Nuclear Magnetic Resonance Shielding Constants Research Articles

On the utmost importance of the geometry factor of accuracy in the quantum chemical calculations of 31P NMR chemical shifts: New efficient pecG-n (n = 1, 2) basis sets for the geometry optimization procedure.

31P nuclear magnetic resonance (NMR) chemical shifts were shown to be very sensitive to the basis set used at the geometry optimization stage. Commonly used energy-optimized basis sets for a phosphorus atom containing only one polarization d-function were shown to be unable to provide correct equilibrium geometries for the calculations of phosphorus chemical shifts. The use of basis sets with at least two polarization d-functions on a phosphorus atom is strongly recommended. In this paper, an idea of creating the basis sets purposed for the geometry optimization that provide the least possible error coming from the geometry factor of accuracy in the resultant NMR shielding constants is proposed. The property-energy consisted algorithm with the target function in the form of the molecular energy gradient relative to P-P bond lengths was applied to create new geometry-oriented pecG-n (n = 1, 2) basis sets for a phosphorus atom. New basis sets have demonstrated by far superior performance as compared to the other commonly used energy-optimized basis sets in massive calculations of 31P NMR chemical shifts carried out at the gauge-including atomic orbital-coupled cluster singles and doubles/pecS-2 level of the theory by taking into account solvent, vibrational, and relativistic corrections.

Nuclear Magnetic Shielding Constants with the Polarizable Density Embedding Model.

We extend the polarizable density embedding (PDE) model to support the calculation of nuclear magnetic resonance (NMR) shielding constants using gauge-including atomic orbitals (GIAOs) within a density functional theory (DFT) framework. The PDE model divides the total system into fragments, describing some by quantum mechanics (QM) and the others through an embedding model. The PDE model uses anisotropic polarizabilities, inter-fragment two-electron Coulomb integrals, and a non-local repulsion operator to emulate the QM effects. The terms involving Coulomb integrals are straightforwardly extended with GIAOs. In contrast, we consider two approaches to handle the gauge dependency of the non-local operator, employing either simple symmetrization or a gauge transformation. We find the latter approach to be most stable with respect to increasing the basis set size of the QM region. We examine the accuracy of the PDE model for calculating NMR shielding constants on several solutes in a water solution. The performance is compared with the classical polarizable embedding (PE) model in addition to supermolecular reference calculations. Based on these systems, we address the basis set convergence characteristics and the QM region size requirements. Furthermore, we investigate the performance of the PDE model for a system with significant electron spill-out. In many cases, we find that the PDE model outperforms the PE model, especially regarding the accuracy of nuclear shielding constants when using small QM region sizes and in systems with significant electron spill-out.

Accurate Prediction of Nuclear Magnetic Resonance Parameters via the XYG3 Type of Doubly Hybrid Density Functionals.

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.

Four-component relativistic calculations of NMR shielding constants of the transition metal complexes. Part 1: Pentaammines of cobalt, rhodium, and iridium.

The nonrelativistic and four-component fully relativistic calculations of 1 H, 15 N, 59 Co, 103 Rh, and 193 Ir shielding constants of pentaammineaquacomplexes of cobalt(III), rhodium(III), and iridium(III) were carried out at the density functional theory (DFT) level of theory. The noticeable deshielding relativistic corrections were observed for nitrogen shielding constants (chemical shifts), whereas those corrections were found to be negligible for protons. For the transition metals cobalt, rhodium, and iridium, relativistic corrections to their nuclear magnetic resonance (NMR) shielding constants were found to be rather small for cobalt and rhodium (some 5-10%), whereas they are essentially larger for iridium (up to 70%).

Segmented Contracted Error-Consistent Basis Sets of Quadruple-ζ Valence Quality for One- and Two-Component Relativistic All-Electron Calculations.

