Quadrupolar polarization

The five second-moment spherical tensor components can also be calculated and are defined as the quadrupolar polarization terms. They can be seen as the ELF basin equivalents to the atomic quadrupole moments introduced by Popelier [32] in the case of an AIM analysis ... 

Figure 6-3. Correlation between the quadrupolar polarization ( M2 ) of CO bonds in selected molecule and of the bond multiplicity...

Another important atomic polarization is measured by the axial components of the quadrupole moment. The quadrupolar polarization of an atomic density measured with respect to the z-axis is given by... 

Flo. 6.1. Pictorial demonstration of quadrupolar polarizations of an electronic charge distribution. 

Information corresponding to the k populations of the orbital model is recovered in the quadrupole polarization of the atomic charge densities, a property of the total charge density. A quadrupolar polarization of the density along the z-axis, eqn (6.48), has the form of a d i orbital, a removal of charge from a plane and its concentration in an axial direction perpendicular to the plane (Fig. 6.1) for < 0. In benzene and ethylene, with the z-axis perpendicular to the plane containing the nuclei, Qjj(C) = — 3.34 and =... 

The director at one of the boundaries of a hybrid cell is aligned homeotropically, at the opposite boundary homogeneously as was shown earlier in Fig. 10.11. Therefore, a hybrid cell has intrinsic bend-splay distortion and must have a projection of the macroscopic polarization along the cell normal. We can clearly see in Figs. 10.11 and 11.25 how the quadrupolar polarization emerges. The molecules may have positive (eo > 0) quadrupoles shown in Fig. 11.25 or negative ones (fio < 0) seen in Inset to Fig. 11.26b. 

In Eq. (8-7), which is Coulomb s law, the charges are to be aeeompanied with their signs. Because of the high-order reciprocal dependence on distance in Eqs. (8-11) and (8-12), these quadrupolar interactions are usually negligible. For uncharged polar molecules the dipole-dipole interaction of Eq. (8-10), which has the dependence, is the most important contributor to the electrostatie potential energy. 

A common feature of many mesogenic molecules is the presence of polar substituents and aromatic cores [3]. The electrostatic interactions between such groups can be incorporated into a molecular potential with the addition of dipolar and quadrupolar terms, respectively. Rather than represent these permanent electrostatic interactions by using a model in which a charge distribution is scattered over the surface of the molecule, it is very common to use one (or more) point multipoles [2,29]. Thus for an electrostatic Gay-Berne model, the pair potential is given by the sum... 

In contrast to the spin-1/2 —> spin-1/2 polarization case, the transfer of polarization between spin-1/2 and quadrupolar nuclei presents a considerable challenge due to the very complex spin dynamics involved in the CP process and the spinlocking of quadrupolar nuclei under MAS. The overall sensitivity is rarely enhanced with respect to the direct polarization method, even if T[ is much shorter than Tf. The usefulness of the CP experiment relies mainly on its ability to probe the interactions between the neighboring nuclei in ID or 2D schemes under MAS or isotropic resolution. The theoretical and practical aspects of spin-locking and CP transfer between spin-1/2 and the SQ or MQ coherences of the quadrupolar nuclei (SQ-CP or MQ-CP) have been thoroughly studied and reviewed [20, 221-227]. Some of the challenges involved in such experiments are summarized below. 

The CP can also be used for polarization transfer to MQ coherences of half-integer quadrupolar nuclei [222, 223, 228-231]. This type of transfer is mainly used in the context of MQMAS [228,229,231], although the spin-locking of MQ coherences is also featured in experiments involving homonuclear dipolar recoupling experiments [232]. 

De Paul, S.M., Ernst, M., Shore, J.S., Stebbins, J.F., and Pines, A. (1997) Cross-polarization from quadrupolar nuclei to silicon using low-radio-frequency amplitudes during magic-angle spinning. /. Phys. 

Note 2 Examples of such interactions that have been noted are dipolar/non-polar, charge-transfer and quadrupolar. 

For large-weight Zn + complexes with broad (50-150 kHz) second-order quadrupolar powder patterns Zn QE NMR may be an experimental challenge. In such cases the sensitivity must be enhanced by isotope enrichment combined with, e.g., cross polarization (CP) from H ", low-temperature acquisition or sampling of the free-induction decay (FID) in the presence of a train of refocusing pulses. ... 

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