Dipole field around

Derive the expression for the electric field around a point dipole, Eq. VI-5, by treating the dipole as two charges separated by a distance d, then moving to distances X d. 

For a quantum mechanical calculation, the single point calculation leads to a wave function for the molecular system and considerably more information than just the energy and gradient are available. In principle, any expectation value might be computed. You can get plots of the individual orbitals, the total (or spin) electron density and the electrostatic field around the molecule. You can see the orbital energies in the status line when you plot an orbital. Finally, the log file contains additional information including the dipole moment of the molecule. The level of detail may be controlled by the PrintLevel entry in the chem.ini file. 

In addition to the dipole-dipole relaxation processes, which depend on the strength and frequency of the fluctuating magnetic fields around the nuclei, there are other factors that affect nOe (a) the intrinsic nature of the nuclei I and S, (b) the internuclear distance (r,s) between them, and (c) the rate of tumbling of the relevant segment of the molecule in which the nuclei 1 and S are present (i.e., the effective molecular correlation time, Tf). 

The most efficient factor in stabilizing the electronic state is the dipole-dipole interaction. This creates a local electric field (reactive field) around the excited dye interacting with its dipole [14]. If the charges are present in its vicinity, they create an electric field that interacts with the dye dipole and induces electrochromic shifts of absorption and fluorescence spectra. The direction of these shifts depends on the relative orientation of the electric field vector and the dye dipole. These effects of electrochromism are overviewed in [15]. 

Natural electrical dipole development around electronic conductors in the earth is theoretically sound, supported by experimentation and well documented through 100 years of field observation. However the problem with it is that it only describes a subset of cases where SP occurs over ore deposits. It cannot account for cases where voltages exceed c. 500 mV (Sato Mooney 1960) and these are not rare. There should also be no response at all over disseminated sulfides yet large porphyry deposits and other disseminated systems produce the largest SP responses so far documented... 

Fig. 1. Electrical dipole development around a conductor crossing redox equipotential lines. Positive current in the country rock (not shown) travels perpendicular to electrical field lines from the anode to the cathode (modified after Govett 1976 and Hamilton 1998).

Debye and Huckel (J) have derived an expression for the work function of an ion in an ion atmosphere in solution. They and others (J, S, 4) have applied this function to various phenomena in liquid media. The authors (2) have previously deduced, in a similar way, the field around a dipole and have combined it with Onsagers (5) theory of polar liquids to obtain an equation that explains the electrostatic effects on the rates of reaction between ions and dipolar molecules (2). The equation has been applied (2,6,7,8) to the rates of several ion-dipolar molecular reactions. 

Ch. Jungen All I can say at this point is that the quantum defect/frame transformation approach appears to work for CaF around n = 14. We have chosen CaF, which is so highly polar, in order to ascertain this, and this is also the reason why we have made ab initio calculations in order to compare experiment and theory. I suppose that the dipole field is averaged out by the rotational motion, and thus one can get away with the customary frame transformation approach. 

This interaction arises from the overlap of the deformation fields around both defects. For weakly anisotropic cubic crystals and isotropic point defects, the long-range (dipole-dipole) contribution obeys equation (3.1.4) with a(, ip) oc [04] (i.e., the cubic harmonic with l = 4). In other words, the elastic interaction is anisotropic. If defects are also anisotropic, which is the case for an H centre (XJ molecule), in alkali halides or crowdions in metals, there is little hope of getting an analytical expression for a [35]. The calculation of U (r) for F, H pairs in a KBr crystal has demonstrated [36] that their attraction energy has a maximum along an (001) axis with (110) orientation of the H centre reaching for 1 nn the value -0.043 eV. However, in other directions their elastic interaction was found to be repulsive. 

Polar molecules develop an electrical field around themselves, therefore they are marked by the ability to attract either mutually themselves or other molecules with unsymmetrical electron structures. In this way we can explain the association of polar molecules (of water for instance) or the solvation of ions (hydration in case of water) caused by drawing in of the dipoles of water molecules into the electrical field of the ions (to be discussed further on). 

Figure 22. Sketch of the electric field lines E0 in the optical near field around the circular subwavelength aperture of a near-field probe with a molecular dipole D at r from the center of the aperture.

It seems natural to assume that polar crystals would be a source of electric fields around them just as magnets are a source of magnetic fields. In practice, however, the net dipole moment is not detectable in ferroelectrics because the surface charges are usually rapidly neutralized by ambient charged particles. 

A polarisable apolar molecule can be represented by a dielectric sphere of radius a and relative permittivity 8, bearing no diarge distribution vdiidi can produce singularities for r g a. An ion or polar molecule situated in the vidnity of this sphere give rise to an induced dipole moment in and hence to an electrostatic field around the dielectric sphere. The solvent around the apolar molecule is considered as a homogeneous medium of relative permittivity s. 

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