1
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Drontschenko V, Ochsenfeld C. Low-Scaling, Efficient and Memory Optimized Computation of Nuclear Magnetic Resonance Shieldings within the Random Phase Approximation Using Cholesky-Decomposed Densities and an Attenuated Coulomb Metric. J Phys Chem A 2024. [PMID: 39239944 DOI: 10.1021/acs.jpca.4c02773] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/07/2024]
Abstract
An efficient method for the computation of nuclear magnetic resonance (NMR) shielding tensors within the random phase approximation (RPA) is presented based on our recently introduced resolution-of-the-identity (RI) atomic orbital RPA NMR method [Drontschenko, V. J. Chem. Theory Comput. 2023, 19, 7542-7554] utilizing Cholesky decomposed density type matrices and employing an attenuated Coulomb RI metric. The introduced sparsity is efficiently exploited using sparse matrix algebra. This allows for an efficient and low-scaling computation of RPA NMR shielding tensors. Furthermore, we introduce a batching method for the computation of memory demanding intermediates that accounts for their sparsity. This extends the applicability of our method to even larger systems that would have been out of reach before, such as, e.g., a DNA strand with 260 atoms and 3408 atomic orbital basis functions.
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Affiliation(s)
- Viktoria Drontschenko
- 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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Adusei EBA, Casetti VT, Goldsmith CD, Caswell M, Alinj D, Park J, Zeller M, Rusakov AA, Kinney ZJ. Bent naphthodithiophenes: synthesis and characterization of isomeric fluorophores. RSC Adv 2024; 14:25120-25129. [PMID: 39139244 PMCID: PMC11318266 DOI: 10.1039/d4ra04850d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2024] [Accepted: 07/26/2024] [Indexed: 08/15/2024] Open
Abstract
Thiophene-containing heteroarenes are one of the most well-known classes of π-conjugated building blocks for photoactive molecules. Isomeric naphthodithiophenes (NDTs) are at the forefront of this research area due to their straightforward synthesis and derivatization. Notably, NDT geometries that are bent - such as naphtho[2,1-b:3,4-b']dithiophene (α-NDT) and naphtho[1,2-b:4,3-b']dithiophene (β-NDT) - are seldom employed as photoactive small molecules. This report investigates how remote substituents impact the photophysical properties of isomeric α- and β-NDTs. The orientation of the thiophene units plays a critical role in the emission: in the α(OHex)R2 series conjugation from the end-caps to the NDT core is apparent, while in the β(Oi-Pent)R2 series minimal change is observed unless strong electron acceptors, such as β(Oi-Pent)(PhCF3)2, are employed. This push-pull acceptor-donor-acceptor (A-D-A) fluorophore exhibits positive fluorosolvatochromism that correlates with increasing solvent polarity parameter, E T(30). In total, these results highlight how remote substituents are able to modulate the emission of isomeric bent NDTs.
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Affiliation(s)
- Emmanuel B A Adusei
- Department of Chemistry, Oakland University Rochester Michigan USA +1-248-370-2347
| | - Vincent T Casetti
- Department of Chemistry, Oakland University Rochester Michigan USA +1-248-370-2347
| | - Calvin D Goldsmith
- Department of Chemistry, Oakland University Rochester Michigan USA +1-248-370-2347
| | - Madison Caswell
- Department of Chemistry, Oakland University Rochester Michigan USA +1-248-370-2347
| | - Drecila Alinj
- Department of Chemistry, Oakland University Rochester Michigan USA +1-248-370-2347
| | - Jimin Park
- Department of Chemistry, Oakland University Rochester Michigan USA +1-248-370-2347
| | - Matthias Zeller
- Department of Chemistry, Purdue University West Lafayette Indiana USA
| | - Alexander A Rusakov
- Department of Chemistry, Oakland University Rochester Michigan USA +1-248-370-2347
| | - Zacharias J Kinney
- Department of Chemistry, Oakland University Rochester Michigan USA +1-248-370-2347
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3
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Fauser S, Drontschenko V, Ochsenfeld C, Görling A. Accurate NMR Shieldings with σ-Functionals. J Chem Theory Comput 2024; 20:6028-6036. [PMID: 38967385 DOI: 10.1021/acs.jctc.4c00512] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/06/2024]
Abstract
In recent years, density-functional methods relying on a new type of fifth-rung correlation functionals called σ-functionals have been introduced. σ-Functionals are technically closely related to the random phase approximation and require the same computational effort but yield distinctively higher accuracies for reaction and transition state energies of main group chemistry and even outperform double-hybrid functionals for these energies. In this work, we systematically investigate how accurate σ-functionals can describe nuclear magnetic resonance (NMR) shieldings. It turns out that σ-functionals yield very accurate NMR shieldings, even though in their optimization, exclusively, energies are employed as reference data and response properties such as NMR shieldings are not involved at all. This shows that σ-functionals combine universal applicability with accuracy. Indeed, the NMR shieldings from a σ-functional using input orbitals and eigenvalues from Kohn-Sham calculations with the exchange-correlation functional of Perdew, Burke and Ernzerhof (PBE) turned out to be the most accurate ones among the NMR shieldings calculated with various density-functional methods including methods using double-hybrid functionals. That σ-functionals can be used for calculating both reliable energies and response properties like NMR shieldings characterizes them as all-purpose functionals, which is appealing from an application point of view.
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Affiliation(s)
- Steffen Fauser
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
| | - Viktoria Drontschenko
- 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
| | - Andreas Görling
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
- Erlangen National High Performance Computing Center (NHR@FAU), Martensstr. 1, D-91058 Erlangen, Germany
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4
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Schattenberg C, Kaupp M. Implementation and First Evaluation of Strong-Correlation-Corrected Local Hybrid Functionals for the Calculation of NMR Shieldings and Shifts. J Phys Chem A 2024; 128:2253-2271. [PMID: 38456430 PMCID: PMC10961831 DOI: 10.1021/acs.jpca.3c08507] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2023] [Revised: 02/01/2024] [Accepted: 02/09/2024] [Indexed: 03/09/2024]
Abstract
Local hybrid functionals containing strong-correlation factors (scLHs) and range-separated local hybrids (RSLHs) have been integrated into an efficient coupled-perturbed Kohn-Sham implementation for the calculation of nuclear shielding constants. Several scLHs and the ωLH22t RSLH have then been evaluated for the first time for the extended NS372 benchmark set of main-group shieldings and shifts and the TM70 benchmark of 3d transition-metal shifts. The effects of the strong-correlation corrections have been analyzed with respect to the spatial distribution of the sc-factors, which locally diminish exact-exchange admixture at certain regions in a molecule. The scLH22t, scLH23t-mBR, and scLH23t-mBR-P functionals, which contain a "damped" strong-correlation factor to retain the excellent performance of the underlying LH20t functional for weakly correlated situations, tend to make smaller corrections to shieldings and shifts than the "undamped" scLH22ta functional. While the latter functional can also deteriorate agreement with the reference data in certain weakly correlated cases, it provides overall better performance, in particular for systems where static correlation is appreciable. This pertains only to a minority of systems in the NS372 main-group test set but to many more systems in the TM70 transition-metal test set, in particular for high-oxidation-state complexes, e.g., Cr(+VI) complexes and other systems with stretched bonds. Another undamped scLH, the simpler LDA-based scLH21ct-SVWN-m, also tends to provide significant improvements in many cases. The differences between the functionals and species can be rationalized on the basis of one-dimensional plots of the strong-correlation factors, augmented by isosurface plots of the fractional orbital density (FOD). Position-dependent exact-exchange admixture is thus shown to provide substantial flexibility in treating response properties like NMR shifts for both weakly and strongly correlated systems.
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Affiliation(s)
- Caspar
Jonas Schattenberg
- Research
Unit of Structural Chemistry & Computational Biophysics, Leibniz-Forschungsinstitut für Molekulare Pharmakologie
(FMP), Robert-Roessle-Str.
10, 13125 Berlin, Germany
| | - Martin Kaupp
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
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5
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Li J, Liang J, Wang Z, Ptaszek AL, Liu X, Ganoe B, Head-Gordon M, Head-Gordon T. Highly Accurate Prediction of NMR Chemical Shifts from Low-Level Quantum Mechanics Calculations Using Machine Learning. J Chem Theory Comput 2024; 20:2152-2166. [PMID: 38331423 DOI: 10.1021/acs.jctc.3c01256] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/10/2024]
Abstract
Theoretical predictions of NMR chemical shifts from first-principles can greatly facilitate experimental interpretation and structure identification of molecules in gas, solution, and solid-state phases. However, accurate prediction of chemical shifts using the gold-standard coupled cluster with singles, doubles, and perturbative triple excitations [CCSD(T)] method with a complete basis set (CBS) can be prohibitively expensive. By contrast, machine learning (ML) methods offer inexpensive alternatives for chemical shift predictions but are hampered by generalization to molecules outside the original training set. Here, we propose several new ideas in ML of the chemical shift prediction for H, C, N, and O that first introduce a novel feature representation, based on the atomic chemical shielding tensors within a molecular environment using an inexpensive quantum mechanics (QM) method, and train it to predict NMR chemical shieldings of a high-level composite theory that approaches the accuracy of CCSD(T)/CBS. In addition, we train the ML model through a new progressive active learning workflow that reduces the total number of expensive high-level composite calculations required while allowing the model to continuously improve on unseen data. Furthermore, the algorithm provides an error estimation, signaling potential unreliability in predictions if the error is large. Finally, we introduce a novel approach to keep the rotational invariance of the features using tensor environment vectors (TEVs) that yields a ML model with the highest accuracy compared to a similar model using data augmentation. We illustrate the predictive capacity of the resulting inexpensive shift machine learning (iShiftML) models across several benchmarks, including unseen molecules in the NS372 data set, gas-phase experimental chemical shifts for small organic molecules, and much larger and more complex natural products in which we can accurately differentiate between subtle diastereomers based on chemical shift assignments.
