energies and reaction energies. We find that the fifth order reaction energies are of CCSD quality and that they are of comparable accuracy to state-of-the-art approximations to the CCSD energy based on local pair natural orbitals. The advantage of the present approach over local correlation methods is the absence of user defined threshold parameters for neglecting or approximating contributions to the correlation energy. Fixed threshold parameters lead to discontinuous energy surfaces, although this effect is often small enough to be ignored, but the present approach has a differentiable energy that will facilitate derivation and implementation of gradients and higher derivatives. A further advantage is that the calculation of the perturbation correction is non-iterative and can, therefore, be calculated in parallel, leading to a short time-to-solution.
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Affiliation(s)
| | - Frank Jensen
- Department of Chemistry, Aarhus University, Langelandsgade 140, DK 8000 Aarhus C, Denmark
| | - Kurt V Mikkelsen
- Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK 2100 Copenhagen Ø, Denmark
| | - Jeppe Olsen
- Department of Chemistry, Aarhus University, Langelandsgade 140, DK 8000 Aarhus C, Denmark
| | - Poul Jørgensen
- Department of Chemistry, Aarhus University, Langelandsgade 140, DK 8000 Aarhus C, Denmark
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3
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Hillers-Bendtsen AE, Mikkelsen KV, Martinez TJ. Tensor Hypercontraction of Cluster Perturbation Theory: Quartic Scaling Perturbation Series for the Coupled Cluster Singles and Doubles Ground-State Energies. J Chem Theory Comput 2024; 20:1932-1943. [PMID: 38380846 DOI: 10.1021/acs.jctc.3c01038] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/22/2024]
Abstract
Even though cluster perturbation theory has been shown to be a robust noniterative alternative to coupled cluster theory, it is still plagued by high order polynomial computational scaling and the storage of higher order tensors. We present a proof-of-concept strategy for implementing a cluster perturbation theory ground-state energy series for the coupled cluster singles and doubles energy with N4 computational scaling using tensor hypercontraction (THC). The reduction in computational scaling by two orders is achieved by decomposing two electron repulsion integrals, doubles amplitudes and multipliers, as well as selected double intermediates to the THC format. Using the outlined strategy, we showcase that the THC pilot implementations retain numerical accuracy to within 1 kcal/mol relative to corresponding conventional and density fitting implementations, and we empirically verify the N4 scaling.
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Affiliation(s)
| | - Kurt V Mikkelsen
- Department of Chemistry, University of Copenhagen, Universitetsparken 5, Copenhagen Ø DK-2100, Denmark
| | - Todd J Martinez
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, United States
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, United States
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4
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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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5
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Corzo HH, Hillers-Bendtsen AE, Barnes A, Zamani AY, Pawłowski F, Olsen J, Jørgensen P, Mikkelsen KV, Bykov D. Corrigendum: Coupled cluster theory on modern heterogeneous supercomputers. Front Chem 2023; 11:1256510. [PMID: 37654900 PMCID: PMC10466216 DOI: 10.3389/fchem.2023.1256510] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2023] [Accepted: 07/11/2023] [Indexed: 09/02/2023] Open
Abstract
[This corrects the article DOI: 10.3389/fchem.2023.1154526.].
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Affiliation(s)
| | | | | | - Abdulrahman Y. Zamani
- Department of Chemistry and Biochemistry and Center for Chemical Computation and Theory, University of California, Merced, CA, United States
| | - Filip Pawłowski
- Department of Chemistry and Biochemistry, Auburn University, Auburn, AL, United States
| | - Jeppe Olsen
- Department of Chemistry, Aarhus University, Aarhus, Denmark
| | - Poul Jørgensen
- Department of Chemistry, Aarhus University, Aarhus, Denmark
| | - Kurt V. Mikkelsen
- Department of Chemistry, University of Copenhagen, Copenhagen, Denmark
| | - Dmytro Bykov
- Oak Ridge National Laboratory, Oak Ridge, TN, United States
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6
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Corzo HH, Hillers-Bendtsen AE, Barnes A, Zamani AY, Pawłowski F, Olsen J, Jørgensen P, Mikkelsen KV, Bykov D. Coupled cluster theory on modern heterogeneous supercomputers. Front Chem 2023; 11:1154526. [PMID: 37388945 PMCID: PMC10303140 DOI: 10.3389/fchem.2023.1154526] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Accepted: 05/11/2023] [Indexed: 07/01/2023] Open
Abstract
This study examines the computational challenges in elucidating intricate chemical systems, particularly through ab-initio methodologies. This work highlights the Divide-Expand-Consolidate (DEC) approach for coupled cluster (CC) theory-a linear-scaling, massively parallel framework-as a viable solution. Detailed scrutiny of the DEC framework reveals its extensive applicability for large chemical systems, yet it also acknowledges inherent limitations. To mitigate these constraints, the cluster perturbation theory is presented as an effective remedy. Attention is then directed towards the CPS (D-3) model, explicitly derived from a CC singles parent and a doubles auxiliary excitation space, for computing excitation energies. The reviewed new algorithms for the CPS (D-3) method efficiently capitalize on multiple nodes and graphical processing units, expediting heavy tensor contractions. As a result, CPS (D-3) emerges as a scalable, rapid, and precise solution for computing molecular properties in large molecular systems, marking it an efficient contender to conventional CC models.
