NMR Metholodogy

In the last century magnetic resonance spectroscopy developed into one of the most powerful tools for probing structure and dynamics in all states of matter. Not surprisingly, there have been many Nobel Prizes for magnetic resonance related research, starting with the work of I. I. Rabi (Physics, 1944) for the magnetic resonance detection method. Since then four other Nobel prizes have been awarded for enhancing the technique beyond all previous expectations (Physics, 1952: F. Bloch and E. M. Purcell for the first detection of nuclear magnetic resonance (NMR) in bulk samples; Chemistry, 1991: R. R. Ernst for developing Fourier transform and multi-dimensional NMR, and most recently, Chemistry, 2002: K. Wuthrich for protein 3D structure methods, and Medicine, 2003: P. C. Lauterbur and P. Mansfield for magnetic resonance imaging).

One of the most active and exciting areas of NMR research today concerns its application to solid and heterogeneous samples. A large part our research interests lies in the substantial methodological advances that have occurred in the last decade that now allow NMR to be used as a probes of structure and dynamics in solids.

NMR Methods for Quadrupolar Nuclei in Solids

All NMR active nuclei possess a magnetic dipole moment. The couping of this magnetic dipole moment to external magnetic fields as well as the magnetic dipole moments of neighboring nuclei, is central to the NMR experiment. Nuclei with a spin angular momentum quantum numbers greater than 1/2 are called quadrupolar nuclei because these nuclei posess, in addition to their magnetic dipole moment, an electric quadrupole moment. The symmetry allowed nuclear moments as a function of spin I are given in the table below.


Quadrupolar nuclei comprise nearly 70% of the NMR active nuclei in the periodic table, as shown below.


An electric quadrupole moment couples to its surrounding electric field gradient, which for a nucleus arises from asymmetric bonding environments. Quite often, this electric quadrupolar coupling is much stronger than the magnetic couplings to neighboring nuclei. In both the liquid and the solid state, the effect of such strong quadrupolar couplings on the NMR spectrum is the same: a significant loss in NMR sensitivity and resolution, although the mechanism for producing this effect is different in each case.

In solution state NMR strong quadrupolar couplings lead to short nuclear spin relaxation times which result in homogeneously broadened resonances that are often indistinguishable from the baseline. One common approach for improving solution-state NMR resolution of quadrupolar nuclei is to collect spectra at elevated temperatures where molecular re-orientational correlation times are much shorter than the NMR time scale, and homogeneous line broadenings due to quadrupolar relaxation is diminished. Unfortunately, the temperature needed to reach this motional narrowing regime is often impractically high for many samples.

For solid state NMR, where molecular re-orientational correlation times are typically much longer than the NMR time scale, quadrupolar nuclei do not suffer from such short relaxation times and large homogeneous line widths. Instead, they suffer from frequency anisotropies on the order of megaHertz, i.e., larger than the bandwidth of most NMR spectrometers. Thus, it can be problematic getting the complete NMR spectrum of a quadrupolar nucleus in a polycrystalline sample. Fortunately, for half-integer spin quadrupolar nuclei, the central m=1/2 -1/2 quantum transition is unaffected by the quadrupolar anisotropy to first order. For example, in the figure below is a simulated 87Rb NMR spectrum at 9.4 Tesla (400 MHz 1H) of a polycrystalline sample with a single 87Rb site with a quadrupolar coupling constant, Cq, of 3.2 MHz and quadrupolar asymmetry parameter, ηq, of 0.2.


Compared to the central transition, the anisotropic broadening of the outer satellite transitions, i.e., m=3/2 1/2 and m=-1/2 -3/2, is so severe in this example that their intensity is reduced by nearly a factor of 50 compared to the central transition.

Although the development of solid-state NMR techniques like Magic-Angle Spinning (MAS) in the 1950's and multiple pulse line narrowing approaches in the mid-1960's have made the observation of isotropic site-resolved spectra of spin 1/2 nuclei in polycrystalline solids routine today, NMR spectroscopists interested in exploiting quadrupolar nuclei with these coherent averaging schemes were often disappointed. The effect of applying conventional speed MAS to the same sample as the Figure above is shown in the figure below.


The satellite transitions are broken up into a centerband and numerous spinning sidebands and only the centerband for the central transition remains at this spinning speed. Notice, however, that while MAS reduces the anisotropic broadening, a high-resolution isotropic spectrum is not obtained for the central nor satellite transitions. Magic-angle spinning and related multiple-pulse techniques were only designed to give isotropic spectra under the conditions that the Zeeman interaction was orders of magnitude stronger than all other spin interactions. When this is not the case, these techniques fail to yield isotropic spectra. Probing a little deeper into the theory one finds that a common assumption in NMR that the quantization axis of the nuclear spin Hamiltonian is along the external magnetic field direction is not always valid for many quadrupolar nuclei. A simplfied picture describing this situation is shown below.


The strong quadrupolar coupling tilts the nuclear spin quantization axis away from the external magnetic field direction. This small tilting results in a more complicated orientation dependence for the NMR transition frequency as well as amplitude. Of course, NMR is significantly more sensitive to frequency than amplitude variations, and it is the frequency anisotropy of quadrupolar nuclei that has presented the greatest challenge to solid-state NMR. Using a well chosen static perturbation theory expansion of the spin eigenvalues and eigenstates, one sees that MAS, by itself, lacks the necessary symmetry in its reorientation trajectory to average away the anisotropy in the higher-order corrections to the NMR frequency for quadrupolar nuclei. Because of these difficulties in both the liquid and solid state, quadrupolar nuclei had never enjoyed the same widespread success as spin 1/2 nuclei in NMR spectroscopy.

Over the last decade solid-state NMR of quadrupolar nuclei has undergone a renaissance starting with techniques such as double rotation (DOR) and dynamic angle spinning (DAS) which provided high resolution isotropic spectra of quadrupolar nuclei for the first time, followed by the subsequent introduction of the transition correlated magic-angle spinning experiments: multiple-quantum MAS (MQ-MAS) and satellite transition MAS (ST-MAS). From a mechanical point of view the transition correlated magic-angle spinning experiments are easier techniques to experimentally implement as they can be performed with most commercial MAS probes and have gained the most widespread use.

While all these techniques are welcome additions to the solid-state NMR spectroscopist's toolbox, the inherently low sensitivity of many quadrupolar nuclei still remains an obstacle to their full exploitation. Our lab has also been involved in developing methods such as Rotor Assisted Population Transfer (RAPT) for enhancing the solid-state NMR central transition (CT) sensitivity of half-integer quadrupolar nuclei by transferring populations from the (unobserved) satellite transitions (ST) through selective saturation of the satellite transitions. An improved RAPT sequence using Frequency-Switched Gaussian pulses (FSG-RAPT) was later designed to provide not only a more robust experimental enhancement but also the ability to measure quadrupolar coupling constants. This approach combines the sensitivity advantage of the central transition with the Cq measurement precision advantage of the satellites. The dependence of the FSG-RAPT enhancement on offset frequency for nuclei with different Cq values was also exploited to design RAPT sequences for the selective excitation or suppression, respectively, of nuclei with large quadrupolar couplings.