Quadrupolar nuclei parameters

Figure 23 Second order shifts in spin-1/2 spectra arising from coupling to a quadrupolar nucleus with S = 5/2, as a function of the parameter %D lu,...

In Section 2.2.6, the nutation frequency of a quadrupolar nucleus was seen to vary from (I + /2)v] when vi << vq to V when V >> vq. The nutation spectra display distinct features in the region where vi vq. Simulation of nutation behaviour has shown that the useful range of rf field-strengths lies with vq/vi in the range 0.05-1. The distinct features of nutation spectra allow the quadrupole parameters to be obtained. This means that only quadrupole frequencies up to a certain limit are accessible with currently available rf-fields of 500 kHz in specially dedicated probeheads, and in fields of around 100 kHz in most commercially available systems. This constraint especially limits the investigation of spin I = 3/2 nuclei such as Na. 

Fig. 5 The effect of magic-angle spinning on the central transition lineshape for a half-integer spin quadrupolar nucleus. Left central transition lineshape under static, i.e., non-spinning conditions. Right the same transition under magic-angle spinning. The asymmetry parameter r is given with each spectrum. Reproduced with permission from [61])...

Since the short relaxation times associated with a quadrupolar nucleus drastically reduce the time delay to be applied in an NMR experiment between two pulses, measuring times are short or, in other words, distinct NMR signals can often be detected with a limited time spent down to micromolar concentrations. Along with this apparent advantage, quadrupolar nuclei provide information in addition to the classical parameters chemical shift (or shielding) and nuclear spin-spin coupling constants. Variations in linewidths for quadrupolar nuclei are another sensitive quantity allowing for the evaluation of the electronic and the steric situation in the first coordination sphere of a vanadium compound, its periphery, its (local) symmetry and its interaction with the matrix, i.e. counter-ions, solvent molecules and other constituents present in solution. 

Under anisotropic conditions, NMR lineshapes for a quadrupolar nucleus are dominated by chemical shielding and (first and second order) quadrupolar interactions. Dipolar interaction is usually a minor contribution only. First-order quadrupole interaction lifts the degeneracy of the allowed 21 (i.e. seven in the case of V / = V2) Zeeman transitions as shown in Figure 3.7, giving rise to seven equidistant lines, viz. a central line (mj = + V2 -V2. unaffected by quadrupole interaction) and six satellite lines. The overall breadth of the spectrum is determined by the size of the nuclear quadrupole coupling constant Cq the deviations from axial symmetry and hence the shape of the spectral envelope are governed by the asymmetry parameter. Static solid-state NMR thus provides additional parameters, in particular the quadrupole coupling constant, which correlates with the electronic situation in a vanadium compound. [ 1 The central component reflects the anisotropy of the chemical shift. 

Following the approach of Werbelow and co-workers, the lineshape of a spin-1/2 nucleus scalar-coupled to a quadrupolar nucleus may be simulated in terms of the relaxation parameters of the quadrupolar nucleus, provided that... 

Such results exemplify the analytic use of NMR of a quadrupolar nucleus. It Is not mandatory to be able to make a detailed Interpretation of the NMR parameters, chemical shifts and llnewldths, for each of the chemlced species In the solution to which the quadrupolar nucleus can attach Itself. If these NMR parameters differ sufficiently between these various species, relative concentrations can be obtained and such Information can be quite valuable. Re rdlng the structure of the ion pairs themselves, at present Na NMR Is restricted to distinguishing between tight, loose or dissociated Ion pairs, which It can do rather reliably (24). But obviously. It Is to be complemented by h and NMR If Information about the geometry and the electron distribution In the anion Is desired (25-27). 

There are several approximate methods often useful in understanding the trends in the quadrupole parameters in a related series of molecules containing the same quadrupolar nucleus. One. due to Townes and Dailey, is essentially a localized orbital approach, in which attention is focused on changes in the orbital populations of the atom containing the quadrupolar nucleus, and polarization of the core electrons (the so-called Sternheimer polarization factor) is assumed to vary negligibly from one molecule to another. In the case for example,... 

Hyperfine Parameters From a quantum chemical point of view, the quantity required for the determination of the nuclear quadrupole-coupling tensor is the electric field gradient at the quadrupolar nucleus. This is a first-order property which can be computed as either the first derivative of the energy with respect to the nuclear quadrupole moment or the expectation value of the corresponding (one-electron) operator... 

Deuterium, whose spin is equal to 1, is a quadrupolar nucleus. Its NMR parameters are almost exclusively governed by the quadrupolar interaction with the electric field tensor (FGT) at the deuteron site. Although the intermolecular contributions to the electric field gradient can be significant, the field gradient usually originates mainly from the electrons in the C- H bond and is considered to a first approximation to be intramolecular. It is found to be axially symmetric about the C- H bond in aliphatic compounds, and to a good approximation in aromatic compounds as well. Thus, information obtained from H NMR on molecular order and dynamics mostly concerns individual C- H bond directions. 

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