Electric Quadrupole Relaxation

We saw in Chapter 7 that the resonance frequency of a quadrupolar nucleus is dependent on the orientation of the molecule in which it resides. Molecular tumbling now causes fluctuating electric fields, which induce transitions among the nuclear quadrupole energy levels. The resulting nuclear relaxation is observed in the NMR just as though the relaxation had occurred by a magnetic mechanism. 

The general theory of quadrupole relaxation is somewhat complex but simplifies for the case of rapid molecular tumbling and axial symmetry of the molecular electric field. The interaction energy between the nucleus and a surrounding electric field gradient (Eq. 7.18) appears quadratically  

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R486 A. M. Souza, A. Gavini-Viana, I. S. Oliveria, R. S. Sarthor, R. Auccaise, E. R. Deazervedo and T. J. Bonagamba, Nuclear Spin 3/2 Electric Quadrupole Relaxation as a Quantum Computational Process , Quantum Inf. Comput.,... 

Although the efg should be zero for symmetrical, octahedral ML and tetrahedral ML4 complexes, significant electric quadrupole relaxation can still be present because of distortions caused by outer sphere interactions or vibrational motion. 

It is worth mentioning that >NH protons may often appear somewhat broader than their -OH counterparts, for another reason >NH protons have another relaxation mechanism available to them (quadrupole relaxation) because the 14N nucleus has an electric quadrupole moment. This extra relaxation capability can lead to a shorter relaxation time for >NH protons, and since the natural linewidth of a peak is inversely proportional to the relaxation time of the proton(s) giving rise to it, a shorter relaxation time will give rise to a broader peak. 

Quadrupolar nuclei Those nuclei, which because of their spin quantum number (which is always >1/2), have asymmetric charge distribution and thus posses an electric quadrupole as well as a magnetic dipole. This feature of the nucleus provides an extremely efficient relaxation mechanism for the nuclei themselves and for their close neighbors. This can give rise to broader than expected signals. 

The main NMR interactions in solution of interest to chemists are the chemical shift relative to some stated standard (6), the indirect coupling constant (7) and the relaxation times T1 (spin-lattice) T2 (spin-spin related to the line width) and T p, the relaxation time in the rotating frame. In the case of solids and oriented samples both the direct dipole-dipole and the electric quadrupole interactions assume greater importance. We shall confine our attention in this chapter to diamagnetic compounds so that we may neglect nuclear interactions with electron spins. 

The procedures for recording spectra of heteronuclei often differ considerably from those for H and (which would today be considered routine ) since it is necessary, even for routine measurements, to adjust the experimental conditions to suit the special properties of the nuclei to be observed. For example, the spin-lattice relaxation times for some nuclides, such as N, are very long, whereas for others (especially those with an electric quadrupole moment, such as N) they are very short. Also, the spectra observed for some nuclides contain interfering signals caused by other materials present, for example the glass of the sample tube ("B, Si), the spectrometer probe unit ( Al) or the transmitter/receiver coil. For many nuclides the sample temperature and its constancy are important factors for example, quadrupolar nuclides such as O give narrower signals when the temperature is increased. 

All of the heteroatoms possess at least one naturally occurring isotope with a magnetic moment (Table 15). The nuclei 14N, 170 and 33S also possess an electric quadrupole moment which interacts with the electric field gradient at the nucleus, providing a very efficient mechanism for relaxing the nuclear spin. The consequence of this facilitation of relaxation is a broadening of the NMR signals so that line widths may be 50-1000 Hz or even wider. To some extent this problem is offset by the more extensive chemical shifts that are observed. The low natural abundances and/or sensitivities have necessitated the use of accumulation techniques for all of these heteroatoms. The relative availability of 170 and 15N enriched... 

Nuclear quadrupole relaxation may also contribute significantly to spin-relaxation and thus lead to line broadening. These effects depend upon the electric-field gradient at the nucleus which is reduced if the radical is symmetrical. 

Another source of microdynamic information comes from the deuterium relaxation rates. The quadrupolar coupling constant (e2qQ/h) expresses the magnitude of the coupling between the electric quadrupole moment Q of the nucleus and the efg q at the nucleus (e is the electronic charge, and h is Planck s constant). It provides a relaxation mechanism for the quadrupolar nucleus of its Fourier component at the Larmor (resonance) frequency for this nucleus is non-negligible. It has such a Fourier component because tumbling of the molecule the quadrupolar nucleus is part of, in a... 

Several reviews on xenon NMR spectroscopy have appeared [1, 2], therefore in this introduction only the most important aspects will be discussed. The xenon atom has two isotopes which are suited for NMR studies, the 129Xe and 131Xe isotopes. For most studies 129Xe is more convenient than 131Xe, while the former nucleus with spin I=V2 does not have an electrical quadrupole moment. In some cases, however, the quadrupolar interaction can provide additional (spectral and relaxation) information. Flere we will only consider the 129Xe isotope. 

Rebane, V.N., Rebane, T.K. and Sherstyuk, A.I. (1981). Possibility of observing the relaxation of higher polarization moments in electric-quadrupole radiation, Optika i Spektroskopiya, 51, 753-755. 

Nuclei with a spin number 7 of one or higher have a nonspherical charge distribution. This asymmetry is described by an electrical quadrupole moment, which, as we shall see later, affects the relaxation time and, consequently, the linewidth of the signal and coupling with neighboring nuclei. In quantum mechanical terms, the spin number 7 determines the number of orientations a nucleus may assume in an external uniform magnetic field in accordance with the formula 27+1. We are concerned with the proton whose spin number 7 is 1/2. 

It is known from nuclear structure theory that nuclei with I > 1 also have an electric quadrupole moment Q, which is a measure of the asphericity of the nucleus. Nuclear quadrupole moments affect the rate of magnetic dipole relaxation, and nuclei with Q 0 are candidates for NQR measurements (see Table 3.3). 

NMR thus, 19F splittings due to UB—19F coupling, and their disappearance at lower temperatures due to quadrupole relaxation of UB, give a measure of the electric field gradient about boron and, hence, of the adduct structure (27, 28). 

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