Anisotropy lineshape analysis

One potential problem with chemical shift anisotropy lineshape analysis (or indeed analysis of lineshapes arising from any nuclear spin interaction) is that the analysis results in a description of the angular reorientation of the chemical-shielding tensor during the motion, not the molecule. To convert this information into details of how the molecule moves, we need to know how the chemical-shielding tensor (or other interaction tensor) is oriented in the molecular frame. A further possible complication with the analysis is that it may not be possible to achieve an experiment temperature at which the motion is completely quenched, and thus it may not be possible to directly measure the principal values of the interaction tensor, i.e. anisotropy, asymmetry and isotropic component. If the motion is complex, lack of certainty about the input tensor parameters leads to an ambiguous lineshape analysis, with several (or even many) possible fits to the experimental data. 

Several methods have been developed to determine the chemical shift anisotropies in the presence of small and large quadrupolar broadenings, including lineshape analysis of CT or CT plus ST spectra measured under static, MAS, or high-resolution conditions [206-210]. These methods allow for determination of the quadrupolar parameters (Cq, i)q) and chemical shift parameters (dcs, //cs> <5CT), as well as the relative orientation of the quadrupolar and chemical shift tensors. In this context, the MQMAS experiment can be useful, as it scales the CSA by a factor of p in the isotropic dimension, allowing for determination of chemical shift parameters from the spinning sideband manifold [211],... 

Motions with rates of the order of the nuclear spin interaction anisotropy can be assessed via lineshape analysis. These are generally motions of intermediate rates, a few kHz to tens of kHz for chemical shift and dipolar interactions, higher for quadrupolar interactions. 

In the review period there have been many studies of molecular motion using analysis of chemical shift anisotropy lineshapes. One that nicely illustrates what is currently possible concerns the motion of 13CO intercalated in C o.9 This is a particularly interesting example as both the CO and C6o molecules undergo reorientation, with the onset of motion occurring at different temperatures for the two species. Furthermore, the work uses a prior calculation of the potential... 

Another study used the VACSY experiment discussed in Section 2.2 to examine the molecular motion in the crystalline region on poly(e-caprolactone) via lineshape analysis of l3C chemical shift anisotropy powder patterns.79... 

Crystalline amino acids have often been used as model compounds for probing functional group interactions in proteins. The 3-site 120° jump motion of the ammonium (-NH3) group in alanine has been studied using 2H NMR lineshape analysis and by considering the anisotropy of the 2H spin-lattice relaxation [182]. The activation energy for this motion was estimated to be 40.5 kj mol-1. 

In contrast to n-paraffins, which exhibit no or only a slight C NMR CSA, aromatics or hydrocarbons with double or triple bonds show a much larger anisotropy. Therefore, benzene (57) and 2-butyne 14) were chosen as suitable probe molecules to study molecular motions by C NMR lineshape analysis. Theoretical lineshapes for different motional states of benzene and 2-butyne molecules are depicted in Figs. 3 and 4. The proton-decoupled C NMR spectra were recorded by means of the homemade NMR spectrometer UDRIS (University of Leipzig) and a BRUKER MSL 400 (Central Institute of Physical Chemistry, Berlin) at frequencies of 22.6 and 100.6 MHz (9,14,57). 

Lineshape analysis of or NMR signals arising from the quadrupolar interaction or chemical shifts anisotropy, respectively, can yield invaluable information about amplitude and motions in the solid [3,150-156]. The quadrupolar interaction, in particular, dominates the spectral pattern in NMR. The frequency of a deuterium resonance in the absence of molecular motion is given by... 

Fig. 2 Experimental analysis of the chemical shift anisotropy of high-silica ZSM-5 zeolite, (a) 29Si MAS NMR and (b) extracted CSA lineshapes from a two-dimensional CSA recoupling sequence dashed lines are simulated lineshapes. Adapted with permission from [79]. Copyright 2008 American Chemical Society...

For this reason, the study in question19 examined a sample of high-density polyethylene that was iso topically labelled with, 3C so as to produce isolated 13C spin pairs. Static 13C powder lineshapes were then observed as a function of temperature. Analysis of these by lineshape simulation shows that, indeed, the polyethylene chains do undergo 180° chain flips. The static lineshapes in this case result from the sum of chemical shift anisotropy and dipolar coupling. However, the chemical shift anisotropy is known and, as mentioned previously,... 

The work of Hong et al.15 discusses the theoretical analysis of the dipolar lineshapes in the limit of rapid, anisotropic motion. The analysis assumes a motionally averaged dipolar coupling tensor, i.e. the average of the tensor over all the sites/orientations visited during the course of the motion, which has an effective anisotropy AD and asymmetry //>... 

There have been several studies of shift anisotropy in paramagnetic solids, obtained from the orientation analysis of powder lineshapes. Bloembergen [76], Rundle [77], and Poulis and Hardeman [78] analyzed the orientation dependent shifts in single crystals of hydrated Cu salts at low temperatures. McGarvey and Nagy [79, 80] have investigated the temperature dependence of static powder spectra of uranocene U(CgHg)2, a system where all the protons are chemically equivalent. 

---