Dipolar distribution, calculation

For these, empirical values are usually not available. One calculates first the wave-function of the excited state. A, using SCF-CI techniques. The charge distribution of this state is obtained, and expressed as a sum of multipolar, multicentric terms, up to quadrupole. From this expression, the electrostatic interactions are calculated as in the ground state. The polarization term is harder to calculate, it is often taken to be equal to the ground-state term. The dispersion term may be calculated approximately by considering the interaction between two dipolar distributions due to the excited states of A and D. This approximation is valid when the first excited state... 

The rather well-defined spin precession frequencies in CePdSn and CePtSn (especially the single frequency in the upper AFM state of CePtSn) are inconsistent with an incommensurately modulated spin structure. Dipolar sum calculations were carried out for the muon stopping site mentioned earlier and the spin structure of the upper AFM state of CePtSn as derived by Kadowaki et al. (1993), in order to elucidate the problem somewhat further (Kalvius et al. 1995b). The calculations generated four fi eld distributions of file type discussed in sect. 3.7 (see eq. 51) ... 

FIGURE 7.57 (a) TSDC spectra of individual water and water located in rat tail vertebrae initially and after additional adsorption of water vapor for 24 h (+6 wt%) (discharging current has the opposite sign to that of the TSD current) and (b) pore size distribution calculated on the basis of the TSDC for initial bone tissue (sample I) for dipolar relaxation at 7 <225 K. (Adapted from Colloids Surf. B Biointerfaces, 48, Turov, V.V., Gun ko, V.M., Zarko, V.I. et al.. Weakly and strongly associated nonfreezable water bound in bones, 167-175, 2006a, Copyright 2006, with permission from Elsevier.)... 

The parameters of the response fuoctioa are dependent on temperature and pressure. The temperature dependence will be discussed here for the Kohlrausch function only. In this fun km. parameter r determines the angular frequency where the dielectric loss and the relaxation lime distribution calculated from Eq. (19) are near to maximum. The temperature dependence of this parameter for such dipolar groups, the thermal motion of which do not influence the main structure appreciably, is... 

This was averaged over the total distribution of ionic and dipolar spheres in the solution phase. Parameters in the calculations were chosen to simulate the Hg/DMSO and Ga/DMSO interfaces, since the mean-spherical approximation, used for the charge and dipole distributions in the solution, is not suited to describe hydrogen-bonded solvents. Some parameters still had to be chosen arbitrarily. It was found that the calculated capacitance depended crucially on d, the metal-solution distance. However, the capacitance was always greater for Ga than for Hg, partly because of the different electron densities on the two metals and partly because d depends on the crystallographic radius. The importance of d is specific to these models, because the solution is supposed (perhaps incorrectly see above) to begin at some distance away from the jellium edge. 

We will consider dipolar interaction in zero field so that the total Hamiltonian is given by the sum of the anisotropy and dipolar energies = E -TEi. By restricting the calculation of thermal equilibrium properties to the case 1. we can use thermodynamical perturbation theory [27,28] to expand the Boltzmann distribution in powers of This leads to an expression of the form [23]... 

A four-pulse DEER measurement of the distance between two tyrosyl radicals on the monomers that make up the R2 subunit of E. coli ribonucleotide reductase gave a point-dipole distance of 33.1 A, which is in good agreement with the X-ray crystal structure.84 Better agreement between the calculated and observed dipolar frequency could be obtained by summing contributions from distributed... 

More refined continuum models—for example, the well-known Fumi-Tosi potential with a soft core and a term for attractive van der Waals interactions [172]—have received little attention in phase equilibrium calculations [51]. Refined potentials are, however, vital when specific ion-ion or ion-solvent interactions in electrolyte solutions affect the phase stability. One can retain the continuum picture in these cases by using modified solvent-averaged potentials—for example, the so-called Friedman-Gumey potentials [81, 168, 173]. Specific interactions are then represented by additional terms in (pap(r) that modify the ion distribution in the desired way. Finally, there are models that account for the discrete molecular nature of the solvent—for example, by modeling the solvent as dipolar hard spheres [174, 175]. 

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