Measuring and modeling anisotropy in the NMR of solids

Abstract

Since the earliest days of nuclear magnetic resonance (NMR) in solids, it has been known that the measurable quantities are inherently anisotropic. This anisotropy means that the measured values depend on the orientation of the individual crystallites in the magnetic field. Perhaps the best-known example is the chemical shift, where measurements in single crystals exhibit strong changes in the shift as the crystal is physically reoriented. This chemical shift anisotropy (CSA) is obscured in most solution studies because rapid reorientation occurs. One of the main advantages of anisotropic measurements is that multiple values can be measured for a single atomic position. In the case of CSA, three shifts per nucleus are typically reported. Likewise, measurements of the electric field gradient (EFG) tensor commonly provide two values per site. For structural studies, the availability of more than one data value for each atomic position greatly enhances the feasibility of accurately characterizing a structure.

In recent years, studies on anisotropy have moved beyond the development of new measurement methodology into detailed structural studies. These analyses typically combine experimental data with computational methods and one of the major conclusions from this work is that the CSA and EFG tensors are extraordinarily sensitive to structure. Indeed, it is now well established that in order to achieve acceptable agreement between experimental and computed values, some refinement of atom positions derived from diffraction studies is necessary. Interestingly, this refinement has been found to be necessary at both hydrogen and nonhydrogen positions.

This special issue focuses on anisotropic studies involving the CSA and EFG tensors. Considerable progress has occurred in the past two decades in terms of measuring, modeling, and employing anisotropy in structural studies. Hereinafter, the work presented is equally divided between those measuring and modeling the CSA and studies involving the EFG tensor. These manuscripts provide an illustration of the wide range of studies now underway and involve a diverse range of nuclides including ¹³C, ¹⁴N, ¹⁵N, ³⁵Cl, and ⁵¹V in diamagnetic and paramagnetic solids. The overall aim of this issue is to emphasize that experimental developments have made the measurement of anisotropy in NMR more accessible and that modern modeling methods provide a general and widely available tool set for relating these measurements to structure.