Quadrupole coupling constant interaction

The interaction energy depends on Gn, and v and the allowed energy levels turn out to depend on eQ q. Division by h gives eqQ jh which we refer to as the quadrupole coupling constant (QCC). 

The effect of probe molecules on the 27A1 NMR has attracted some attention recently. In particular, the determination of the quadrupole coupling constant, Cq, is a sensitive means to learn more about the bonding situation at the aluminum in acid sites, and how it reflects the interaction with basic probe molecules. If one of the four oxygen atoms in an AIO4 tetrahedral coordination is protonated, as in a zeolitic acid site, the coordination is somewhat in between a trigonal and a tetrahedral A1 environment [232]. The protonated oxygen decreases its bond order to A1 to approximately half of its size compared to an unprotonated zeolite. 

In this section analytical expressions for ENDOR transition frequencies and intensities will be given, which allow an adequate description of ENDOR spectra of transition metal complexes. The formalism is based on operator transforms of the spin Hamiltonian under the most general symmetry conditions. The transparent first and second order formulae are expressed as compact quadratic and bilinear forms of simple equations. Second order contributions, and in particular cross-terms between hf interactions of different nuclei, will be discussed for spin systems possessing different symmetries. Finally, methods to determine relative and absolute signs of hf and quadrupole coupling constants will be summarized. 

Numerous X-ray investigations have unravelled the solid state structure of contact and solvent-separated ion pairs. It was therefore considered to be of interest to evaluate also the potential of solid state NMR as a tool for the investigation of this structural problem. In addition to the study of chemical shifts discussed above (Section II.B), the quadrupole coupling constant of the nuclide Li, x( Li), was expected to be an ideal sensor for the bonding situation around the lithium cation because, due to its dependence on the electric field gradient, the quadrupolar interaction for this spin-3/2 nucleus is strongly influenced by local symmetry, as exemplified in Section II.C.3. This is also shown with some model calculations in Section ILF. 

The strength of the quadrupole interaction is usually expressed as the quadrupole coupling constant, and is given by... 

While the nuclei 3H and 13C relax predominantly by the DD mechanism, relaxation of a quadrupole nucleus such as deuterium essentially involves fluctuating fields arising from interaction between the quadrupole moment and the electrical field gradient at the quadrupole nucleus [16]. If the molecular motion is sufficiently fast (decreasing branch of the correlation function, Fig. 3.20), the 2H spin-lattice relaxation time is inversely proportional to the square of the quadrupole coupling constant e2q Q/H of deuterium and the effective correlation time [16] ... 

While S relaxation behaviour can provide interesting information about interactions in solution, nuclear quadrupole coupling constants are a very sensitive probe in the study of the electronic distribution around the sulphur nucleus. 

Bersohn 76) has calculated the crystal field created by the molecular dipoles in the lattice of CH3C1. The static dipole moment of the molecules induces through the polarizability of the molecules an additional dipole moment which increases the dipole moment of the free molecule by a factor of about 1.05. This in turn means that the C—Cl bond has increased in ionic character under the influence of the intermolecular electric fields and therefore (see Eq. (II.9 the quadrupole coupling constant will be lower relative to the gaseous state. Besides the dipole moment induced in the direction of the static dipole, a perpendicular partial moment should be induced, too. Therefore the axial symmetry of the C—Cl bond will be disturbed and the asymmetry parameter 77 may become unequal zero. A small asymmetry parameter 17 = 0.028 has been observed for the nuclear quadrupole interaction in solid CH3I. Bersohn also calculated from the known crystal structure of 1,3,5-trichlorobenzene the induced... 

The matrix elements of the quadrupole interaction are calculated in various places, for different coupling cases, in the main text. Here we shall carry out the calculation in a case (a) coupled representation, which will enable us to define the nuclear quadrupole moment, the electric field gradient, and the quadrupole coupling constant. 

The axial component of the total magnetic hyperfine interaction, A 3/2, in the 2n3/2 component is equal to a+ (b + c)/2, where a, b and c are the Frosch and Foley [192] constants. In the 2n1/2 component the axial hyperfine constant, h /2, is equal to a — (b + c)/2. Since both fine-structure components can usually be studied by pure microwave experiments, a partial separation of the magnetic hyperfine constants can be achieved. The electric quadrupole coupling constant, eq0 Q, is obtained for both isotopes. 

The most interesting hyperfine interaction in the three molecules is that of55 Mn in the MnO molecule, illustrated in figure 10.91. The Frosch and Foley [192] hyperfine constants and the electric quadrupole coupling constant are found to have the following values (in MHz) ... 

Comparison of the observed value of by with the known contact interaction constant of the Mn+ ion gives a value for cf of0.573. In other words the 3da and 4s hybridisation is a nearly perfect one-to-one mixture. The dipolar hyperfine constant c depends upon a sum of contributions from the 3d unpaired electrons in the 9atomic orbitals, a value which agrees well with the measured value of —48.199 MHz. As we have commented elsewhere, the quadrupole coupling constant involves all of the electrons, and is not readily amenable to a simple semi-empirical treatment. 

As we have shown in Appendix 8.5, and elsewhere, to is the axial component of the dipolar interaction obtained from the fourth term in equation (11.2). The large value of the Fermi contact constant is consistent with a model in which the unpaired electron occupies a a-type molecular orbital which has 45% N atom, v character. Radford produced convincing arguments to show that the model is also consistent with the small dipolar hyperfine constant, and also the electric quadrupole coupling constant. 

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