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Affiliation(s)
- Jie Li
- Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Jiashu Liang
- Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Zhe Wang
- Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Aleksandra L Ptaszek
- Christian Doppler Laboratory for High-Content Structural Biology and Biotechnology, Department of Structural and Computational Biology, Max Perutz Laboratories, University of Vienna, Campus Vienna Biocenter 5, Vienna 1030, Austria
- Laboratory for Computer-Aided Molecular Design, Division of Medicinal Chemistry, Otto Loewi Research Center, Medical University Graz, Neue Stiftingtalstrasse 6/III, Graz 8010, Austria
| | - Xiao Liu
- Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Brad Ganoe
- Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Martin Head-Gordon
- Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Teresa Head-Gordon
- Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Departments of Bioengineering and Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, California 94720, United States
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6
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Kleine Büning JB, Grimme S, Bursch M. Machine learning-based correction for spin-orbit coupling effects in NMR chemical shift calculations. Phys Chem Chem Phys 2024; 26:4870-4884. [PMID: 38230684 DOI: 10.1039/d3cp05556f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2024]
Abstract
As one of the most powerful analytical methods for molecular and solid-state structure elucidation, NMR spectroscopy is an integral part of chemical laboratories associated with a great research interest in its computational simulation. Particularly when heavy atoms are present, a relativistic treatment is essential in the calculations as these influence also the nearby light atoms. In this work, we present a Δ-machine learning method that approximates the contribution to 13C and 1H NMR chemical shifts that stems from spin-orbit (SO) coupling effects. It is built on computed reference data at the spin-orbit zeroth-order regular approximation (ZORA) DFT level for a set of 6388 structures with 38 740 13C and 64 436 1H NMR chemical shifts. The scope of the methods covers the 17 most important heavy p-block elements that exhibit heavy atom on the light atom (HALA) effects to covalently bound carbon or hydrogen atoms. Evaluated on the test data set, the approach is able to recover roughly 85% of the SO contribution for 13C and 70% for 1H from a scalar-relativistic PBE0/ZORA-def2-TZVP calculation at virtually no extra computational costs. Moreover, the method is transferable to other baseline DFT methods even without retraining the model and performs well for realistic organotin and -lead compounds. Finally, we show that using a combination of the new approach with our previous Δ-ML method for correlation contributions to NMR chemical shifts, the mean absolute NMR shift deviations from non-relativistic DFT calculations to experimental values can be halved.
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Affiliation(s)
- Julius B Kleine Büning
- Mulliken Center for Theoretical Chemistry, Clausius Institute for Physical and Theoretical Chemistry, University of Bonn, Beringstr. 4, 53115 Bonn, Germany.
| | - Stefan Grimme
- Mulliken Center for Theoretical Chemistry, Clausius Institute for Physical and Theoretical Chemistry, University of Bonn, Beringstr. 4, 53115 Bonn, Germany.
| | - Markus Bursch
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany.
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7
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Franzke YJ, Bruder F, Gillhuber S, Holzer C, Weigend F. Paramagnetic Nuclear Magnetic Resonance Shifts for Triplet Systems and Beyond with Modern Relativistic Density Functional Methods. J Phys Chem A 2024; 128:670-686. [PMID: 38195394 DOI: 10.1021/acs.jpca.3c07093] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2024]
Abstract
An efficient framework for the calculation of paramagnetic NMR (pNMR) shifts within exact two-component (X2C) theory and (current-dependent) density functional theory (DFT) up to the class of local hybrid functionals (LHFs) is presented. Generally, pNMR shifts for systems with more than one unpaired electron depend on the orbital shielding contribution and a temperature-dependent term. The latter includes zero-field splitting (ZFS), hyperfine coupling (HFC), and the g-tensor. For consistency, we calculate these three tensors at the same level of theory, i.e., using scalar-relativistic X2C augmented with spin-orbit perturbation theory. Results for pNMR chemical shifts of transition-metal complexes reveal that this X2C-DFT framework can yield good results for both the shifts and the individual tensor contributions of metallocenes and related systems, especially if the HFC constant is large. For small HFC constants, the relative error is often large, and sometimes the sign may be off. 4d and 5d complexes with more complicated structures demonstrate the limitations of a fully DFT-based approach. Additionally, a Co-based complex with a very large ZFS and pronounced multireference character is not well described. Here, a hybrid DFT-multireference framework is necessary for accurate results. Our results show that X2C is sufficient to describe relativistic effects and computationally cheaper than a fully relativistic approach. Thus, it allows use of large basis sets for converged HFCs. Overall, current-dependent meta-generalized gradient approximations and LHFs show some potential; however, the currently available functionals leave a lot to be desired, and the predictive power is limited.
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Affiliation(s)
- Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany
| | - Florian Bruder
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany
| | - Sebastian Gillhuber
- Institute of Inorganic Chemistry, Karlsruhe Institute of Technology (KIT), Engesserstraße 15, 76131 Karlsruhe, Germany
| | - Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany
| | - Florian Weigend
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany
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8
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Schattenberg C, Wodyński A, Åström H, Sundholm D, Kaupp M, Lehtola S. Revisiting Gauge-Independent Kinetic Energy Densities in Meta-GGAs and Local Hybrid Calculations of Magnetizabilities. J Phys Chem A 2023; 127:10896-10907. [PMID: 38100678 PMCID: PMC10758120 DOI: 10.1021/acs.jpca.3c06244] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2023] [Revised: 10/27/2023] [Accepted: 11/08/2023] [Indexed: 12/17/2023]
Abstract
In a recent study [J. Chem. Theory Comput. 2021, 17, 1457-1468], some of us examined the accuracy of magnetizabilities calculated with density functionals representing the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA (mGGA), as well as global hybrid (GH) and range-separated (RS) hybrid functionals by assessment against accurate reference values obtained with coupled-cluster theory with singles, doubles, and perturbative triples [CCSD(T)]. Our study was later extended to local hybrid (LH) functionals by Holzer et al. [J. Chem. Theory Comput. 2021, 17, 2928-2947]; in this work, we examine a larger selection of LH functionals, also including range-separated LH (RSLH) functionals and strong-correlation LH (scLH) functionals. Holzer et al. also studied the importance of the physically correct handling of the magnetic gauge dependence of the kinetic energy density (τ) in mGGA calculations by comparing the Maximoff-Scuseria formulation of τ used in our aforementioned study to the more physical current-density extension derived by Dobson. In this work, we also revisit this comparison with a larger selection of mGGA functionals. We find that the newly tested LH, RSLH, and scLH functionals outperform all of the functionals considered in the previous studies. The various LH functionals afford the seven lowest mean absolute errors while also showing remarkably small standard deviations and mean errors. Most strikingly, the best two functionals are scLHs that also perform remarkably well in cases with significant multiconfigurational character, such as the ozone molecule, which is traditionally excluded from statistical error evaluations due to its large errors with common density functionals.
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Affiliation(s)
- Caspar
J. Schattenberg
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Artur Wodyński
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Hugo Åström
- Department
of Chemistry, Faculty of Science, University
of Helsinki, P.O. Box 55
(A.I. Virtanens plats 1), University of Helsinki FI-00014, Finland
| | - Dage Sundholm
- Department
of Chemistry, Faculty of Science, University
of Helsinki, P.O. Box 55
(A.I. Virtanens plats 1), University of Helsinki FI-00014, Finland
| | - Martin Kaupp
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Susi Lehtola
- Department
of Chemistry, Faculty of Science, University
of Helsinki, P.O. Box 55
(A.I. Virtanens plats 1), University of Helsinki FI-00014, Finland
- Molecular
Sciences Software Institute, Blacksburg, Virginia 24061, United States
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9
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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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10
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Franzke YJ, Holzer C. Exact two-component theory becoming an efficient tool for NMR shieldings and shifts with spin-orbit coupling. J Chem Phys 2023; 159:184102. [PMID: 37937936 DOI: 10.1063/5.0171509] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2023] [Accepted: 09/04/2023] [Indexed: 11/09/2023] Open
Abstract
We present a gauge-origin invariant exact two-component (X2C) approach within a modern density functional framework, supporting meta-generalized gradient approximations such as TPSS and range-separated hybrid functionals such as CAM-B3LYP. The complete exchange-correlation kernel is applied, including the direct contribution of the field-dependent basis functions and the reorthonormalization contribution from the perturbed overlap matrix. Additionally, the finite nucleus model is available for the electron-nucleus potential and the vector potential throughout. Efficiency is ensured by the diagonal local approximation to the unitary decoupling transformation in X2C as well as the (multipole-accelerated) resolution of the identity approximation for the Coulomb term (MARI-J, RI-J) and the seminumerical exchange approximation. Errors introduced by these approximations are assessed and found to be clearly negligible. The applicability of our implementation to large-scale calculations is demonstrated for a tin pincer-type system as well as low-valent tin and lead complexes. Here, the calculation of the Sn nuclear magnetic resonance shifts for the pincer-type ligand with about 2400 basis functions requires less than 1 h for hybrid density functionals. Further, the impact of spin-orbit coupling on the nucleus-independent chemical shifts and the corresponding ring currents of all-metal aromatic systems is studied.
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Affiliation(s)
- Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany
| | - Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany
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11
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Wilson DJD. Extreme NMR shielding in fluoro-nitrogen cations. Phys Chem Chem Phys 2023; 25:25420-25434. [PMID: 37706351 DOI: 10.1039/d3cp03399f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/15/2023]
Abstract
The structure and NMR shielding of a set of N-F containing cations is reported to near-quantitative accuracy from extensive ab initio calculations. Currently, the shortest experimentally confirmed N-F bond is 1.2461(10) Å in NNF+, however CCSD(T)-F12b/cc-pVQZ-F12 optimised geometries suggest that even shorter N-F bonds are possible for both monocations (1.236 Å, HNF+) and dications (1.098 Å, NF2+). NMR shielding constants have been calculated in a composite manner with individual components from coupled-cluster expansions up to CCSDTQP and basis sets up to aug-cc-pCV8Z, together with vibrational and relativistic corrections. 15N and 19F NMR chemical shifts correlate well with available experimental data. Extreme 19F chemical shifts are predicted for HNF+ (1628.9 ppm) and NH2F2+ (1298.0 ppm), which are by far the largest 19F chemical shifts ever reported and well outside the known range of +865 ppm (F2O2) to -448 ppm (ClF). The 15N chemical shift of -1283.07 ppm in HNF+ is similarly extreme, being well outside the known range of 15N chemical shifts of -730 to 260 ppm (CH3NO2 reference). This work highlights the application of state-of-the-art theoretical techniques, and provides accurate NMR properties of both isolated and yet unknown N-F cations, which can serve to guide and supplement NMR experimentation.
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Affiliation(s)
- David J D Wilson
- Department of Chemistry, La Trobe Institute for Molecular Science, La Trobe University, Melbourne, Victoria 3086, Australia.
