1
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Drontschenko V, Bangerter FH, Ochsenfeld C. Analytical Second-Order Properties for the Random Phase Approximation: Nuclear Magnetic Resonance Shieldings. J Chem Theory Comput 2023; 19:7542-7554. [PMID: 37863033 DOI: 10.1021/acs.jctc.3c00542] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2023]
Abstract
A method for the analytical computation of nuclear magnetic resonance (NMR) shieldings within the direct random phase approximation (RPA) is presented. As a starting point, we use the RPA ground-state energy expression within the resolution-of-the-identity approximation in the atomic-orbital formalism. As has been shown in a recent benchmark study using numerical second derivatives [Glasbrenner, M. J. Chem. Theory Comput. 2022, 18, 192], RPA based on a Hartree-Fock reference shows accuracies comparable to coupled cluster singles and doubles (CCSD) for NMR chemical shieldings. Together with the much lower computational cost of RPA, it has emerged as an accurate method for the computation of NMR shieldings. Therefore, we aim to extend the applicability of RPA NMR to larger systems by introducing analytical second-order derivatives, making it a viable method for the accurate and efficient computation of NMR chemical shieldings.
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Affiliation(s)
- Viktoria Drontschenko
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
| | - Felix H Bangerter
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
- Max Planck Institute for Solid State Research, D-70569 Stuttgart, Germany
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2
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Iuliucci RJ, Hartman JD, Beran GJO. Do Models beyond Hybrid Density Functionals Increase the Agreement with Experiment for Predicted NMR Chemical Shifts or Electric Field Gradient Tensors in Organic Solids? J Phys Chem A 2023; 127:2846-2858. [PMID: 36940431 DOI: 10.1021/acs.jpca.2c07657] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/22/2023]
Abstract
Ab initio predictions of chemical shifts and electric field gradient (EFG) tensor components are frequently used to help interpret solid-state nuclear magnetic resonance (NMR) experiments. Typically, these predictions employ density functional theory (DFT) with generalized gradient approximation (GGA) functionals, though hybrid functionals have been shown to improve accuracy relative to experiment. Here, the performance of a dozen models beyond the GGA approximation are examined for the prediction of solid-state NMR observables, including meta-GGA, hybrid, and double-hybrid density functionals and second-order Møller-Plesset perturbation theory (MP2). These models are tested on organic molecular crystal data sets containing 169 experimental 13C and 15N chemical shifts and 114 17O and 14N EFG tensor components. To make these calculations affordable, gauge-including projector augmented wave (GIPAW) Perdew-Burke-Ernzerhof (PBE) calculations with periodic boundary conditions are combined with a local intramolecular correction computed at the higher level of theory. Within the context of typical NMR property calculations performed on a static, DFT-optimized crystal structure, the benchmarking finds that the double-hybrid DFT functionals produce errors versus experiment that are no smaller than those of hybrid functionals in the best cases, and they can be larger. MP2 errors versus experiment are even bigger. Overall, no practical advantages are found for using any of the tested double-hybrid functionals or MP2 to predict experimental solid-state NMR chemical shifts and EFG tensor components for routine organic crystals, especially given the higher computational cost of those methods. This finding likely reflects error cancellation benefiting the hybrid functionals. Improving the accuracy of the predicted chemical shifts and EFG tensors relative to experiment would probably require more robust treatments of the crystal structures, their dynamics, and other factors.
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Affiliation(s)
- Robbie J Iuliucci
- Department of Chemistry, Washington and Jefferson College, Washington, Pennsylvania 15301 United States
| | - Joshua D Hartman
- Department of Chemistry, University of California, Riverside, California 92521 United States
| | - Gregory J O Beran
- Department of Chemistry, University of California, Riverside, California 92521 United States
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3
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DFT calculations of 1H- and 13C-NMR chemical shifts of 3-methyl-1-phenyl-4-(phenyldiazenyl)-1H-pyrazol-5-amine in solution. Sci Rep 2022; 12:17798. [PMID: 36273019 PMCID: PMC9588065 DOI: 10.1038/s41598-022-22900-y] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2022] [Accepted: 10/20/2022] [Indexed: 01/19/2023] Open
Abstract
Geometries of the 3-methyl-1-phenyl-4-(phenyldiazenyl)-1H-pyrazol-5-amine azo-dye compound and its tautomer were optimized using B3LYP and M06-2X functionals in coupling with TZVP and 6-311 + G(d,p) basis sets. The 1H- and 13C-NMR chemical shifts of all species were predicted using 13 density functional theory (DFT) approaches in coupling with TZVP and 6-311 + G(d,p) basis sets at the different optimized geometries by applying the using GIAO method using the eight geometries. The selected functionals are characterized by having different amount of Hartree-Fock exchange. The selected DFT methods were B3LYP, M06-2X, BP86, B97XD, TPSSTPSS, PBE1PBE, CAM-B3LYP, wB97XD, LSDA, HSEH1PBE, PW91PW91, LC-WPBE, and B3PW91. The results obtained were compared with the available experimental data using different statistical descriptors such as root mean square error (RMSE) and maximum absolute error (MAE). Results revealed that the prediction of the 1H-NMR chemical shifts has more significant dependence on the applied geometry than that of the prediction of the 13C-NMR chemical shifts. Among all the examined functionals, B97D and TPSSTPSS functionals were found to be the most accurate ones, while the M06-2X functional is the least accurate one. Results also revealed that the prediction of NMR chemical shifts using TZVP basis sets results is more accurate results than 6-311 + G(2d,p) basis set.