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Affiliation(s)
| | | | | | - Abdulrahman Y. Zamani
- Department of Chemistry and Biochemistry and Center for Chemical Computation and Theory, University of California, Merced, CA, United States
| | - Filip Pawłowski
- Department of Chemistry and Biochemistry, Auburn University, Auburn, AL, United States
| | - Jeppe Olsen
- Department of Chemistry, Aarhus University, Aarhus, Denmark
| | - Poul Jørgensen
- Department of Chemistry, Aarhus University, Aarhus, Denmark
| | - Kurt V. Mikkelsen
- Department of Chemistry, University of Copenhagen, Copenhagen, Denmark
| | - Dmytro Bykov
- Oak Ridge National Laboratory, Oak Ridge, TN, United States
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7
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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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8
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Westheimer BM, Gordon MS. Scalable ab initio fragmentation methods based on a truncated expansion of the non-orthogonal molecular orbital model. J Chem Phys 2021; 155:154101. [PMID: 34686043 DOI: 10.1063/5.0064864] [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
An alternative formulation of the non-orthogonal molecular orbital model of electronic structure theory is developed based on the expansion of the inverse molecular orbital overlap matrix. From this model, a hierarchy of ab initio fragment-based quantum chemistry methods, referred to as the nth-order expanded non-orthogonal molecular orbital methods, are developed using a minimal number of approximations, each of which is frequently employed in intermolecular interaction theory. These novel methods are compared to existing fragment-based quantum chemistry methods, and the implications of those significant differences, where they exist, between the methods developed herein and those already existing methods are examined in detail. Computational complexities and theoretical scaling are also analyzed and discussed. Future extensions for the hierarchy of methods, to account for additional intrafragment and interfragment interactions, are outlined.
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Affiliation(s)
| | - Mark S Gordon
- Department of Chemistry, Iowa State University, Ames, Iowa 50011, USA
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9
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Hansen AS, Aurbakken E, Pedersen TB. Smooth potential-energy surfaces in fragmentation-based local correlation methods for periodic systems. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1896046] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- A. S. Hansen
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, Oslo, Norway
| | - E. Aurbakken
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, Oslo, Norway
| | - T. B. Pedersen
- Department of Chemistry, Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, Oslo, Norway
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10
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Pierce K, Rishi V, Valeev EF. Robust Approximation of Tensor Networks: Application to Grid-Free Tensor Factorization of the Coulomb Interaction. J Chem Theory Comput 2021; 17:2217-2230. [PMID: 33780616 DOI: 10.1021/acs.jctc.0c01310] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Approximation of a tensor network by approximating (e.g., factorizing) one or more of its constituent tensors can be improved by canceling the leading-order error due to the constituents' approximation. The utility of such robust approximation is demonstrated for robust canonical polyadic (CP) approximation of a (density-fitting) factorized two-particle Coulomb interaction tensor. The resulting algebraic (grid-free) approximation for the Coulomb tensor, closely related to the factorization appearing in pseudospectral and tensor hypercontraction approaches, is efficient and accurate, with significantly reduced rank compared to the naive (nonrobust) approximation. Application of the robust approximation to the particle-particle ladder term in the coupled-cluster singles and doubles reduces the size complexity from O (N6) to O (N5) with robustness ensuring negligible errors in chemically relevant energy differences using CP ranks approximately equal to the size of the density-fitting basis.
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Affiliation(s)
- Karl Pierce
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Varun Rishi
- 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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11
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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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12
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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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13
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Datta D, Saitow M, Sandhöfer B, Neese F. 57Fe Mössbauer parameters from domain based local pair-natural orbital coupled-cluster theory. J Chem Phys 2020; 153:204101. [PMID: 33261496 DOI: 10.1063/5.0022215] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report on applications of the domain based local pair-natural orbital (PNO) coupled-cluster method within the singles and doubles approximation (DLPNO-CCSD) to the calculation of 57Fe isomer shifts and quadrupole splittings in a small training set of iron complexes consisting of large molecular ligands and iron atoms in varying charge, spin, and oxidation states. The electron densities and electric field gradients needed for these calculations were obtained within the recently implemented analytic derivative scheme. A method for the direct treatment of scalar relativistic effects in the calculation of effective electron densities is described by using the first-order Douglas-Kroll-Hess Hamiltonian and a Gaussian charge distribution model for the nucleus. The performance of DLPNO-CCSD is compared with four modern-day density functionals, namely, RPBE, TPSS, B3LYP, and B2PLYP, as well as with the second-order Møller-Plesset perturbation theory. An excellent correlation between the calculated electron densities and the experimental isomer shifts is attained with the DLPNO-CCSD method. The correlation constant a obtained from the slope of the linear correlation plot is found to be ≈-0.31 a.u.3 mm s-1, which agrees very well with the experimental calibration constant α = -0.31 ± 0.04 a.u.3 mm s-1. This value of a is obtained consistently using both nonrelativistic and scalar relativistic DLPNO-CCSD electron densities. While the B3LYP and B2PLYP functionals achieve equally good correlation between theory and experiment, the correlation constant a is found to deviate from the experimental value. Similar trends are observed also for quadrupole splittings. The value of the nuclear quadrupole moment for 57Fe is estimated to be 0.15 b at the DLPNO-CCSD level. This is consistent with previous results and is here supported by a higher level of theory. The DLPNO-CCSD results are found to be insensitive to the intrinsic approximations in the method, in particular the PNO occupation number truncation error, while the results obtained with density functional theory (DFT) are found to depend on the choice of the functional. In a statistical sense, i.e., on the basis of the linear regression analysis, however, the accuracies of the DFT and DLPNO-CCSD results can be considered comparable.