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12
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Cheng CY, Wibowo-Teale AM. Semiempirical Methods for Molecular Systems in Strong Magnetic Fields. J Chem Theory Comput 2023; 19:6226-6241. [PMID: 37672773 PMCID: PMC10536997 DOI: 10.1021/acs.jctc.3c00671] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2023] [Indexed: 09/08/2023]
Abstract
A general scheme is presented to extend semiempirical methods to include the effects of arbitrary strength magnetic fields, while maintaining computational efficiency. The approach utilizes three main modifications; a London atomic orbital (LAO) basis set is introduced, field-dependent kinetic energy corrections are added to the model Hamiltonian, and spin-Zeeman interaction energy terms are included. The approach is applied to the widely available density-functional tight-binding method GFN1-xTB. Considering the basis set requirements for the kinetic energy corrections in a magnetic field leads to two variants: a single-basis approach GFN1-xTB-M0 and a dual-basis approach GFN1-xTB-M1. The LAO basis in the latter includes the appropriate nodal structure for an accurate representation of the kinetic energy corrections. The variants are assessed by benchmarking magnetizabilities and nuclear magnetic resonance shielding constants calculated using weak magnetic fields. Remarkably, the GFN1-xTB-M1 approach also exhibits excellent performance for strong fields, |B | ≤ 0.2B0 (B0 = 2.3505 × 105 T), recovering exotic features such as the para- to dia-magnetic transition in the BH molecule and the preferred electronic configuration, molecular conformation, and orientation of benzene. At stronger field strengths, |B | > 0.2B0, a degradation in the quality of the results is observed. The utility of GFN1-xTB-M1 is demonstrated by performing conformer searches in a range of field strengths for the cyclooctatetraene molecule, with GFN1-xTB-M1 capturing the transition from tub to planar conformations at high field, consistent with much more computationally demanding current-density functional theory calculations. Magnetically induced currents are also shown to be well described for the benzene and infinitene molecules, the latter demonstrating the flexibility and computational efficiency of the approach. The GFN1-xTB-M1 approach is a useful tool for the study of structure, conformation, and dynamics of large systems in magnetic fields at the semiempirical level as well as for preoptimization of molecular structure in ab initio calculations, enabling more efficient exploration of complex potential energy surfaces and reactivity in the presence of external fields.
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Affiliation(s)
- Chi Y. Cheng
- School
of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, U.K.
| | - Andrew M. Wibowo-Teale
- School
of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, U.K.
- 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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13
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Kleine Büning JB, Grimme S. Computation of CCSD(T)-Quality NMR Chemical Shifts via Δ-Machine Learning from DFT. J Chem Theory Comput 2023. [PMID: 37262324 DOI: 10.1021/acs.jctc.3c00165] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
NMR spectroscopy undoubtedly plays a central role in determining molecular structures across different chemical disciplines, and the accurate computational prediction of NMR parameters is highly desirable. In this work, a new Δ-machine learning approach is presented to correct DFT-computed NMR chemical shifts using input features from the calculation and in addition highly accurate reference data at the CCSD(T)/pcSseg-2 level of theory with a basis set extrapolation scheme. The model is trained on a data set containing 1000 optimized and geometrically distorted structures of small organic molecules comprising most elements of the first three periods and containing data for 7090 1H and 4230 13C NMR chemical shifts. Applied to the PBE0/pcSseg-2 method, the mean absolute deviation (MAD) on the internal NMR shift test set is reduced by 81% for 1H and 92% for 13C at virtually no additional computational cost. For 12 different DFT functional and basis set combinations, the MAD of the ML-corrected NMR shifts ranges from 0.021 to 0.039 ppm (1H) and from 0.38 to 1.07 ppm (13C). Importantly, the new method consistently outperforms the simple and widely used linear regression correction technique. This behavior is reproduced on three different external benchmark sets, confirming the generality and robustness of the correction scheme, which can easily be applied in DFT-based spectral simulations.
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Affiliation(s)
- Julius B Kleine Büning
- Mulliken Center for Theoretical Chemistry, Clausius Institute for Physical and Theoretical Chemistry, University of Bonn, Beringstr. 4, 53115 Bonn, Germany
| | - Stefan Grimme
- Mulliken Center for Theoretical Chemistry, Clausius Institute for Physical and Theoretical Chemistry, University of Bonn, Beringstr. 4, 53115 Bonn, Germany
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14
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Wong J, Ganoe B, Liu X, Neudecker T, Lee J, Liang J, Wang Z, Li J, Rettig A, Head-Gordon T, Head-Gordon M. An in-silico NMR laboratory for nuclear magnetic shieldings computed via finite fields: Exploring nucleus-specific renormalizations of MP2 and MP3. J Chem Phys 2023; 158:164116. [PMID: 37114707 PMCID: PMC10148725 DOI: 10.1063/5.0145130] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2023] [Accepted: 04/10/2023] [Indexed: 04/29/2023] Open
Abstract
We developed and implemented a method-independent, fully numerical, finite difference approach to calculating nuclear magnetic resonance shieldings, using gauge-including atomic orbitals. The resulting capability can be used to explore non-standard methods, given only the energy as a function of finite-applied magnetic fields and nuclear spins. For example, standard second-order Møller-Plesset theory (MP2) has well-known efficacy for 1H and 13C shieldings and known limitations for other nuclei such as 15N and 17O. It is, therefore, interesting to seek methods that offer good accuracy for 15N and 17O shieldings without greatly increased compute costs, as well as exploring whether such methods can further improve 1H and 13C shieldings. Using a small molecule test set of 28 species, we assessed two alternatives: κ regularized MP2 (κ-MP2), which provides energy-dependent damping of large amplitudes, and MP2.X, which includes a variable fraction, X, of third-order correlation (MP3). The aug-cc-pVTZ basis was used, and coupled cluster with singles and doubles and perturbative triples [CCSD(T)] results were taken as reference values. Our κ-MP2 results reveal significant improvements over MP2 for 13C and 15N, with the optimal κ value being element-specific. κ-MP2 with κ = 2 offers a 30% rms error reduction over MP2. For 15N, κ-MP2 with κ = 1.1 provides a 90% error reduction vs MP2 and a 60% error reduction vs CCSD. On the other hand, MP2.X with a scaling factor of 0.6 outperformed CCSD for all heavy nuclei. These results can be understood as providing renormalization of doubles amplitudes to partially account for neglected triple and higher substitutions and offer promising opportunities for future applications.
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Affiliation(s)
- Jonathan Wong
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Brad Ganoe
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Xiao Liu
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Tim Neudecker
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Joonho Lee
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Jiashu Liang
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Zhe Wang
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Jie Li
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Adam Rettig
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
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15
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Hoyt EM, Smith LO, Crittenden DL. Simple, accurate, adjustable-parameter-free prediction of NMR shifts for molecules in solution. Phys Chem Chem Phys 2023; 25:9952-9957. [PMID: 36951928 DOI: 10.1039/d3cp00721a] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/24/2023]
Abstract
Accurate prediction of NMR shifts is invaluable for interpreting and assigning NMR spectra, especially for complex applications such as determining the identity of unknown substances or resolving stereochemical assignments. Statistical linear regression models have proven effective for accurately correlating density functional theory predictions of chemical shieldings with experimentally-measured shifts, but lack transferability - they must be reparameterised using a reasonably extensive training set at each level of theory and for each choice of NMR solvent. We have previously introduced a novel two-point "shift-and-scale" correction procedure for gas phase shieldings that overcomes these limitations without significant loss of accuracy. In this work, we demonstrate that this approach is equally applicable for predicting solution-phase shifts from computed gas phase shieldings, using acetaldehyde as an experimentally and computationally convenient reference system. We also present all of the required experimental reference data to enable this approach to be used for any target analyte in a range of commonly used NMR solvents (chloroform, dichloromethane, acetonitrile, methanol, acetone, DMSO, D2O, benzene, pyridine).
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Affiliation(s)
- Emlyn M Hoyt
- School of Physical and Chemical Sciences, University of Canterbury, Christchurch 8140, New Zealand.
| | - Lachlan O Smith
- School of Physical and Chemical Sciences, University of Canterbury, Christchurch 8140, New Zealand.
| | - Deborah L Crittenden
- School of Physical and Chemical Sciences, University of Canterbury, Christchurch 8140, New Zealand.
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16
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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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17
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Liu X, McKemmish L, Pérez-Ríos J. The performance of CCSD(T) for the calculation of dipole moments in diatomics. Phys Chem Chem Phys 2023; 25:4093-4104. [PMID: 36651174 DOI: 10.1039/d2cp05060a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
This work analyzes the accuracy of the coupled cluster with single, double, and perturbative triple excitation [CCSD(T)] method for predicting dipole moments. In particular, we benchmark CCSD(T) predictions for the equilibrium bond length, vibrational frequency, and dipole moment versus accurate experimental data. As a result, we find that CCSD(T) leads to accurate dipole moments. However, in some cases, it disagrees with the experimental values, and the disagreement can not be satisfactorily explained via relativistic or multi-reference effects. Therefore, our results indicate that benchmark studies for energy and geometry properties do not accurately describe other electron density magnitudes.
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Affiliation(s)
- Xiangyue Liu
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
| | - Laura McKemmish
- School of Chemistry, UNSW Sydney, Sydney, NSW 2052, Australia
| | - Jesús Pérez-Ríos
- Department of Physics and Astronomy, Stony Brook University, Stony Brook 11794, New York, USA. .,Institute for Advanced Computational Science, Stony Brook University, Stony Brook, NY 11794-3800, USA
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18
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Manian A, Hudson RJ, Ramkissoon P, Smith TA, Russo SP. Interexcited State Photophysics I: Benchmarking Density Functionals for Computing Nonadiabatic Couplings and Internal Conversion Rate Constants. J Chem Theory Comput 2023; 19:271-292. [PMID: 36490305 DOI: 10.1021/acs.jctc.2c00888] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
We present the first benchmarking study of nonadiabatic matrix coupling elements (NACMEs) calculated using different density functionals. Using the S1 → S0 transition in perylene solvated in toluene as a case study, we calculate the photophysical properties and corresponding rate constants for a variety of density functionals from each rung of Jacob's ladder. The singlet photoluminescence quantum yield (sPLQY) is taken as a measure of accuracy, measured experimentally here as 0.955. Important quantum chemical parameters such as geometries, absorption, emission, and adiabatic energies, NACMEs, Hessians, and transition dipole moments were calculated for each density functional basis set combination (data set) using density functional theory based multireference configuration interaction (DFT/MRCI) and compared to experiment where possible. We were able to derive simple relations between the TDDFT and DFT/MRCI photophysical properties; with semiempirical damping factors of ∼0.843 ± 0.017 and ∼0.954 ± 0.064 for TDDFT transition dipole moments and energies to DFT/MRCI level approximations, respectively. NACMEs were dominated by out-of-plane derivative components belonging to the center-most ring atoms with weaker contributions from perturbations along the transverse and longitudinal axes. Calculated theoretical spectra compared well to both experiment and literature, with fluorescence lifetimes between 7.1 and 12.5 ns, agreeing within a factor of 2 with experiment. Internal conversion (IC) rates were then calculated and were found to vary wildly between 106-1016 s-1 compared with an experimental rate of the order 107 s-1. Following further testing by mixing data sets, we found a strong dependence on the method used to obtain the Hessian. The 5 characterized data sets ranked in order of most promising are PBE0/def2-TZVP, ωB97XD/def2-TZVP, HCTH407/TZVP, PBE/TZVP, and PBE/def2-TZVP.