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4
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Bangerter F, Glasbrenner M, Ochsenfeld C. Tensor-Hypercontracted MP2 First Derivatives: Runtime and Memory Efficient Computation of Hyperfine Coupling Constants. J Chem Theory Comput 2022; 18:5233-5245. [PMID: 35943450 PMCID: PMC9476664 DOI: 10.1021/acs.jctc.2c00118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
We employ our recently introduced tensor-hypercontracted (THC) second-order Møller-Plesset perturbation theory (MP2) method [Bangerter, F. H., Glasbrenner, M., Ochsenfeld, C. J. Chem. Theory Comput. 2021, 17, 211-221] for the computation of hyperfine coupling constants (HFCCs). The implementation leverages the tensor structure of the THC factorized electron repulsion integrals for an efficient formation of the integral-based intermediates. The computational complexity of the most expensive and formally quintic scaling exchange-like contribution is reduced to effectively subquadratic, by making use of the intrinsic, exponentially decaying coupling between tensor indices through screening based on natural blocking. Overall, this yields an effective subquadratic scaling with a low prefactor for the presented THC-based AO-MP2 method for the computation of isotropic HFCCs on DNA fragments with up to 500 atoms and 5000 basis functions. Furthermore, the implementation achieves considerable speedups with up to a factor of roughly 600-1000 compared to previous implementations [Vogler, S., Ludwig, M., Maurer, M., Ochsenfeld, C. J. Chem. Phys. 2017, 147, 024101] for medium-sized organic radicals, while also significantly reducing storage requirements.
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Affiliation(s)
- Felix
H. Bangerter
- Chair
of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
| | - Michael Glasbrenner
- Chair
of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair
of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany,Max
Planck Institute for Solid State Research, D-70569 Stuttgart, Germany,
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5
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Poidevin C, Stoychev GL, Riplinger C, Auer AA. High Level Electronic Structure Calculation of Molecular Solid-State NMR Shielding Constants. J Chem Theory Comput 2022; 18:2408-2417. [PMID: 35353527 PMCID: PMC9009078 DOI: 10.1021/acs.jctc.1c01095] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
In this work, we
present a quantum mechanics/molecular mechanics
(QM/MM) approach for the computation of solid-state nuclear magnetic
resonance (SS-NMR) shielding constants (SCs) for molecular crystals.
Besides applying standard-DFT functionals like GGAs (PBE), meta-GGAs
(TPSS), and hybrids (B3LYP), we apply a double-hybrid (DSD-PBEP86)
functional as well as MP2, using the domain-based local pair natural
orbital (DLPNO) formalism, to calculate the NMR SCs of six amino acid
crystals. All the electronic structure methods used exhibit good correlation
of the NMR shieldings with respect to experimental chemical shifts
for both 1H and 13C. We also find that local
electronic structure is much more important than the long-range electrostatic
effects for these systems, implying that cluster approaches using
all-electron/Gaussian basis set methods might offer great potential
for predictive computations of solid-state NMR parameters for organic
solids.
