Determination of the antisymmetric part of the chemical shift anisotropy tensor via spin relaxation in nuclear magnetic resonance

Abstract

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.

Lanthanide-induced relaxation anisotropy

“…It wasn't until 2016 that violations were seen: 36 in reality, Curie relaxation rates also depend on the angle that the lanthanide-nucleus vector makes with the principal axes of the magnetic susceptibility tensor. [35][36][37] There is also a deeper aspect: paramagnetic chemical shielding tensors are unusual because of their large asymmetry, 37 which is negligible in diamagnetic cases, 60 but becomes very important for the systems reported here -the product of two symmetric matrices is only symmetric when they commute, which is not the case for D and χ .…”

“…Guéron 26 did not consider susceptibility anisotropy. The other reason is that the antisymmetric component of the chemical shielding tensor, usually ignored in diamagnetic systems due to its small amplitude, 60 is significant here -the product of two symmetric matrices is only symmetric when they commute, which is not the case for D and aniso χ . We therefore have the antisymmetric term in the shielding tensor that is actually of the same order of magnitude as the symmetric term, and must therefore be included into the analysis of the nuclear relaxation.…”

Expanding the utility of NMR restraints with paramagnetic compounds: Background and practical aspects

“…The total chemical shielding tensor σ is a non-symmetric tensor that can be decomposed into three independent tensors: an isotropic component, a traceless symmetric component, and a traceless antisymmetric component [116–118]: $$\sigma ={\sigma }^{\text{italiciso}}+{\sigma }^{\text{italicsym}}+{\sigma }^{\text{italicanti}}$$ …”

A Magic‐Angle‐Spinning NMR Spectroscopy Method for the Site‐Specific Measurement of Proton Chemical‐Shift Anisotropy in Biological and Organic Solids

“…Since the antisymmetric part of the tensor is known not to yield measurable contributions to the resonance frequencies, it can in general be ignored. [23] However, in the fast-motion limit it can make a sizable contribution to relaxation rates in liquids [24–25] and should, in principle, be taken into account when relaxation measurements are used for the determination of proton shift tensors. The size of this effect on cross-correlated relaxation rates (see below) was estimated by Sharma et al based on DFT calculations of amide-proton shift tensors in a protein and was found to be negligible.…”