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Affiliation(s)
- Dipayan Datta
- Department of Chemistry and Ames Laboratory, Iowa State University, 201 Spedding Hall, 2416 Pammel Drive, Ames, Iowa 50011-2416, USA
| | - Masaaki Saitow
- 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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14
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Scott CJC, Di Remigio R, Crawford TD, Thom AJW. Theory and implementation of a novel stochastic approach to coupled cluster. J Chem Phys 2020; 153:144117. [DOI: 10.1063/5.0026513] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Charles J. C. Scott
- Department of Physics, King’s College London, Strand, London WC2R 2LS, United Kingdom
| | - Roberto Di Remigio
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - T. Daniel Crawford
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
- Molecular Sciences Software Institute, Blacksburg, Virginia 24060, USA
| | - Alex J. W. Thom
- Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
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15
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Frank MS, Schmitz G, Hättig C. Implementation of the iterative triples model CC3 for excitation energies using pair natural orbitals and Laplace transformation techniques. J Chem Phys 2020; 153:034109. [PMID: 32716174 DOI: 10.1063/5.0012597] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a pair natural orbital (PNO)-based implementation of CC3 excitation energies, which extends our previously published state-specific PNO ansatz for the solution of the excited state eigenvalue problem to methods including connected triple excitations. A thorough analysis of the equations for the excited state triples amplitudes is presented from which we derive a suitable state-specific triple natural orbital basis for the excited state triples amplitudes, which performs equally well for local and non-local excitations. The accuracy of the implementation is evaluated using a large and diverse test set. We find that for states with small contributions from double excitations, a T0 approximation to PNO-CC3 yields accurate results with a mean absolute error (MAE) for TPNO = 10-7 in the range of 0.02 eV. However, for states with larger double excitation contributions, the T0 approximation is found to yield significantly less accurate results, while the Laplace-transformed variant of PNO-CC3 shows a uniform accuracy for singly and doubly excited states (MAE and maximum error of 0.01 eV and 0.07 eV for TPNO = 10-7, respectively). Finally, we apply PNO-CC3 to the calculation of the first excited state of berenil at a S1 minimum geometry, which is shown to be close to a conical intersection. This calculation in the aug-cc-pVTZ basis set (more than 1300 basis functions) is the largest calculation ever performed with CC3 on excitation energies.
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Affiliation(s)
- Marius S Frank
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44801 Bochum, Germany
| | - Gunnar Schmitz
- Deparment of Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark
| | - Christof Hättig
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44801 Bochum, Germany
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16
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Lang J, Antalík A, Veis L, Brandejs J, Brabec J, Legeza Ö, Pittner J. Near-Linear Scaling in DMRG-Based Tailored Coupled Clusters: An Implementation of DLPNO-TCCSD and DLPNO-TCCSD(T). J Chem Theory Comput 2020; 16:3028-3040. [PMID: 32275424 DOI: 10.1021/acs.jctc.0c00065] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
We present a new implementation of density matrix renormalization group based tailored coupled clusters method (TCCSD), which employs the domain-based local pair natural orbital approach (DLPNO). Compared to the previous local pair natural orbital (LPNO) version of the method, the new implementation is more accurate, offers more favorable scaling, and provides more consistent behavior across the variety of systems. On top of the singles and doubles, we include the perturbative triples correction (T), which is able to retrieve even more dynamic correlation. The methods were tested on three systems: tetramethyleneethane, oxo-Mn(Salen), and iron(II)-porphyrin model. The first two were revisited to assess the performance with respect to LPNO-TCCSD. For oxo-Mn(Salen), we retrieved between 99.8 and 99.9% of the total canonical correlation energy which is an improvement of 0.2% over the LPNO version in less than 63% of the total LPNO runtime. Similar results were obtained for iron(II)-porphyrin. When the perturbative triples correction was employed, irrespective of the active space size or system, the obtained energy differences between two spin states were within the chemical accuracy of 1 kcal/mol using the default DLPNO settings.