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Affiliation(s)
- Corentin Poidevin
- Institut des Sciences Chimiques de Rennes, Av. Général Leclerc, 357000 Rennes, France
| | - Georgi L Stoychev
- Max-Planck-Institut für Kohlenforschung, 45470 Mülheim an der Ruhr, Germany
| | | | - Alexander A Auer
- Max-Planck-Institut für Kohlenforschung, 45470 Mülheim an der Ruhr, Germany
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6
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Glasbrenner M, Vogler S, Ochsenfeld C. Efficient low-scaling computation of NMR shieldings at the second-order Møller-Plesset perturbation theory level with Cholesky-decomposed densities and an attenuated Coulomb metric. J Chem Phys 2021; 155:224107. [PMID: 34911319 DOI: 10.1063/5.0069956] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A method for the computation of nuclear magnetic resonance (NMR) shieldings with second-order Møller-Plesset perturbation theory (MP2) is presented which allows to efficiently compute the entire set of shieldings for a given molecular structure. The equations are derived using Laplace-transformed atomic orbital second-order Møller-Plesset perturbation theory as a starting point. The Z-vector approach is employed for minimizing the number of coupled-perturbed self-consistent-field equations that need to be solved. In addition, the method uses the resolution-of-the-identity approximation with an attenuated Coulomb metric and Cholesky decomposition of pseudo-density matrices. The sparsity in the three-center integrals is exploited with sparse linear algebra approaches, leading to reduced computational cost and memory demands. Test calculations show that the deviations from NMR shifts obtained with canonical MP2 are small if appropriate thresholds are used. The performance of the method is illustrated in calculations on DNA strands and on glycine chains with up to 283 atoms and 2864 basis functions.
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Affiliation(s)
- Michael Glasbrenner
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
| | - Sigurd Vogler
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
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7
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Glasbrenner M, Graf D, Ochsenfeld C. Benchmarking the Accuracy of the Direct Random Phase Approximation and σ-Functionals for NMR Shieldings. J Chem Theory Comput 2021; 18:192-205. [PMID: 34898213 DOI: 10.1021/acs.jctc.1c00866] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A method for computing NMR shieldings with the direct random phase approximation (RPA) and the closely related σ-functionals [Trushin, E.; Thierbach, A.; Görling, A. Toward chemical accuracy at low computational cost: density functional theory with σ-functionals for the correlation energy. J. Chem. Phys. 2021, 154, 014104] is presented, which is based on a finite-difference approach. The accuracy is evaluated in benchmark calculations using high-quality coupled cluster values as a reference. Our results show that the accuracy of the computed NMR shieldings using direct RPA is strongly dependent on the density functional theory reference orbitals and improves with increasing amounts of exact Hartree-Fock exchange in the functional. NMR shieldings computed with direct RPA using a Hartree-Fock reference are significantly more accurate than MP2 shieldings and comparable to CCSD shieldings. Also, the basis set convergence is analyzed and it is shown that at least triple-zeta basis sets are required for reliable results.
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Affiliation(s)
- Michael Glasbrenner
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
| | - Daniel Graf
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany.,Max Planck Institute for Solid State Research, Heisenbergstr. 1, D-70569 Stuttgart, Germany
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8
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Burger S, Lipparini F, Gauss J, Stopkowicz S. NMR chemical shift computations at second-order Møller-Plesset perturbation theory using gauge-including atomic orbitals and Cholesky-decomposed two-electron integrals. J Chem Phys 2021; 155:074105. [PMID: 34418917 DOI: 10.1063/5.0059633] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
We report on a formulation and implementation of a scheme to compute nuclear magnetic resonance (NMR) shieldings at second-order Møller-Plesset (MP2) perturbation theory using gauge-including atomic orbitals (GIAOs) to ensure gauge-origin independence and Cholesky decomposition (CD) to handle unperturbed and perturbed two-electron integrals. We investigate the accuracy of the CD for the derivatives of the two-electron integrals with respect to an external magnetic field and for the computed NMR shieldings, before we illustrate the applicability of our CD-based GIAO-MP2 scheme in calculations involving up to about 100 atoms and more than 1000 basis functions.
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Affiliation(s)
- Sophia Burger
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Filippo Lipparini
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, I-56124 Pisa, Italy
| | - Jürgen Gauss
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Stella Stopkowicz
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
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9
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Stoychev GL, Auer AA, Gauss J, Neese F. DLPNO-MP2 second derivatives for the computation of polarizabilities and NMR shieldings. J Chem Phys 2021; 154:164110. [PMID: 33940835 DOI: 10.1063/5.0047125] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a derivation and efficient implementation of the formally complete analytic second derivatives for the domain-based local pair natural orbital second order Møller-Plesset perturbation theory (MP2) method, applicable to electric or magnetic field-response properties but not yet to harmonic frequencies. We also discuss the occurrence and avoidance of numerical instability issues related to singular linear equation systems and near linear dependences in the projected atomic orbital domains. A series of benchmark calculations on medium-sized systems is performed to assess the effect of the local approximation on calculated nuclear magnetic resonance shieldings and the static dipole polarizabilities. Relative deviations from the resolution of the identity-based MP2 (RI-MP2) reference for both properties are below 0.5% with the default truncation thresholds. For large systems, our implementation achieves quadratic effective scaling, is more efficient than RI-MP2 starting at 280 correlated electrons, and is never more than 5-20 times slower than the equivalent Hartree-Fock property calculation. The largest calculation performed here was on the vancomycin molecule with 176 atoms, 542 correlated electrons, and 4700 basis functions and took 3.3 days on 12 central processing unit cores.
