Electron density fluctuations

Intensity Level Between SAXS and WAXS Electron Density Fluctuations... 

If the number Z/v of electrons in each particle is constant, electron density fluctuation... 

If a S> 1, collective effects play an important role and the light scattering is no longer caused by individual electrons but by electron density fluctuations 280), Jn this case the spectrum shows a central line at Xq and two narrow lines located symmetrically about Xq, at a distance governed by the electron plasma frequency. The linewidth is smaller than in the case X < 1 and is determined rather by the thermal motion of the ions, not that of the electrons. The line shape depends on the ratio of electron to ion temperatures. Therefore, a measurement of the shape and width of this central line allows, under certain assumptions, a direct determination of the ion temperature. 

In Sections 17.2 and 17.3, we have reviewed the QM/MM approach based on the real-space grids [40,41,58,59,60,61,62] and the novel theory of solutions [14,15,16], respectively. As has been suggested, the theory of energy representation is readily applicable to a solute that is quantum chemically described. The present section is devoted to the details of the methodology, referred to as QM/MM-ER, developed by combining the QM/MM approach with the theory of energy representation [19]. The point of the method is to divide the total solvation free energy into the contributions due to the pairwise additive interaction between the solute and the solvent and the residual contribution due to the electron density fluctuation. A focus will be placed on the treatment of the many-body interaction inherent in the quantum chemical object. 

In this subsection, we presented an approximate scheme to evaluate the contribution S/u. of the electron density fluctuation to the excess chemical potential. Although we saw that this contribution is minor for a QM water molecule in ambient and supercritical water, it should emphasized that 8p, can be treated quantitatively in the method of energy representation. Actually, the treatment of the electron density fluctuation is not directly possible in the PCM and RISM-SCF methods. Furthermore, the approximate 8p, is exact to second order in the solvent density and in the electron density fluctuation. Thus, when the effect of the electron density fluctuation is weak, the calculation of 5p, is expected to be accurate. 

P3) The effect of the electron density fluctuation can be approximately estimated by performing additional QM/MM simulations that compute distribution functions Po (K) and p (p) with respect to the energy coordinate p = v(n, x,) —u ( , x,). These distribution functions are used as inputs to the approximate functional. 

In practical implementation of QM/MM-ER, the procedures (PI) and (P2) would be sufficient to compute the free energies with substantial accuracy. As was demonstrated in the previous paper [60], delocalization of electron distribution in space significantly affects the energetics of solvation. The effect of the electron density fluctuation can be safely neglected when one computes the free energy differences between reactants and products in chemical reactions in solution since the cancellations of the effect will take place. 

K is a constant containing all the optical parameters for light, electron density fluctuations for X-rays and scattering length difference for neutrons. The exact definitions of K are given as ... 

Here N, Ep, and W are all functions of position. This gives us the electron density in terms of the potential. We may now use Poisson s equation to write the screening potential, (5fP(r) - in terms of the electron density fluctuation,... 

State energy calculations are also assisted by TDDFT. This development principally concerns the van der Waals (vdW) or dispersion-force component of the groundstate energy. The usual groundstate LDA and its various gradient extensions [227] do not give an adequate description of vdW forces [228], presumably because these forces arise (in one picture at least see below) from the correlations between dynamic electron density fluctuations in widely separated positions. This makes the usual local or near-local approximations invalid. The approach to be introduced here facilitates the derivation of van der Waals functionals via a frequency integration over dynamic susceptibilities. 

This technique provides information regarding the periodicity and magnitude of electron density fluctuations. The technique has been used on segmented polyurethanes and related polymers to study domain spacing, phase purity, and the width of the transition zone between dissimilar domains (10,11,12). ... 

If one could reach spotsizes at the sample of 0.1 0.1 pm2 then one would get into the range of the electron density fluctuation due to the morphology of lamellar... 

The dispersion force is due to induced dipole interaction between atoms or molecules through electron density fluctuations. According to London, the potential energy of interaction London is given by... 

Because of the poorer packing of protofibrils at band locations, these should be more readily invaded by foreign substances. Large invading molecules may actually increase the distortions of protofibrils at bands or actually pry open the structure to increase the spread of distortion along the fibril. On the other hand, molecules which are small compared to protofibril diameters may serve to smooth out the kinks and increase perfection, or perhaps to fill in the holes and reduce the electron-density fluctuations at the imperfect cross sections, thus causing similar reduction in the diffraction evidence of imperfection. Chemical attack on the fibril should most easily be accomplished at band locations. 

Figure 2.15. Electron density fluctuations close to the surface (one-dimensionat). and p(z) can be evaluated from Eq.(2,84a) to give ...

The intensity is determined by the mean scattering power of the system which is given the designation r 2 or mean square electron density fluctuation. For a two-phase system of volume V with volume fractions x and X and with the respective electron densities pj and P2, it can be shown that... 

Faivre, A., David, L., VassoUle, R., Vigier, G., Etienne, S., and Geissler, E., Electronic density fluctuations in disordered systems 1. Effect of thermal treatments bon the dynamics and local microstructure of poly(methyl methacrylate). Macromolecules, 29, 8387-8390 (1996). 

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