Field quadrupolar

Isotopes with />l/2 are called quadrupolar nuclei. The nucleus responds to both magnetic and electric fields. Quadrupolar nuclei respond to the electric field gradient at the nucleus through the quadrupole coupling, X . 

Intramolecular quadrupolar 2 Reorientation of the electric field gradient principal axis Dominant for />1 (covalently bonded) [14]... 

Intermolecular quadrupolar 2 Fluctuation of the electric field gradient, moving multipoles Common for />1 In free Ions In solution [la... 

Unlike simple deflections or accelerations of ions in magnetic and electric fields (Chapter 25), the trajectory of an ion in a quadrupolar field is complex, and the equations of motion are less easy to understand. Accordingly, a simplified version of the equations is given here, with a fuller discussion in the Appendix at the end of this chapter. 

Relationship between a and q. The shaded area indicates regions of stable ion motion through the quadrupolar field. 

Once an approximation to the wavefunction of a molecule has been found, it can be used to calculate the probable result of many physical measurements and hence to predict properties such as a molecular hexadecapole moment or the electric field gradient at a quadrupolar nucleus. For many workers in the field, this is the primary objective for performing quantum-mechanical calculations. But from... 

The first Ni Mossbauer spectrum of nickel in a bioinorganic compound with determinable EFG and isomer shift was reported for a nickel complex compound with planar [NiSJ core and considered as a model compound for hydrogenase. This Mossbauer spectrum from the formal Ni compound is presented in Fig. 7.16. The observed quadrupolar interaction can be understood in terms of ligand field theory. In this approach, the b g and levels (d y2 and d ) are not occupied which is expected to cause a large negative EFG contribution [32]. 

NMR spectroscopy is a powerful technique to study molecular structure, order, and dynamics. Because of the anisotropy of the interactions of nuclear spins with each other and with their environment via dipolar, chemical shift, and quadrupolar interactions, the NMR frequencies depend on the orientation of a given molecular unit relative to the external magnetic field. NMR spectroscopy is thus quite valuable to characterize partially oriented systems. Solid-state NMR... 

The strength of the quadrupolar interaction is proportional to the quadrupole moment Q of a nucleus and the electric field gradient (EFG) [21-23]. The size of Q depends on the effective shape of the ellipsoid of nuclear charge distribution, and a non-zero value indicates that it is not spherically symmetric (Fig. 1). 

Fig. 1 (a) Schematic representation of the spherical and non-spherical charge distribution in a nucleus. The value of electric quadrupole moment Q for the quadrupolar nucleus depends on the isotope under consideration, (b) The quadrupolar interaction arises from the interaction of Q with surrounding electric field gradient (EFG)... 

During an rf-field irradiation, the Hamiltonian governing a quadrupolar spin system can be written in the rotating frame as... 

Since the second-order quadrupolar broadening is inversely proportional to the Larmor frequency [(35) and (36)], one obvious means for improving the resolution is to employ the highest available magnetic field strength [94], The use of several spectrometers operated at different magnetic field strengths can be helpful in... 

The quadrupolar effects of order higher than two (7) are usually assumed to be negligible, especially at high magnetic fields. However, once the first- and second-order effects are removed, the measurement of third-order contributions becomes realistic. It can be easily shown that, similar to the first-order case, the CT and all symmetric MQ transitions (q = 0) are free of the third-order contribution, which thus can be safely ignored in DAS, DOR, and MQMAS experiments [161,162]. This is not the case for transitions between non-symmetric spin states, such as the STs. Indeed, numerical simulations of the third-order effect have explained the spectral features that have been observed in 27A1 STMAS spectra of andalusite mineral [161]. 

Vosegaard and Massiot [144] showed that it is possible to create a high-resolution 2D spectrum correlating the chemical shifts with the second-order quadrupolar lineshapes from several spectra recorded at different magnetic field strengths using a projection-reconstruction method called chemical shift-quadrupolar projection-reconstruction of one-dimensional spectra (CQ-PRODI). 

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