Quadrupole couplings

Nuclei with / 1 have an electric quadrupole moment q that is a measure of the deviation of the nuclear charge distribution from spherical symmetry. The intensity of the electrostatic field gradient is given the symbol Q, and the electric quadrupole interaction is given by 

In this equation e is the charge on the electron, / is the spin quantum number of the nucleus, and Av is the separation between adjacent lines of the 2/-component multiplet. This spectrum arises because the quadrupolar interaction pushes some energy levels up and some down the transitions between adjacent energy levels (recall that the only allowed transitions are between adjacent levels) are shifted by amounts proportional to mz. The center of gravity of the spectrum is not affected to first order. Equation (15.6) applies only to axially symmetric electric field gradient tensors, such as those experienced by 2H in a typical C-D bond. The 

There is a redeeming instance that often makes partial spectra of quadrupolar nuclei observable. For odd-half integral nuclei, such as 23Na (7=2), the mz = to m. = -2 transition is not affected by the quadrupolar interaction to first order and remains relatively sharp, while the satellite transitions, such as mz = to mz = 2 and m. = —2 to mz = -2, are broadened by the powder distribution. There is a substantial second-order effect of the quadrupole coupling that broadens even the central transition, but this broadening is often only a few kilohertz to a few tens of kilohertz—large but much smaller than Megahertz. 

Another special case occurs if the nucleus is at a site of cubic point symmetry (actually tetrahedral symmetry or higher will do). If this condition holds, the electric field gradient must by symmetry disappear, and the quadrupole coupling vanishes. Common examples are tetrahedral ions such as SO -, MoO -, TcOj, and simple salts, such as NaCl, in which the ions reside in sites of cubic symmetry. Unfortunately, this situation almost never occurs for the quadrupolar nuclei, such as l70, l4N, and 35C1, that one might wish to study in organic compounds. The only possible exceptions are symmetrically tetrasubstituted ammonium salts. 

Of course, in single crystals the spectrum consists of discrete lines whose frequencies move with crystal orientation. In some cases involving large couplings it is possible to track the positions of these discrete lines as the crystals are rotated by retuning the spectrometer and probe at each crystal orientation. In that manner a spectral width of several megahertz may be covered in smaller, more practical pieces of bandwidth. This method has been used to determine the sequence and tertiary structure of crystalline proteins by observing the l4N resonances of the amide backbones. 

There is a redeeming instance that often makes partial spectra of quadrupolar nuclei observable. For odd-half integral nuclei, such as Na (/= ), the j fo = - j transi- 

The spectra discussed in Chapter 4 were analyzed by neglecting the effects of nuclear quadrupole coupling on the nuclear hyperfine structure. Presented here is the way such effects may be incorporated into the spectra using perturbation theory. 

The quadrupole coupling term in the spin Hamiltonian can be written as  

Assuming identical principal axes for A and P, the Hamiltonian term would have the form in the (x , y , z ) coordinate system  

Note that transformation by a general coordinate transformation matrix leaves the quadrupole matrix symmetrical, i.e., Py = Pp and with zero trace, 

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Dechter J J, Henriksson U, Kowalewski J and Nilsson A-C 1982 Metal nucleus quadrupole coupling constants in aluminum, gallium and indium acetylacetonates J. Magn. Reson. 48 503-11... 

From accurate measurements of the Stark effect when electrostatic fields are applied, information regarding the electron distribution is obtained. Further Information on this point is obtained from nuclear quadrupole coupling effects and Zeeman effects (74PMH(6)53). 

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

T. P. Das and E. L. Hahn, Nuclear Quadrupole Resonance Spectroscopy, Academic Press, New York, 1958, 223 pp E. A. C. Lucken, Nuclear Quadrupole Coupling Constants, Academic Press, London, 1969, 360 pp. 

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). 

Quadrupole coupling constants for molecules are usually determined from the hyperfine structure of pure rotational spectra or from electric-beam and magnetic-beam resonance spectroscopies. Nuclear magnetic resonance, electron spin resonance and Mossbauer spectroscopies are also routes to the property. There is a large amount of experimental data for and halogen-substituted molecules. Less data is available for deuterium because the nuclear quadrupole is small. 

