Lineshape dipolar

When a large nurWber of spins interact, the numerous lines of the splitting pattern overlap and merge into a continuous lineshape whose functional form cannot be obtained from theory. Yet this shape contains useful geometrical information. One means of representing this dipolar lineshape g(w) is by a moment expansion... 

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 //>... 

Fig. 11. The LG-CP experiment of Fig. 9(a) applied to - C dipolar couplings in polycarbonate.15 (a) The full two-dimensional spectrum, (b) The LG-CP dipolar lineshape for the quaternary 13C (carbon 4), which as expected shows only very small - C dipolar couplings (as evidenced by the lack of observable splitting of the lineshape). (c) The LG-CP dipolar lineshape for carbon 3. (d) The best-fit simulation to the lineshape in (c). The motion used in this simulation (fast limit) assumes that the phenyl ring containing the carbon reorients about the local twofold axis of the ring through an angle of 120°, with the reorientation axis wobbling with an amplitude of 20°.

NMR quadrupolar/ Chemical shift anisotropy/ Magnetic dipolar lineshapes Infrared/ Raman spectroscopy Inelastic x-ray/Neutron scattering... 

In molecularly rigid systems, the direct (through-space) dipole-dipole interaction between nuclear spins I = fe is normally the dominant source of broadening of the NMR lineshape. For a pair of similar nuclear spins i and j in a magnetic field Hq the dipolar splitting in their spectrum is given by... 

Multiple-pulse measurements were performed on both the LP and HP samples at 20° and — 80° C, and when no differences were noted, lower temperature measurements were performed only on the LP sample. Multiple-pulse spectra for the LP sample are illustrated in Figure 4 together with the eight-pulse spectrum of the reference used for the low-temperature measurements, Ca(OH)2. The lineshapes observed are quite broad, and the line center is a function of temperature. The line width was separated into three contributions by performing three related multiple-pulse measurements (I). These indicated that the main contributions to the linewidth came from both relaxation and second-order dipolar effects. The maximum possible field inhomogeneity Hamiltonian is estimated to be less than 16 ppm by this means, which indicates that the com-... 

Figure 6 is a plot of the proton NMR spectrum obtained from H2Os3(CO)io when using an eight-pulse cycle (5, 6,16,17,18) to suppress the effects of proton-proton dipolar interactions. The curve results from a computer fit that assumes the lineshape is caused by the chemical shift tensor. The center of the spectrum is near r = 19 ppm, and thus it agrees reasonably with that expected from the solution NMR results (r = 21.7 ppm (37)). The three principal values of the tensor, according to this fit, are at r values 5.6 ppm, 19.9 ppm, and 31.6 ppm. Since approximately one-third of the proton pairs interact with a near... 

Spectral lineshapes were first expressed in terms of autocorrelation functions by Foley39 and Anderson.40 Van Kranendonk gave an extensive review of this and attempted to compute the dipolar correlation function for vibration-rotation spectra in the semi-classical approximation.2 The general formalism in its present form is due to Kubo.11 Van Hove related the cross section for thermal neutron scattering to a density autocorrelation function.18 Singwi et al.41 have applied this kind of formalism to the shape of Mossbauer lines, and recently Gordon15 has rederived the formula for the infrared bandshapes and has constructed a physical model for rotational diffusion. There also exists an extensive literature in magnetic resonance where time-correlation functions have been used for more than two decades.8... 

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. 

Fig. 3. Example spectra from the one-dimensional dipolar-shift experiment taken from reference 7. (a) (Top) Experimental l3C chemical shift anisotropy powder pattern for Ru(C5H5)2 and (below) for comparison, the dipolar shift l3C spectrum for the same compound, (b) Calculated dipolar-shift lineshapes for different angles (indicated) between the lH-13C dipolar and chemical shift anisotropy tensor principal z-axes.

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,... 

In the review period there have been several papers on 2H lineshape analysis. One of the most important is that discussing the validity of Markov models for modelling molecular dynamics6 discussed previously. Another important paper discusses the effect of dipolar coupling on 2H lineshapes, with particular emphasis on ND and ND2 groups.34 The effect of any dipolar... 

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