Electric quadrupole coupling

Electrostatic energy is minimized by appropriate alignment of a quadrupole in a field gradient (in contrast to dipolar energy, which depends directly on the field). In a molecule, there is an electric field gradient (efg) at the nucleus because of asymmetry 

The nuclear quadrupole coupling constant (NQCC) is a tensor quantity related to the efg tensor. In frequency units 

Since the NQCC depends not only on the nuclear quadrupole moment Q, but also on the chemical environment of the nucleus, quadrupole couplings can vary greatly for the same nucleus. Moreover, the NQCC tensor contains useful chemical information on the disposition of bonding and nonbonding electrons which determine the efg. Thus for N, with 7=1, the NQCC is small (a few kHz) in the symmetrical environment of the ammonium ion NH/, small also in linear groups (as in R — N s C), but larger (about 9 MHz) in very asymmetric locations, as in NHFj. 

In solid-state NMR spectroscopy the quadrupolar interaction, if less than 100 kHz, say, can be taken as a perturbation of the Zeeman interaction (the high-field case ). Perturbation theory then gives the contribution to the energy (for axial symmetry of the efg, with = 0) as follows  

Thus a spin-1 nucleus ( H, Li, N) gives a doublet with the splitting (for rj = 0) 

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E. M. Dickson and E. F. W. Seymour, Knight shift and electric quadrupole coupling in Mg metal. /. Phys. C Solid State Phys., 1970, 3,666-670. 

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... 

This discussion shows that the most accurate interpretation of the electric quadrupole coupling constant is obtained by evaluating... 

Short of the ab initio calculations, there are several semi-empirical approaches to the calculation and interpretation of electric quadrupole coupling constants. These were developed originally by Townes and Dailey [47, 48] and are well documented in the book by Gordy and Cook [49], They are based on the linear combination of atomic orbitals approximation for molecular orbitals, mentioned earlier in equation (7.266) and described in more detail in chapter 6 ... 

The alkali halide molecules have been studied comprehensively by molecular beam electric resonance methods. Table 8.14 presents a summary with references. In most cases the electric quadrupole coupling constants have been determined, and usually also the nuclear spin-rotation constants. 

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) ... 

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. 

Comparison can be made with the predictions of this simple molecular orbital model. The Fermi contact constant, for example, is expected to be small because the molecular orbital containing the unpaired electron has predominantly 2p atomic character. The observed contact interaction corresponds to only 6%, v character. The dipolar interaction is also in good agreement with this simple description. The electric quadrupole coupling is much more difficult to describe in simple terms because it involves all electrons. 

Electric quadrupole coupling constants, nuciear-spin rotation coupling constants, tensor and scalar nuclear spin-spin coupling constants, Fermi contact and anisotropic hyperfine parameters, magnetic nuclear-orbital coupling constants... 

In absence of experimental data on the relaxation rate in sites (c) and (d) in Cl, these were calculated from estimated electric quadrupole coupling constants and rotational correlation times. The excess line width of the chloride NMR signal was experimentally observed to be directly proportional to the total concentration... 

The three main anisotropic Interactions are (i) the magnetic dipole-dipole coupling, (ii) the electric quadrupole coupling (I > 1/2), and (iii) the magnetic shielding (chemical shift). These will be dealt with in turn with the emphasis being on qualitative understanding since quantitative expositions abound elsewhere (1-4). 

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