Electric quadrupole moment of nucleus

In addition, the electron cloud in an atom may have an electrostatic interaction with the electric quadrupole moment of the nucleus, if one exists. This effect is very small (of the order of 10 cm. ). Finally there is the energy of the direct interaction of the nuclear moment with the external magnetic field ( 10 cm. ) as in NMR. 

Figure 2.16 Experimental values of the electric quadrupole moment of nuclei. The lines are drawn through the data to emphasize the trends from M. A. Preston, Physics of the Nucleus. Copyright 1962 by Addison-Wesley Publishing Company. Reprinted by permission of Pearson Education, Inc.

The predominant interaction for a 2H spin system is the quadrupolar interaction, which couples the electric quadrupole moment of the 2H nucleus to its electronic surrounding. This interaction is a second-rank tensor Hq which lies approximately along the C-2H bond in organic molecules. Thus, in practice, 2H nuclei may be considered to be isolated. It shows that the 2H NMR formalism is similar to that of an isolated proton pair [8] ... 

Those on a nitrogen (14N) atom are subject to partial or complete decoupling by the electrical quadrupole moment of the, 4N nucleus, whose spin number is one. 

The common 14N nucleus has a spin number I of 1 and, in accordance with the formula 21 + 1, should cause a proton attached to it and a proton on an adjacent carbon atom to show three equally intense peaks. There are two factors, however, that complicate the picture the rate of exchange of the proton on the nitrogen atom and the electrical quadrupole moment of the 14N nucleus (see Section 3.2.1). 

Protons are not coupled to chlorine, bromine, or iodine nuclei because of the strong electrical quadrupole moments of these halogen nuclei. For example, proton-proton coupling in CH3CH2C1 is unaffected by the presence of a chlorine nucleus the triplet and quartet are sharp. 

The quadrupole coupling interaction is represented by the first term of Eqn. (4), in which Q, is the quadrupole moment of nucleus i and VE, is the electric field gradient at this nucleus due to the other charges in the molecule. The second term gives the magnetic dipole-dipole interaction of two nuclei with magnetic moments p, and pj5 separated by a distance R. 

Nuclear quadrupole resonance spectroscopy (NQR) is a very direct and experimentally quite simple method for studying the interaction between the electric quadrupole moment of a nucleus and the electric field gradient at its site. Since the discovery of the method by Dehmelt and Kruger 3>6) in 1950, a large amount of experimental material has been collected, most of which has been interpreted within the frame of semiempirical theories. 

The spacing of the different energy levels studied by NQR is due to the interaction of the nuclear quadrupole moment and the electric field gradient at the site of the nucleus considered. Usually the electric quadrupole moment of the nucleus is written eQ, where e is the elementary charge Q has the dimension of an area and is of the order of 10 24 cm2. More exactly, the electric quadrupole moment of the nucleus is described by a second order tensor. However, because of its symmetry and the validity of the Laplace equation, the scalar quantity eQ is sufficient to describe this tensor. 

Absolute value of the electronic charge Electric quadrupole moment of a nucleus Atomic nuclear quadrupole coupling constant Nuclear quadrupole coupling constant Ionic character of a bond Nuclear spin... 

If the NH exchange rate is low, the NH peak is still broad because the electrical quadrupole moment of the nitrogen nucleus induces a moderately efficient spin relaxation and, thus, an intermediate lifetime for the spin states of the nitrogen nucleus. The proton thus sees three spin states of the nitrogen nucleus (spin number = 1), which are changing at a moderate rate, and the proton responds by giving a broad peak. In this case, coupling of the NH proton to the adjacent protons is observed. Such is the case for pyrroles, indoles, secondary and primary amides, and carbamates (Fig. 4.34). 

If we again refer to Table 7.1, we find that neither of the two isotopes of nitrogen is ideal for NMR. The most abundant isotope of nitrogen, 14N, which represents greater than 99% of nitrogen s natural abundance, possesses a spin of 1 and hence an electric quadrupole moment. This nucleus has an inherent low sensitivity and a very broad line because of quadrupolar relaxation. We shall not consider it any further. 

What kinds of fields Any kind which will interact with the nucleus strongly enough and there are two such randomly fluctuating fields effective in NMR relaxation. One is a time varying magnetic field which can interact with the nuclear magnetic dipole moments and the other is an EFG which can interact with an electric quadrupole moment of the nucleus if it has one. [Only those with l> can have electric quadrupole moments. ] The magnetic field interaction is the same as that which is utilized in the NMR experiment to cause transitions, for example, by a n/2 pulse. 

In nonspherical nuclei (/ > i) there exists a nonzero quadrupole moment for the nuclear charge density that contributes to the quadrupolar term (fourth term) in Eq. (1). In the expression for the electrostatic interaction energy for the nucleus in the potential produced by the electrons, the electric quadrupole moment of the nucleus is coupled to the gradient of the electric field at the nuclear site. This field gradient is, of course, due to the electrons. In diagonalized form one may write... 

The interaction between the electric quadrupole moment of a nucleus with I > Vi and the electric field gradient from the surrounding medium is usually difficult to extract from ESR spectra. By contrast, the influence of quadrupole couplings is clearly shown by the appearance of more than one ENDOR line for each electron spin quantum number ms of a species with electron spin S and nuclear spin I > Vi. In the common case of an 5 = Vi species with an nqc that is small compared to the hfc the frequencies are given by an equation of the type (see Chapter 3) ... 

Often the velocity spectrum of a sample consists of two lines even if all atoms of the absorber are in the same state of chemical bonding and in corresponding lattice positions. The quadrupole splitting of the resonance line in the case of iron is caused by the interaction of the electric field gradient around the nucleus with the electric quadrupole moment of the excited Fe-nucleus (1=3/2), The field gradient around the nucleus depends on the electronic configuration of the nucleus and on its environment. 

Electric quadrupole interaction between electric quadrupole moment of the nucleus and electric field gradient at the nuclear site Quadrupole splitting A q a. Molecular symmetry b. Oxidation slate (nominal valency) c. Spin Slate d. Bonding properties... 

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