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Affiliation(s)
- Anjay Manian
- ARC Centre of Excellence in Exciton Science, School of Science, RMIT University, Melbourne3000, Australia
| | - Rohan J Hudson
- ARC Centre of Excellence in Exciton Science, School of Chemistry, University of Melbourne, Parkville3010, Australia
| | - Pria Ramkissoon
- ARC Centre of Excellence in Exciton Science, School of Chemistry, University of Melbourne, Parkville3010, Australia
| | - Trevor A Smith
- ARC Centre of Excellence in Exciton Science, School of Chemistry, University of Melbourne, Parkville3010, Australia
| | - Salvy P Russo
- ARC Centre of Excellence in Exciton Science, School of Science, RMIT University, Melbourne3000, Australia
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19
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Liang J, Wang Z, Li J, Wong J, Liu X, Ganoe B, Head-Gordon T, Head-Gordon M. Efficient Calculation of NMR Shielding Constants Using Composite Method Approximations and Locally Dense Basis Sets. J Chem Theory Comput 2023. [PMID: 36594660 DOI: 10.1021/acs.jctc.2c00933] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
This paper presents a systematic study of applying composite method approximations with locally dense basis sets (LDBS) to efficiently calculate NMR shielding constants in small and medium-sized molecules. The pcSseg-n series of basis sets are shown to have similar accuracy to the pcS-n series when n ≥ 1 and can slightly reduce computational costs. We identify two different LDBS partition schemes that perform very effectively for density functional calculations. We select a large subset of the recent NS372 database containing 290 H, C, N, and O shielding values evaluated by reference methods on 106 molecules to carefully assess methods of the high, medium, and low computational costs to make practical recommendations. Our assessment covers conventional electronic structure methods (density functional theory and wave function) with global basis calculations, as well as their use in one of the satisfactory LDBS approaches, and a range of composite approaches, also with and without LDBS. Altogether 99 methods are evaluated. On this basis, we recommend different methods to reach three different levels of accuracy and time requirements across the four nuclei considered.
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Affiliation(s)
- Jiashu Liang
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California94720, United States
| | - Zhe Wang
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California94720, United States
| | - Jie Li
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California94720, United States
| | - Jonathan Wong
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California94720, United States
| | - Xiao Liu
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California94720, United States
| | - Brad Ganoe
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California94720, United States
| | - Teresa Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California94720, United States
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California94720, United States.,Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California94720, United States
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20
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Rzepiela K, Kaminský J, Buczek A, Broda MA, Kupka T. Electron Correlation or Basis Set Quality: How to Obtain Converged and Accurate NMR Shieldings for the Third-Row Elements? Molecules 2022; 27:8230. [PMID: 36500321 PMCID: PMC9737175 DOI: 10.3390/molecules27238230] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2022] [Revised: 11/17/2022] [Accepted: 11/22/2022] [Indexed: 11/29/2022] Open
Abstract
The quality of theoretical NMR shieldings calculated at the quantum-chemical level depends on various theoretical aspects, of which the basis set type and size are among the most important factors. Nevertheless, not much information is available on the basis set effect on theoretical shieldings of the NMR-active nuclei of the third row. Here, we report on the importance of proper basis set selection to obtain accurate and reliable NMR shielding parameters for nuclei from the third row of the periodic table. All calculations were performed on a set of eleven compounds containing the elements Na, Mg, Al, Si, P, S, or Cl. NMR shielding tensors were calculated using the SCF-HF, DFT-B3LYP, and CCSD(T) methods, combined with the Dunning valence aug-cc-pVXZ, core-valence aug-cc-pCVXZ, Jensen polarized-convergent aug-pcSseg-n and Karlsruhe x2c-Def2 basis set families. We also estimated the complete basis set limit (CBS) values of the NMR parameters. Widely scattered nuclear shieldings were observed for the Dunning polarized-valence basis set, which provides irregular convergence. We show that the use of Dunning core-valence or Jensen basis sets effectively reduces the scatter of theoretical NMR results and leads to their exponential-like convergence to CBS. We also assessed the effect of vibrational, temperature, and relativistic corrections on the predicted shieldings. For systems with single bonds, all corrections are relatively small, amounting to less than 4% of the CCSD(T)/CBS value. Vibrational and temperature corrections were less reliable for H3PO and HSiCH due to the high anharmonicity of the molecules. An abnormally high relativistic correction was observed for phosphorus in PN, reaching ~20% of the CCSD(T)/CBS value, while the correction was less than 7% for other tested molecules.
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Affiliation(s)
- Kacper Rzepiela
- Faculty of Chemistry, University of Opole, 48 Oleska Street, 46-052 Opole, Poland
| | - Jakub Kaminský
- Institute of Organic Chemistry and Biochemistry of the CAS, Flemingovo nám. 2, 166 10 Prague, Czech Republic
| | - Aneta Buczek
- Faculty of Chemistry, University of Opole, 48 Oleska Street, 46-052 Opole, Poland
| | - Małgorzata A. Broda
- Faculty of Chemistry, University of Opole, 48 Oleska Street, 46-052 Opole, Poland
| | - Teobald Kupka
- Faculty of Chemistry, University of Opole, 48 Oleska Street, 46-052 Opole, Poland
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21
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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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22
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Zhang T, Zhang C, Ma X, Quan H. Substitution Effects on the Reactivity and Thermostability of Five-Membered Ring Fluorides. ACS OMEGA 2022; 7:25476-25490. [PMID: 35910138 PMCID: PMC9330182 DOI: 10.1021/acsomega.2c02461] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Recently, five-membered ring fluorides (c-C5Fs) have been significantly desirable in green chlorofluorocarbon substitutes due to their practically flexible application in various fields and environmental friendliness. Detailed knowledge regarding different substitution effects on their environmental properties and thermal stability is very limited due to their high-cost experiments. Here, comprehensive density functional theory and ab initio molecular dynamics calculations were performed to explore the relative electrophilic and nucleophilic reactivity and thermostability of c-C5F chemicals. The electronic properties induced by substitution effects of c-C5Fs were first explored. The environmental friendliness of c-C5Fs including 1,1,2,2,3,3-hexafluorocyclopentane (F6A), 1,1,2,2,3,3,4-heptafluorocyclopentane (F7A), cis-1,1,2,2,3,3,4,5-octafluorocyclopentane (F8A), 3,3,4,4,5,5-hexafluorocyclopentene (F6E), 1,3,3,4,4,5,5-heptafluorocyclopentene (F7E), octafluorocyclopentene (F8E), 1-chloro-3,3,4,4,5,5-hexafluorocyclopent-1-ene (F6-1), and 1-chloro-2,3,3,4,4,5,5-heptafluorocyclopent-1-ene (F7-1) was validly confirmed. Besides, their thermal stabilities at 600 K temperature were concluded due to their flexible carbon skeletons, where both in-plane stability and slight aromaticity of F6E were in peculiar found to contribute substantially. We also would like to stress the future application of F6-1 due to its significant out-plane stability. This study may pave the way for the development of chlorofluorocarbon substitutes.
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Affiliation(s)
- Tongyun Zhang
- School
of Chemical Engineering, Northwest University, 229 Taibai North Road, Xi’an, Shaanxi 710069, China
| | - Chengping Zhang
- School
of Chemistry and Chemical Engineering, Beijing
Institute of Technology, 5 South Zhongguancun Street, Beijing 100081, China
| | - Xiaoxun Ma
- School
of Chemical Engineering, Northwest University, 229 Taibai North Road, Xi’an, Shaanxi 710069, China
| | - Hengdao Quan
- School
of Chemistry and Chemical Engineering, Beijing
Institute of Technology, 5 South Zhongguancun Street, Beijing 100081, China
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23
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Bernatowicz P, Szymanski S. Molecular Zeeman interactions in NMR spectra of methyl groups. J Chem Phys 2022; 157:074312. [DOI: 10.1063/5.0107637] [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
Methyl groups in organic solids generally behave as uniaxial quantum rotors. The existing NMR theory appears to be complete, capable of describing even the finest details of the temperature-dependent spectra of such objects. However, the once re-ported temperature effects in the carbon spectra of the 13C-labeled methyl group in a single crystal of acetylsalicylic acid have still not been explained. As the temperature decreases, in the quartet corresponding to the rapid motional averaging regime, the inner lines first begin to broaden but then narrow again, so that at 6 K a pattern similar to that at room temperature was observed. In the present work, these puzzling effects are explained quantitatively by invoking the molecular Zeeman (MZ) interaction. Like the spin-rotation (SR) interaction long known to occur in methyl groups, it engages the magnetic moments generated by their torsional motions. How-ever, it has not been considered in NMR spectroscopy until now. This is a surprising situation because in the magnetic fields currently used in NMR spectroscopy, the MZ interaction is orders of magnitude stronger than the (magnetic field independent) SR effects.