Segmented contracted basis sets of quadruple-ζ quality for exact two-component (X2C) calculations are presented for the elements H-Rn. These sets are the all-electron relativistic counterparts of the Karlsruhe "def2" and "dhf" systems of bases, which were designed for Hartree-Fock and density functional treatments and-with a somewhat extended set-also for correlated treatments. The bases were optimized with analytical basis set gradients and the finite nucleus model based on a Gaussian charge distribution at the scalar-relativistic X2C level. Extensions are provided for self-consistent two-component treatments to describe spin-orbit coupling, polarization effects, and nuclear magnetic resonance (NMR) shielding constants. The basis sets were designed to yield comparable errors in atomization energies, orbital energies, dipole moments, and NMR shielding constants all across the periodic table of elements. A test set of more than 360 molecules representing (nearly) all elements in their common oxidation states was utilized for the valence properties, and a test set of more than 250 closed-shell molecules was employed for the NMR shielding constants. The quality of the developed basis sets is compared to other frequently used relativistic all-electron bases.

Calculations of nuclear magnetic shielding constants based on the exact two-component relativistic method.

From the matrix representation of the modified Dirac equation based on the restricted magnetically balanced gauge-including atomic orbital (RMB-GIAO) basis, previously one of the authors (Yoshizawa) and co-workers derived the two-component normalized elimination of the small component (2c-NESC) formulas for 2c relativistic calculations of nuclear magnetic resonance (NMR) shielding tensors. In the present study, at the Hartree-Fock (HF) level, we numerically confirm that for several molecules the RMB-GIAO-based 2c-NESC method provides gauge-origin independent NMR shielding values. Moreover, we investigate the accuracy of the 2c-NESC method by comparison with the 4c relativistic NMR calculations at the HF level. For noble gas dimers and Hg compounds, it is shown that the 2c-NESC method reproduces the 4c relativistic NMR shielding constants within errors of 0.12%-0.31% of the 4c relativistic values and yields chemical shifts sufficiently close to the 4c relativistic results. Also, we discuss the basis set convergence of NMR shielding constants calculated with the 2c-NESC and 4c relativistic methods.

Accurate Prediction of NMR Chemical Shifts in Macromolecular and Condensed-Phase Systems with the Generalized Energy-Based Fragmentation Method.

The generalized energy-based fragmentation (GEBF) method is extended to allow calculations of nuclear magnetic resonance (NMR) chemical shifts of macromolecular and condensed-phase systems feasible at a low computational cost. In this approach, NMR shielding constants in a large system are evaluated as a linear combination of the corresponding quantities from a series of small "electrostatically embedded" subsystems. Comparison of NMR shielding constants from the GEBF-X method [where X is an electronic structure method, such as Hartree-Fock (HF), density functional theory (DFT), ...] with those from the conventional quantum chemistry method for two representative systems verifies that the GEBF approach can reproduce the results of the conventional quantum chemistry method very well. This procedure has further been applied to compute NMR shielding constants of a large foldamer and a supramolecular aggregate, and the 15N shielding constant for CH3CN in the CHCl3 solvent. For the former two systems, the predicted 1H chemical shifts are in good agreement with the experimental data. For the CH3CN/CHCl3 solution, the 15N shielding constant of CH3CN is evaluated as the ensemble average of up to 200 sufficiently large CH3CN/CHCl3 clusters from either classical or QM/MM (quantum mechanics/molecular mechanics) molecular dynamics (MD) simulations. Our results reveal that the gas-to-solution shift of 15N (from an isolated CH3CN to the CH3CN/CHCl3 solution) based on PM6-DH+/MM MD simulation is in good accord with the experimental value, outperforming those based on classical MD simulation and the previous polarizable continuum model using integral equation formalism (IEF-PCM) study. This study unravels that the generation of representative liquid structures is critical in evaluating the NMR shielding constants of condensed-phase systems.

Linking the Character of the Metal–Ligand Bond to the Ligand NMR Shielding in Transition-Metal Complexes: NMR Contributions from Spin–Orbit Coupling

