Charge quantum-mechanical considerations

On the other hand, in aromatic compounds, particularly in benzene, a decrease is apparent in the molar refraction. This depression is specific to the aromatic character and is consistent with the fact that, on account of the ring arrangement of the three double bonds within the nuclear framework, a definite distribution of negative charge density occurs. The same consequence was deduced from quantum-mechanical considerations by the far-reaching studies of Hiickel, Pauling and Slater. It... 

The first set of screening constants was obtained from the discussion of the motion of an electron in the field of the nucleus and its surrounding electron shells, idealized as electrical charges uniformly distributed over spherical surfaces of suitably chosen radii. This idealization of electron shells was first used by Schrodinger3), and later by Heisenberg4) and Unsold5), who pointed out that it is justified to a considerable extent by the quantum mechanics. The radius of a shell of electrons with principal quantum number nt is taken as... 

In recent years, electrochemical charge transfer processes have received considerable theoretical attention at the quantum mechanical level. These quantal treatments are pivotal in understanding underlying processes of technological importance, such as electrode kinetics, electrocatalysis, corrosion, energy transduction, solar energy conversion, and electron transfer in biological systems. 

Nuclei with spin I > are not, as a rule, perfectly spherical distributions of charge, as may be shown by quite general quantum mechanical symmetry considerations (89). All nuclei possess the spin axis as a sym-... 

According to these considerations three subregions are defined as depicted in Fig. 1. The inner and outer parts of the QM region are termed the QM core and QM layer zone, respectively. As discussed solutes in the QM core do not require the application of non-Coulombic potentials—composite species with complex potential energy surfaces can be treated in a straightforward way, while complex potential functions are required in the case of classical and even conventional QM/MM simulation studies. Interactions at close solute-solvent distances are treated exclusively via quantum mechanics and account for polarization, charge transfer, as well as many-body effects. The solute-solvent... 

If a solution, being in contact with an electrode, contains photosensitive atoms or molecules, irradiation of such a system may lead to photoelectro-chemical reactions or, to be more exact, electrochemical reactions with excited particles involved. In such reactions the electrons pass either from an excited particle to the electrode (the anodic process) or from the electrode to an excited particle (the cathodic process). In this case, an elementary act of charge transfer has much in common with ordinary (dark) electrochemical redox reactions, which opens a possibility of interpreting certain aspects of photochemical processes under consideration with the use of concepts developed for general quantum mechanical description of electrode processes. 

Measurement of electron density by X-ray diffraction cannot distinguish each electron in different orbitals however, it provides overall information on the asphericity of the d electron distribution in a molecule as well as on the redistribution of electrons upon chemical bond formation. At the present stage, experimental charge distributions can be compared only qualitatively with theoretical calculations. The method, however, will be of considerable value in clarifying poorly understood bonding situations. If the electron-density distribution and the geometrical arrangement of the atomic nuclei in a complex are known, it is possible, at least in principle, to predict all its physical and chemical properties on the basis of quantum mechanics. 

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