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Affiliation(s)
- Georgi L Stoychev
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Alexander A Auer
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Jürgen Gauss
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, 55128 Mainz, Germany
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
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10
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Jinger R, Fliegl H, Bast R, Dimitrova M, Lehtola S, Sundholm D. Spatial Contributions to Nuclear Magnetic Shieldings. J Phys Chem A 2021; 125:1778-1786. [PMID: 33605721 PMCID: PMC8023705 DOI: 10.1021/acs.jpca.0c10884] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2020] [Revised: 02/05/2021] [Indexed: 01/09/2023]
Abstract
We develop a methodology for calculating, analyzing, and visualizing nuclear magnetic shielding densities which are calculated from the current density via the Biot-Savart relation. Atomic contributions to nuclear magnetic shielding constants can be estimated within our framework with a Becke partitioning scheme. The new features have been implemented in the GIMIC program and are applied in this work to the study of the 1H and 13C nuclear magnetic shieldings in benzene (C6H6) and cyclobutadiene (C4H4). The new methodology allows a visual inspection of the spatial origins of the positive (shielding) and negative (deshielding) contributions to the nuclear magnetic shielding constant of a single nucleus, something which has not been hitherto easily accomplished. Analysis of the shielding densities shows that diatropic and paratropic current-density fluxes yield both shielding and deshielding contributions, as the shielding or deshielding is determined by the direction of the current-density flux with respect to the studied nucleus instead of the tropicity. Becke partitioning of the magnetic shieldings shows that the magnetic shielding contributions mainly originate from the studied atom and its nearest neighbors, confirming the localized character of nuclear magnetic shieldings.
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Affiliation(s)
- Rahul
Kumar Jinger
- Indian
Institute of Science Education and Research, Dr. Homi Bhabha Road, Pashan, Pune 411008, India
| | - Heike Fliegl
- Karlsruhe
Institute of Technology, Institute of Nanotechnology, Hermann-von-Helmholtz Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany
| | - Radovan Bast
- Department
Information Technology, UiT Arctic University
Norway, Tromsø, Norway
| | - Maria Dimitrova
- Department
of Chemistry, Faculty of Science, University
of Helsinki, P.O. Box 55, FI-00014 Helsinki, Finland
| | - Susi Lehtola
- Department
of Chemistry, Faculty of Science, University
of Helsinki, P.O. Box 55, FI-00014 Helsinki, Finland
- Molecular
Sciences Software Institute, Blacksburg, Virginia 24061, United States
| | - Dage Sundholm
- Department
of Chemistry, Faculty of Science, University
of Helsinki, P.O. Box 55, FI-00014 Helsinki, Finland
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11
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Gräfenstein J. Efficient calculation of NMR isotopic shifts: Difference-dedicated vibrational perturbation theory. J Chem Phys 2019; 151:244120. [PMID: 31893883 DOI: 10.1063/1.5134538] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
We present difference-dedicated second-order vibrational perturbation theory (VPT2) as an efficient method for the computation of nuclear magnetic resonance (NMR) isotopic shifts, which reflect the geometry dependence of the NMR property in combination with different vibration patterns of two isotopologues. Conventional calculations of isotopic shifts, e.g., by standard VPT2, require scanning the geometry dependence over the whole molecule, which becomes expensive rapidly as the molecule size increases. In DD-VPT2, this scan can be restricted to a small region around the substitution site. At the heart of DD-VPT2 is a set of localized vibration modes common to the two isotopologues and designed such that the difference between the vibration patterns is caught by a small subset of them (usually fewer than 10). We tested the DD-VPT2 method for a series of molecules with increasing size and found that this method provides results with the same quality as VPT2 and in good agreement with the experiment, with computational savings up to 95% and less numerical instabilities. The method is easy to automatize and straightforward to generalize to other molecular properties.
