Properties electric quadrupole moment

Molecular electric quadrupole moments are more elusive animals, and they are not particularly easy to determine experimentally. Prior to 1970, the only direct routes to these quantities were from the Kerr and Cotton-Mouton effects. They can now be obtained from microwave Zeeman spectroscopy, to fair accuracy. It is fair to say that direct calculation offers a faster and more reliable route to this property than experiment. 

Equation (4.15) would be extremely onerous to evaluate by explicit treatment of the nucleons as a many-particle system. However, in Mossbauer spectroscopy, we are dealing with eigenstates of the nucleus that are characterized by the total angular momentum with quantum number 7. Fortunately, the electric quadrupole interaction can be readily expressed in terms of this momentum 7, which is called the nuclear spin other properties of the nucleus need not to be considered. This is possible because the transformational properties of the quadrupole moment, which is an irreducible 2nd rank tensor, make it possible to use Clebsch-Gordon coefficients and the Wigner-Eckart theorem to replace the awkward operators 3x,xy—(5,yr (in spatial coordinates) by angular momentum operators of the total... 

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. 

For I > 1/2, nuclei also possess an electric quadrupole moment, Q. Quadrupolar nuclei exchange energy with electric fields in the rest of the molecule in which they are located causing profound effects on NMR spectra. Table 3.3 lists properties for some nuclei found in bioinorganic systems. 

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. 

Vanadium-51 is a spin 7/2 nucleus, and consequently it has a quadrupole moment and is frequently referred to as a quadrupolar nucleus. The nuclear quadrupole moment is moderate in size, having a value of -0.052 x 10 2S m2. Vanadium-51 is about 40% as sensitive as protons toward NMR observation, and therefore spectra are generally easily obtained. The NMR spectroscopy of vanadium is influenced strongly by the quadrupolar properties, which derive from charge separation within the nucleus. The quadrupole moment interacts with its environment by means of electric field gradients within the electron cloud surrounding the nucleus. The electric field gradients arise from a nonspherical distribution of electron density about the... 

Among the molecular properties introduced above are the permanent electric dipole moment /xa and traceless electric quadrupole moment a(8, the electric dipole polarizability aajg(—w to) [aiso(to) = aaa(—or, o>)], the magnetizability a(8, the dc Kerr first electric dipole hyperpolarizability jBapy(—(o a>, 0) and the dc Kerr second electric-dipole hyperpolarizability yapys(— ( >, 0,0). The more exotic mixed hypersusceptibilities are defined, with the formalism of modern response theory [9]... 

Birefringences are mostly observed in condensed phases, especially pure liquids or solutions, since the strong enhancement of the effects allows for reduced dimensions (much shorter optical paths) of the experimental apparatus. Nowadays measurements of linear birefringences can be carried out on liquid samples with desktop-size instruments. Such measurements may yield information on the molecular properties, molecular multipoles and their polarizabilities. In some instances, for example KE, CME and BE, measurements (in particular of their temperature dependence) have been carried out simultaneously on some systems. From the combination of data, information on electric dipole polarizabilities, dipole and quadrupole moments, magnetizabilities and higher order properties were then obtained. 

Differences in CC bond lengths of the aromatic moiety, which are less than 0.025 A are indeed small if compared to distances of 1.48 A and 1.33 A characterising C(sp2)-C(sp2) single and C(sp2)=C(sp2) double bonds, respectively, as usually pointed out by X-ray researchers. However, they are quite significant for many properties which critically depend on interatomic distances like e.g. molecular quadrupole moments, electric field gradients, spin-spin coupling constants of directly bonded atoms etc. A... 

Nuclei with spin 7 1 display another problem arising from the electric quadrupole moment which interacts with the electric field gradient created by the surrounding electrons. This property leads to a decrease of the relaxation times and, accordingly, an increase of the linewidths. This situation theoretically limits the use of NMR to nuclei with highly symmetric environments. The cluster effect , as suggested by Rehder [8], sometimes leads to important exceptions to this rule, as shown below. 

Ritchie, G.L.D. Field-gradient induced birefringence a direct route to molecular quadrupole moments. In Clary, D.C., Orr, B., (eds) Optical, Electric and Magnetic Properties of Molecules, pg. 67, Elsevier, Amsterdam, The Netherlands (1997)... 

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