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Affiliation(s)
- Jakub Lang
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic.,Faculty of Sciences, Charles University, Albertov 6, 128 00 Prague 2, Czech Republic
| | - Andrej Antalík
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic.,Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 12116 Prague 2, Czech Republic
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Jan Brandejs
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic.,Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 12116 Prague 2, Czech Republic
| | - Jiří Brabec
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Örs Legeza
- Strongly Correlated Systems "Lendület" Research group, Wigner Research Centre for Physics, H-1525 Budapest, Hungary
| | - Jiří Pittner
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
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17
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Schmitz G, Elm J. Assessment of the DLPNO Binding Energies of Strongly Noncovalent Bonded Atmospheric Molecular Clusters. ACS OMEGA 2020; 5:7601-7612. [PMID: 32280904 PMCID: PMC7144154 DOI: 10.1021/acsomega.0c00436] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2020] [Accepted: 03/11/2020] [Indexed: 05/03/2023]
Abstract
This work assesses the performance of DLPNO-CCSD(T0), DLPNO-MP2, and density functional theory methods in calculating the binding energies of a representative test set of 45 atmospheric acid-acid, acid-base, and acid-water dimer clusters. The performance of the approximate methods is compared to high level explicitly correlated CCSD(F12*)(T)/complete basis set (CBS) reference calculations. Out of the tested density functionals, ωB97X-D3(BJ) shows the best performance with a mean deviation of 0.09 kcal/mol and a maximum deviation of 0.83 kcal/mol. The RI-CC2/aug-cc-pV(T+d)Z level of theory severely overpredicts the cluster binding energies with a mean deviation of -1.31 kcal/mol and a maximum deviation up to -3.00 kcal/mol. Hence, RI-CC2/aug-cc-pV(T+d)Z should not be utilized for studying atmospheric molecular clusters. The DLPNO variants are tested both with and without the inclusion of explicit correlation (F12) in the wavefunction, with different pair natural orbital (PNO) settings (loosePNO, normalPNO, and tightPNO) and using both double and triple zeta basis sets. The performance of the DLPNO-MP2 methods is found to be independent of PNO settings and yield low mean deviations of -0.84 kcal/mol or below. However, DLPNO-MP2 requires explicitly correlated wavefunctions to yield maximum deviations below 1.40 kcal/mol. For obtaining high accuracy, with maximum deviation below ∼1.0 kcal/mol, either DLPNO-CCSD(T0)/aug-cc-pVTZ (normalPNO) calculations or DLPNO-CCSD(T0)-F12/cc-pVTZ-F12 (normalPNO) calculations are required. The most accurate level of theory is found to be DLPNO-CCSD(T0)-F12/cc-pVTZ-F12 using a tightPNO criterion which yields a mean deviation of 0.10 kcal/mol, with a maximum deviation of 0.20 kcal/mol, compared to the CCSD(F12*)(T)/CBS reference.
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Affiliation(s)
- Gunnar Schmitz
- Department
of Chemistry, Aarhus University, Langelandsgade 140, 8000 Aarhus C, Denmark
| | - Jonas Elm
- Department
of Chemistry and iClimate, Aarhus University, Langelandsgade 140, 8000 Aarhus C, Denmark
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18
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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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19
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Miyagawa K, Kawakami T, Suzuki Y, Isobe H, Shoji M, Yamanaka S, Okumura M, Nakajima T, Yamaguchi K. Domain-based local pair natural orbital CCSD(T) calculations of strongly correlated electron systems: Examination of dynamic equilibrium models based on multiple intermediates in S1 state of photosystem II. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1666171] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- K. Miyagawa
- Institute for Scientific and Industrial Research, Osaka University, Osaka 567-0047, Japan
| | - T. Kawakami
- Graduate School of Science, Osaka University, Toyonaka 560-0043, Japan
- RIKEN Center for Computational Science, Kobe, Hyogo 650-0047, Japan
| | - Y. Suzuki
- Graduate School of Science, Osaka University, Toyonaka 560-0043, Japan
| | - H. Isobe
- Graduate School of Natural Science and Technology, Okayama University, Okayama 700-8530, Japan
| | - M. Shoji
- Center of Computational Sciences, Tsukuba University, Tsukuba, Ibaraki 305-8577, Japan
| | - S. Yamanaka
- Graduate School of Science, Osaka University, Toyonaka 560-0043, Japan
| | - M. Okumura
- Graduate School of Science, Osaka University, Toyonaka 560-0043, Japan
| | - T. Nakajima
- RIKEN Center for Computational Science, Kobe, Hyogo 650-0047, Japan
| | - K. Yamaguchi
- Institute for Scientific and Industrial Research, Osaka University, Osaka 567-0047, Japan
- RIKEN Center for Computational Science, Kobe, Hyogo 650-0047, Japan
- Insitute for Nanoscience Design, Osaka University, Toyonaka 560-0043, Japan
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20
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Antalík A, Veis L, Brabec J, Demel O, Legeza Ö, Pittner J. Toward the efficient local tailored coupled cluster approximation and the peculiar case of oxo-Mn(Salen). J Chem Phys 2019; 151:084112. [PMID: 31470730 DOI: 10.1063/1.5110477] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
We introduce a new implementation of the coupled cluster method with single and double excitations tailored by the matrix product state wave functions (DMRG-TCCSD), which employs the local pair natural orbital (LPNO) approach. By exploiting locality in the coupled cluster stage of the calculation, we were able to remove some of the limitations that hindered the application of the canonical version of the method to larger systems and/or with larger basis sets. We assessed the accuracy of the approximation using two systems: tetramethyleneethane (TME) and oxo-Mn(Salen). Using the default cut-off parameters, we were able to recover over 99.7% and 99.8% of the canonical correlation energy for the triplet and singlet state of TME, respectively. In the case of oxo-Mn(Salen), we found that the amount of retrieved canonical correlation energy depends on the size of the complete active space (CAS)-we retrieved over 99.6% for the larger 27 orbital CAS and over 99.8% for the smaller 22 orbital CAS. The use of LPNO-TCCSD allowed us to perform these calculations up to quadruple-ζ basis set, amounting to 1178 basis functions. Moreover, we examined dependence of the ground state of oxo-Mn(Salen) on the CAS composition. We found that the inclusion of 4dxy orbital plays an important role in stabilizing the singlet state at the DMRG-CASSCF level via double-shell effect. However, by including dynamic correlation, the ground state was found to be triplet regardless of the size of the basis set or the composition of CAS, which is in agreement with previous findings by canonical DMRG-TCCSD in smaller basis.