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Affiliation(s)
- Jürgen Gräfenstein
- Department of Chemistry and Molecular Biology, University of Gothenburg, SE-412 96 Göteborg, Sweden
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12
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Pinski P, Neese F. Analytical gradient for the domain-based local pair natural orbital second order Møller-Plesset perturbation theory method (DLPNO-MP2). J Chem Phys 2019; 150:164102. [DOI: 10.1063/1.5086544] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Affiliation(s)
- Peter Pinski
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
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13
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Yuan M, Zhang Y, Qu Z, Xiao Y, Liu W. Sublinear scaling quantum chemical methods for magnetic shieldings in large molecules. J Chem Phys 2019; 150:154113. [DOI: 10.1063/1.5083193] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Minghong Yuan
- Beijing National Center for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Yong Zhang
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao 266237, China
| | - Zhi Qu
- Beijing National Center for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Yunlong Xiao
- Beijing National Center for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao 266237, China
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14
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15
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Stoychev GL, Auer AA, Neese F. Efficient and Accurate Prediction of Nuclear Magnetic Resonance Shielding Tensors with Double-Hybrid Density Functional Theory. J Chem Theory Comput 2018; 14:4756-4771. [DOI: 10.1021/acs.jctc.8b00624] [Citation(s) in RCA: 51] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Georgi L. Stoychev
- Max-Planck-Institut für Kohlenforschung, Mülheim an der Ruhr 45470, Germany
| | - Alexander A. Auer
- Max-Planck-Institut für Kohlenforschung, Mülheim an der Ruhr 45470, Germany
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Mülheim an der Ruhr 45470, Germany
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16
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Vogler S, Savasci G, Ludwig M, Ochsenfeld C. Selected-Nuclei Method for the Computation of Hyperfine Coupling Constants within Second-Order Møller-Plesset Perturbation Theory. J Chem Theory Comput 2018; 14:3014-3024. [PMID: 29762028 DOI: 10.1021/acs.jctc.8b00116] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
We introduce a new ansatz to compute hyperfine coupling constants of selected nuclei at the level of second-order Møller-Plesset perturbation (MP2) and double-hybrid density functional theory with reduced computational effort, opening the route to the analyis of hyperfine coupling constants of large molecular structures. Our approach is based on a reformulation of the canonical MP2 term in atomic orbitals, thus exploiting the locality of electron correlation. We show that a perturbation-including integral screening reduces the scaling behavior of the number of significant two-electron integrals to sublinear. This selected-nuclei approach allows for an efficient computation within scaled-opposite spin (SOS) RI-MP2 on massively parallelized architectures such as graphical processor units (GPUs), thus enabling studies on the influence of the environment on hyperfine coupling constants.
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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) , Butenandtstrasse 7 , 81377 Munich , Germany
| | - Gökcen Savasci
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , Butenandtstrasse 7 , 81377 Munich , Germany.,Max Planck Institute for Solid State Research, Heisenbergstrasse 1 , 70569 Stuttgart , Germany
| | - Martin Ludwig
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , Butenandtstrasse 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) , Butenandtstrasse 7 , 81377 Munich , Germany.,Max Planck Institute for Solid State Research, Heisenbergstrasse 1 , 70569 Stuttgart , Germany
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17
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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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18
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Hoffmann F, Li DW, Sebastiani D, Brüschweiler R. Improved Quantum Chemical NMR Chemical Shift Prediction of Metabolites in Aqueous Solution toward the Validation of Unknowns. J Phys Chem A 2017; 121:3071-3078. [PMID: 28388058 DOI: 10.1021/acs.jpca.7b01954] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
A quantum-chemistry based protocol, termed MOSS-DFT, is presented for the prediction of 13C and 1H NMR chemical shifts of a wide range of organic molecules in aqueous solution, including metabolites. Molecular motif-specific linear scaling parameters are reported for five different density functional theory (DFT) methods (B97-2/pcS-1, B97-2/pcS-2, B97-2/pcS-3, B3LYP/pcS-2, and BLYP/pcS-2), which were applied to a large set of 176 metabolite molecules. The chemical shift root-mean-square deviations (RMSD) for the best method, B97-2/pcS-3, are 1.93 and 0.154 ppm for 13C and 1H chemical shifts, respectively. Excellent results have been obtained for chemical shifts of methyl and aromatic 13C and 1H that are not directly bonded to a heteroatom (O, N, S, or P) with RMSD values of 1.15/0.079 and 1.31/0.118 ppm, respectively. This study not only demonstrates how NMR chemical shift in aqueous environment can be improved over the commonly used global linear scaling approach, but also allows for motif-specific error estimates, which are useful for an improved chemical shift-based verification of metabolite candidates of metabolomics samples containing unknown components.
