Dipolar order under fast magic-angle spinning

Second-order dipolar order in magic-angle spinning nuclear magnetic resonance

Generating dipolar order under magic-angle spinning (MAS) conditions is explored for different pulse sequences and dipolar-coupling networks. It is shown that under MAS second-order dipolar order can be generated reliably with 10% to 30% efficiency using the Jeener-Broekaert sequence in systems where the second-order average Hamiltonian is a (near) constant of the motion. When using adiabatic demagnetization and remagnetization, second-order dipolar order can be generated and reverted back to Zeeman order with up to 60% efficiency. This requires a maximum field strength with a nutation frequency that is less than one-quarter of the rotor frequency, and that the spin system can be properly spinlocked under such conditions. A simple coherent description accounts for the principal features of the spin dynamics, even using the smallest possible system of three coupled spins. For the systems investigated, the lifetime of second-order dipolar order under MAS was found to be on the order of T(1).

Cross-correlations between low-γ nuclei in solids via a common dipolar bath

Correlation of chemical shifts of low-γ nuclei (such as 15N) is an important method for assignment of resonances in uniformly-labeled biological solids. Under static experimental conditions, an efficient mixing of low-γ nuclear spin magnetization can be achieved by a thermal contact to the common reservoir of dipole-dipole interactions in order to create 15N-15N, 13C-13C, or 15N-13C cross-peaks in a 2D correlation spectrum. A thermodynamic approach can be used to understand the mechanism of magnetization mixing in various 2D correlation pulse sequences. This mechanism is suppressed under magic-angle spinning, when mixing via direct cross-polarization with protons becomes more efficient. Experimental results are presented for single-crystalline and powder samples of 15N-labeled N-acetyl-L-15N-valyl-L-15N-leucine (NAVL). In addition to the thermodynamic analysis of mixing pulse sequences, two different new mixing sequences utilizing adiabatic pulses are also experimentally demonstrated.

Origins of linewidth in 1H magic-angle spinning NMR

A detailed study of the factors determining the linewidth (and hence resolution) in 1H solid-state magic-angle spinning NMR is described. Although it has been known from the early days of magic-angle spinning (MAS) that resolution of spectra from abundant nuclear spins, such as 1H, increases approximately linearly with increasing sample rotation rate, the difficulty of describing the dynamics of extended networks of coupled spins has made it difficult to predict a priori the resolution expected for a given sample. Using recently developed, highly efficient methods of numerical simulation, together with experimental measurements on a variety of test systems, we propose a comprehensive picture of 1H resolution under MAS. The "homogeneous" component of the linewidth is shown to depend primarily on the ratio between an effective local coupling strength and the spin rate, modified by geometrical factors which loosely correspond to the "dimensionality" of the coupling network. The remaining "inhomogeneous" component of the natural linewidth is confirmed to have the same properties as in dilute-spin NMR. Variations in the NMR frequency due to chemical shift effects are shown to have minimal impact on 1H resolution. The implications of these results for solid-state NMR experiments involving 1H and other abundant-spin nuclei are discussed.

Constants of motion in NMR spectroscopy

We present a general method for constructing a subset of the constants of motion in terms of products of spin operators. These operators are then used to give insight into the multi-spin orders comprising the quasi-equilibrium state formed under a Jeener-Broekaert sequence in small, dipolar-coupled, spin systems. We further show that constants of motion that represent single-quantum coherences are present due to the symmetry of the dipolar Hamiltonian under 180 degrees spin rotations, and that such coherences contribute a DC component to the FID which vanishes in the absence of the flip-flop terms and is only present for spin clusters with an odd number of spins.