Nuclear Magnetic Resonance Shielding Research Articles

NMR chemical shift computations at second-order Møller-Plesset perturbation theory using gauge-including atomic orbitals and Cholesky-decomposed two-electron integrals.

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.

Absolute NMR shielding scales in methyl halides obtained from experimental and calculated nuclear spin-rotation constants

The nonrelativistic ``Ramsey-Flygare relationship'' is the most used procedure to obtain semiexperimental nuclear magnetic resonance (NMR) absolute shieldings by a correspondence between NMR shieldings ($\mathbit{\ensuremath{\sigma}}$) and nuclear spin-rotation constants ($\mathbit{M}$). One of its generalizations to the relativistic framework is known as the M-V model, which was proposed few year ago by some of the authors of the present work and right now is only applied to linear molecules. This model includes terms that do not have nonrelativistic counterparts and also include the paramagnetic contribution to the NMR shielding of nuclei in free atoms. All this ensures that its results fit quite well with those of four-component (4c) calculations. The first application of the M-V model to nonlinear molecules, like methyl halides or ${\mathrm{CH}}_{3}X$ molecules ($X=\mathrm{F}$, Cl, Br, and I), is given here. The analysis of each electronic mechanism of $\mathbit{\ensuremath{\sigma}}$ shows that most of their electron correlation effects are strongly related with the same effects in $\mathbit{M}$. By including experimental data of $M$ in the M-V model most of the correlation effects are accurately taken into account for the absolute values of $\mathbit{\ensuremath{\sigma}}$. Calculations of ${\mathbit{M}}_{Y}$ and ${\mathbit{\ensuremath{\sigma}}}_{Y}$ ($Y=\mathrm{H}$, C, and $X$) were carried out within the linear response formalism at the random-phase level of approach and density functional theory in both 4c and nonrelativistic frameworks. The best fits between calculations of $\mathbit{M}$ and experimental data are obtained from calculations at 4c-PBE0 level of theory in all cases, but not for ${M}_{\ensuremath{\parallel},\mathrm{Cl}}$, which suggests that a revision of the available experimental data may be necessary. There is an additional advantage of using the M-V model: one can indirectly calculate shieldings of open-shell free atoms, which cannot be obtained at the moment by applying 4c methods.

DLPNO-MP2 second derivatives for the computation of polarizabilities and NMR shieldings.

We present a derivation and efficient implementation of the formally complete analytic second derivatives for the domain-based local pair natural orbital second order Møller-Plesset perturbation theory (MP2) method, applicable to electric or magnetic field-response properties but not yet to harmonic frequencies. We also discuss the occurrence and avoidance of numerical instability issues related to singular linear equation systems and near linear dependences in the projected atomic orbital domains. A series of benchmark calculations on medium-sized systems is performed to assess the effect of the local approximation on calculated nuclear magnetic resonance shieldings and the static dipole polarizabilities. Relative deviations from the resolution of the identity-based MP2 (RI-MP2) reference for both properties are below 0.5% with the default truncation thresholds. For large systems, our implementation achieves quadratic effective scaling, is more efficient than RI-MP2 starting at 280 correlated electrons, and is never more than 5-20 times slower than the equivalent Hartree-Fock property calculation. The largest calculation performed here was on the vancomycin molecule with 176 atoms, 542 correlated electrons, and 4700 basis functions and took 3.3 days on 12 central processing unit cores.

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.

Investigating solvent effects on the magnetic properties of molybdate ions () with relativistic embedding

AbstractWe investigate the ability of mechanical and electronic density functional theory‐based embedding approaches to describe the solvent effects on nuclear magnetic resonance (NMR) shielding constants of the 95Mo nucleus in the molybdate ion in aqueous solution. From the description obtained from calculations with two‐ and four‐component relativistic Hamiltonians, we find that, for such systems, spin‐orbit coupling effects are clearly important for absolute shielding values, but for relative quantities, a scalar relativistic treatment provides sufficient estimation of the solvent effects. We find that the electronic contributions to the solvent effects are relatively modest yet decisive to provide a more accurate magnetic response of the system when compared to reference supermolecular calculations. We analyze the errors in the embedding calculations by statistical methods, as well as through a real‐space representation of NMR shielding densities, which are shown to provide a clear picture of the physical processes at play.

Investigation of 205Tl NMR shielding, structural, and electronical properties in thallium halides by applying PBE‐GGA, YS‐PBE0 and mBJ functionals

We report the structural, electronical, and heavy nuclear 205 Tl Nuclear Magnetic Resonance (NMR) shielding properties of thallium halides TlX (X = F, Cl, Br, and I) by the first principles calculation. The Perdew-Burke-Ernzerhof Generalized Gradient Approximation, Yukawa Screened-PBE0 hybrid functional, and modified Becke-Johnson (mBJ) functionals including the relativistic and spin-orbit coupling effects are applied for calculation of the exchange-correlation potentials. Calculated PDOS spectra display that the valence band is composed of the X-s, Tl-5d, X-p, and Tl-6s states, and these states play an important role in 205 Tl NMR shielding. Our findings indicate that the nuclear magnetic shielding parameters depend on the electronic properties. Obtained results by mBJ show that there is a close agreement between the experimental and the calculated NMR parameters.