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Affiliation(s)
- Felix Hoffmann
- Institute of Chemistry, Martin-Luther-University Halle-Wittenberg , von-Danckelmann-Platz 4, 06120 Halle, Germany
| | - Da-Wei Li
- Campus Chemical Instrument Center, The Ohio State University , Columbus, Ohio 43210, United States
| | - Daniel Sebastiani
- Institute of Chemistry, Martin-Luther-University Halle-Wittenberg , von-Danckelmann-Platz 4, 06120 Halle, Germany
| | - Rafael Brüschweiler
- Campus Chemical Instrument Center, The Ohio State University , Columbus, Ohio 43210, United States.,Department of Chemistry and Biochemistry, The Ohio State University , Columbus, Ohio 43210, United States.,Department of Biological Chemistry and Pharmacology, The Ohio State University , Columbus, Ohio 43210, United States
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19
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Sundholm D, Rauhalahti M, Özcan N, Mera-Adasme R, Kussmann J, Luenser A, Ochsenfeld C. Nuclear Magnetic Shieldings of Stacked Aromatic and Antiaromatic Molecules. J Chem Theory Comput 2017; 13:1952-1962. [PMID: 28287722 DOI: 10.1021/acs.jctc.6b01250] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Dage Sundholm
- Department
of Chemistry, University of Helsinki, P.O. Box 55, A.I. Virtanens plats
1, FIN-00014 Helsinki, Finland
| | - Markus Rauhalahti
- Department
of Chemistry, University of Helsinki, P.O. Box 55, A.I. Virtanens plats
1, FIN-00014 Helsinki, Finland
| | - Nergiz Özcan
- Department
of Chemistry, University of Helsinki, P.O. Box 55, A.I. Virtanens plats
1, FIN-00014 Helsinki, Finland
| | - Raúl Mera-Adasme
- Departamento
de Ciencias del Ambiente, Universidad de Santiago de Chile (USACH), Av. Libertador Bernardo O’Higgins 3363, 9170022 Estación Central, Chile
| | - Jörg Kussmann
- Department
of Chemistry, University of Munich (LMU), München D-81377, Germany
| | - Arne Luenser
- Department
of Chemistry, University of Munich (LMU), München D-81377, Germany
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20
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Kumar C, Kjærgaard T, Helgaker T, Fliegl H. Nuclei-selected atomic-orbital response-theory formulation for the calculation of NMR shielding tensors using density-fitting. J Chem Phys 2016; 145:234108. [DOI: 10.1063/1.4972212] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Affiliation(s)
- Chandan Kumar
- Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, 0315 Oslo, Norway
| | - Thomas Kjærgaard
- Department of Chemistry, Aarhus University, Langelandsgade 140, 8000 Aarhus C, Denmark
| | - Trygve Helgaker
- Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, 0315 Oslo, Norway
| | - Heike Fliegl
- Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, 0315 Oslo, Norway
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21
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Hartman J, Day GM, Beran GJO. Enhanced NMR Discrimination of Pharmaceutically Relevant Molecular Crystal Forms through Fragment-Based Ab Initio Chemical Shift Predictions. CRYSTAL GROWTH & DESIGN 2016; 16:6479-6493. [PMID: 27829821 PMCID: PMC5095663 DOI: 10.1021/acs.cgd.6b01157] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2016] [Revised: 09/09/2016] [Indexed: 05/10/2023]
Abstract
Chemical shift prediction plays an important role in the determination or validation of crystal structures with solid-state nuclear magnetic resonance (NMR) spectroscopy. One of the fundamental theoretical challenges lies in discriminating variations in chemical shifts resulting from different crystallographic environments. Fragment-based electronic structure methods provide an alternative to the widely used plane wave gauge-including projector augmented wave (GIPAW) density functional technique for chemical shift prediction. Fragment methods allow hybrid density functionals to be employed routinely in chemical shift prediction, and we have recently demonstrated appreciable improvements in the accuracy of the predicted shifts when using the hybrid PBE0 functional instead of generalized gradient approximation (GGA) functionals like PBE. Here, we investigate the solid-state 13C and 15N NMR spectra for multiple crystal forms of acetaminophen, phenobarbital, and testosterone. We demonstrate that the use of the hybrid density functional instead of a GGA provides both higher accuracy in the chemical shifts and increased discrimination among the different crystallographic environments. Finally, these results also provide compelling evidence for the transferability of the linear regression parameters mapping predicted chemical shieldings to chemical shifts that were derived in an earlier study.
