Interactions quadrupolar

7 Quadrupolar Interactions. - Quadrupolar coupling constants are sensitive probes of hydrogen bonding. Their accurate knowledge is a major prerequisite when trying to extract dynamical information from relaxation data of quadrupo- 

Muller et presented an novel approach that allows NMR relaxation rates to be determined for a complex mixture, and it is applied to a dimethyl sulfox-ide/water solution. It involves use of a predetermined, quantum mechanical, multidimensional property surface in a simulation. The results are used in conjunction with simulated rotational correlation time to calculated the DQCC, in an analogous approach to the one used by experimentalists, and to examine the surprising experimental findings for the composition dependence of the DQCC in the dimethyl sulfoxide/water mixture. In this respect, Muller and Huber showed that the contributions of solvent molecules to NMR properties of the solute molecule in liquids is approximately pair-additive. Because water is an extreme case, the authors assume that for other systems an even better additivity might be found. 

Gill et al measured copper quadrupole coupling constants in binary mixtures of acetonitrile with some other nitriles. Victor et investigated magnetic 

Magnetic multipoles of rank higher than one become active in spin systems with I 5 and their contribution to relaxation depends on dynamics. The appearance of multipole terms complicates the relaxation description and supports the multiexponential behavior of relaxation. Nosel et al. presented the effects of high rank multipoles on lineshape and longitudinal relaxation of 7=3 systems. Results obtained from both numerical simulation and experimental data show that longitudinal and transverse relaxation are strongly influenced by these multipole terms, especially at lower temperatures where, due to molecular mobility, the extreme narrowing condition is not fulfilled. 

Vaara and Pyykko presented a theory for the magnetic-field-dependent quadrupole splitting in the Xe NMR spectra in isotropic media and tested it by ab initio electronic structure calculations. Evidence exists only for even-power magnetic field dependence. The dominant mechanism is verified to be the electric field gradient caused by the diamagnetic distortion of the atomic electron cloud, quadratic in the magnetic field. NQCC for diatomic molecules were calculated by Bryce and Wasylishen. Turner et al performed a systematic computational study of the geometrical dependence of the deuteron quadrupole interaction parameters (DQCC and asymmetry parameter) for the water-formaldehyde model system. Bematowicz and Szymanski studied NMR spectra of a spin nucleus scalar coupled to two equivalent spin-1 nuclei 

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This compound has two crystallographically distinct vanadium sites. While the static spectrum is a superposition of two powder patterns of the kind shown in Figure 3, MAS leads to well-resolved sharp resonances. Weak peaks denoted by asterisks are spinning sidebands due to the quadrupolar interaction. 

There is arbitr iriness in describing phenomena as either physical or chemical, but in some sense the nuclear relaxation mechanisms we have discussed to this point are physical mechanisms, based as they are on rotational motions of molecules, magnetic dipole-dipole interactions, quadrupolar interactions, and so on. Now we discuss a nuclear relaxation mechanism that is chemical in origin. 

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 similar model has been used to study the effect of a quadrupolar interaction on a system of Gay-Berne discs [27]. In this case, the bare Gay-Berne model... 

Thus the formation of tilted analogues of the smectic A phases, i.e. monolayer Cl and bilayer C2, is possible for mesogens with relatively large electric quadrupoles. In the case of strongly sterically asymmetric molecules (e.g., zigzag shaped or dumbell shaped molecules, Fig. 3b) these quadrupolar interactions may be steric in origin. From this point of view observation of molecular tilt in the molecular dynamics simulations for a one-layer film of DOBAMBC in the absence of electrostatic interactions is not so surprising [106]. 

From the applications of Ni Mossbauer spectroscopy in solid-state research, it is clear that (1) information from isomer shift studies is generally not very reliable because of the smallness of the observed isomer shifts and the necessity of SOD shift corrections which turn out to be difficult, and (2) useful information about magnetic properties and site symmetry is obtained from spectra reflecting magnetic and/or quadrupolar interactions. 

The first Ni Mossbauer spectrum of nickel in a bioinorganic compound with determinable EFG and isomer shift was reported for a nickel complex compound with planar [NiSJ core and considered as a model compound for hydrogenase. This Mossbauer spectrum from the formal Ni compound is presented in Fig. 7.16. The observed quadrupolar interaction can be understood in terms of ligand field theory. In this approach, the b g and levels (d y2 and d ) are not occupied which is expected to cause a large negative EFG contribution [32]. 

For example, Marder and co-workers [10] (among others) have studied liquid crystal mesophases induced by the presence of quadrupolar interactions between non-mesomorphic phenyl- and perfluorophenyl-containing moieties (e.g. 1). 

Quadrupolar interactions (termed complementary polytopic interactions by the authors) are also responsible for mesophase induction and modification in a series of disc-like materials (e.g. 2 and 3) as described by, for example, Bushby and co-workers [11-13]. 

Fast motions of the molecules in the liquid state average all these interactions. Chemical shifts and J values are measured as discrete averages, and the dipolar and quadrupolar interactions are averaged to zero. 

NMR spectroscopy is a powerful technique to study molecular structure, order, and dynamics. Because of the anisotropy of the interactions of nuclear spins with each other and with their environment via dipolar, chemical shift, and quadrupolar interactions, the NMR frequencies depend on the orientation of a given molecular unit relative to the external magnetic field. NMR spectroscopy is thus quite valuable to characterize partially oriented systems. Solid-state NMR... 

Figure 5. Energy level diagram for a spin 5/2 nucleus showing the effect of the first-order quadrupolar interaction on the Zeeman energy levels. The (m V2 m = -V2) transition (shown in bold) is independent of the quadrupolar interaction to...

The strength of the quadrupolar interaction is proportional to the quadrupole moment Q of a nucleus and the electric field gradient (EFG) [21-23]. The size of Q depends on the effective shape of the ellipsoid of nuclear charge distribution, and a non-zero value indicates that it is not spherically symmetric (Fig. 1). 

The Hamiltonian describing the quadrupolar interaction in the laboratory frame (L), in the units of radians/s, can be written using the spherical tensor formalism as [1,6, 24]... 

Fig. 1 (a) Schematic representation of the spherical and non-spherical charge distribution in a nucleus. The value of electric quadrupole moment Q for the quadrupolar nucleus depends on the isotope under consideration, (b) The quadrupolar interaction arises from the interaction of Q with surrounding electric field gradient (EFG)... 

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