Line-broadening in NMR

Line broadening in nmr experiments has been used to determine self-exchange rates for [Ru(4,4 -Me2bipy)(hfac)2] , [Ru(4,4 -Me2bipy)-(acac)2] and [Ru(hfac)3] in acetonitrite solution. The reactions are outer-sphere in nature and vary with solvent dielectric according to Marcus expectations. 

Slowly tumbling large molecules, such as proteins, undergo rapid transverse relaxation, which causes line broadening in the NMR spectrum. This imposes an upper limit on the size of molecules whose structures can be usefully interpreted by NMR. Small molecules tumble at high rates and have much slower relaxation rates, and therefore a sharper well-resolved NMR spectrum. 

We have referred to the various interactions which can cause line broadening in the solid state. One of these, which is normally not a problem in liquid state NMR, is due to the fact that the chemical shift itself is a tensor, i.e. in a coordinate system with orthogonal axes x, y and z its values along these axes can be very different. This anisotropy of the chemical shift is proportional to the magnetic field of the spectrometer (one reason why ultra-high field spectrometers are not so useful), and can lead in solid state spectra to the presence of a series of spinning sidebands, as shown in the spectra of solid polycrystalline powdered triphenylphosphine which follows (Fig. 49). In the absence of spinning, the linewidth of this sample would be around 75 ppm ... 

The nucleus is quadrupolar (spin 7/2, natural abundance 99.76%), and thus, the spectra can be affected by both the first- and second-order quadru-pole interaction, though the second-order broadening is generally not the largest source of line broadening in these materials. In general, three major anisotropic interactions influence the line shapes seen in the NMR spectra of solid samples (i) the qua-... 

Ichikawa, K. and Matsumoto, T., An aluminium-27 NMR study of chemical exchange and NMR line broadening in molten butylpyridinium chloride + AlClg ll,/. Magn. Reson., 63,445,1985. 

A. Meissner, P. Bloch, E. Humpfer, M. Spraul and O. W. Sorensen, Reduction of inhomogeneous line broadening in two-dimensional high-resolution MAS NMR spectra of molecules attached to swelled resins in solid-phase synthesis, J. Am. Chem. Soc., 1997, 119, 1787-1788. 

The frequency differences between ESR hyperfine components are much greater than NMR spin-spin splittings, so that the N14 quadrupole moment does not give line broadening in ESR spectra. 

In a study of rates of degenerate 1,2-shifts in tertiary carbocations, Saunders and Kates854 used higher-field (67.9 MHz) 13C NMR line broadening in the fast-exchange limit. The 2-butyl cation showed no broadening at — 140°C. Assuming the hypothetical frozen out chemical shift difference between C(2) and C(3) to be 227 ppm, an upper limit for AG was calculated to be 2.4 kcal mol 1. 

An even closer parallel is found in the work of Kreilick (33, 34), who prepared the ketal derived from 2,6-di-tert-butyl-4-acetoxyphenol. From a study of the effect of temperature on line broadening in the NMR spectrum of this compound he concluded that rearrangement occurs both by dissociation to radicals and recombination and by a direct intramolecular process. The former corresponds to the key reaction of the redistribution mechanism, while the latter is entirely analogous to the ketal rearrangement mechanism (Reaction 15). 

The dipole-dipole coupling and the inhomogeneities are responsible for line broadening in a NMR spectrum when the molecular motions are slow. From line width and form of the spectrum data may be obtained of nuclear positions. Hence, T2 determines the width of the resonance line, but has no correspondence with the saturation or the overall degree of occupation of the nuclear energy levels, like Ti has. T2 is always less than or equal to Ti (see Table 12.6). 

Before going into some detail on the applied techniques, we shall first summarise the causes of line broadening in the spectra of solids. Line broadening in 13C NMR spectra of solids will be discussed below. 

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