Evaluation of Spin Relaxation Induced by Chemical Shielding Anisotropy: A Comment on the Importance of the Antisymmetric Component (original) (raw)
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Chemical Physics Letters, 1990
The first experimental detection of an antisymmetrical component (u') in the NMR shielding tensor of a nucleus is reported. The 13C NMR relaxation rates ( I /T, and 1 /T,) of the ethyledic carbons in tetrachlorocyclopropeene in toluene-d, at about -90°C are dominated at high fields by the shielding tensor modulated by random molecular rotation. We find that T2 is circa 1.1 T, in contrast to that in "CS*, where u' is zero by symmetry and where the measured Tz is not greater than the maximum (O.S57r, ) allowed for this case. The present results are in qualitative agreement with previous ab initio IGLO calculations showing thaf the ethylenic carbons in cyclopropenes have unusually large antisymmetric components in their shielding tensors.
The Journal of Chemical Physics, 2010
Relaxation processes induced by the antisymmetric part of the chemical shift anisotropy tensor ͑henceforth called anti-CSA͒ are usually neglected in NMR relaxation studies. It is shown here that anti-CSA components contribute to longitudinal relaxation rates of the indole 15 N nucleus in tryptophan in solution at different magnetic fields and temperatures. To determine the parameters of several models for rotational diffusion and internal dynamics, we measured the longitudinal relaxation rates R 1 =1/ T 1 of 15 N, the 15 N-1 H dipole-dipole ͑DD͒ cross-relaxation rates ͑Overhauser effects͒, and the cross-correlated CSA/DD relaxation rates involving the second-rank symmetric part of the CSA tensor of 15 N at four magnetic fields B 0 = 9.4, 14.1, 18.8, and 22.3 T ͑400, 600, 800, and 950 MHz for protons͒ over a temperature range of 270Ͻ T Ͻ 310 K. A good agreement between experimental and theoretical rates can only be obtained if the CSA tensor is assumed to comprise first-rank antisymmetric ͑anti-CSA͒ components. The magnitude of the hitherto neglected antisymmetric components is of the order of 10% of the CSA.
The journal of physical chemistry letters, 2016
The broadly accepted procedure to obtain the experimental absolute scale of NMR magnetic shieldings, σ, is well-known for nonheavy atom-containing molecules. It was uncovered more than 40 years ago by the works of Ramsey and Flygare. They found a quite accurate relationship among σ and the nuclear spin-rotation constants. Its relativistic extension was very recently proposed, although it has an intrinsic weakness because a new SO-S two-component term needs to be considered. We show how to overcome this problem. We found that (νY(S) - νY(atom,S)) generalizes the SO-S term, where νY(S) = ⟨⟨[((r - rY) × α)/(|r - rY|(3))]; S((4))⟩⟩, r - rY is the electron position with respect to the position of nucleus Y, and S((4)) is the four-component total electron spin. When including this new term, one finds that the best of our relativistic Flygare-like models fits quite well with the results of the most accurate method available at the moment. We also show that the difference among the parallel...
The shielding tensor part II: Understanding its strange effects on relaxation
Concepts in Magnetic Resonance, 1992
The shielding tensor can be nonsymmetric and thus in general has both symmetric and antisymmetric parts. Relaxation by these two parts of the shielding tensor (chemical shift anisotropy or CSA relaxation) are reviewed and compared with relaxation by the dipole-dipole (DD) mechanism. It is explained how T, can be equal to (6/7)T1 or to 2T1 in limiting situations for relaxation that involves the shielding tensor.
Recent Advances in Theoretical and Physical Aspects of NMR Chemical Shifts
Kimika, 2015
In the first part of this review, theoretical aspects of nuclear magnetic shielding include (a) general theory, for example, newly developed approaches in relativistic theory of nuclear shielding, the relation between the spin-rotation tensor and shielding in relativistic theory, ab initio methods for treating open shell systems and a complete theory of chemical shifts in paramagnetic systems, the link between the definitions of the elusive concepts aromaticity and anti-aromaticity and the magnetic properties: the magnetizability tensor and the nuclear magnetic shielding tensor via delocalized electron currents and electron current maps, (b) ab initio and DFT calculations, both relativistic and non-relativistic, for various nuclei in various molecular systems using various levels of theoretical treatment. Physical aspects include (a) anisotropy of the shielding tensor, usually from solid state measurements, and calculations to support these, (b) shielding surfaces and rovibrational averaging, paying special attention to the sensitive relationship between shielding and bond angles or torsion angles that makes shielding such a powerful tool for structural/conformational determination in macromolecules, (c) chemical shifts that arise from isotopic substitution of NMR nucleus or neighboring nuclei, (d) intermolecular effects on nuclear shielding, and (e) absolute shielding scales.