Comparison between optoelectronic spectra and NMR shielding in tellurium based compounds: a FP-LAPW study

The Nuclear Magnetic Resonance (NMR) of 125Te atom and optoelectronic spectra in the X2TeO3 (X = Na, K, Ag) and PbTeO3 compounds are investigated by the modified Becke-Johnson (mBJ) potential. Obtained magnetic shielding and the experimental chemical shifts are in close agreement. The X ions control polarity of the magnetic shielding around the 125Te nucleus and σiso(X) increases from Na2TeO3 to PbTeO3 compounds. Calculated band gap of X2TeO3 (X = Na, K, Ag) and PbTeO3 compounds are 3.23, 0.24, 3.63 and 3.95 eV, respectively. Density of states results show that the X1,2-p states in the bottom of the valence band have an essential role in the value of 125Te NMR chemical shielding. The magnetic shielding of X atoms governs on the optical properties, such as the static dielectric function, refractive indexes and plasmon energies.

Phosphorus mononitride: A difficult case for theory

AbstractPhosphorus nitride (PN) is the simplest molecule formed solely by phosphorus and nitrogen. It represents an interesting model for materials, where phosphorus is directly attached to nitrogen. Nevertheless, both theoretical and experimental studies often provide an incomplete picture on the structural, electronic, and spectral properties of PN. Theoretical predictions often suffer from insufficient level of theory, incomplete basis set, or from neglecting several effects, for example, zero‐point vibrational correction (ZPVC). Therefore, we performed an extensive benchmark study on structural, electronic, and spectral properties of PN at the Hartree‐Fock, density functional theory (DFT), or even the coupled‐cluster levels. We paid special attention to the basis set effect. We tested three variants of Dunning's aug‐cc‐pVXZ basis sets with the size from double‐ζ to sextuple‐ζ, as well as Jensen's aug‐pc‐n, aug‐pcJ‐n, and aug‐pcSseg‐n basis sets, where n = 1‐4. Obtained energetics, PN distance, dipole moment, vibrational frequencies, and nuclear magnetic resonance (NMR) parameters were extrapolated to the complete basis set limit (CBS) using three‐ or two‐parameter formulas. The 31P NMR shieldings estimated with the aug‐cc‐pVXZ and aug‐cc‐pV(X + d)Z basis sets strongly depend on the basis set size providing scattered convergence patterns toward CBS. The Hartree‐Fock self‐consistent field (HF‐SCF) NMR parameters evinced similar behavior as the coupled‐cluster data. The only smooth convergence was achieved using the aug‐cc‐pCVXZ basis sets that include core‐valence effects. The KT3 functional underestimated the phosphorus CBS shieldings by about 12 ppm compared to coupled cluster with singles and doubles (CCSD) (T). Nevertheless, KT3 unambiguously surpasses the HF‐SCF and CCSD levels that provide 31P shieldings that are lower by about 150 ppm and 24 ppm compared to CCSD(T). The convergence of nitrogen shieldings was regular for all basis set hierarchies and all theoretical methods. Relativistic and vibrational effects on selected properties were also discussed.

Microscopic Sources of Solid-State NMR Shielding in Titanate of Alkaline Earth Perovskite Metals

Nuclear magnetic resonance (NMR) parameters are calculated and analyzed in a series of titanate of alkaline earth perovskites to explore microscopic sources of their magnetic shieldings using a full-potential-based NMR scheme. In this method, there is no approximation to calculate the induced current density. The slope of the correlation between various approaches and available experimental data is successfully reproduced very close to the required ideal value (−1). Our NMR results are consistent with the experimental data and the available theoretical results calculated by the gauge-including projector augmented-wave (GIPAW) method. Moreover, we have predicted the chemical shifts of the compounds in which their experimental values have not been measured yet. Isotropic and anisotropic chemical shift parameters as well as associated asymmetries are analyzed. The analysis explores the relation between atomic and orbital characters of the valence and conduction bands wave functions as well as the 17O NMR shi...

