Nuclear Magnetic Resonance Volume 41

By K. Kamienska-Trela, Jacek Wójcik

The Royal Society of Chemistry

Copyright © 2012 The Royal Society of Chemistry
All rights reserved.
ISBN: 978-1-84973-373-1

Contents

Preface K. Kamienska-Trela, v,
Books and reviews Wojciech Schlif, 1,
Theoretical and physical aspects of nuclear shielding Cynthia J. Jameson and Angel C. De Dios, 38,
Applications of nuclear shielding Shigeki Kuroki, Tsunenori Kameda and Hidekazu Yasunaga, 56,
Theoretical aspects of indirect spin-spin couplings Jaroslaw Jazwinski, 119,
Applications of spin-spin couplings Krystyna Kamienska-Trela and Jacek Wójcik, 148,
Nuclear spin relaxation in liquids and gases Jozef Kowalewski, 196,
Solid state NMR spectroscopy A. E. Aliev and R. V. Law, 244,
NMR of proteins and nucleic acids Peter J. Simpson, 290,
NMR of lipids and membranes Ewa Swiezewska and Jacek Wójcik, 320,
NMR in living systems M. J. W. Prior, 348,
A specialist periodical report on nuclear magnetic resonance (2011/8) synthetic macromolecules Hiromichi Kurosu and Takeshi Yamanobe, 386,
NMR of liquid crystals and micellar solutions Gerardino D’Errico and Luigi Paduano, 429,

CHAPTER 1

Theoretical and physical aspects of nuclear shielding

Cynthia J. Jameson and Angel C. De Dios

DOI: 10.1039/9781849734851-00038

1 Theoretical aspects of nuclear shielding

1.1 General theory

Several recent relativistic studies involve the shielding in molecules containing Cl, Br, and I, with special attention to the investigation of heavy atom effect on itself, the heavy atom effects on vicinal heavy atoms, and the heavy atom effects on light atoms. The importance of relativistic effects on NMR shielding constants and chemical shifts of linear HgL2 (L=Cl, Br, I, CH3) compounds has been investigated using three different relativistic methods: the fully relativistic four-component approach and the two- component approximations, linear response elimination of small component (LR-ESC) and zeroth-order regular approximation (ZORA). The calculations were performed at the level of HF and DFT theories. DFT calculations employed three different functionals (GGA/BP86 and the hybrid functionals B3LYP and PBE0). It is found that LR-ESC reproduces successfully the four-component results for the C shielding constant in Hg(CH3)2 within 6 ppm, but fails to reproduce the Hg shielding constants and chemical shifts. The latter is mainly due to an underestimation of the change in spin-orbit contribution. Even though ZORA underestimates the absolute Hg NMR shielding constants by ~2100 ppm, the differences between Hg chemical shift values obtained using ZORA and the four-component approach without spin-density contribution to the exchange-correlation (XC) kernel are less than 60 ppm for all compounds using three different functionals, BP86, B3LYP, and PBE0. However, larger deviations (up to 366 ppm) occur for Hg chemical shifts in HgBr2 and HgI2 when ZORA results are compared with four-component calculations with noncollinear spin-density contribution to the XC kernel. For the ZORA calculations it is necessary to use large basis sets (QZ4P) and the TZ2P basis set may give errors of ~500 ppm for the Hg chemical shifts, despite deceivingly good agreement with experimental data. The largest possible basis set, QZ4P, also contains the largest number of high-exponent functions, important for the calculation of shielding constants and especially the spin-orbit term. The effect of using a Gaussian charge distribution model for the nuclear Coulomb potential as opposed to a point charge model was also investigated. A Gaussian nucleus model for the Coulomb potential reduces the Hg absolute shielding values by ~100–500 ppm and the Hg chemical shifts by 1–143 ppm compared to the point nucleus model depending on the atomic number Z of the coordinating atom and the level of theory. The effect on the shielding constants of the lighter nuclei (C, Cl, Br, I) is, however, negligible. Although ZORA underestimates Hg absolute shielding values by ~2100 ppm, the differences between Hg chemical shift values obtained using ZORA and four-component approaches (without spin-density contribution to the XC kernel) are less than 60 ppm and are similar for all three. This is in a good agreement with the conclusion made by Autschbach that ZORA is a reliable tool for the investigation of chemical shifts as a “valence” property due to very accurate hyperfine integrals for the valence shells of heavy atoms in contrast to inner-most core shells which are important for absolute shielding values.