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Affiliation(s)
- Joshua
D. Hartman
- Department
of Chemistry, University of California, Riverside, California 92521 United States
| | - Graeme M. Day
- School
of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
| | - Gregory J. O. Beran
- Department
of Chemistry, University of California, Riverside, California 92521 United States
- E-mail:
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22
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Reid DM, Kobayashi R, Collins MA. Systematic Study of Locally Dense Basis Sets for NMR Shielding Constants. J Chem Theory Comput 2015; 10:146-52. [PMID: 26579898 DOI: 10.1021/ct4007579] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
This paper presents a systematic study of partitioning schemes for locally dense basis sets in the context of NMR shielding calculations. The partitionings explored were based exclusively on connectivity and utilized the basis sets from the pcS-n series. Deviations from pcS-4 shieldings were calculated for a set of 28 organic molecules at the HF, B3LYP, and KT3 levels of theory, with the primary goal being the determination of an efficient scheme that achieves maximal deviations of 0.1 ppm for (1)H and 1 ppm for (13)C. Both atom based and group based divisions of basis sets were examined, with the latter providing the most promising results. It is demonstrated that for the systems studied, at least pcS-1 is required for all parts of the molecule. This, coupled with pcS-3 on the group of interest and pcS-2 on the adjacent groups, is sufficient to achieve the desired level of accuracy at a minimal computational expense. In addition, the suitability of the pcS-n basis sets for post-SCF methods was confirmed through a comparison with other standard basis sets at the MP2 level.
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Affiliation(s)
- David M Reid
- Research School of Chemistry, The Australian National University , Acton ACT 0200, Australia
| | - Rika Kobayashi
- Australian National University Supercomputer Facility, The Australian National University , Acton ACT 0200, Australia
| | - Michael A Collins
- Research School of Chemistry, The Australian National University , Acton ACT 0200, Australia
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23
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Hartman JD, Beran GJO. Fragment-Based Electronic Structure Approach for Computing Nuclear Magnetic Resonance Chemical Shifts in Molecular Crystals. J Chem Theory Comput 2015; 10:4862-72. [PMID: 26584373 DOI: 10.1021/ct500749h] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
First-principles chemical shielding tensor predictions play a critical role in studying molecular crystal structures using nuclear magnetic resonance. Fragment-based electronic structure methods have dramatically improved the ability to model molecular crystal structures and energetics using high-level electronic structure methods. Here, a many-body expansion fragment approach is applied to the calculation of chemical shielding tensors in molecular crystals. First, the impact of truncating the many-body expansion at different orders and the role of electrostatic embedding are examined on a series of molecular clusters extracted from molecular crystals. Second, the ability of these techniques to assign three polymorphic forms of the drug sulfanilamide to the corresponding experimental (13)C spectra is assessed. This challenging example requires discriminating among spectra whose (13)C chemical shifts differ by only a few parts per million (ppm) across the different polymorphs. Fragment-based PBE0/6-311+G(2d,p) level chemical shielding predictions correctly assign these three polymorphs and reproduce the sulfanilamide experimental (13)C chemical shifts with 1 ppm accuracy. The results demonstrate that fragment approaches are competitive with the widely used gauge-invariant projector augmented wave (GIPAW) periodic density functional theory calculations.
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Affiliation(s)
- Joshua D Hartman
- Department of Chemistry, University of California , Riverside, California 92521, United States
| | - Gregory J O Beran
- Department of Chemistry, University of California , Riverside, California 92521, United States
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24
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Hartman JD, Monaco S, Schatschneider B, Beran GJO. Fragment-based (13)C nuclear magnetic resonance chemical shift predictions in molecular crystals: An alternative to planewave methods. J Chem Phys 2015; 143:102809. [PMID: 26374002 DOI: 10.1063/1.4922649] [Citation(s) in RCA: 55] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We assess the quality of fragment-based ab initio isotropic (13)C chemical shift predictions for a collection of 25 molecular crystals with eight different density functionals. We explore the relative performance of cluster, two-body fragment, combined cluster/fragment, and the planewave gauge-including projector augmented wave (GIPAW) models relative to experiment. When electrostatic embedding is employed to capture many-body polarization effects, the simple and computationally inexpensive two-body fragment model predicts both isotropic (13)C chemical shifts and the chemical shielding tensors as well as both cluster models and the GIPAW approach. Unlike the GIPAW approach, hybrid density functionals can be used readily in a fragment model, and all four hybrid functionals tested here (PBE0, B3LYP, B3PW91, and B97-2) predict chemical shifts in noticeably better agreement with experiment than the four generalized gradient approximation (GGA) functionals considered (PBE, OPBE, BLYP, and BP86). A set of recommended linear regression parameters for mapping between calculated chemical shieldings and observed chemical shifts are provided based on these benchmark calculations. Statistical cross-validation procedures are used to demonstrate the robustness of these fits.
