Dipole localized

Aqvist, J., Luecke, H., (Juiocho, F.A. and Warshel, A. (1991) Dipoles localized at helix termini of proteins stabilize charges. Proc. Natl. Acad. Sci. USA, 88,2026-2050. 

The tensors f and f in Eq. (6-2) may be represented by Eqs. (6-3) and (6-4) [33, 90], assuming that the solvent can be approximated to a homogeneous and isotropic dielectric, where the solute molecules are localized in a spherical cavity (then the tensor fe is reduced to the scalar f.), and approximating the dipole moment of the solute molecule by a point dipole localized in the center of this sphere ... 

Pp Pcoil C-FPp K-D Re Hp M-P P-P IIlong dipole /LOCAL /NON-LOCAL NMR shift... 

At the linear level, the microscopic induced dipole vector on a single molecule in the local Cartesian... 

The polarization P is given in tenns of E by the constitutive relation of the material. For the present discussion, we assume that the polarization P r) depends only on the field E evaluated at the same position r. This is the so-called dipole approximation. In later discussions, however, we will consider, in some specific cases, the contribution of a polarization that has a non-local spatial dependence on the optical field. Once we have augmented the system of equation B 1.5.16. equation B 1.5.17. equation B 1.5.18. equation B 1.5.19 and equation B 1.5.20 with the constitutive relation for the dependence of Pon E, we may solve for the radiation fields. This relation is generally characterized tlirough the use of linear and nonlinear susceptibility tensors, the subject to which we now turn. 

In order to describe the second-order nonlinear response from the interface of two centrosynnnetric media, the material system may be divided into tlnee regions the interface and the two bulk media. The interface is defined to be the transitional zone where the material properties—such as the electronic structure or molecular orientation of adsorbates—or the electromagnetic fields differ appreciably from the two bulk media. For most systems, this region occurs over a length scale of only a few Angstroms. With respect to the optical radiation, we can thus treat the nonlinearity of the interface as localized to a sheet of polarization. Fonnally, we can describe this sheet by a nonlinear dipole moment per unit area, -P ", which is related to a second-order bulk polarization by hy P - lx, y,r) = y. Flere z is the surface nonnal direction, and the... 

The higher-order bulk contribution to the nonlmear response arises, as just mentioned, from a spatially nonlocal response in which the induced nonlinear polarization does not depend solely on the value of the fiindamental electric field at the same point. To leading order, we may represent these non-local tenns as bemg proportional to a nonlinear response incorporating a first spatial derivative of the fiindamental electric field. Such tenns conespond in the microscopic theory to the inclusion of electric-quadnipole and magnetic-dipole contributions. The fonn of these bulk contributions may be derived on the basis of synnnetry considerations. As an example of a frequently encountered situation, we indicate here the non-local polarization for SFIG in a cubic material excited by a plane wave (co) ... 

We now come back to the important example of two spin 1/2 nuclei with the dipole-dipole interaction discussed above. In simple physical tenns, we can say that one of the spins senses a fluctuating local magnetic field originatmg from the other one. In tenns of the Hamiltonian of equation B 1.13.8. the stochastic fiinction of time F l t) is proportional to Y2 (9,( ))/rjo, where Y, is an / = 2 spherical hannonic and r. is the... 

Barium titanate [12047-27-7] has five crystaUine modifications. Of these, the tetragonal form is the most important. The stmcture is based on corner-linked oxygen octahedra, within which are located the Ti" " ions. These can be moved from their central positions either spontaneously or in an apphed electric field. Each TiO octahedron may then be regarded as an electric dipole. If dipoles within a local region, ie, a domain, are oriented parallel to one another and the orientation of all the dipoles within a domain can be changed by the appHcation of an electric field, the material is said to be ferroelectric. At ca 130°C, the Curie temperature, the barium titanate stmcture changes to cubic. The dipoles now behave independentiy, and the material is paraelectric (see Ferroelectrics). 

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