The four-component calculations using the relativistic polarization propagator formalism and also the two-component LR-ESC method were employed by Melo et al. to investigate Sn and Pb shielding in SnH2XY and PbH2XY with X,Y being F, Cl, Br, and I. At the same time they also examined the halogen nuclear shieldings in these molecules. The two-component results are about 20% smaller than the benchmark 4-component results. The non-relativistic behavior of σ(Sn) is that the nucleus becomes less shielded with heavier substituents. The relativistic results in SnH2X2 exhibit the same decreasing behavior of σ(Sn) in going from F to Cl, but this is followed by an increase in going from Cl to Br to I. Most of the relativistic correction terms are not sensitive to the chemical environment; only three of the correction terms vary with substitution, of which the spin-orbit – Fermi contact term is the most variable. Electron correlation effects on σ(Sn) in these molecules are significant in the non- relativistic treatment, but are not significant for the relativistic results. The results are in qualitative agreement with earlier results by Nakatsuji et al. and by Bagno et al.

Halogen substituent effects on La shielding in LaX3 molecules have been investigated using two-component DFT based on the zeroth-order regular approximation. A detailed analysis of the inverse halogen dependence of σ(La) was carried out via decomposition of the shielding tensor elements into contributions from localized and delocalized molecular orbitals. As with σ(Pb) in PbH2XY, both the relativistic effects of the heavy atom on itself and the relativistic effects of heavy atoms on the vicinal heavy atom are significant, the latter increasing in going from Cl to Br to I. Analysis shows that the cancellation of spin-orbit contributions of opposite sign from La itself and from the halogen leads to the trend which is the so-called inverse halogen dependence, the σ(La) in LaX3 decreasing in going from F to I. In decomposing the shielding contributions to σ(La) in LaX3 molecules, the diamagnetic component is almost identical across the series, the paramagnetic and spin-orbit contributions reinforce one another in going from Cl to I, with the paramagnetic term being the dominant contribution. This is in contrast to the σ(C) in CH3X, for example, where the so-called normal halogen dependence arises from the spin orbit effect from the halogen, a heavy atom effect on the shielding of a light atom, increasing in going from Cl to I, so that σ(C) in the series of CH3X molecules increases in this order. The calculated values are in agreement with the earlier calculations by Ooms et al. The calculated values for the gas phase molecules give too large a σ(La) shielding difference between the Cl and I compounds in comparison with the solid state observations, but this is expected. Ooms et al. had found that simulating the solid environment with a [LaX9]-6 cluster leads to a significantly reduced shielding difference. The heavier the halogen is, the more anisotropic is σ(La), in agreement with 139La solid state experiments.

We recall that in non-relativistic theory, with gauge origin anywhere along the line of centers, σ||p is identically zero for a linear molecule. How large is the deviation from zero in relativistic theory? We have reviewed in Vol. 38 of this series the experimental evidence for the significance of relativistic effects on shielding in linear molecule such as XeF2, where it was established experimentally by Forgeron et al., that identity relationships which had been derived for non-relativistic treatments of nuclear magnetic shielding no longer hold. They had found that

σ||(N in linear molecule) – σdiam(N in free atom)≈0

did not hold for Xe in XeF2; this quantity differed from zero by -1000 ppm.

And they had found that

[MATHEMATICAL EXPRESSION OMITTED]

did not hold for Xe in XeF2, where the quantity on the left hand side was different by about 1430 ppm from the quantity on the right hand side.