Computational Study of Y NMR Shielding in Intermetallic Yttrium Compounds

Density functional theory (DFT) calculations of the magnetic shielding for solid state nuclear magnetic resonance (NMR) provide an important contribution for the understanding of experimentally observed signals. In this work, we present calculations of the Y NMR shielding in intermetallic compounds (YMg, YT, YTX, YT2X, YT2X2, Y2TB6, and Y2TSi3 where T represents various transition metals and X refers to group IV elements C, Si, Ge, Sn, Pb). The total shielding σ of this selection varies by about 2500 ppm and correlates very well with the experimentally observed shifts except for YMg and YZn. These two simple compounds have a spike in the DOS at EF and a corresponding huge spin susceptibility which leads to the disagreement. It could be a problem of DFT (neglect of spin fluctuations), but we would interpret the discrepancies as caused by disorder which could be present in the experimental samples because disorder removes the spike in the DOS. The diamagnetic contribution σo (chemical shift) is by no means ...

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.

The role of electrostatic interactions and solvent polarity on the 15N NMR shielding of azines

The nitrogen-15 nuclear magnetic resonance (15N NMR) shielding of azines is very sensitive to the chemical environment. Theoretically, specific interactions are important on the calculation of their spectroscopic properties. However, the choice of the solvent model for the description of NMR shielding constants is still a subject of discussion. In this context, we analyse the role of electrostatic interactions on 15N NMR shielding as function of solvent polarity using the sequential-Quantum Mechanics/Molecular Mechanics approach methodology. Excellent agreement with experimental data of the NMR shielding was obtained without the inclusion of explicit solvent molecules either for polar or non polar solvents.

Absorption mechanism, structural and electronic properties of MC19 (M = B and Si) fullerenes with 1-acetylpiperazine

The interaction mechanisms of undoped, silicon- and boron-doped C20 fullerenes and 1-acetylpiperazine (1-ap) were investigated. Stability, electronic properties, influence of water on the solubility and stability, molecular parameters, descriptive vibrational bands and nuclear magnetic resonance shielding values are reported. The quantum mechanical calculations were carried out using the M06-2X functional and the 6-31G(d) basis set. It is observed that all the complexes are more stabilized in water compared to the gas phase. The most stable complex was found as silicon-doped fullerene interacting with the carbonyl edge of 1-ap releasing energy of 64.13 kcal/mol in water.

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.

127I NMR calculations in binary metal iodides by PBE-GGA, YS-PBE0 and mBJ exchange correlation potentials

We have calculated Nuclear Magnetic Resonance (NMR) spectroscopy for 127I (quadrupolar nuclei I=5/2) in binary metal iodides XI (X=Li, Na, K, Rb and Cs) by using PBE- GGA, YS- PBE0 and mBJ exchange correlation potentials. The results show that the nature of bonds between Iodine and metal atoms are ionic. The main contribution in NMR spectroscopy is related to the induced current inside the atomic sphere and the remainder of the unit cell volume contributes only a few ppm. Obtained NMR shifts are compared with the NMR shielding data and the NMR shielding for metal-p band varies across the series about 221ppm. Density of states results indicate that the largest contribution in the shielding comes from the I-core electrons (1s and 4d). The NMR shielding graphs show that there are negative linear correlation with slope −1.18, −1.16 and −1.01 by PBE- GGA, YS- PBE0 and mBJ, respectively. The computed results by mBJ are in good agreement with the experimental values.

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.

Big picture of relativistic molecular quantum mechanics

AbstractAny quantum mechanical calculation on electronic structure ought to choose first an appropriate Hamiltonian H and then an Ansatz for parameterizing the wave function Ψ, from which the desired energy/property E(λ) can finally be calculated. Therefore, the very first question is: what is the most accurate many-electron Hamiltonian H? It is shown that such a Hamiltonian i.e. effective quantum electrodynamics (eQED) Hamiltonian, can be obtained naturally by incorporating properly the charge conjugation symmetry when normal ordering the second quantized fermion operators. Taking this eQED Hamiltonian as the basis, various approximate relativistic many-electron Hamiltonians can be obtained based entirely on physical arguments. All these Hamiltonians together form a complete and continuous ‘Hamiltonian ladder’, from which one can pick up the right one according to the target physics and accuracy. As for the many-electron wave function Ψ, the most intriguing questions are as follows. (i) How to do relativistic explicit correlation? (ii) How to handle strong correlation? Both general principles and practical strategies are outlined here to handle these issues. Among the electronic properties E(λ) that sample the electronic wave function nearby the nuclear region, nuclear magnetic resonance (NMR) shielding and nuclear spin-rotation (NSR) coupling constant are especially challenging: they require body-fixed molecular Hamiltonians that treat both the electrons and nuclei as relativistic quantum particles. Nevertheless, they have been formulated rigorously. In particular, a very robust ‘relativistic mapping’ between the two properties has been established, which can translate experimentally measured NSR coupling constants to very accurate absolute NMR shielding scales that otherwise cannot be obtained experimentally. Since the most general and fundamental issues pertinent to all the three components of the quantum mechanical equation HΨ = EΨ (i.e. Hamiltonian H, wave function Ψ, and energy/property E(λ)) have fully been understood, the big picture of relativistic molecular quantum mechanics can now be regarded as established.

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.