Anisotropic interaction

Another important application of perturbation theory is to molecules with anisotropic interactions. Examples are dipolar hard spheres, in which the anisotropy is due to the polarity of tlie molecule, and liquid crystals in which the anisotropy is due also to the shape of the molecules. The use of an anisotropic reference system is more natural in accounting for molecular shape, but presents difficulties. Hence, we will consider only... 

In the purely non-adiabatic limit the phase (5.52) coincides with that calculated in [203] and for very long flights (rt b,v" v) or high energies (.E e) it reduces to what can be obtained from the approximation of rectilinear trajectories. However, there is no need for these simplifications. The SCS method enables us to account for the adiabaticity of collisions and consider the curvature of the particle trajectories. The only demerit is that this curvature is not subjected to anisotropic interaction and is not affected by transitions in the rotational spectrum of the molecule. 

Intermolecular recognition and self-assembly processes both in the solid, liquid, and gas phases are the result of the balanced action of steric and electronic factors related to shape complementarity, size compatibility, and specific anisotropic interactions. Rather than pursuing specific and definitive rules for recognition and self-assembly processes, we will afford some heuristic principles that can be used as guidelines in XB-based supramolecular chemistry. 

The special case of isotropic g and hyperfine interaction will now be considered. This simplification is valid when the anisotropic interactions are averaged by rapid tumbling. The quadrupole interaction will be omitted because it is purely anisotropic. The resulting simplified spin Hamiltonian is given in Equation (9). 

In this review, we focus on the effect of anisotropic interactions, in particular parallel attractions, and demonstrate that the inclusion of such interactions in a model leads to a great richness in possible polymer phase behavior. From a practical point of view, the model that we describe has the advantage that it is computationally very cheap—although this advantage comes at the price of sacrificing the greater realism of an off-lattice model. 

Hu W, Frenkel D (2005) Polymer crystallization driven by anisotropic interactions. Adv Polym Sci (in this volume)... 

Tensor correlation methods refer to the selection of two anisotropic interactions so that the pattern of the 2D correlation spectrum can reveal the magnitudes and relative orientation of the two tensorial interactions. Below we will discuss many different SSNMR techniques suggested for the determination of peptide backbone... 

Echo Formation Between Two Correlated Anisotropic Interactions... 

The terms in (la) and (lb) both involve sums of single nuclear spin operators Iz. In contrast, the terms in (lc) involve pairwise sums over the products of the nuclear spin operators of two different nuclei, and are thus bilinear in nuclear spin. If the two different nuclei are still of the same isotope and have the same NMR resonant frequency, then the interactions are homonuclear if not, then heteronuclear. The requirements of the former case may not be met if the two nuclei of the same isotope have different frequencies due to different chemical or Knight shifts or different anisotropic interactions, and the resulting frequency difference exceeds the strength of the terms in (lc). In this case, the interactions behave as if they were heteronuclear. The dipolar interaction is proportional to 1/r3, where r is the distance between the two nuclei. Its angular dependence is described below, after discussing the quadrupolar term. 

The first approach has successfully been applied to the study of amorphous as well as to macroscopically ordered solids. Examples of applications include the determination of backbone geometries in fibrous proteins [4] or the determination of protein-backbone, side-chain, and bound-ligand orientation with respect to the membrane normal in membrane-bound proteins [5-8]. Membranes, bilayers, bicelles, or liposomes are neither solid nor liquid systems but have aspects of both and are sometimes liquid crystalline. In most of these systems, time-independent anisotropic interactions play an important role,... 

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