The author concerns himself with a comparison between theoretical and experimental studies of simple molecules containing the C = N linkage. A large number of spectroscopic studies have been made for XCN molecules, and in the majority of cases many isotopic species have been studied. The experimental data is very accurate. An interesting feature of such molecules is that the C s N distances are equal to within experimental error, and one might expect that the quadrupole coupling constants would be similar. This is not the case, as shown in Table 16.4. 

The deuteron solid state spectra are completely dominated by the quadrupole coupling of the deuteron I = 1 spin, the NMR frequency being given by lS)... 

In presence of molecular motion the NMR line shape will change. A particularly simple situation arises, if the motion is rapid on timescale defined by the inverse width of the spectrum in absence of motion 6 1. In this fast exchange limit, which in 2H NMR is reached for correlation times tc < 1CT7 s, the motion leads to a partially averaged quadrupole coupling and valuable information about the type of motion can directly be obtained from analysis of the resulting line shapes. The NMR frequency is then given by... 

Sb Mossbauer spectra of SbSBr, SbSI, SbSeBr, SbSel, and SbTel have been obtained at 4.2 K. The quadrupole coupling-constant of the iodides decreases in the order SbSI > SbSel > SbTel, becoming nega-... 

Schwerdtfeger, P., Pernpointner, M. and Nazarewicz, W. (2004) Calculation of Nuclear Quadrupole Coupling Constants, in Calculation ofNMR and EPR Parameters Theory and Applications, (eds M. Kaupp M. Biihl and V.G. Malkin), Wiley-VCH Verlag GmbH, Weinheim, pp. 279-291. 

Lantto, P. and Vaara, J. (2006) Calculations of nuclear quadrupole coupling in noble gas-noble metal fluorides Interplay of relativistic and electron correlation effects. Journal of Chemical Physics, 125, 174315-1-174315-7. 

The experimentally observed quadrupole splitting AEq for Fe in inorganic compounds, metals, and solids reaches from 0 to more than 6 mm s [30, 32]. The range of AEq for other Mossbauer isotopes may be completely different because of the different nuclear quadrupole moment Q of the respective Mossbauer nucleus, and also because the EFG values may be intrinsically different due to markedly different radial distributions of the atomic orbitals (vide infra). As Q is constant for a given isotope, variations in the quadrupole coupling constants eQV can only arise from... 

RBa2Cu40g (R = Sm, Y, Er) Nuclear-quadrupole coupling parameters at the rare-earth metal and copper sites from Cu ( Zn) and Ga( Zn) Mossbauer emission spectroscopy, EEG tensor in comparison with point charge model, shows that holes in lattices are localized primarily at chain-oxygen sites... 

Chemical information from hafnium Mossbauer spectroscopy can primarily be deduced from the quadrupole-splitting parameter. In Table 7.4, we have listed the quadrupole coupling constants eQV for some hafnium compounds. Schafer et al. 

Table 7.4 Quadrupole coupling constant eQV z and asymmetry parameter r) for hafnium compounds...

W(VI) compounds with 5cP electronic configuration, the EFG is reasonably weU described by the lattice contribution only. The regular octahedral WOs structure yields zero EFG in agreement with experiment, while the deformed tetrahedral W04 strucmre results in significant quadrupole coupling constants of either sign, e Q > 0 and also <0, depending on the distortion of the O4 tetrahedron. 

Table 7.7 Quadrupole coupling constants e qQ (mm 7 = Kti — VyyiVzz, and experimental line width tungsten compounds...

Their results show that quadrupole coupling persists in domains at high dilution, for which a reasonably accurate magnitude and the sign may be determined, even in more concentrated systems and even in the presence of substantial... 

Table 10 BH HLYP/aug-cc-pVTZ calculated nuclear quadrupole coupling constants /(N) and /(Hal) [MHz] of the complexes XY- -NH3 a ...

Other key properties of these complexes relevant for comparison with experiment are the nuclear quadrupole coupling constants. Theoretical NQCC values, as calculated via electric field gradients, are discussed exhaustively in several recent theoretical investigations [26,28,30,33,34] and in experimental work [4-11]. BH HLYP/aug-cc-pVTZ calculated NQCCs [30,34], as evaluated for XY- -NH3 complexes, are listed in Table 10. 

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