Examples of anisotropic nuclear interactions Two directionally dependent interactions commonly found in solid-state NMR are the chemical shift anisotropy (CSA) and the internuclear dipolar coupling. Many more such interactions exist, such as the anisotropic J-coupling in NMR, or in related fields, such as the g-tensor in electron spin resonance. In mathematical terms, all these interactions can be described using the same formalism.
Experimental background Anisotropic interactions modify the nuclear spin energy levels (and hence the resonance frequency) of all sites in a molecule, and often contribute to a line-broadening effect in NMR spectra. However, there is a range of situations when their presence can either not be avoided, or is even particularly desired, as they encode structural parameters, such as orientation information, on the molecule of interest.
High-resolution conditions in solids (in a wider sense) can be established using magic angle spinning (MAS), macroscopic sample orientation, combinations of both of these techniques, enhancement of mobility by highly viscous sample conditions, and a variety of radio frequency (RF) irradiation patterns. While the latter allows decoupling of interactions in spin space, the others facilitate averaging of interactions in real space. In addition, line-broadening effects from microscopic inhomogeneities can be reduced by appropriate methods of sample preparation.
Under decoupling conditions, isotropic interactions can report on the local structure, e.g. by the isotropic chemical shift. In addition, decoupled interactions can be selectively re-introduced (recoupling"), and used, for example, for controlled de-phasing or transfer of polarization, which allows to derive a number of structural parameters.
Solid-state NMR line widths The residual line width (full width at half max) of 13C nuclei under MAS conditions at 5–15 kHz spinning rate is typically in the order of 0.5–2 ppm, and may be comparable to solution-state NMR conditions. Even at MAS rates of 20 kHz and above, however, non linear groups (not a straight line) of the same nuclei linked via the homonuclear dipolar interactions can only be suppressed partially, leading to line widths of 0.5 ppm and above, which is considerably more than in optimal solution state NMR conditions. Other interactions such as the quadrupolar interaction can lead to line widths of 1000's of ppm due to the strength of the interaction. The first-order quadrupolar broadening is largely suppressed by sufficiently fast MAS, but the second-order quadrupolar broadening has a different angular dependence and cannot be removed by spinning at one angle alone. Ways to achieve isotropic lineshapes for quadrupolar nuclei include spinning at two angles simultaneously (DOR), sequentially (DAS), or through refocusing the second-order quadrupolar interaction with a two-dimensional experiment such as MQMAS or STMAS.
Anisotropic interactions in solution-state NMR From the perspective of solution-state NMR, it can be desirable to reduce motional averaging of dipolar interactions by alignment media. The order of magnitude of these residual dipolar couplings (RDCs) are typically of only a few rad/Hz, but do not destroy high-resolution conditions, and provide a pool of information, in particular on the orientation of molecular domains with respect to each other.
Dipolar truncation The dipolar coupling between two nuclei is inversely proportional to the cube of their distance. This has the effect that the polarization transfer mediated by the dipolar interaction is cut off in the presence of a third nucleus (all of the same kind, e.g. 13C) close to one of these nuclei. This effect is commonly referred to as dipolar truncation. It has been one of the major obstacles in efficient extraction of internuclear distances, which are crucial in the structural analysis of biomolecular structure. By means of labeling schemes or pulse sequences, however, it has become possible to circumvent this problem in a number of ways.
Specifically, the external magnetic field induces currents of the electrons in molecular orbitals. These induced currents create local magnetic fields that often vary across the entire molecular framework such that nuclei in distinct molecular environments usually experience unique local fields from this effect.
Nuclear spins exhibit a dipole moment, which interacts with the dipole moment of other nuclei (dipolar coupling). The magnitude of the interaction is dependent on the spin species, the internuclear distance, and the orientation of the vector connecting the two nuclear spins with respect to the external magnetic field B (see figure). The maximum dipolar coupling is given by the dipolar coupling constant d,
History of discoveries of NMR phenomena, and the development of solid-state NMR spectroscopy:
Purcell, Torrey and Pound: "nuclear induction" on 1H in paraffin 1945, at about the same time Bloch et al. on 1H in water.
A fundamental RF pulse sequence and building-block in most solid-state NMR experiments is cross-polarization (CP) [Waugh et al]. It can be used to enhance the signal of nuclei with a low gyromagnetic ratio (e.g. 13C, 15N) by magnetization transfer from nuclei with a high gyromagnetic ratio (e.g. 1H), or as spectral editing method (e.g. directed 15N→13C CP in protein spectroscopy). In order to establish magnetization transfer, the RF pulses applied on the two frequency channels must fulfill the Hartmann–Hahn condition [Hartmann, 1962]. Under MAS, this condition defines a relationship between the voltage through the RF coil and the rate of sample rotation. Experimental optimization of such conditions is one of the routine tasks in performing a (solid-state) NMR experiment.
CP is a basic building block of most pulse sequences in solid-state NMR spectroscopy. Given its importance, a pulse sequence employing direct excitation of 1H spin polarization, followed by CP transfer to and signal detection of 13C, 15N) or similar nuclei, is itself often referred to as CP experiment, or, in conjunction with MAS, as CP-MAS [Schaefer and Stejskal, 1976]. It is the typical starting point of an investigation using solid-state NMR spectroscopy.
A technique that can substantially reduce or remove the chemical shift anisotropy, the dipolar coupling is sample rotation (most commonly magic angle spinning, but also off-magic angle spinning).
Homonuclear RF decoupling decouples spin interactions of nuclei which are the same as those which are being detected. Heteronuclear RF decoupling decouples spin interactions of other nuclei.
Although the broaden lines are often not desired, dipolar couplings between atoms in the crystal lattice can also provide very useful information. Dipolar coupling are distance dependent, and so they may be used to calculate interatomic distances in isotopically labelled molecules.
Because most dipolar interactions are removed by sample spinning, recoupling experiments are needed to re-introduce desired dipolar couplings so they can be measured.
An example of a recoupling experiment is the Rotational Echo DOuble Resonance (REDOR) experiment [Gullion and Schaefer, 1989].