
R. Kurbanov, T. Zinkevich, A.
Krushelnitsky.
The nuclear magnetic resonance relaxation data analysis in solids: General R1/R1 rho equations and the modelfree approach
J. Chem. Phys. 135, (2011).
Abstract
The advantage of the solid state NMR for studying molecular dynamics is the capability to study slow motions without limitations: in the liquid state, if orienting media are not used, all anisotropic magnetic interactions are averaged out by fast overall Brownian tumbling of a molecule and thus investigation of slow internal conformational motions (e. g., of proteins) in solution can be conducted using only isotropic interactions. One of the main tools for obtaining amplitudes and correlation times of molecular motions in the mu s time scale is measuring relaxation rate R1 rho. Yet, there have been a couple of unresolved problems in the quantitative analysis of the relaxation rates. First, when the resonance offset of the spinlock pulse is used, the spinlock field can be oriented under an arbitrary angle in respect to B0. Second, the spinlock frequency can be comparable or even less than the magic angle spinning rate. Up to now, there have been no equations for R1 rho that would be applicable for any values of the spinlock frequency, magic angle spinning rate and resonance offset of the spinlock pulse. In this work such equations were derived for two most important relaxation mechanisms: heteronuclear dipolar coupling and chemical shift anisotropy. The validity of the equations was checked by numerical simulation of the R1 rho experiment using SPINEVOLUTION program. In addition to that, the applicability of the wellknown modelfree approach to the solid state NMR relaxation data analysis was considered. For the wobbling in a cone at 30 degrees and 90 degrees cone angles and twosite jump models, it has been demonstrated that the autocorrelation functions G(0)(t), G(1)(t), G(2)(t), corresponding to different spherical harmonics, for isotropic samples (powders, polycrystals, etc.) are practically the same regardless of the correlation time of motion. This means that the modelfree approach which is widely used in liquids can be equally applied, at least assuming these two motional models, to the analysis of the solid state NMR relaxation data.
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