Second-order quadrupole splittings

Fig. 7.2. Powder patterns for I = 3/2 showing (a) NMR spectrum in the presence of first-order quadrupole effects and (b) the effect on the central component in the spectrum of second-order effects. The spectra are shown relative to the central point, with Ap and denoting first- and second-order quadrupole splittings,...

Here p is the probability for occupation of site i characterized by the field gradient q and the order parameter S. For a powder sample the second-order "quadrupole splitting" is given by... 

The resonance position is slightly solvent dependent,and the temperature gradient is 0.29 ppm/deg. Second-order quadrupole splitting was observed in the [Mo(CO)4] powder spectrum [NQCC = 0.021(0.0023) MHz, > <0.1 =... 

Equation (16) is very important because it imcovers two central ideas. First, the second-order frequency splitting depends inversely on the Larmor frequency, thus the importance of this term diminishes with increasing external magnetic field strength. Second, the k=0 term has no orientation dependence (Do 0 = 1) or, in other words, it is an isotropic term. This means that the isotropic shift observed in the NMR spectriun of a quadrupolar nucleus has, in addition to the usual isotropic chemical shift, a contribution from the quadrupole cou-phng, which is given by... 

It should be noted that for anisotropic liquid crystals the NMR signal is split into 21 component signals due to first-order static quadrupole interactions but that, in the absence of second-order quadrupole effects, the width of the central line gives the transverse relaxation rate both for powder samples and for macroscopically aligned samples (see further Chapter 7). 

A first-order quadrupole interaction pattern is observed in the partly ordered liquid crystal systems [NbCp(CO)4]/nematic phase 4 (nine-line pattern). Polycrystalline [NbCp(CO)4] exhibits a comparable spectrum at 1.53 T but a second-order pattern (split central component) arises at 0.27 T. ... 

Malononitrile is particularly interesting as it shows a second-order transition 2 ) no discontinuity of the pure quadrupole resonance is detected, but, over a limited temperature range, each line splits into two components, whose separation varies with temperature in a continuous manner, from zero to a maximum and then back to zero, without any hysteresis. 

Figure 5.1 The effect of quadrupole interactions on an / = 3/2 nucleus in a magnetic field. The Zeeman interaction splits the levels by an equal amount, cot, (the Larmor frequency in frequency units). The central +1 /2 to -1 /2 transition is unaffected by first order coupling co j however, second order coupling, co , affects all transitions.

High pressure applied to a-FcaOs causes the expected pressure-induced change in the second-order Doppler shift [9]. The electron density at the iron is effectively independent of pressure. However, the sign of the quadrupole splitting reverses at 30 kbar, the data suggesting that, in addition to a spin-flip transition, there is also some alteration in the local site symmetry. 

Fig. 18. 35 GHz cw ENDOR signal from O (/ = f) of nitrile hydratase in 35% enriched H2 0, taken at the high-held edge ( 3) of the EPR envelope. The quintet shown represents the v+ branch of the 0 ENDOR pattern that is centered at the O Larmor frequency, 7.3 MHz (filled triangle). The quadrupole splittings and hyperfine values calculated are estimated using second-order perturbation theory in the nuclear quadrupole interaction for an O nucleus. Conditions 12,650 G, 34.92 GHz, 0.16 mW microwave power, 1 G modulation amplitude, 0.5 MHz/sec if scan speed, 2 K. (Adapted from Jin et al. )...

The ratios of the quadrupole splitting for the two isotopes 151/153 are 0.3857(2), but a small correction for second-order effects of the magnetic hyperfine structure increases the ratio to 0.3900(8). This is slightly higher than the ratio of 0.3874(3) found by Erickson and Sharma (1981) from measurements on Eu " in YAIO3, but bisects the two ratios of the quadrupole constants B listed in table 3. 

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