Electron distribution inhomogeneities

In the local density approximation it is assumed that at each point r in the inhomogeneous electron distribution (i.e. in the system of interest) where the density is p(r) then Vxc[p(r)] and Sxc p )) have the same values as in the homogeneous electron gas. In other words, the real electron density surrounding a volume element at position r is replaced by a constant electron density with the same value as at r. However, this constant electron density is different for each point in space (Figure 3.6). 

An electron in a MO is thus distributed inhomogeneously over the molecule. Calculate this distribution over the three carbon atoms for an electron in and for an electron in I 2. 

FIGURE 5.4 The differences in electron localization functions (ELFs) between the Becke-Edgecombe (BE) and Markovian (Ml) and (M2) formulations of Eqs. (5.388), (5.416), and (5.417), in left and right respectively, versus the homogeneous (/j-parameter) and inhomogeneous (g-parameter) influences on electronic distribution (Putz, 2009). 

Early LSDA static pseudopotential approaches to sodium microclusters date back approximately 20 years [122], see Appendix C. It would be misleading to consider LDA calculations as the natural extension of jellium models. However, the global validity of the latter cannot but anticipate the success of the former. Clearly, these should also clarify the role of the atomic structure in determining the electronic behavior of the clusters and the extent to which the inhomogeneity of the electron distribution is reflected in the measurable properties. Many structural determinations are by now available for the smaller aggregates, made at different levels of approximation and of accuracy (e.g. [110, 111], see Appendix C). The most extensive investigation of sodium clusters so far is the LDA-CP study of Ref. [123] (see Appendix C), which makes use of all the features of the CP method. Namely, it uses dynamical SA to explore the potential-energy surface, MD to simulate clusters at different temperatures, and detailed analysis of the one-electron properties, which can be compared to the predictions of jellium-based models. 

A nucleus possesses a nuelear quadrupole moment if it has a spin I greater than 1/2. In this case, its energy levels will be affected by an electric field gradient (EFG) at the nucleus, which leads to sphtting of the Mossbauer line. To detect this it is sufficient if at least one of the nuclear states involved in y-ray excitation possesses a quadrupole moment eQ, and that the electric field at the nucleus is inhomogeneous. This is usually the case if there is a non-cubic valence electron distribution or non-cubic lattice-site symmetry. 

Myers A B, Tchenio P and Moerner W E 1994 Vibronic spectroscopy of single molecules exploring electronic-vibrational frequency correlations within an inhomogeneous distribution J. Lumin. 58 161-7... 

Preliminary measurements with space-resolved PMC techniques have shown that PMC images can be obtained from nanostructured dye sensitization cells. They showed a chaotic distribution of PMC intensities that indicate that local inhomogeneities in the preparation of the nanostructured layer affect photoinduced electron injection. A comparison of photocurrent maps taken at different electrode potentials with corresponding PMC maps promises new insight into the function of this unconventional solar cell type. 

The interface is, from a general point of view, an inhomogeneous dielectric medium. The effects of a dielectric permittivity, which need not be local and which varies in space, on the distribution of charged particles (ions of the electrolyte), were analyzed and discussed briefly by Vorotyntsev.78 Simple models for the system include, in addition to the image-force interaction, a potential representing interaction of ions with the metal electrons. 

The inner and outer potential differ by the surface potential Xa — (fa — ipa- This is caused by an inhomogeneous charge distribution at the surface. At a metal surface the positive charge resides on the ions which sit at particular lattice sites, while the electronic density decays over a distance of about 1 A from its bulk value to zero (see Fig. 2.1). The resulting dipole potential is of the order of a few volts and is thus by no means negligible. Smaller surface potentials exist at the surfaces of polar liquids such as water, whose molecules have a dipole moment. Intermolecular interactions often lead to a small net orientation of the dipoles at the liquid surface, which gives rise to a corresponding dipole potential. 

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