Relativistic effects significantly affect various spectroscopic properties of compounds containing heavy elements. Particularly in Nuclear Magnetic Resonance (NMR) spectroscopy, the heavy atoms strongly influence the NMR shielding constants of neighboring light atoms. In this account we analyze paramagnetic contributions to NMR shielding constants and their modulation by relativistic spin-orbit effects in a series of transition-metal complexes of Pt(II), Au(I), Au(III), and Hg(II). We show how the paramagnetic NMR shielding and spin-orbit effects relate to the character of the metal-ligand (M-L) bond. A correlation between the (back)-donation character of the M-L bond in d10 Au(I) complexes and the propagation of the spin-orbit (SO) effects from M to L through the M-L bond influencing the ligand NMR shielding via the Fermi-contact mechanism is found and rationalized by using third-order perturbation theory. The SO effects on the ligand NMR shielding are demonstrated to be driven by both the electronic structure of M and the nature of the trans ligand, sharing the σ-bonding metal orbital with the NMR spectator atom L. The deshielding paramagnetic contribution is linked to the σ-type M-L bonding orbitals, which are notably affected by the trans ligand. The SO deshielding role of σ-type orbitals is enhanced in d10 Hg(II) complexes with the Hg 6p atomic orbital involved in the M-L bonding. In contrast, in d8 Pt(II) complexes, occupied π-type orbitals play a dominant role in the SO-altered magnetic couplings due to the accessibility of vacant antibonding σ-type MOs in formally open 5d-shell (d8). This results in a significant SO shielding at the light atom. The energy- and composition-modulation of σ- vs π-type orbitals by spin-orbit coupling is rationalized and supported by visualizing the SO-induced changes in the electron density around the metal and light atoms (spin-orbit electron deformation density, SO-EDD).

Automated Fragmentation Polarizable Embedding Density Functional Theory (PE-DFT) Calculations of Nuclear Magnetic Resonance (NMR) Shielding Constants of Proteins with Application to Chemical Shift Predictions.

Full-protein nuclear magnetic resonance (NMR) shielding constants based on ab initio calculations are desirable, because they can assist in elucidating protein structures from NMR experiments. In this work, we present NMR shielding constants computed using a new automated fragmentation (J. Phys. Chem. B 2009, 113, 10380-10388) approach in the framework of polarizable embedding density functional theory. We extend our previous work to give both basis set recommendations and comment on how large the quantum mechanical region should be to successfully compute 13C NMR shielding constants that are comparable with experiment. The introduction of a probabilistic linear regression model allows us to substantially reduce the number of snapshots that are needed to make comparisons with experiment. This approach is further improved by augmenting snapshot selection with chemical shift predictions by which we can obtain a representative subset of snapshots that gives the smallest predicted error, compared to experiment. Finally, we use this subset of snapshots to calculate the NMR shielding constants at the PE-KT3/pcSseg-2 level of theory for all atoms in the protein GB3.

Nuclei-selected atomic-orbital response-theory formulation for the calculation of NMR shielding tensors using density-fitting

An atomic orbital density matrix based response formulation of the nuclei-selected approach of Beer, Kussmann, and Ochsenfeld [J. Chem. Phys. 134, 074102 (2011)] to calculate nuclear magnetic resonance (NMR) shielding tensors has been developed and implemented into LSDalton allowing for a simultaneous solution of the response equations, which significantly improves the performance. The response formulation to calculate nuclei-selected NMR shielding tensors can be used together with the density-fitting approximation that allows efficient calculation of Coulomb integrals. It is shown that using density-fitting does not lead to a significant loss in accuracy for both the nuclei-selected and the conventional ways to calculate NMR shielding constants and should thus be used for applications with LSDalton.

Crystal Structures of Tiotropium Bromide and Its Monohydrate in View of Combined Solid-state Nuclear Magnetic Resonance and Gauge-Including Projector-Augmented Wave Studies

Tiotropium bromide is an anticholinergic bronchodilator used in the management of chronic obstructive pulmonary disease. The crystal structures of this compound and its monohydrate have been previously solved and published. However, in this paper, we showed that those structures contain some major errors. Our methodology based on combination of the solid-state nuclear magnetic resonance (NMR) spectroscopy and quantum mechanical gauge-including projector-augmented wave (GIPAW) calculations of NMR shielding constants enabled us to correct those errors and obtain reliable structures of the studied compounds. It has been proved that such approach can be used not only to perform the structural analysis of a drug substance and to identify its polymorphs, but also to verify and optimize already existing crystal structures.