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Affiliation(s)
- Andrej Antalík
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Jiří Brabec
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Ondřej Demel
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Örs Legeza
- Strongly Correlated Systems "Lendület" Research Group, Wigner Research Centre for Physics, H-1525 Budapest, Hungary
| | - Jiří Pittner
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
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21
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Mihm TN, McIsaac AR, Shepherd JJ. An optimized twist angle to find the twist-averaged correlation energy applied to the uniform electron gas. J Chem Phys 2019; 150:191101. [PMID: 31117769 DOI: 10.1063/1.5091445] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Abstract
We explore an alternative to twist averaging in order to obtain more cost-effective and accurate extrapolations to the thermodynamic limit (TDL) for coupled cluster doubles (CCD) calculations. We seek a single twist angle to perform calculations at, instead of integrating over many random points or a grid. We introduce the concept of connectivity, a quantity derived from the nonzero four-index integrals in an MP2 calculation. This allows us to find a special twist angle that provides appropriate connectivity in the energy equation, which yields results comparable to full twist averaging. This special twist angle effectively makes the finite electron number CCD calculation represent the TDL more accurately, reducing the cost of twist-averaged CCD over Ns twist angles from Ns CCD calculations to Ns MP2 calculations plus one CCD calculation.
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Affiliation(s)
- Tina N Mihm
- Department of Chemistry, University of Iowa, Iowa City, Iowa 52242-1002, USA
| | - Alexandra R McIsaac
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - James J Shepherd
- Department of Chemistry, University of Iowa, Iowa City, Iowa 52242-1002, USA
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22
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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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23
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Scott CJC, Di Remigio R, Crawford TD, Thom AJW. Diagrammatic Coupled Cluster Monte Carlo. J Phys Chem Lett 2019; 10:925-935. [PMID: 30724572 DOI: 10.1021/acs.jpclett.9b00067] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We propose a modified coupled cluster Monte Carlo algorithm that stochastically samples connected terms within the truncated Baker-Campbell-Hausdorff expansion of the similarity-transformed Hamiltonian by construction of coupled cluster diagrams on the fly. Our new approach-diagCCMC-allows propagation to be performed using only the connected components of the similarity-transformed Hamiltonian, greatly reducing the memory cost associated with the stochastic solution of the coupled cluster equations. We show that for perfectly local, noninteracting systems diagCCMC is able to represent the coupled cluster wavefunction with a memory cost that scales linearly with system size. The favorable memory cost is observed with the only assumption of fixed stochastic granularity and is valid for arbitrary levels of coupled cluster theory. Significant reduction in memory cost is also shown to smoothly appear with dissociation of a finite chain of helium atoms. This approach is also shown not to break down in the presence of strong correlation through the example of a stretched nitrogen molecule. Our novel methodology moves the theoretical basis of coupled cluster Monte Carlo closer to deterministic approaches.
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Affiliation(s)
- Charles J C Scott
- Department of Chemistry , University of Cambridge , Cambridge CB2 1TN , United Kingdom
| | - Roberto Di Remigio
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry , University of Tromsø - The Arctic University of Norway , N-9037 Tromsø , Norway
- Department of Chemistry , Virginia Tech , Blacksburg , Virginia 24061 , United States
| | - T Daniel Crawford
- Department of Chemistry , Virginia Tech , Blacksburg , Virginia 24061 , United States
| | - Alex J W Thom
- Department of Chemistry , University of Cambridge , Cambridge CB2 1TN , United Kingdom
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24
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Lang J, Brabec J, Saitow M, Pittner J, Neese F, Demel O. Perturbative triples correction to domain-based local pair natural orbital variants of Mukherjee's state specific coupled cluster method. Phys Chem Chem Phys 2019; 21:5022-5038. [PMID: 30762044 DOI: 10.1039/c8cp03577f] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this article we report an implementation of the perturbative triples correction to Mukherjee's state-specific multireference coupled cluster method based on the domain-based pair natural orbital approach (DLPNO-MkCC). We tested the performance of DLPNO-MkCCSD(T) in calculations involving tetramethyleneethane and isomers of naphthynes. These tests show that more than 97% of triples energy was recovered with respect to the canonical MkCCSD(T) method, which together with the DLPNO-MkCCSD part accounts for about 99.70-99.85% of the total correlation energy. The applicability of the method was demonstrated on calculations of singlet-triplet gaps for several large systems: triangulene, dynemicin A, and a beryllium complex.
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Affiliation(s)
- Jakub Lang
- J. Heyrovský Institute of Physical Chemistry, v.v.i., Academy of Sciences of the Czech Republic, Dolejškova 3, 18223 Prague 8, Czech Republic.