We assume that we can still use the identity

[MATHEMATICAL EXPRESSION OMITTED]

but C||N (which is not observed experimentally in spin-rotation interactions since axes of molecular rotation of a linear molecule are only those perpendicular to the line of centers) is no longer zero, and [MATHEMATICAL EXPRESSION OMITTED] is no longer zero, in a relativistic treatment. Gomez and Aucar have studied the magnitude of [MATHEMATICAL EXPRESSION OMITTED] in diatomic FX molecules using the RPA level of the polarization propagator formalism and four-component functions. For σ(F) in FX, [MATHEMATICAL EXPRESSION OMITTED] is 1.5, 19.7, 52.9, 17.9, -684.7 ppm for F2, FCl, FBr, FI, FAt respectively. For σ(X) in FX, [MATHEMATICAL EXPRESSION OMITTED] is 1.5, 26.6, -8.9, -447.4, -1819.2 ppm for F2, FCl, FBr, FI, FAt respectively. We see that the error in assuming that [MATHEMATICAL EXPRESSION OMITTED] vanishes for linear molecules is not monotonic with the increasing size of the heavy atom, but clearly is significant for FBr and FI. There are no problems with chemical shift scales on an absolute basis (that is, relative to the bare nucleus) when the absolute shielding scale is based on the absolute shielding calculated from the experimental spin rotation constant in a molecule constituted of light atoms and the measured chemical shifts in the gas phase relative to this reference, as in the case of 19F where the reference molecule is HF, for example.

The unusually negative 1H NMR chemical shifts of hydrogen atoms directly bonded to a transition metal center (with values ranging up to ca. -50 ppm in certain diamagnetic iridium complexes), and their dependence on the other ligands present at the metal site, led Buckingham and Stephens to suggest an explanation model already in 1964. On the basis of ligand field theory and the Ramsey formula of NMR chemical shifts, they argued that the local diamagnetic term of the hydride cannot account fully for such large shifts. Instead, paramagnetic ring currents within the incomplete valence d-shell of the transition metal site were invoked, which are experienced as an effective diamagnetic (diatropic in modern terminology) current at the off-center position of the hydrogen nucleus. Recently, relativistic four-component DFT-GIAO based calculations by Kaupp and co-workers of 1H NMR chemical shifts of a series of 3d, 4d, and 5d transition-metal hydrides have revealed significant spin-orbit-induced heavy atom effects on the hydride shifts, in particular for several 4d and 5d complexes. These calculations reveal that spin-orbit (SO) effects provide substantial, in some cases even the dominant, contributions to the well-known characteristic high-field (greater shielding) hydride shifts of complexes with a partially filled d-shell. The Buckingham-Stephens model of off-center paramagnetic ring currents to explain the characteristic and important high-field 1H shifts of transition-metal hydride complexes remains valid but has to be augmented by consideration of the sizable spin-orbit effects, particularly for 4d and 5d complexes. The spin-orbit contributions affect mainly the perpendicular shielding tensor contributions, thereby enhancing the “Buckingham-Stephens-type” terms. In contrast, complexes with a 4d10 and 5d10 configuration exhibit large deshielding SO effects on their hydride 1H NMR shifts. The differences between the two classes of complexes are attributed by Kaupp and co-workers to the dominance of π-type d-orbitals for the true transition-metal systems, compared to σ-type orbitals for the d10 systems.