Mechanism of Spin–Orbit Effects on the Ligand NMR Chemical Shift in Transition-Metal Complexes: Linking NMR to EPR

Relativistic effects play an essential role in understanding the nuclear magnetic resonance (NMR) chemical shifts in heavy-atom compounds. Particularly interesting from the chemical point of view are the relativistic effects due to heavy atom (HA) on the NMR chemical shifts of the nearby light atoms (LA), referred to as the HALA effects. The effect of Spin-Orbit (SO) interaction originating from HA on the nuclear magnetic shielding at a neighboring LA, σ(SO), is explored here in detail for a series of d(6) complexes of iridium. Unlike the previous findings, the trends in σ(SO) observed in this study can be fully explained neither in terms of the s-character of the HA-LA bonding nor by trends in the energy differences between occupied and virtual molecular orbitals (MOs). Rather, the σ(SO) contribution to the total NMR shielding is found to be modulated by the d-orbital participation of the heavy atom (Ir) in the occupied and virtual spin-orbit active MOs, i.e., those which contribute significantly to the σ(SO). The correlation between the d-character of σ(SO)-active MOs and the size of the corresponding SO contribution to the nuclear magnetic shielding constant at LA is so tight that the magnitude of σ(SO) can be predicted in a given class of compounds on the basis of d-orbital character of relevant MO with relative error smaller than 15%. This correspondence is supported by an analogy between the perturbation theory expressions for the spin-orbit induced NMR σ-tensor and those for the EPR g-tensor as well as the A-tensor of the ligand. This correlation is demonstrated on a series of d(5) complexes of iridium. Thus, known qualitative relationships between electronic structure and EPR parameters can be newly applied to reproduce, predict, and understand the SO-induced contributions to NMR shielding constants of light atoms in heavy-atom compounds.

NMR shielding constants of CuX, AgX, and AuX (X = F, Cl, Br, and I) investigated by density functional theory based on the Douglas–Kroll–Hess Hamiltonian

Two-component relativistic density functional theory (DFT) with the second-order Douglas-Kroll-Hess (DKH2) one-electron Hamiltonian was applied to the calculation of nuclear magnetic resonance (NMR) shielding constant. Large basis set dependence was observed in the shielding constant of Xe atom. The DKH2-DFT-calculated shielding constants of I and Xe in HI, I2, CuI, AgI, and XeF2 agree well with those obtained by the four-component relativistic theory and experiments. The Au NMR shielding constant in AuF is extremely more positive than in AuCl, AuBr, and AuI, as reported recently. This extremely positive shielding constant arises from the much larger Fermi contact (FC) term of AuF than in others. Interestingly, the absolute values of the paramagnetic and the FC terms are considerably larger in CuF and AuF than in others. The large paramagnetic term of AuF arises from the large d-components in the Au dπ -F pπ and Au sdσ-F pσ molecular orbitals (MOs). The large FC term in AuF arises from the small energy difference between the Au sdσ + F pσ and Au sdσ-F pσ MOs. The second-order magnetically relativistic effect, which is the effect of DKH2 magnetic operator, is important even in CuF. This effect considerably improves the overestimation of the spin-orbit effect calculated by the Breit-Pauli magnetic operator.

NMR Shielding Constants in PH3, Absolute Shielding Scale, and the Nuclear Magnetic Moment of 31P

Ab initio values of the absolute shielding constants of phosphorus and hydrogen in PH(3) were determined, and their accuracy is discussed. In particular, we analyzed the relativistic corrections to nuclear magnetic resonance (NMR) shielding constants, comparing the constants computed using the four-component Dirac-Hartree-Fock approach, the four-component density functional theory (DFT), and the Breit-Pauli perturbation theory (BPPT) with nonrelativistic Hartree-Fock or DFT reference functions. For the equilibrium geometry, we obtained σ(P) = 624.309 ppm and σ(H) = 29.761 ppm. Resonance frequencies of both nuclei were measured in gas-phase NMR experiments, and the results were extrapolated to zero density to provide the frequency ratio for an isolated PH(3) molecule. This ratio, together with the computed shielding constants, was used to determine a new value of the nuclear magnetic dipole moment of (31)P: μ(P) = 1.1309246(50) μ(N).

On the Accuracy of Density Functional Theory to Predict Shifts in Nuclear Magnetic Resonance Shielding Constants due to Hydrogen Bonding.

