Nuclear electric quadrupole

Nuclear electric quadrupole QCC (quadrupole coupling constant), (asymmetry parameter) Line-shape analysis, nutation NMR Coordination symmetry... 

Nuclear electric quadrupole moment of ground (g) and excited (e) state (in... 

Bleaney, B., Bowers, K.D., and Pryce, M.H.L. 1955. Paramagnetic resonance in dilute copper salts III. Theory, and evaluation of the nuclear electric quadrupole moments of 63Cu and 65Cu. Proceedings of the Royal Society of London A 228 166-174. 

Extraframework cations are needed in anionic zeolites for charge balance, and for several zeolite topologies their locations are well investigated [281, 282]. Different cations have been investigated by solid state NMR in the past with different NMR properties and different project targets. We restrict this section to a tutorial example on sodium cation motion in sodalite and cancrinite structures [283-285], 23Na has a nuclear electric quadrupole moment, and quadrupolar interaction is useful to investigate jump processes, especially when they are well defined. 

The spin interactions, dipole-dipole (D), nuclear electric quadrupole (Q) and chemical shielding (C.S), may be formally written in terms of irreducible tensors of rank l34 in Hz ... 

G. W. Proctor and W. H. Tanttila, Saturation of nuclear electric quadrupole energy levels by ultrasonic excitation, Phys. Rev., 1955, 98, 1854. 

In other words, isotopes having a spin value equal to, or greater than one exhibit an ellipsoidal charge distribution and have spin. They invariably possess a nuclear electric quadrupole moment, designated as Q ... 

A discussion of nuclear electric quadrupole coupling in the vinyl halides has led to the estimate of about 6 percent double-bond character for the C—Cl bond in vinyl chioride and 3 percent for the C—I bond in vinyl iodide.87 Values of electric dipole moments of mono-halogenated benzenes have been interpreted as corresponding to 4 percent of double-bond character for the C—X bonds.68... 

The energy of the nuclear electric quadrupole in an inhomogeneous electric field varies with the orientation of the quadrupole moment. The electric field E at a particular nucleus in the molecule is determined by the electronic wave function and the electric fields produced by the other nuclei. There is no reason for E to be constant over the region around any nucleus. Rather, the components of E will vary, and we will have nonzero values of 3 x/dx, 3 x /dy, etc. The electric potential V(x,y,z) at a point (x,y,z) in space can be defined such that E= — grad V, or [Halliday and Resnick, Section 29-7]... 

There is another common cause of line splittings in microwave spectroscopy. Nuclei with spin I > 1 have an electric quadrupole moment. An electric quadrupole moment arises from a nonspherically symmetric charge distribution for example, a uniformly charged ellipsoid of revolution has no electric dipole moment, but does have an electric quadrupole moment. The nuclear electric quadrupole moment is16... 

The interaction between the nuclear electric quadrupole moment and the electrons of the molecule couples the nuclear spin I to the rotational angular momentum J, giving a resultant total angular momentum F, of... 

Yi and Ys - gyromagnetic ratio of spin 1 and spin S nuclear spin, rJS = intemuclear distance, tr= rotational correlation time, x< = reorientation correlation time, xj = angular momentum correlation time, Cs = concentration of spin S, Cq = e2qzzQ/h = quadrupole coupling constant, qzz = the electric field gradient, Q = nuclear electric quadrupole moment in 10 24 cm2, Ceff = effective spin-rotational coupling constant, a = closest distance of appropriate of spin 1 and spin S, D = (DA+DB)/2 = mutual translational self diffusion coefficient of the molecules containing I and S, Ij = moment of inertia of the molecule, Ao = a// - ol-... 

Static quadrupole effects in NMR are observed in solids (9) and also in anisotropic liquid crystals (10, 11, 12). For nuclei with spin quantum numbers, I, greater than V2, the distribution of positive charge over the nucleus can be nonspherical and the situation can be described in terms of a nuclear electric quadrupole moment. The interaction between the quadrupole moment, eQ and electric field gradients, eq, shifts the energy levels of the nuclear spin states. 

NMR spectra of quadrupolar nuclei are influenced by the interaction of the nuclear electric quadrupole moment with electrostatic field gradients generated at the nuclear sites by asymmetric electron distributions due to chemical bonding. To a first order... 

Table 3.3 Nuclear Spin /, Nuclear Gyromagnetic Ratio gN, Isotopic Abundance, Nuclear Electric Quadrupole Moment Q, and NMR Resonance Frequency v at 1 Tesla (10,000 Gauss) for Nuclei of Interest to NMR and NQRa...

Nuclear electric quadrupole moment interaction with electric field gradient... 

For chemically interesting nuclei, Table 11.10 lists values of the nuclear spin quantum number I, the nuclear gyromagnetic ratio gN/ the nuclear electric quadrupole moment Q, and the nuclear magnetic resonance frequency v (Hz, for H0 = 1 tesla). 

Nuclear Quadrupole Resonance (NQR) [50-54], Nuclear (electric) quadrupole resonance (NQR) was invented in 1950 [55] and is applicable to nuclei with nonzero nuclear electric quadrupoles eQ, which are 3x3 tensors, whose significant components are the quadrupole coupling constant QCC ... 

The term in equation (4.54) represents the nuclear electric quadrupole interaction. 

The form of the nuclear electric quadrupole interaction in the effective Hamiltonian for a diatomic molecule is given in equations (7.158) and (7.161), with the latter applying only to molecules in n electronic states. The two parameters which can be determined from a fit of the experimental data are eqo Q and et/i Q respectively. Since the electric quadrupole moment eQ is known for most nuclei, an experimental observation gives information on q0 (and perhaps qi), the electric field gradient at the nucleus. This quantity depends on the electronic structure of the molecule according to the expression... 

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