Localized electrons, definition

The surface basicity of a solid catalyst can be defined in a way analogous to that applied to conventional bases. Thus, a surface Lewis base site is one that is able to donate an electron pair to an adsorbed molecule. If we take the definition of surface basicity in a more general way, it could be said that the active surface corresponds to sites with relatively high local electron densities. This general definition will include not only Lewis basicity but also single electron donor sites. We emphasize that the literature of heterogeneous catalysis often reports that both single-electron and electron-pair donor sites exist on basic catalysts. 

We have assumed a classical model for molecules in which the majority of the electrons are localized on definite atoms or in definite two center bonds. Although this assumption works well in practice, it certainly needs justification, for in a correct LCAO MO description of a typical molecule, each MO is composed of AO s contributed by all the atoms present and there is nothing in this description that corresponds even remotely to the classical idea of localized bonds. 

Is resonance a real phenomenon The answer is quite definitely no. We cannot say that the molecule has either one or the other structure or even that it oscillates between them. .. Putting it in mathematical terms, there is just one full, complete and proper solution of the Schrodinger wave equation which describes the motion of the electrons. Resonance is merely a way of dissecting this solution or, indeed, since the full solution is too complicated to work out in detail, resonance is one way - and then not the only way - of describing the approximate solution. It is a calculus , if by calculus we mean a method of calculation but it has no physical reality. It has grown up because chemists have become used to the idea of localized electron pair bonds that they are loath to abandon it, and prefer to speak of a superposition of definite structures, each of which contains familiar single or double bonds and can be easily visualizable. [30]... 

F 2p character than F 2s character and is also bonding with respect to the FI orbital. This set of orbitals (2cr, 3a) illustrates a central feature of the MO approach. Whereas a simple Lewis structure or valence picture would draw a localized electron pair interaction between two orbitals, the MO picture attributes some bonding character to two separate molecular orbitals. This simple MO diagram illustrates the difficulty of determining a meaningful definition for bond order in a polyatomic molecule. No single MO completely represents the bonding between two atoms. 

Still there is no chance to find some experimental criterion for checking each of the described theories. It should be stressed that the polaron model of the cavity with the localized electron is definitely proved by the volume expansion of ammonia when adding the alkali metal to it (38). Besides, on the basis of any of the cavity theories it becomes comparatively easy to explain the results of investigation of e tr photoannealing—i.e., the dispersion of the trap depths, and temperature dependence of ExmaX of the electrons. In this connection it is rather desirable to find some approach to determining the sizes of the cavities for the electrons in the irradiated polar systems, as it has been done for the metal-ammonia solutions. 

We briefly report here a few definitions coneerning global and local electron counting procedures, remembering also that the number of cluster valence electrons (CVE) strongly determines the stoichiometry and the cluster shape, while the correct local valence electrons (LVE) distribution influences the ligand conformation. For a BMCC ... 

During last decades, the concept of the photon DOS is extensively discussed with respect to elementary photon emission and scattering events. Formulation of the photon DOS concept was promoted by pioneering papers by Purcell in 1947 [19], and Bykov in 1972 [20]. They predicted the considerable modification of spontaneous emission rate in cavities and in periodic medium, respectively. Today, the modification of spontaneous emission and scattering of light constitutes a body of modern nanophotonics (see e.g. [21] and refs, therein). Local photonic DOS which in many instances is an optical counterpart of local electronic DOS in doped semiconductors still lacks a solid definition [22]. 

As we have seen above chemical bonding in crystals (as well as in molecules) is analyzed in terms of the local properties of the electronic structure, obtained from the one-electron density matrix, written in a localized basis. Since local properties of electronic structure are essential ingredients of a number of theories and models (for example, the numerical values of atomic charges are used in the atom-atom potentials of the shell model), their estimation is of great importance. TVaditionally, the same AO basis is used both in LCAO SCF calculations and in the local properties definition, as was noted above. However, this approach is not always reliable, since the results of the population analyses are often strongly dependent on an inclusion of diffuse orbitals into the basis (useful for the electronic-structure calculations) and on the scheme chosen for the population analysis. 

This proposed mechanism is based upon the idea that a protein is a semiconductor, in which, as in a metal, certain electrons are not strictly localized to definite points in the macromolecule, but are, to a certain degree,... 

It is absolutely vital for our discussion to have a good definition of a localized electronic state as opposed to one which is delocalized. The later will also be referred to as a quasi-free electron. Our primary definition will be that the localized electron is characterized by a wave function which decays exponentially with distance the same type of definition used for simple atomic wave functions. The quasi-free electron... 

Since in liquid alcanes a localized electron in the conduction band can be relatively easily thermally excited into an extended state, we would expect F to be only slightly higher in the liquid than in the solid. We could go one step further and argue that polyethylene, since it is partially amorphous, resembles a liquid alcane and also is expected to exhibit F 1 MV/cm. This is definitely not confirmed by experiment. Polyethylene can withstand fields up to - 5 MV/cm (O Dwyer, 1973). 

The observations described in this section are particularly relevant for the definition of the transport mechanism because they all hint to a major role of the non-local electron phonon coupling. If the intermolecular coupling is so sensitive to the relative position of the molecules, there must be vibrations that modulate very effectively the intermolecular coupling and these are described by the term... 

The mathematical formulation and definition of GRDs provide information about the overall properties of the chemical systems and are also useful for analysing the thermodynamic aspects of chemical reactions. However, the GRDs caimot identify the reactive part or site of the molecule. Most of the chemical reactions are primarily concerned with the atoms, group of atoms or a specific site in a molecule. The important issues relate to the effect of charge or density fluctuations in chemical reactivity and the observed reactivity trends. The chemical reactivity for a system is determined by the sensitivity of electron density to the perturbations. Therefore, an appropriate definition was required in addition to the global descriptors [18]. A basic local descriptor is related to the change of the local electron density to the chemical potential of the system. This is known as local softness. 

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