If parity violation contributions are neglected, NMR spectroscopy cannot be directly used to determine the absolute configuration of chiral molecules in isotropic media, as the observable shielding and spin-spin coupling tensors are exactly the same for the two enantiomers of a chiral molecule. It has been shown that the shielding tensors in the L and R molecules have identical (observable) diagonal components and only differ in the signs of the off-diagonal elements of the symmetric part of the tensor and the antisymmetric part of the tensor, that is, all elements of the shielding tensors are either identical for L and R, or differ by a rotation dependent sign. In the presence of both a static electric field and a static magnetic field, a pseudo scalar quantity, σchiral, the chiral portion of the shielding, manifests itself as a term σchiralS · B × E in which σchiral has the same magnitude but opposite signs for the L and the R molecules, but still undetectable in conventional NMR spectroscopy where only the tensor component along the static magnetic field is observed. Buckingham, and Buckingham and Fischer have pointed out that the chiral portion of the shielding for molecules in both a static electric field and a static magnetic field depend on the electronic properties which are the electric polarizability of the shielding tensor. Thus, there has been a renewed interest in the calculations of the latter quantities. The non-vanishing components of the derivatives of the nuclear magnetic shielding with respect to the electric field and gradient of the amide N and H atoms of the isolated N-methyl acetamide molecule were calculated using the augmented basis set series introduced for these properties by Jensen, using various DFT exchange correlation functionals: B3LYP, KT3, PBE0 and compared with Hartree-Fock results. It is found that the electric field derivatives of the shielding depend more on the inclusion of augmented functions than the field-free shielding. Actually, there is better chance for observing the chiral part of the spin-spin coupling, due to the fact that the homonuclear pseudoscalar spin-spin coupling commutes with the Zeeman Hamiltonian, unlike the pseudoscalar nuclear shielding term so calculations of electric polarizability of J coupling have also received attention recently.

DFT has turned out to be an excellent compromise between the accuracy and computational efficiency that is particularly important when dealing with nuclear shielding calculations in larger systems. The underlying exchange-correlation (XC) functional is known to be the principal factor determining the accuracy of a DFT calculation, therefore, research on improvements on the currently available exchange correlation functionals remains an important and active area of theoretical research. An important role is currently played by hybrid XC functionals first introduced by Becke. Hybrid functionals include some admixture of the exact exchange energy. Despite the great success of global hybrid functionals, for example, B3LYP and PBE0, in predicting various molecular properties, they turned out not to be sufficiently flexible: it is usually not possible to find a unique constant for the amount of exact exchange admixture that provides consistently high accuracy for different properties as well as for different classes of systems. Local hybrids are a promising new generation of exchange-correlation functionals. In contrast to the constant exact exchange admixture of global hybrids, local hybrids include exact exchange in a position-dependent way, governed by a “local mixing function” (LMF). Therefore, considerable effort has been spent recently in developing hybrid functionals in which the extent of exact exchange admixture is introduced by a mixing function which determines the position-dependence of the exact exchange admixture. Recently, Arbuznikov and Kaupp reviewed the advances in hybrid functionals, discussed different strategies to construct LMFs (semiempirical vs. ab initio), different levels of the implementation of local hybrids (self-consistent vs. nonself-consistent), and some methodological aspects associated with the calculation of second-order magnetic properties (a coupled-perturbed scheme for general hyper-GGA functionals). They provide some examples for the performance of local hybrids in the description of NMR properties. A more detailed examination of the performance of local hybrid functionals for NMR properties is given in ref. 31 where recent work in the field of occupied-orbital dependent (OOD) exchange-correlation functionals in density functional theory is reviewed, with emphasis on the development of local hybrid functionals, and on the nontrivial self-consistent implementation of complex OOD functionals. Recently proposed LMFs have provided local hybrids of high accuracy in the computation of thermochemical data and with good performance for some magnetic-resonance parameters. These local hybrids require very few semi-empirical parameters. Two levels of the self-consistent implementation of OOD functional are discussed: one may either stop after the derivation of the functional derivatives with respect to the orbitals, leading to nonlocal potentials. This is discussed for local hybrids and for general OOD functionals up to and including the complicated B05 real-space model of non-dynamical correlation. Alternatively, one may append an additional transformation to local and multiplicative potentials based on the optimized effective potential (OEP) approach or of approximations to the OEP. Numerical results for various properties including nuclear magnetic shielding are reviewed.

(Continues…)Excerpted from Nuclear Magnetic Resonance Volume 41 by K. Kamienska-Trela, Jacek Wójcik. Copyright © 2012 The Royal Society of Chemistry. Excerpted by permission of The Royal Society of Chemistry.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.