Electron, free, confinement

Thus, one-electron transfer causes cis -> trans isomerization. It is quite effective with free migration of an unpaired electron over the molecular framework. It is less effective when the unpaired electron is confined within the limits of a coordination complex. Such fixation of the unpaired electron hinders the rotation around the C=C bond. In a similar manner, a ball tied to a... 

Calculated geometries for a small number of diatomic and small polyatomic free radicals are compared with experimental structures in Table 5-18. These have been drawn from a somewhat larger collection provided in Appendix A5 (Tables A5-50 to A5-57). Except for triplet oxygen, all radicals possess a single unpaired electron (they are doublets). The usual set of theoretical models has been examined. All calculations involve use of the unrestricted open-shell SCF approach, where electrons of different spin occupy different orbitals, as opposed to the restricted open-shell SCF approach, where paired electrons are confined to the same orbital (see Chapter 2 for more detailed discussion). 

The eigenspectrum of the free-electron gas confined within a sphere of... 

Fig. 5.1 The eigenspectrum of a free-electron gas confined to a cube (left-hand panel) or a sphere (right-hand panel). The magic numbers corresponding to shell closings are given in the middle panel.

It is interesting that the electron cloud confined in the octahedron formed by the Na+ neighbors can be approximately treated as a free electron in a box of such dimensions. The straightforward calculation... 

The description of electrostatic phenomena in condensed molecular environments rests on the observation that charges appear in two kinds. First, molecular electrons are confined to the molecular volume so that molecules move as neutral polarizable bodies. Second, free mobile charges (e.g. ions) may exist. In a continuum description the effect of the polarizable background is expressed by the dielectric response of such environments. 

Such a modified picture is definitely not contradictory to the formulations [Rb902] 5 e" and [Csn03] + 5 e used in Chapter IV.l., because the reduction of the net charges of the clusters does not mean a reduction of the free electron concentration. Indeed, this result is equivalent to an assumption used by Burt and Heine (47) to explain the low work functions of CS11O3 (see V.4.). These authors emphasize that the iimer part of the clusters due to the concentrated negative charges of the Onions are hi ly repulsive for electrons. Therefore, the free electrons are confined to the periphery of the clusters. This assumption is visualized by the very simple picture of an ionic character of the iimer part of each Cs atom in the cluster and a metallic character of the outer part of each Cs atom. 

Our approach to the absorber design makes use of the optical excitation of surface plasmonsin small metal particles. In general, the free electron portion in metals is responsible for the typical brightness of metallic surfaces. The situation is quite different in small metal particles with a size of only a few nanometers. Here motion of the previously free electrons is confined inside a particle, so that electrons behave optically in a similar maimer like bound electrons - they show resonant absorption behaviour and are therefore a natural choice for a selective absorber material. 

At energies near the electrons are confined to channels and are thus not typical three dimensional free electrons. But, we have ignored quantum mechanics and in reality the electrons can tunnel from one channel to another and between various allowed regions. Furthermore as already indicated if we allow the electrons to hop there will be an additional component due to thermally assisted processes (or phonon... 

Sharp drops after certain sizes in the abundance spectrum indicate enhanced stability of these clusters compared to neighboring sizes. We will try to understand this phenomenon from the behavior of valence electrons in the clusters by invoking simple quantum mechanical models. The simplest model one uses for valence electrons inside a bulk metal is the free-electron theory valence electrons of all the atoms are free to move over the entire volume occupied by the solid [11]. One can use a similar free electron model in case of metal clusters. As the simplest approximation, shape of the cluster can be taken as spherical, and the electrons strictly confined within the sphere. In this hard sphere model, the Schrbdinger equation describing the valence electrons is... 

TTus is the energy of a free electron (not confined to a crystal). Note that this energy is continuous (not quantized) and that it goes as k. ... 

ScHERMANN, J. P Maior, F. G. Characteristics of electron-free plasma confinement in an rf quadrupole field. AppL Phys. 1978, 16, 225. 

Electronic effects on surfaces can generate preferential adsorption sites, as illustrated for step edges. However, a necessary condition for this to occnr on snrfaces is the availability of free charge as well as states for the free charge to occnpy. The closed-packed (111) surfaces allow for a greater orbital overlap of the surface atoms. This greater electron freedom leads to a two-dimensional free-electron gas confined to the surface. However, such surface states do not exist for the (110) and (100) surfaces. Studies on CgHg adsorbed on Ag(llO) reveals that the terraces and the (001) steps remain completely free of molecules. 

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