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Affiliation(s)
- Joshua D Hartman
- Department of Chemistry, University of California, Riverside, California 92521, USA
| | - Stephen Monaco
- The Pennsylvania State University, The Eberly Campus, 2201 University Dr, Lemont Furnace, Pennsylvania 15456, USA
| | - Bohdan Schatschneider
- The Pennsylvania State University, The Eberly Campus, 2201 University Dr, Lemont Furnace, Pennsylvania 15456, USA
| | - Gregory J O Beran
- Department of Chemistry, University of California, Riverside, California 92521, USA
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25
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Maurer M, Ochsenfeld C. Spin component-scaled second-order Møller-Plesset perturbation theory for calculating NMR shieldings. J Chem Theory Comput 2015; 11:37-44. [PMID: 26574201 DOI: 10.1021/ct5007295] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Spin component-scaled and scaled opposite-spin second-order Møller-Plesset perturbation approaches (SCS-MP2 and SOS-MP2) are introduced for calculating NMR chemical shifts in analogy to the well-established scaled approaches for MP2 energies. Gauge-including atomic orbitals (GIAO) are employed throughout this work. The GIAO-SCS-MP2 and GIAO-SOS-MP2 methods typically show superior performance to nonscaled MP2 and are closer to the coupled-cluster singles doubles perturbative triples (CCSD(T))/cc-pVQZ reference values. In addition, the pragmatic use of mixed basis sets for the Hartree-Fock and the correlated part of NMR chemical shift calculations is shown to be beneficial.
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Affiliation(s)
- Marina Maurer
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU) , Butenandtstrasse 7, D-81377 Munich, Germany.,Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU) , Butenandtstrasse 5-13, D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU) , Butenandtstrasse 7, D-81377 Munich, Germany.,Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU) , Butenandtstrasse 5-13, D-81377 Munich, Germany
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26
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Reid DM, Collins MA. Calculating nuclear magnetic resonance shieldings using systematic molecular fragmentation by annihilation. Phys Chem Chem Phys 2015; 17:5314-20. [DOI: 10.1039/c4cp05116e] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Systematic fragmentation accurately predicts theoretical chemical shieldings.
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Affiliation(s)
- David M. Reid
- Research School of Chemistry
- The Australian National University
- ACT
- Australia
| | - Michael A. Collins
- Research School of Chemistry
- The Australian National University
- ACT
- Australia
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27
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Maurer SA, Clin L, Ochsenfeld C. Cholesky-decomposed density MP2 with density fitting: Accurate MP2 and double-hybrid DFT energies for large systems. J Chem Phys 2014; 140:224112. [DOI: 10.1063/1.4881144] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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28
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Flaig D, Maurer M, Hanni M, Braunger K, Kick L, Thubauville M, Ochsenfeld C. Benchmarking Hydrogen and Carbon NMR Chemical Shifts at HF, DFT, and MP2 Levels. J Chem Theory Comput 2014; 10:572-8. [DOI: 10.1021/ct400780f] [Citation(s) in RCA: 126] [Impact Index Per Article: 12.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Denis Flaig
- Chair of Theoretical Chemistry,
Department of Chemistry, University of Munich (LMU), Butenandtstr.
7, D-81377 Munich, Germany
- Center for Integrated Protein
Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5-13, D-81377 Munich, Germany
| | - Marina Maurer
- Chair of Theoretical Chemistry,
Department of Chemistry, University of Munich (LMU), Butenandtstr.
7, D-81377 Munich, Germany
- Center for Integrated Protein
Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5-13, D-81377 Munich, Germany
| | - Matti Hanni
- Chair of Theoretical Chemistry,
Department of Chemistry, University of Munich (LMU), Butenandtstr.
7, D-81377 Munich, Germany
- Center for Integrated Protein
Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5-13, D-81377 Munich, Germany
| | - Katharina Braunger
- Chair of Theoretical Chemistry,
Department of Chemistry, University of Munich (LMU), Butenandtstr.
7, D-81377 Munich, Germany
- Center for Integrated Protein
Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5-13, D-81377 Munich, Germany
| | - Leonhard Kick
- Chair of Theoretical Chemistry,
Department of Chemistry, University of Munich (LMU), Butenandtstr.
7, D-81377 Munich, Germany
- Center for Integrated Protein
Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5-13, D-81377 Munich, Germany
| | - Matthias Thubauville
- Chair of Theoretical Chemistry,
Department of Chemistry, University of Munich (LMU), Butenandtstr.
7, D-81377 Munich, Germany
- Center for Integrated Protein
Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5-13, D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry,
Department of Chemistry, University of Munich (LMU), Butenandtstr.
7, D-81377 Munich, Germany
- Center for Integrated Protein
Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5-13, D-81377 Munich, Germany
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