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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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Jin Y, Bartlett RJ. Perturbation Improved Natural Linear-Scaled Coupled-Cluster Method and Its Application to Conformational Analysis. J Phys Chem A 2019; 123:371-381. [PMID: 30585491 DOI: 10.1021/acs.jpca.8b07947] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The fragment-based coupled-cluster (CC) theory utilizing the transferable functional groups through natural localized molecular orbital (NLMO), that is, the natural linear-scaled coupled-cluster (NLSCC) has been further developed to take the extra-fragment interactions into account. The correction to the interaction energies sacrificed during the fragmentation process for the previous NLSCC method is computed by a computationally efficient perturbation theory that maintains the original scaling. The new linear-scaled coupled-cluster for the singles and doubles (CCSD) method is applied to the analysis of relative energies of delicate conformational problems of polypeptides. By adding a perturbation correction, results accurate to less than a kcal/mol are obtained for the alanine tetramer.
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Affiliation(s)
- Yifan Jin
- Quantum Theory Project and Departments of Chemistry and Physics , University of Florida , Gainesville , Florida 32611 , United States
| | - Rodney J Bartlett
- Quantum Theory Project and Departments of Chemistry and Physics , University of Florida , Gainesville , Florida 32611 , United States
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27
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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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28
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Saitow M, Neese F. Accurate spin-densities based on the domain-based local pair-natural orbital coupled-cluster theory. J Chem Phys 2018; 149:034104. [PMID: 30037259 DOI: 10.1063/1.5027114] [Citation(s) in RCA: 44] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
Exploiting locality in the electron correlation reduces the computational cost for solving the Coupled-Cluster (CC) equations. This is important for making CC theory applicable to routine computational chemistry applications where it promises to deliver results of "gold-standard" quality. Recently, we have proposed a series of CC formulations in the domain-based local pair-natural orbital framework [DLPNO-coupled-cluster with singles and doubles (CCSD) and DLPNO-coupled-cluster singles and doubles with perturbative triples] which are designed to reproduce approximately 99.9% of the canonical correlation energy. In our previous work, the DLPNO-CCSD method has been extended to the high-spin open-shell reference and shown to possess comparable accuracy to the closed-shell counterpart [M. Saitow et al., J. Chem. Phys. 146, 164105 (2017)]. The so-called Λ-equations have been formulated in the DLPNO framework for the closed-shell species as an exact derivative of the DLPNO-CCSD Lagrangian with respect to the PNO-based cluster amplitudes [D. Datta et al., J. Chem. Phys. 145, 114101 (2016)]. In this paper, we extend the DLPNO-based Lagrangian scheme to the high-spin open-shell reference cases, thus enabling the accurate computation of the electron- and spin-densities for large open-shell species. We apply this newly developed approach to various first-order electronic and magnetic properties such as isotropic and anisotropic components in the hyperfine coupling interactions and the electric field gradient. We demonstrate that the DLPNO-CCSD results converge toward the respective canonical CC density and also that the DLPNO-CCSD-based properties are more accurate than the conventional density functional theory (DFT) results in real-life applications. The additional computational cost is not more than one energy evaluation in the DLPNO-CCSD framework.
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Affiliation(s)
- Masaaki Saitow
- Max-Planck-Institut für Chemische Energiekonversion, Stiftstr. 34-36, D-45470 Mülheim an der Ruhr, Germany
| | - Frank Neese
- Max-Planck-Institut für Chemische Energiekonversion, Stiftstr. 34-36, D-45470 Mülheim an der Ruhr, Germany
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29
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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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30
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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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31
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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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32
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Vogler S, Ludwig M, Maurer M, Ochsenfeld C. Low-scaling first-order properties within second-order Møller-Plesset perturbation theory using Cholesky decomposed density matrices. J Chem Phys 2018; 147:024101. [PMID: 28711065 DOI: 10.1063/1.4990413] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An efficient implementation of energy gradients and of hyperfine coupling constants in second-order Møller-Plesset perturbation theory (MP2) is presented based on our fully atomic orbital (AO)-based approach. For the latter, an unrestricted AO-based MP2 formulation is introduced. A reduction in the dependency of the computational efficiency on the size of the basis set is achieved by a Cholesky decomposition and the prefactor is reduced by the resolution-of-the-identity approximation. Significant integral contributions are selected based on distance-including integral estimates (denoted as QQR-screening) and its reliability as a fully controlled screening procedure is demonstrated. The rate-determining steps are shown via model computations to scale cubically in the computation of energy gradients and quadratically in the case of hyperfine coupling constants. Furthermore, a significant speed-up of the computational time with respect to the canonical formulation is demonstrated.