The Journal of Chemical Physics, 2002
This work investigates the nature of second order effects resulting in solid state nuclear magnetic resonance ͑NMR͒, from cross-correlations between the quadrupolar and shielding couplings. Using an average Hamiltonian theory, it is shown that these effects can bring the nonsecular terms of the shielding interaction into the realm of conventional detection. Such terms include the antisymmetric components of the chemical shift tensor, which, although postulated to exist, have hitherto eluded direct experimental measurement. As numerical calculations supported these analytical derivations, an experimental study was undertaken to measure such components from the single-crystal rotation plot of a half-integer quadrupolar nucleus. A custom-made probehead was built, a data analysis procedure developed, and together these were used to analyze the satellite transition spectra arising from a 59 Co single crystal of cobalt͑III͒tris͑acetylacetonate͒. The results of repetitive studies on such sample are reported.
Nuclear spin relaxation due to chemical shift anisotropy of gas-phase 129Xe
Physical Chemistry Chemical Physics, 2011
Nuclear spin relaxation provides detailed dynamical information on molecular systems and materials. Here, first-principles modeling of the chemical shift anisotropy (CSA) relaxation time for the prototypic monoatomic 129 Xe gas is carried out, both complementing and predicting the results of NMR measurements. Our approach is based on molecular dynamics simulations combined with pre-parametrized ab initio binary nuclear shielding tensors, an ''NMR force field''. By using the Redfield relaxation formalism, the simulated CSA time correlation functions lead to spectral density functions that, for the first time, quantitatively determine the experimental spin-lattice relaxation times T 1 . The quality requirements on both the Xe-Xe interaction potential and binary shielding tensor are investigated in the context of CSA T 1 . Persistent dimers Xe 2 are found to be responsible for the CSA relaxation mechanism in the low-density limit of the gas, completely in line with the earlier experimental findings. 1312, +358-(0)8-553 1343 w Electronic supplementary information (ESI) available: Details of Redfield theory for CSA relaxation; computational details; error sources and antisymmetric terms in CSA-induced nuclear spin relaxation; supporting figures and tables. See
Physical Review A
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 (σ) and nuclear spin-rotation constants (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 CH 3 X molecules (X = F, Cl, Br, and I), is given here. The analysis of each electronic mechanism of σ shows that most of their electron correlation effects are strongly related with the same effects in 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 σ. Calculations of M Y and σ Y (Y = 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 M and experimental data are obtained from calculations at 4c-PBE0 level of theory in all cases, but not for M ,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.
Molecular Physics, 2000
The 'Gauge Including Atomic Orbitals' (CIAO) approach is used to investigate the question of intramolecular rotation. Ab initio CIAO calculations of NMR chemical shielding tensors carried out with GAUSSIAN 94 within the SCF-Hartree-Fock approximation are described. In order to compare the calculated chemical shifts with experimental ones, it is important to use consistent nuclear shieldings for NMR reference compounds like TMS. The influence of rotating functional groups X=CH3, CHO, NO2, NH2, CONH2, COOH or C6H5 on the shielding tensors in seven vinylic derivatives H2C=CH-X is studied; the molecules are propene, acrolein, nitroethylene, ethyleneamine, acrylamide, acrylic acid and styrene. We observe a marked dependence of nuclear shielding and chemical shift on the torsional movement. Different Boltzmann averages over the conformational states are considered and compared for gas phase, liquid and solid state NMR. Their applicability to model cases for rigid or freely rotating molecules and for fixed molecules (e.g. polymers or proteins) with rapidly rotating groups is discussed and simple calculation models are presented. On the basis of this work it can be concluded that intramolecular rotation clearly affects the observed averages. Effects of up to 2 ppm have been observed for isotropic chemical shifts, and up to 17 ppm difference have been observed for individual tensor components, for example, of the carboxylic I3C atom in acrylic acid. The variation of the shielding tensor on a nucleus in a fixed molecular backbone resulting from an attached rotating group furthermore leads to a new relaxation mechanism by chemical shift anisotropy.