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24
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Palivec V, Pohl R, Kaminský J, Martinez-Seara H. Efficiently Computing NMR 1H and 13C Chemical Shifts of Saccharides in Aqueous Environment. J Chem Theory Comput 2022; 18:4373-4386. [PMID: 35687789 DOI: 10.1021/acs.jctc.2c00127] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Determining the structure of saccharides in their native environment is crucial to understanding their function and more accurately targeting their utilization. Nuclear magnetic resonance observables such as the nuclear Overhauser effect or spin-spin coupling constants are routinely utilized to study saccharides in their native water environment. However, while highly sensitive to the local environment, chemical shifts are mostly overlooked, despite being commonly measured for compounds identification. Although chemical shifts carry considerable structural information, their direct association with structure is notoriously difficult. This is mostly due to the similarity in the chemical nature of most saccharides causing similar physicochemical environments close to sugar C and H atoms, resulting in comparable chemical shifts. The rise of computational power allows one to compute reliable chemical shifts and use them to determine atomistic details of these sugars in solution. However, any prediction is severely limited by the computational protocol used and its accuracy. In this work, we studied a set of 31 saccharides on which we evaluated various computational protocols to calculate the total number of 375 1H and 327 13C chemical shifts of sugars in an aqueous environment. Our study proposes two cost-effective protocols for simulating 1H and 13C chemical shifts that we recommend for further use. These protocols can help with the interpretation of experimental spectra, but we also show that they are also capable of structure prediction independently. This is possible because of the low mean absolute deviations of calculated shifts from the experiment (0.06 ppm for 1H and 1.09 ppm for 13C). We explore different solvation methods, basis sets, and optimization schemes to reach such accuracy. A correct sampling of the conformation phase space of flexible sugar molecules is also key to obtaining accurately converged theoretical chemical shifts. The linear regression method was applied to convert the calculated isotropic nuclear magnetic shielding constants to simulated chemical shifts comparable with the experiment. The achieved level of accuracy can help in utilizing chemical shifts for elucidating the 3D atomistic structure of saccharides in aqueous solutions. All linear regression parameters obtained on our extensive set of sugars for all the tested protocols can be reutilized in future works.
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Affiliation(s)
- Vladimír Palivec
- Institute of Organic Chemistry and Biochemistry, Czech Academy of Sciences, Flemingovo námĕstí 542/2, Prague 6 CZ166 10, Czech Republic
| | - Radek Pohl
- Institute of Organic Chemistry and Biochemistry, Czech Academy of Sciences, Flemingovo námĕstí 542/2, Prague 6 CZ166 10, Czech Republic
| | - Jakub Kaminský
- Institute of Organic Chemistry and Biochemistry, Czech Academy of Sciences, Flemingovo námĕstí 542/2, Prague 6 CZ166 10, Czech Republic
| | - Hector Martinez-Seara
- Institute of Organic Chemistry and Biochemistry, Czech Academy of Sciences, Flemingovo námĕstí 542/2, Prague 6 CZ166 10, Czech Republic
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25
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Yan W, Xu X. Accurate Prediction of Nuclear Magnetic Resonance Parameters via the XYG3 Type of Doubly Hybrid Density Functionals. J Chem Theory Comput 2022; 18:2931-2946. [PMID: 35467852 DOI: 10.1021/acs.jctc.2c00055] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful and versatile tools in elucidating molecular structures. To eliminate ambiguities of experimental assignments, accurate calculations of NMR spectra are of great importance. Here, a method for theoretical evaluation of the NMR shielding constants by analytic derivatives using gauge including atomic orbitals (GIAO) has been implemented for the XYG3 type of doubly hybrid density functionals (xDH), namely, the GIAO-xDH method. Benchmark calculations on shielding constants and chemical shifts demonstrate the remarkable accuracy of the GIAO-xDH method, compared to the accurate CCSD(T) references. It is shown here that the XYGJ-OS functional is able to give a mean absolute deviation (MAD) of ∼3.0 ppm in the calculated shielding constants for 13C, 15N, 17O, 19F, while both XYGJ-OS and xDH-PBE0 functionals are able to provide a satisfactory estimation of chemical shifts with MADs of ∼0.03 and 1.0 ppm for 1H and 13C, respectively. The basis set influence upon the method has been examined and a computational scheme considering both accuracy and efficiency has been proposed and tested to predict the experimental 13C chemical shifts of five medium-sized natural product molecules, yielding a MAD of ∼1.0 ppm, which demonstrates the practical feasibility of the GIAO-xDH method.
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Affiliation(s)
- Wenjie Yan
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai, 200433, China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai, 200433, China
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Imamura K, Higashi M, Kobayashi Y, Kageyama H, Sato H. Chemical Shift of Solvated Hydride Ion: Comparative Study with Solvated Fluoride Ion. J Phys Chem B 2022; 126:3090-3098. [DOI: 10.1021/acs.jpcb.2c00326] [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)
- Kosuke Imamura
- Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan
| | - Masahiro Higashi
- Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan
- Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyoto 615-8520, Japan
| | - Yoji Kobayashi
- King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia
| | - Hiroshi Kageyama
- Department of Energy & Hydrocarbon Chemistry, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan
| | - Hirofumi Sato
- Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan
- Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyoto 615-8520, Japan
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan
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27
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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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Franzke YJ, Yu JM. Quasi-Relativistic Calculation of EPR g Tensors with Derivatives of the Decoupling Transformation, Gauge-Including Atomic Orbitals, and Magnetic Balance. J Chem Theory Comput 2022; 18:2246-2266. [PMID: 35354319 DOI: 10.1021/acs.jctc.1c01175] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
We present an exact two-component (X2C) ansatz for the EPR g tensor using gauge-including atomic orbitals (GIAOs) and a magnetically balanced basis set expansion. In contrast to previous X2C and four-component relativistic ansätze for the g tensor, this implementation results in a gauge-origin-invariant formalism. Furthermore, the derivatives of the relativistic decoupling matrix are incorporated to form the complete analytical derivative of the X2C Hamiltonian. To reduce the associated computational costs, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The quasi-relativistic X2C and DLU-X2C Hamiltonians accurately reproduce the results of the parent four-component relativistic theory when accounting for two-electron picture-change effects with the modified screened nuclear spin-orbit approximation in the respective one-electron integrals and integral derivatives. According to our benchmark studies, the uncontracted Dyall and segmented-contracted Karlsruhe x2c-type basis sets perform well when compared to large even-tempered basis sets. Moreover, (range-separated) hybrid density functional approximations such as LC-ωPBE and ωB97X-D are needed to match the experimental findings. The impact of the GIAOs depends on the distribution of the spin density, and their use may change the Δg shifts by 10-50% as shown for [(C5Me5)2Y(μ-S)2Mo(μ-S)2Y(C5Me5)2]-. Routine calculations of large molecules are possible with widely available and comparably low-cost hardware as demonstrated for [Pt(C6Cl5)4]- with 3003 basis functions and three spin-(1/2) La(II) and Lu(II) compounds, for which we observe good agreement with the experimental findings.
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Affiliation(s)
- Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, 35032 Marburg, Germany
| | - Jason M Yu
- Department of Chemistry, University of California─Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
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Bharadwaj VS, Westawker LP, Crowley MF. Towards Elucidating Structure–Spectra Relationships in Rhamnogalacturonan II: Computational Protocols for Accurate 13C and 1H Shifts for Apiose and Its Borate Esters. Front Mol Biosci 2022; 8:756219. [PMID: 35141275 PMCID: PMC8820409 DOI: 10.3389/fmolb.2021.756219] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2021] [Accepted: 11/24/2021] [Indexed: 11/13/2022] Open
Abstract
Apiose is a naturally occurring, uncommon branched-chain pentose found in plant cell walls as part of the complex polysaccharide Rhamnogalacturonan II (RG-II). The structural elucidation of the three-dimensional structure of RG-II by nuclear magnetic resonance (NMR) spectroscopy is significantly complicated by the ability of apiose to cross-link via borate ester linkages to form RG-II dimers. Here, we developed a computational approach to gain insight into the structure–spectra relationships of apio–borate complexes in an effort to complement experimental assignments of NMR signals in RG-II. Our protocol involved structure optimizations using density functional theory (DFT) followed by isotropic magnetic shielding constant calculations using the gauge-invariant atomic orbital (GIAO) approach to predict chemical shifts. We evaluated the accuracy of 23 different functional–basis set (FBS) combinations with and without implicit solvation for predicting the experimental 1H and 13C shifts of a methyl apioside and its three borate derivatives. The computed NMR predictions were evaluated on the basis of the overall shift accuracy, relative shift ordering, and the ability to distinguish between dimers and monomers. We demonstrate that the consideration of implicit solvation during geometry optimizations in addition to the magnetic shielding constant calculations greatly increases the accuracy of NMR chemical shift predictions and can correctly reproduce the ordering of the 13C shifts and yield predictions that are, on average, within 1.50 ppm for 13C and 0.12 ppm for 1H shifts for apio–borate compounds.
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Crittenden DL. A new double-reference correction scheme for accurate and efficient computation of NMR chemical shieldings. Phys Chem Chem Phys 2022; 24:27055-27063. [DOI: 10.1039/d2cp03992c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Abstract
Our novel correction procedure yields high-accuracy DFT predictions of absolute NMR shieldings and enables outliers due to relativistic effects or manifestly inadequate modelling of electron correlation to be easily and unambiguously identified.
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Affiliation(s)
- Deborah L. Crittenden
- School of Physical and Chemical Sciences, University of Canterbury, Christchurch, 8140, New Zealand
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Makulski W. Absolute 13C Nuclear Magnetic Shielding of Simple Isolated Molecules from Gas Phase Measurements. Phys Chem Chem Phys 2022; 24:8950-8961. [DOI: 10.1039/d2cp00231k] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The new experimental value of 13C absolute shielding constant in an isolated 13CO molecule was evaluated from the 13C and 3He gas phase NMR measurements performed for 3He/13CO mixtures. The...
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32
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de Wijs GA, Kresse G, Havenith RWA, Marsman M. Comparing GIPAW with numerically exact chemical shieldings: The role of two-center contributions to the induced current. J Chem Phys 2021; 155:234101. [PMID: 34937373 DOI: 10.1063/5.0069637] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In this study, we benchmark density functional theory gauge-including projector-augmented-wave (GIPAW) chemical shieldings against molecular shieldings for which basis set completeness has been achieved [Jensen et al., Phys. Chem. Chem. Phys. 18, 21145 (2016)]. We demonstrate the importance of two-center corrections for GIPAW hydrogen shieldings. For the other nuclei studied, standard GIPAW is sufficiently accurate. We find that GIPAW can be pushed to closely approach the basis set limit. The only source of small inaccuracies lies in the contribution to the shielding that is caused by surface currents, which we estimate comparing GIPAW susceptibilities to converged molecular magnetizabilities.