We present the first systematic investigation of shifts in the nuclear magnetic resonance (NMR) shielding constant due to hydrogen bonding using either the series of wave function based methods, Hartree-Fock (HF), second-order Møller-Plesset perturbation theory (MP2), Coupled Cluster Singles and Doubles (CCSD) and CCSD extended with an approximate description of triples (CCSD(T)), or Density Functional Theory (DFT) employing either the B3LYP, PBE0, or KT3 exchange correlation (xc) functionals. The molecular systems considered are (i) the water dimer and (ii) formaldehyde in complex with two water molecules. Specially for the (17)O in formaldehyde we observe significant differences between the DFT and CCSD(T) predictions. However, the extent of these deviations depends crucially on the applied xc functional. Compared to CCSD(T) we find the KT3 functional to provide accurate results, whereas both B3LYP and PBE0 are in significant error. Potential consequences of this observation are discussed in the context of general predictions of NMR shielding constants in condensed phase.

NMR shieldings from sum-over-states density-functional-perturbation theory: Further testing of the “Loc.3” approximation

The development and implementation of sum-over-states density-functional-perturbation theory (SOS-DFPT) [V.G. Malkin, O.L. Malkina, M.E. Casida, and D.R. Salahub, J. Am. Chem. Soc. 116, 5898 (1994)] has allowed a significant improvement in the accuracy of nuclear magnetic resonance (NMR) chemical shift values over the Hartree–Fock approximation. Furthermore, due to its computational efficiency, SOS-DFPT has opened the way to the study of systems of increased size compared to those that may be approached by more sophisticated but also computationally more intensive methods, such as Møller–Plesset perturbation theory or coupled-cluster theory. The success of SOS-DFPT relies on the introduction of an ad hoc correction to the excitation energy that improves the calculation of the paramagnetic component of the NMR shielding tensor. The lack of a clear physical basis for this approximation has left the SOS-DFPT open to some criticism. We have shown in a previous article [E. Fadda, M.E. Casida, and D.R. Salahub, Int. J. Quantum Chem. 91, 67 (2003)] that the electric field and magnetic field responses are given by equivalent expressions within the Tamm–Dancoff approximation of time-dependent density-functional theory (TD-DFT). This provides an SOS-DFPT expression which, upon restriction to diagonal contributions, yields a new rigorous “Loc.3” approximation. In this article, we more than double our original test set of 10 molecules for C13, N15, and O17 chemical shifts to a set of 25 molecules. In addition, we compare the results of “Loc.3” SOS-DFPT with the results of promising recent functionals for DFT calculations of chemical shifts. The results show not only that the “Loc.3” approximation represents the rigorous physical connection between SOS-DFPT and TD-DFT, but also that it has very good potential for the prediction of NMR shielding constants, opening the way to further developments in DFT-based NMR parameter calculations.

Multiconfigurational self-consistent field calculations of nuclear magnetic resonance indirect spin–spin coupling constants

Ab initio calculations of all the nuclear magnetic resonance (NMR) indirect nuclear spin–spin coupling constants in the HN3 molecule and in four isomers of CH2N2 are described. For each molecule, SCF and two multiconfiguration self-consistent field (MCSCF) wave functions that take into account valence shell correlation effects are applied. All mechanisms contributing to the coupling constants are included. While the SCF results are meaningless, the agreement of the correlated values with those known from experiment is satisfactory. Our most accurate calculations are carried out with the wave functions previously used successfully to compute the NMR shielding constants. All parameters determining the NMR spectra of these molecules have thus been obtained at uniform accuracy from the same reference wave function.

EXACT NUCLEAR MAGNETIC RESONANCE SHIELDING CONSTANTS FOR HYDRIDE, HELIUM, LITHIUM(I), OXYGEN(VI)1

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTEXACT NUCLEAR MAGNETIC RESONANCE SHIELDING CONSTANTS FOR HYDRIDE, HELIUM, LITHIUM(I), OXYGEN(VI)1R. E. GlickCite this: J. Phys. Chem. 1961, 65, 10, 1871–1872Publication Date (Print):October 1, 1961Publication History Published online1 May 2002Published inissue 1 October 1961https://doi.org/10.1021/j100827a045RIGHTS & PERMISSIONSArticle Views25Altmetric-Citations10LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (231 KB) Get e-Alerts