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Affiliation(s)
- Sigurd Vogler
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, 81377 Munich, Germany
| | - Martin Ludwig
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, 81377 Munich, Germany
| | - Marina Maurer
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, 81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, 81377 Munich, Germany
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33
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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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34
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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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35
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Fiedler B, Himmel D, Krossing I, Friedrich J. More Stable Template Localization for an Incremental Focal-Point Approach—Implementation and Application to the Intramolecular Decomposition of Tris-perfluoro- tert-butoxyalane. J Chem Theory Comput 2018; 14:557-571. [DOI: 10.1021/acs.jctc.7b00707] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Benjamin Fiedler
- Institut
für Chemie, Technische Universität Chemnitz, 09111 Chemnitz, Germany
| | - Daniel Himmel
- Institut
für Anorganische und Analytische Chemie, Albert-Ludwigs-Universität Freiburg, 79104 Freiburg, Germany
| | - Ingo Krossing
- Institut
für Anorganische und Analytische Chemie, Albert-Ludwigs-Universität Freiburg, 79104 Freiburg, Germany
| | - Joachim Friedrich
- Institut
für Chemie, Technische Universität Chemnitz, 09111 Chemnitz, Germany
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36
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Brabec J, Lang J, Saitow M, Pittner J, Neese F, Demel O. Domain-Based Local Pair Natural Orbital Version of Mukherjee’s State-Specific Coupled Cluster Method. J Chem Theory Comput 2018; 14:1370-1382. [DOI: 10.1021/acs.jctc.7b01184] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jiri Brabec
- J. Heyrovský Institute of Physical Chemistry, v.v.i., Academy of Sciences of the Czech Republic, Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Jakub Lang
- J. Heyrovský Institute of Physical Chemistry, v.v.i., Academy of Sciences of the Czech Republic, Dolejškova 3, 18223 Prague 8, Czech Republic
- Department of Physical and Macromolecular Chemistry, Faculty of Science, Charles University in Prague, Hlavova 2030, 12840 Prague 2, Czech Republic
| | - Masaaki Saitow
- Max Planck Institute for Chemical Energy Conversion, 45470 Mülheim an der Ruhr, Germany
| | - Jiří Pittner
- J. Heyrovský Institute of Physical Chemistry, v.v.i., Academy of Sciences of the Czech Republic, Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Frank Neese
- Max Planck Institute for Chemical Energy Conversion, 45470 Mülheim an der Ruhr, Germany
| | - Ondřej Demel
- J. Heyrovský Institute of Physical Chemistry, v.v.i., Academy of Sciences of the Czech Republic, Dolejškova 3, 18223 Prague 8, Czech Republic
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37
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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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38
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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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39
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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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40
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Kjærgaard T, Baudin P, Bykov D, Kristensen K, Jørgensen P. The divide–expand–consolidate coupled cluster scheme. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2017. [DOI: 10.1002/wcms.1319] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
| | - Pablo Baudin
- Department of ChemistryAarhus UniversityAarhusDenmark
| | - Dmytro Bykov
- Department of ChemistryAarhus UniversityAarhusDenmark
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41
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Schmitz G, Hättig C. Accuracy of Explicitly Correlated Local PNO-CCSD(T). J Chem Theory Comput 2017; 13:2623-2633. [DOI: 10.1021/acs.jctc.7b00180] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Gunnar Schmitz
- Department
of Chemistry, Aarhus Universitet, Aarhus 8000, Denmark
| | - Christof Hättig
- Arbeitsgruppe
Quantenchemie, Ruhr-Universität, Bochum 44780, Germany
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42
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Kjærgaard T. The Laplace transformed divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation (DEC-LT-RIMP2) theory method. J Chem Phys 2017; 146:044103. [PMID: 28147513 DOI: 10.1063/1.4973710] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation (DEC-RI-MP2) theory method introduced in Baudin et al. [J. Chem. Phys. 144, 054102 (2016)] is significantly improved by introducing the Laplace transform of the orbital energy denominator in order to construct the double amplitudes directly in the local basis. Furthermore, this paper introduces the auxiliary reduction procedure, which reduces the set of the auxiliary functions employed in the individual fragments. The resulting Laplace transformed divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation method is applied to the insulin molecule where we obtain a factor 9.5 speedup compared to the DEC-RI-MP2 method.
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Affiliation(s)
- Thomas Kjærgaard
- qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
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43
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Peng C, Calvin JA, Pavošević F, Zhang J, Valeev EF. Massively Parallel Implementation of Explicitly Correlated Coupled-Cluster Singles and Doubles Using TiledArray Framework. J Phys Chem A 2016; 120:10231-10244. [DOI: 10.1021/acs.jpca.6b10150] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Chong Peng
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Justus A. Calvin
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Fabijan Pavošević
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - 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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44
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Bykov D, Kjaergaard T. The GPU-enabled divide-expand-consolidate RI-MP2 method (DEC-RI-MP2). J Comput Chem 2016; 38:228-237. [DOI: 10.1002/jcc.24678] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2016] [Revised: 10/27/2016] [Accepted: 11/01/2016] [Indexed: 01/16/2023]
Affiliation(s)
- Dmytro Bykov
- Department of Chemistry; qLeap Center for Theoretical Chemistry, University of Aarhus; DK-8000 Århus C Denmark
| | - Thomas Kjaergaard
- Department of Chemistry; qLeap Center for Theoretical Chemistry, University of Aarhus; DK-8000 Århus C Denmark
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45