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Affiliation(s)
- Gilles A de Wijs
- Radboud University, Institute for Molecules and Materials, Heyendaalseweg 135, NL-6525 AJ Nijmegen, The Netherlands
| | - Georg Kresse
- University of Vienna, Faculty of Physics and Center for Computational Materials Science, Kolingasse 14-16, A-1090 Vienna, Austria
| | - Remco W A Havenith
- Stratingh Institute for Chemistry, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, NL-9747 AG Groningen, The Netherlands
| | - Martijn Marsman
- University of Vienna, Faculty of Physics and Center for Computational Materials Science, Kolingasse 14-16, A-1090 Vienna, Austria
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Franzke YJ, Yu JM. Hyperfine Coupling Constants in Local Exact Two-Component Theory. J Chem Theory Comput 2021; 18:323-343. [PMID: 34928142 DOI: 10.1021/acs.jctc.1c01027] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We present a highly efficient implementation of the electron-nucleus hyperfine coupling matrix within the one-electron exact two-component (X2C) theory. The complete derivative of the X2C Hamiltonian is formed, that is, the derivatives of the unitary decoupling transformation are considered. This requires the solution of the response and Sylvester equations, consequently increasing the computational costs. Therefore, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The finite nucleus model is employed for both the scalar potential and the vector potential. Two-electron picture-change effects are modeled with the (modified) screened nuclear spin-orbit approach. Our implementation is fully integral direct and OpenMP-parallelized. An extensive benchmark study regarding the Hamiltonian, the basis set, and the density functional approximation is carried out for a set of 12-17 transition-metal compounds. The error introduced by DLU is negligible, and the DLU-X2C Hamiltonian accurately reproduces its four-component "fully" relativistic parent results. Functionals with a large amount of Hartree-Fock exchange such as CAM-QTP-02 and ωB97X-D are generally favorable. The pure density functional r2SCAN performs remarkably and even outperforms the common hybrid functionals TPSSh and CAM-B3LYP. Fully uncontracted basis sets or contracted quadruple-ζ bases are required for accurate results. The capability of our implementation is demonstrated for [Pt(C6Cl5)4]- with more than 4700 primitive basis functions and four rare-earth single-molecule magnets: [La(OAr*)3]-, [Lu(NR2)3]-, [Lu(OAr*)3]-, and [TbPc2]-. Here, the results with the spin-orbit DLU-X2C Hamiltonian are in an excellent agreement with the experimental findings of all Pt, La, Lu, and Tb molecules.
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Affiliation(s)
- Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany
| | - Jason M Yu
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
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Schattenberg CJ, Kaupp M. Extended Benchmark Set of Main-Group Nuclear Shielding Constants and NMR Chemical Shifts and Its Use to Evaluate Modern DFT Methods. J Chem Theory Comput 2021; 17:7602-7621. [PMID: 34797677 DOI: 10.1021/acs.jctc.1c00919] [Citation(s) in RCA: 34] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
An extended theoretical benchmark set, NS372, for light main-group nuclear shieldings and NMR shifts has been constructed based on high-level GIAO-CCSD(T)/pcSseg-3//CCSD(T)/cc-pVQZ reference data. After removal of the large static-correlation cases O3, F3-, and BH from the statistical evaluations for the 17O, 19F, and 11B subsets, the benchmark comprises overall 372 shielding values in 117 molecules with a wide range of electronic-structure situations, containing 124 1H, 14 11B, 93 13C, 43 15N, 31 17O, 47 19F, 14 31P, and 6 33S shielding constants. The CCSD(T)/pcSseg-3 data are shown to be close to the basis-set and method limit and thus provide an excellent benchmark to evaluate more approximate methods, such as density functional approaches. This dataset has been used to evaluate Hartree-Fock (HF) and MP2, and a wide range of exchange-correlation functionals from local density approximation (LDA) to generalized gradient approximations (GGAs) and meta-GGAs (focusing on their current-density functional implementations), as well as global hybrid, range-separated hybrid, local hybrid, and double-hybrid functionals. Starting with absolute shielding constants, the DSD-PBEP86 double hybrid is confirmed to provide the highest accuracy, with an aggregate relative mean absolute error (rel. MAE) of only 0.9%, followed by MP2 (1.1%). MP2 and double hybrids only show larger errors for a few systems with the largest static-correlation effects. The double-hybrid B2GP-PLYP, the two local hybrids cLH12ct-SsirPW92 and cLH12ct-SsifPW92, and the current-density functional meta-GGA cB97M-V follow closely behind (all 1.5%), as do some further functionals, cLH20t and cMN15-L (both 1.6%), as well as B2PLYP and KT3 (both 2.0%). Functionals on the lower rungs of the usual ladder offer the advantage of lower computational cost and access to larger molecules. Closer examination also reveals the best-performing methods for individual nuclei in the test set. Different ways of treating τ-dependent functionals are evaluated. When moving from absolute shielding constants to chemical shifts, some of the methods can benefit from systematic error compensation, and the overall error range somewhat narrows. Further methods now achieve the 2% threshold of relative MAEs, including functionals based on TPSS (TPSSh, cmPSTS).
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Affiliation(s)
- Caspar Jonas Schattenberg
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Martin Kaupp
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
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35
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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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36
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de Oliveira MT, Alves JMA, Braga AAC, Wilson DJD, Barboza CA. Do Double-Hybrid Exchange-Correlation Functionals Provide Accurate Chemical Shifts? A Benchmark Assessment for Proton NMR. J Chem Theory Comput 2021; 17:6876-6885. [PMID: 34637284 DOI: 10.1021/acs.jctc.1c00604] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
A benchmark density functional theory (DFT) study of 1H NMR chemical shifts for data sets comprising 200 chemical shifts, including complex natural products, has been carried out to assess the performance of DFT methods. Two new benchmark data sets, NMRH33 and NMRH148, have been established. The meta-GGA revTPSS performs remarkably well against the NMRH33 benchmark set (mean absolute deviation (MAD), 0.10 ppm; maximum deviation (max), 0.26 ppm) with the smallest MAD of all evaluated functionals. The best-performing double-hybrid density functional (DHDF), revDSD-BLYP (MAD, 0.16 ppm; max, 0.35 ppm), performs similarly to hybrid-GGA methods (e.g., mPW1PW91/6-311G(d) (MAD, 0.15 ppm; max, 0.36 ppm)), but at a considerably higher computational cost. The results indicate that currently available double-hybrid DFT methods offer no benefit over GGA (including hybrid and meta) functionals in the calculation of 1H NMR chemical shifts.
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Affiliation(s)
- Marcelo T de Oliveira
- Department of Chemistry and Physics, La Trobe Institute of Molecular Sciences, La Trobe University, Melbourne, Victoria 3086, Australia.,Chemistry Institute of São Carlos, University of São Paulo, Avenida Trabalhador São Carlense 400, 13566-590 São Carlos, São Paulo, Brazil
| | - Júlia M A Alves
- Chemistry Institute of São Carlos, University of São Paulo, Avenida Trabalhador São Carlense 400, 13566-590 São Carlos, São Paulo, Brazil
| | - Ataualpa A C Braga
- Instituto de Química, Universidade de São Paulo, Avenida Prof. Lineu Prestes 748, 05508-000 São Paulo, Brazil
| | - David J D Wilson
- Department of Chemistry and Physics, La Trobe Institute of Molecular Sciences, La Trobe University, Melbourne, Victoria 3086, Australia
| | - Cristina A Barboza
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, Warsaw 02-668, Poland
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Wong ZC, Ungur L. Exploring vibronic coupling in the benzene radical cation and anion with different levels of the GW approximation. Phys Chem Chem Phys 2021; 23:19054-19070. [PMID: 34612443 DOI: 10.1039/d1cp02795f] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The linear vibronic coupling constants of the benzene radical cation and anion have been obtained with different levels of the GW approximation, including G0W0, eigenvalue self-consistent GW, and quasiparticle self-consistent GW, as well as DFT with the following exchange-correlation functionals: BLYP, B3LYP, CAM-B3LYP, tuned CAM-B3LYP, and an IP-tuned CAM-B3LYP functional. The vibronic coupling constants were calculated numerically using the gradients of the eigenvalues of the degenerate HOMOs and LUMOs of the neutral benzene molecule for DFT, while the numerical gradients of the quasiparticle energies were used in the case of GW. The results were evaluated against those of high level wave function methods in the literature, and the approximate self-consistent GW methods and G0W0 with long-range corrected functionals were found to yield the best results on the whole.
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Affiliation(s)
- Zi Cheng Wong
- Department of Chemistry, National University of Singapore, Block S8 Level 3, 3 Science Drive 3, 117543, Singapore.
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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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Zarycz MNC, Schiel MA, Angelina E, Enriz RD. Covalence and π-electron delocalization influence on hydrogen bonds in proton transfer process of o-hydroxy aryl Schiff bases: A combined NMR and QTAIM analysis. J Chem Phys 2021; 155:054307. [PMID: 34364326 DOI: 10.1063/5.0058422] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Within the framework of the density functional theory approach, we studied the relationship between the chemical nature of intramolecular hydrogen bonds (HBs) and nuclear magnetic resonance (NMR) parameters, J-couplings and 1H-chemical shifts [δ(1H)], of the atoms involved in such bonds in o-hydroxyaryl Schiff bases during the proton transfer process. For the first time, the shape of the dependence of the degree of covalence in HBs on 1J(N-H), 1J(O-H), 2hJ(O-N), and δ(1H) during the proton transfer process in o-hydroxyaryl Schiff bases was analyzed. Parameters obtained from Bader's theory of atoms in molecules were used to assess the dependence of covalent character in HBs with both the NMR properties. The influence of π-electronic delocalization on 2hJ(N-O) under the proton transfer process was investigated. 2hJ(O-N) in a Mannich base was also studied in order to compare the results with an unsaturated system. In addition, substituent effects on the phenolic ring were investigated. Our results indicate that the covalent character of HBs on both sides of the transition state undergoes a smooth exponential increase as the δ(1H) moves downfield. The degree of covalence of the N⋯H (O⋯H) bond increases linearly as 1J(N-H) (1J(O-H)) becomes more negative, even after reaching the transition state. Non-vanishing values of spin dipolar (SD) and paramagnetic spin orbital terms of 2hJ(O-N) show that π-electronic delocalization has a non-negligible effect on tautomeric equilibrium and gives evidence of the presence of the resonance assisted HB.Variation of the SD term of 2hJ(O-N) follows a similar pattern as the change in the para-delocalization aromaticity index of the chelate ring.
