Valence electron, charge redistribution

The efficient screening approximation means essentially that the final state of the core, containing a hole, is a completely relaxed state relative to its immediate surround-ing In the neighbourhood of the photoemission site, the conduction electron density of charge redistributes in such a way to suit the introduction of a core in which (differently from the normal ion cores of the metal) there is one hole in a deep bound state, and one valence electron more. The effect of a deep core hole (relative to the outer electrons), may be easily described as the addition of a positive nuclear charge (as, e.g. in P-radioactive decay). Therefore, the excited core can be described as an impurity in the metal. If the normal ion core has Z nuclear charges (Z atomic number) and v outer electrons (v metallic valence) the excited core is similar to an impurity having atomic number (Z + 1) and metalhc valence (v + 1) (e.g., for La ion core in lanthanum metal, the excited core is similar to a Ce impurity). 

Physically Eq. (1) implies that the valence electron wave functions are strongly localized within the space between the bonded atoms, and that electrons belonging to spatially separated valence bonds do not interact with each other. In practice this condition is never fulfilled and the deformation of a given bond results in charge-density redistribution over the entire molecule, which is man-... 

Given the quality of data described above, it is possible to go beyond the neutral spherical atom model, and to determine the redistribution of valence electrons due to chemical bonding. In other words, we can develop a description of the electron density distribution that includes charge transfer and non-spherical atoms. 

Entropy production during chemical change has been interpreted [7] as the result of resistance, experienced by electrons, accelerated in the vacuum. The concept is illustrated by the initiation of chemical interaction in a sample of identical atoms subject to uniform compression. Reaction commences when the atoms, compacted into a symmetrical array, are further activated into the valence state as each atom releases an electron. The quantum potentials of individual atoms coalesce spontaneously into a common potential field of non-local intramolecular interaction. The redistribution of valence electrons from an atomic to a metallic stationary state lowers the potential energy, apparently without loss. However, the release of excess energy, amounting to Au = fivai — fimet per atom, into the environment, requires the acceleration of electronic charge from a state of rest, and is subject to radiation damping [99],... 

Vcore(v) is the potential associated with the interaction between valence and core electrons and VexchangeC-v) is the exchange potential between valence electrons. The exchange potential accounts for the repulsive interaction between electrons of like spin (Pauli exclusion principle) and electrons of either spin (correlation interaction). Both of these potentials are experienced in the bulk as well as at the surface. Vdipoie(v) is specific to the surface and arises from charge redistribution at the asymmetric surface. 

Electron removal from, and electron transfer to a compound is related to conformational and configurational changes as well as to an alteration of the reactivity. This was shown, e.g., in Sect. 2.3 entitled ET-induced rearrangements of cyclopropanes and consecutive reactions 132). The effect of charge redistribution within a carban-ion , resulting from different ion pair situations, on the conformations of the car-banion was also illustrated by the examples given in the last section. In this section electron transfer valence tautomerism , as proposed by Staley 133), is reviewed, and the reader will recognize the similarity of the phenomena discussed here to those outlined in Sect. 6. 

The method works as follows. The mass velocity, Darwin and spin-orbit coupling operators are applied as a perturbation on the non-relativistic molecular wave-functions. The redistribution of charge is then used to compute revised Coulomb and exchange potentials. The corrections to the non-relativistic potentials are then included as part of the relativistic perturbation. This correction is split into a core correction, and a valence electron correction. The former is taken from atomic calculations, and a frozen core approximation is applied, while the latter is determined self-consistently. In this way the valence electrons are subject to the direct influence of the relativistic Hamiltonian and the indirect effects arising from the potential correction terms, which of course mainly arise from the core contraction. 

Although the surface atomic stmcture varies little from the ideal, the redistribution of electrons at the surface can be expectedly significant because of the covalent nature of Fe-S bonding in pyrite. An ideal starting point is to consider the predictions of the electron counting principles of autocompensation, which uses the formal charges on the atoms. Each Fe atom contributes two valence electrons to six Fe-S bonds, or 1/3 e per bond. Each S atom contributes six valence electrons to three Fe-S and one S-S bond. Taking one electron from each S to form the S-S bond, 10 are left for the six Fe bonds... 

Consider first the weak charge redistribution such as for the reaction of a hydrogen atom with a hydrogen molecule. Here, Ta,bc ab,c he constructed as the product of the electronic wave function of a free atom and a diatomic molecule, the latter being expressed by the Heitler-London approximation [133, 162]. Then V corresponds to the interaction between two valence structures, one for spin coupling of electrons localized on protons B and C, and the other for those localized on A and B. Calculation yields the London expression for the interaction energy of free atoms in the S state [280]. 

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