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Menezes F, Kats D, Werner HJ. Local complete active space second-order perturbation theory using pair natural orbitals (PNO-CASPT2). J Chem Phys 2016; 145:124115. [DOI: 10.1063/1.4963019] [Citation(s) in RCA: 68] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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46
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Datta D, Kossmann S, Neese F. Analytic energy derivatives for the calculation of the first-order molecular properties using the domain-based local pair-natural orbital coupled-cluster theory. J Chem Phys 2016. [DOI: 10.1063/1.4962369] [Citation(s) in RCA: 51] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Dipayan Datta
- Max-Planck-Institut für Chemische Energiekonversion, Stiftstrasse 34-36, D-45470 Mülheim an der Ruhr, Germany
| | - Simone Kossmann
- Max-Planck-Institut für Chemische Energiekonversion, Stiftstrasse 34-36, D-45470 Mülheim an der Ruhr, Germany
| | - Frank Neese
- Max-Planck-Institut für Chemische Energiekonversion, Stiftstrasse 34-36, D-45470 Mülheim an der Ruhr, Germany
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47
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Bykov D, Kristensen K, Kjærgaard T. The molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory: The DEC-RI-MP2 gradient. J Chem Phys 2016; 145:024106. [DOI: 10.1063/1.4956454] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Dmytro Bykov
- Department of Chemistry, qLeap Center for Theoretical Chemistry, University of Aarhus, DK-8000 Århus C, Denmark
| | - Kasper Kristensen
- Department of Chemistry, qLeap Center for Theoretical Chemistry, University of Aarhus, DK-8000 Århus C, Denmark
| | - Thomas Kjærgaard
- Department of Chemistry, qLeap Center for Theoretical Chemistry, University of Aarhus, DK-8000 Århus C, Denmark
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48
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Fiedler B, Coriani S, Friedrich J. Molecular Dipole Moments within the Incremental Scheme Using the Domain-Specific Basis-Set Approach. J Chem Theory Comput 2016; 12:3040-52. [PMID: 27300371 DOI: 10.1021/acs.jctc.6b00076] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
We present the first implementation of the fully automated incremental scheme for CCSD unrelaxed dipole moments using the domain-specific basis-set approach. Truncation parameters are varied, and the accuracy of the method is statistically analyzed for a test set of 20 molecules. The local approximations introduce small errors at second order and negligible ones at third order. For a third-order incremental CCSD expansion with a CC2 error correction, a cc-pVDZ/SV domain-specific basis set (tmain = 3.5 Bohr), and the truncation parameter f = 30 Bohr, we obtain a mean error of 0.00 mau (-0.20 mau) and a standard deviation of 1.95 mau (2.17 mau) for the total dipole moments (Cartesian components of the dipole vectors). By analyzing incremental CCSD energies, we demonstrate that the MP2 and CC2 error correction schemes are an exclusive correction for the domain-specific basis-set error. Our implementation of the incremental scheme provides fully automated computations of highly accurate dipole moments at reduced computational cost and is fully parallelized in terms of the calculation of the increments. Therefore, one can utilize the incremental scheme, on the same hardware, to extend the basis set in comparison to standard CCSD and thus obtain a better total accuracy.
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Affiliation(s)
- Benjamin Fiedler
- Institute for Chemistry, Technische Universität Chemnitz , Straße der Nationen 62, D-09111 Chemnitz, Germany
| | - Sonia Coriani
- Dipartimento di Scienze Chimiche e Farmaceutiche, Università degli Studi di Trieste , Via L. Giorgieri 1, I-34127 Trieste, Italy.,Aarhus Institute of Advanced Studies, Aarhus University , Høegh-Guldbergs Gade 6B, DK-8000 Aarhus C, Denmark
| | - Joachim Friedrich
- Institute for Chemistry, Technische Universität Chemnitz , Straße der Nationen 62, D-09111 Chemnitz, Germany
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49
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Baudin P, Ettenhuber P, Reine S, Kristensen K, Kjærgaard T. Efficient linear-scaling second-order Møller-Plesset perturbation theory: The divide-expand-consolidate RI-MP2 model. J Chem Phys 2016; 144:054102. [PMID: 26851903 DOI: 10.1063/1.4940732] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Resolution of the Identity second-order Møller-Plesset perturbation theory (RI-MP2) method is implemented within the linear-scaling Divide-Expand-Consolidate (DEC) framework. In a DEC calculation, the full molecular correlated calculation is replaced by a set of independent fragment calculations each using a subset of the total orbital space. The number of independent fragment calculations scales linearly with the system size, rendering the method linear-scaling and massively parallel. The DEC-RI-MP2 method can be viewed as an approximation to the DEC-MP2 method where the RI approximation is utilized in each fragment calculation. The individual fragment calculations scale with the fifth power of the fragment size for both methods. However, the DEC-RI-MP2 method has a reduced prefactor compared to DEC-MP2 and is well-suited for implementation on massively parallel supercomputers, as demonstrated by test calculations on a set of medium-sized molecules. The DEC error control ensures that the standard RI-MP2 energy can be obtained to the predefined precision. The errors associated with the RI and DEC approximations are compared, and it is shown that the DEC-RI-MP2 method can be applied to systems far beyond the ones that can be treated with a conventional RI-MP2 implementation.
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Affiliation(s)
- Pablo Baudin
- qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Patrick Ettenhuber
- qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Simen Reine
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033, N-1315 Blindern, Norway
| | - Kasper Kristensen
- qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Thomas Kjærgaard
- qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
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50
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Wang YM, Hättig C, Reine S, Valeev E, Kjærgaard T, Kristensen K. Explicitly correlated second-order Møller-Plesset perturbation theory in a Divide-Expand-Consolidate (DEC) context. J Chem Phys 2016; 144:204112. [DOI: 10.1063/1.4951696] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yang Min Wang
- qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Christof Hättig
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum, Germany
| | - Simen Reine
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033, N-1315 Blindern, Norway
| | - Edward Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Thomas Kjærgaard
- qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Kasper Kristensen
- qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
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