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Affiliation(s)
- M Natalia C Zarycz
- Facultad de Química, Bioquímica y Farmacia, Universidad Nacional de San Luis; Instituto Multidisciplinario de Investigaciones Biológicas (IMIBIO-SL). CONICET, Ejército de los Andes 950, 5700 San Luis, Argentina
| | - M Ayelén Schiel
- Facultad de Química, Bioquímica y Farmacia, Universidad Nacional de San Luis; Instituto Multidisciplinario de Investigaciones Biológicas (IMIBIO-SL). CONICET, Ejército de los Andes 950, 5700 San Luis, Argentina
| | - Emilio Angelina
- Laboratorio de Estructura Molecular y Propiedades, Facultad de Ciencias Exactas y Naturales y Agrimensura, Universidad Nacional del Nordeste; Instituto de Química Básica y Aplicada (IQUIBA-NEA). CONICET, Avda. Libertad 5460, 3400 Corrientes, Argentina
| | - Ricardo D Enriz
- Facultad de Química, Bioquímica y Farmacia, Universidad Nacional de San Luis; Instituto Multidisciplinario de Investigaciones Biológicas (IMIBIO-SL). CONICET, Ejército de los Andes 950, 5700 San Luis, Argentina
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41
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Borges R, Colby SM, Das S, Edison AS, Fiehn O, Kind T, Lee J, Merrill AT, Merz KM, Metz TO, Nunez JR, Tantillo DJ, Wang LP, Wang S, Renslow RS. Quantum Chemistry Calculations for Metabolomics. Chem Rev 2021; 121:5633-5670. [PMID: 33979149 PMCID: PMC8161423 DOI: 10.1021/acs.chemrev.0c00901] [Citation(s) in RCA: 40] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2020] [Indexed: 02/07/2023]
Abstract
A primary goal of metabolomics studies is to fully characterize the small-molecule composition of complex biological and environmental samples. However, despite advances in analytical technologies over the past two decades, the majority of small molecules in complex samples are not readily identifiable due to the immense structural and chemical diversity present within the metabolome. Current gold-standard identification methods rely on reference libraries built using authentic chemical materials ("standards"), which are not available for most molecules. Computational quantum chemistry methods, which can be used to calculate chemical properties that are then measured by analytical platforms, offer an alternative route for building reference libraries, i.e., in silico libraries for "standards-free" identification. In this review, we cover the major roadblocks currently facing metabolomics and discuss applications where quantum chemistry calculations offer a solution. Several successful examples for nuclear magnetic resonance spectroscopy, ion mobility spectrometry, infrared spectroscopy, and mass spectrometry methods are reviewed. Finally, we consider current best practices, sources of error, and provide an outlook for quantum chemistry calculations in metabolomics studies. We expect this review will inspire researchers in the field of small-molecule identification to accelerate adoption of in silico methods for generation of reference libraries and to add quantum chemistry calculations as another tool at their disposal to characterize complex samples.
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Affiliation(s)
- Ricardo
M. Borges
- Walter
Mors Institute of Research on Natural Products, Federal University of Rio de Janeiro, Rio de Janeiro 21941-901, Brazil
| | - Sean M. Colby
- Biological
Science Division, Pacific Northwest National
Laboratory, Richland, Washington 99352, United States
| | - Susanta Das
- Department
of Chemistry, Michigan State University, East Lansing, Michigan 48824, United States
| | - Arthur S. Edison
- Departments
of Genetics and Biochemistry and Molecular Biology, Complex Carbohydrate
Research Center and Institute of Bioinformatics, University of Georgia, Athens, Georgia 30602, United States
| | - Oliver Fiehn
- West
Coast Metabolomics Center for Compound Identification, UC Davis Genome
Center, University of California, Davis, California 95616, United States
| | - Tobias Kind
- West
Coast Metabolomics Center for Compound Identification, UC Davis Genome
Center, University of California, Davis, California 95616, United States
| | - Jesi Lee
- West
Coast Metabolomics Center for Compound Identification, UC Davis Genome
Center, University of California, Davis, California 95616, United States
- Department
of Chemistry, University of California, Davis, California 95616, United States
| | - Amy T. Merrill
- Department
of Chemistry, University of California, Davis, California 95616, United States
| | - Kenneth M. Merz
- Department
of Chemistry, Michigan State University, East Lansing, Michigan 48824, United States
| | - Thomas O. Metz
- Biological
Science Division, Pacific Northwest National
Laboratory, Richland, Washington 99352, United States
| | - Jamie R. Nunez
- Biological
Science Division, Pacific Northwest National
Laboratory, Richland, Washington 99352, United States
| | - Dean J. Tantillo
- Department
of Chemistry, University of California, Davis, California 95616, United States
| | - Lee-Ping Wang
- Department
of Chemistry, University of California, Davis, California 95616, United States
| | - Shunyang Wang
- West
Coast Metabolomics Center for Compound Identification, UC Davis Genome
Center, University of California, Davis, California 95616, United States
- Department
of Chemistry, University of California, Davis, California 95616, United States
| | - Ryan S. Renslow
- Biological
Science Division, Pacific Northwest National
Laboratory, Richland, Washington 99352, United States
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42
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Holzer C, Franzke YJ, Kehry M. Assessing the Accuracy of Local Hybrid Density Functional Approximations for Molecular Response Properties. J Chem Theory Comput 2021; 17:2928-2947. [PMID: 33914504 DOI: 10.1021/acs.jctc.1c00203] [Citation(s) in RCA: 39] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A comprehensive overview of the performance of local hybrid functionals for molecular properties like excited states, ionization potentials within the GW framework, polarizabilities, magnetizabilities, NMR chemical shifts, and NMR spin-spin coupling constants is presented. We apply the generalization of the kinetic energy, τ, with the paramagnetic current density to all magnetic properties and the excitation energies from time-dependent density functional theory. This restores gauge invariance for these properties. Different ansätze for local mixing functions such as the iso-orbital indicator, the correlation length, the Görling-Levy second-order limit, and the spin polarization are compared. For the latter, we propose a modified version of the corresponding hyper-generalized gradient approximation functional of Perdew, Staroverov, Tao, and Scuseria (PSTS) [Phys. Rev. A 2008, 78, 052513] to allow for a numerically stable evaluation of the exchange-correlation kernel and hyperkernel. The PSTS functional leads to a very consistent improvement compared to the related TPSSh functional. It is further shown that the "best" choice of the local mixing function depends on the studied property and molecular class. While functionals based on the iso-orbital indicator lead to rather accurate excitation energies and ionization energies, the results are less impressive for NMR properties, for which a considerable dependence on the considered molecular test set and nuclei is observed. Johnson's local hybrid functional based on the correlation length yields remarkable results for NMR shifts of compounds featuring heavy elements and also for the excitation energies of organic compounds.
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Affiliation(s)
- Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
| | - Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, 35032 Marburg, Germany.,Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
| | - Max Kehry
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
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43
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Rusakova IL, Rusakov YY. Quantum chemical calculations of 77 Se and 125 Te nuclear magnetic resonance spectral parameters and their structural applications. MAGNETIC RESONANCE IN CHEMISTRY : MRC 2021; 59:359-407. [PMID: 33095923 DOI: 10.1002/mrc.5111] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2020] [Revised: 09/01/2020] [Accepted: 10/07/2020] [Indexed: 06/11/2023]
Abstract
An accurate quantum chemical (QC) modeling of 77 Se and 125 Te nuclear magnetic resonance (NMR) spectra is deeply involved in the NMR structural assignment for selenium and tellurium compounds that are of utmost importance both in organic and inorganic chemistry nowadays due to their huge application potential in many fields, like biology, medicine, and metallurgy. The main interest of this review is focused on the progress in QC computations of 77 Se and 125 Te NMR chemical shifts and indirect spin-spin coupling constants involving these nuclei. Different computational methodologies that have been used to simulate the NMR spectra of selenium and tellurium compounds since the middle of the 1990s are discussed with a strong emphasis on their accuracy. A special accent is placed on the calculations resorting to the relativistic methodologies, because taking into account the relativistic effects appreciably influences the precision of NMR calculations of selenium and, especially, tellurium compounds. Stereochemical applications of quantum chemical calculations of 77 Se and 125 Te NMR parameters are discussed so as to exemplify the importance of integrated approach of experimental and computational NMR techniques.
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Affiliation(s)
- Irina L Rusakova
- A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russian Federation
| | - Yuriy Yu Rusakov
- A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russian Federation
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44
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Schattenberg CJ, Kaupp M. Implementation and Validation of Local Hybrid Functionals with Calibrated Exchange-Energy Densities for Nuclear Shielding Constants. J Phys Chem A 2021; 125:2697-2707. [PMID: 33730855 DOI: 10.1021/acs.jpca.1c01135] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A recently reported coupled-perturbed Kohn-Sham implementation to compute nuclear shielding constants with gauge-including atomic orbitals and local hybrid functionals has been extended to cover higher derivatives of the density in the local mixing function (LMF) of the local hybrid as well as the calibration function (CF) needed to deal with the ambiguity of exchange-energy densities. This allowed the first evaluation of state-of-the-art local hybrids with "calibrated" exchange-energy densities for nuclear shieldings. Compared to previously evaluated simpler local hybrids without a CF, appreciable improvements are found for proton shieldings. Furthermore, the recent LH20t functional is still competitive with the outstanding performance of the uncalibrated LH12ct-SsirSVWN and LH12ct-SsifSVWN LHs for heavier nuclei, suggesting that LH20t is possibly the most robust choice of any rung-four functional for computing the nuclear shieldings of main-group nuclei so far. Interestingly, the presence of a CF in the functional significantly reduces the number of artifacts introduced by the widely used Maximoff-Scuseria framework to treat the local kinetic energy τ. The latter occurs in so-called t-LMFs used in many of the present local hybrids. In any case, the use of Dobson's current-density functional framework is also recommended with more advanced calibrated τ-dependent local hybrid functionals.
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Affiliation(s)
- Caspar Jonas Schattenberg
- Theoretische Chemie/Quantenchemie, Institut für Chemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Martin Kaupp
- Theoretische Chemie/Quantenchemie, Institut für Chemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
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45
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Lehtola S, Dimitrova M, Fliegl H, Sundholm D. Benchmarking Magnetizabilities with Recent Density Functionals. J Chem Theory Comput 2021; 17:1457-1468. [PMID: 33599491 PMCID: PMC8023670 DOI: 10.1021/acs.jctc.0c01190] [Citation(s) in RCA: 36] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2020] [Indexed: 12/21/2022]
Abstract
We have assessed the accuracy of the magnetic properties of a set of 51 density functional approximations, including both recently published and already established functionals. The accuracy assessment considers a series of 27 small molecules and is based on comparing the predicted magnetizabilities to literature reference values calculated using coupled-cluster theory with full singles and doubles and perturbative triples [CCSD(T)] employing large basis sets. The most accurate magnetizabilities, defined as the smallest mean absolute error, are obtained with the BHandHLYP functional. Three of the six studied Berkeley functionals and the three range-separated Florida functionals also yield accurate magnetizabilities. Also, some older functionals like CAM-B3LYP, KT1, BHLYP (BHandH), B3LYP, and PBE0 perform rather well. In contrast, unsatisfactory performance is generally obtained with Minnesota functionals, which are therefore not recommended for calculations of magnetically induced current density susceptibilities and related magnetic properties such as magnetizabilities and nuclear magnetic shieldings. We also demonstrate that magnetizabilities can be calculated by numerical integration of magnetizability density; we have implemented this approach as a new feature in the gauge-including magnetically induced current (GIMIC) method. Magnetizabilities can be calculated from magnetically induced current density susceptibilities within this approach even when analytical approaches for magnetizabilities as the second derivative of the energy have not been implemented. The magnetizability density can also be visualized, providing additional information that is not otherwise easily accessible on the spatial origin of magnetizabilities.
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Affiliation(s)
- Susi Lehtola
- Department
of Chemistry, University of Helsinki, P.O. Box 55, A.I. Virtanens plats
1, FI-00014 University
of Helsinki, Finland
- Molecular
Sciences Software Institute, Blacksburg, Virginia 24061, United States
| | - Maria Dimitrova
- Department
of Chemistry, University of Helsinki, P.O. Box 55, A.I. Virtanens plats
1, FI-00014 University
of Helsinki, Finland
| | - Heike Fliegl
- Institute
of Nanotechnology, KIT, Hermann-von-Helmholtz Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany
| | - Dage Sundholm
- Department
of Chemistry, University of Helsinki, P.O. Box 55, A.I. Virtanens plats
1, FI-00014 University
of Helsinki, Finland
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46
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Ryley MS, Withnall M, Irons TJP, Helgaker T, Teale AM. Robust All-Electron Optimization in Orbital-Free Density-Functional Theory Using the Trust-Region Image Method. J Phys Chem A 2021; 125:459-475. [PMID: 33356245 DOI: 10.1021/acs.jpca.0c09502] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present a Gaussian-basis implementation of orbital-free density-functional theory (OF-DFT) in which the trust-region image method (TRIM) is used for optimization. This second-order optimization scheme has been constructed to provide benchmark all-electron results with very tight convergence of the particle-number constraint, associated chemical potential, and electron density. It is demonstrated that, by preserving the saddle-point nature of the optimization and simultaneously optimizing the density and chemical potential, an order of magnitude reduction in the number of iterations required for convergence is obtained. The approach is compared and contrasted with a new implementation of the nested optimization scheme put forward by Chan, Cohen, and Handy. Our implementation allows for semilocal kinetic-energy (and exchange-correlation) functionals to be handled self-consistently in all-electron calculations. The all-electron Gaussian-basis setting for these calculations will enable direct comparison with a wide range of standard high-accuracy quantum-chemical methods as well as with Kohn-Sham density-functional theory. We expect that the present implementation will provide a useful tool for analyzing the performance of approximate kinetic-energy functionals in finite systems.
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Affiliation(s)
- Matthew S Ryley
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, U.K
| | - Michael Withnall
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, U.K
| | - Tom J P Irons
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, U.K
| | - Trygve Helgaker
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Andrew M Teale
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, U.K.,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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47
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Valentine AJ, Geer AM, Taylor LJ, Teale AM, Wood KE, Williams HEL, Lewis W, Argent SP, McMaster J, Kays DL. Structural and electronic studies of substituted m-terphenyl lithium complexes. Dalton Trans 2021; 50:722-728. [DOI: 10.1039/d0dt03972a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Spectroscopic and computational investigation of the effects of para-substituted m-terphenyl lithium complexes reveals significant electronic differences at the metal centre.
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Affiliation(s)
| | - Ana M. Geer
- Departamento de Química Inorgánica
- Instituto de Síntesis Química y Catálisis Homogénea (ISQCH)
- CSIC
- Universidad de Zaragoza
- 50009 Zaragoza
| | | | - Andrew M. Teale
- School of Chemistry
- University of Nottingham
- University Park
- Nottingham
- UK
| | - Katherine E. Wood
- School of Chemistry
- University of Nottingham
- University Park
- Nottingham
- UK
| | - Huw E. L. Williams
- Centre for Biomolecular Sciences
- University of Nottingham
- University Park
- Nottingham
- UK
| | - William Lewis
- School of Chemistry
- The University of Sydney
- Sydney
- Australia
| | - Stephen P. Argent
- School of Chemistry
- University of Nottingham
- University Park
- Nottingham
- UK
| | - Jonathan McMaster
- School of Chemistry
- University of Nottingham
- University Park
- Nottingham
- UK
| | - Deborah L. Kays
- School of Chemistry
- University of Nottingham
- University Park
- Nottingham
- UK
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48
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Sethio D, Raggi G, Lindh R, Erdélyi M. Halogen Bond of Halonium Ions: Benchmarking DFT Methods for the Description of NMR Chemical Shifts. J Chem Theory Comput 2020; 16:7690-7701. [PMID: 33136388 PMCID: PMC7726912 DOI: 10.1021/acs.jctc.0c00860] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2020] [Indexed: 12/20/2022]
Abstract
Because of their anisotropic electron distribution and electron deficiency, halonium ions are unusually strong halogen-bond donors that form strong and directional three-center, four-electron halogen bonds. These halogen bonds have received considerable attention owing to their applicability in supramolecular and synthetic chemistry and have been intensely studied using spectroscopic and crystallographic techniques over the past decade. Their computational treatment faces different challenges to those of conventional weak and neutral halogen bonds. Literature studies have used a variety of wave functions and DFT functionals for prediction of their geometries and NMR chemical shifts, however, without any systematic evaluation of the accuracy of these methods being available. In order to provide guidance for future studies, we present the assessment of the accuracy of 12 common DFT functionals along with the Hartree-Fock (HF) and the second-order Møller-Plesset perturbation theory (MP2) methods, selected from an initial set of 36 prescreened functionals, for the prediction of 1H, 13C, and 15N NMR chemical shifts of [N-X-N]+ halogen-bond complexes, where X = F, Cl, Br, and I. Using a benchmark set of 14 complexes, providing 170 high-quality experimental chemical shifts, we show that the choice of the DFT functional is more important than that of the basis set. The M06 functional in combination with the aug-cc-pVTZ basis set is demonstrated to provide the overall most accurate NMR chemical shifts, whereas LC-ωPBE, ωB97X-D, LC-TPSS, CAM-B3LYP, and B3LYP to show acceptable performance. Our results are expected to provide a guideline to facilitate future developments and applications of the [N-X-N]+ halogen bond.
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Affiliation(s)
- Daniel Sethio
- Department of Chemistry—BMC, Uppsala University, Box 576, 751 23 Uppsala, Sweden
| | - Gerardo Raggi
- Department of Chemistry—BMC, Uppsala University, Box 576, 751 23 Uppsala, Sweden
| | - Roland Lindh
- Department of Chemistry—BMC, Uppsala University, Box 576, 751 23 Uppsala, Sweden
| | - Máté Erdélyi
- Department of Chemistry—BMC, Uppsala University, Box 576, 751 23 Uppsala, Sweden
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49
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Raynaud C, Norbert-Agaisse E, James BR, Eisenstein O. 31P Chemical Shifts in Ru(II) Phosphine Complexes. A Computational Study of the Influence of the Coordination Sphere. Inorg Chem 2020; 59:17038-17048. [PMID: 33156986 DOI: 10.1021/acs.inorgchem.0c02256] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
The NMR chemical shift has been the most versatile marker of chemical structures, by reflecting global and local electronic structures, and is very sensitive to any change within the chemical species. In this work, Ru(II) complexes with the same five ligands and a variable sixth ligand L (none, H2O, H2S, CH3SH, H2, N2, N2O, NO+, C═CHPh, and CO) are studied by using as the NMR reporter the phosphorus PA of a coordinated bidentate PA-N ligand (PA-N = o-diphenylphosphino-N,N'-dimethylaniline). The chemical shift of PA in RuCl2(PA-N)(PR3)(L) (R = phenyl, p-tolyl, or p-FC6H4) was shown to increase as the Ru-PA bond distance decreases, an observation that was not rationalized. This work, using density functional theory (DFT) calculations, reproduces reasonably well the observed 31P chemical shifts for these complexes and the correlation between the shifts and the Ru-PA bond distance as L varies. An interpretation of this correlation is proposed by using a natural chemical shift (NCS) analysis based on the natural bonding orbital (NBO) method. This analysis of the principal components of the chemical shift tensors shows how the σ-donating properties of L have a particularly high influence on the phosphine chemical shifts.
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Affiliation(s)
| | | | - Brian R James
- Department of Chemistry, University of Vancouver, Vancouver, BC V6T 1Z1, Canada
| | - Odile Eisenstein
- ICGM, Université de Montpellier, CNRS, ENSCM, Montpellier 34095, France.,Department of Chemistry and Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, Oslo 0315, Norway
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50
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Abstract
Magnetic shielding depends on molecular structure and noncovalent interactions. This study shows that it is also measurably dependent on the electric field generated by surrounding molecules. This effect has been observed explicitly for 31P nucleus using the adduct under field approach. The results obtained indicate that the field strength experienced by molecules in crystals consisting of molecules with large dipole moments is similar to that in polar solvents. Therefore, magnetic shielding should explicitly depend on solvent polarity. It is important to note that this effect cannot be reproduced correctly within the polarizable continuum model approach.
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Affiliation(s)
- Ilya G Shenderovich
- Institute of Organic Chemistry, University of Regensburg, Universitaetstrasse 31, 93053 Regensburg, Germany
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