Electronic charge distribution theoretical calculation

There is another aspect that makes measurements of transition probabilities very attractive with regard to a more detailed knowledge of molecular structure. Transition probabilities derived from computed wave functions of upper and lower states are much more sensitive to approximation errors in these functions than are the energies of these states. Experimentally determined transition probabilities are therefore well suited to test the validity of calculated approximate wave functions. A comparison with computed probabilities allows theoretical models of electronic charge distributions in excited molecular states to be improved [2.19,2.20]. 

Theoretical calculations of the electronic structure of phosphorin indicate that the Tr-charge-distribution is different to that of pyridine and cannot be explained by simple resonance theory. 

In all liquids, the free-ion yield increases with the external electric field E. An important feature of the Onsager (1938) theory is that the slope-to-intercept ratio (S/I) of the linear increase of free-ion yield with the field at small values of E is given by e3/2efeB2T2, where is the dielectric constant of the medium, T is its absolute temperature, and e is the magnitude of electronic charge. Remarkably S/I is independent of the electron thermalization distance distribution or other features of electron dynamics in fact, it is free of adjustable parameters. The theoretical value of S/I can be calculated accurately with a known value of the dielectric constant it has been well verified experimentally in a number of liquids, some at different temperatures (Hummel and Allen, 1967 Dodelet et al, 1972 Terlecki and Fiutak, 1972). 

Unlike the oxymercuration of acyclic olefins, oxymercuration of bicyclic olefins often gives jy -addition products. Norbornenes 93, for example, show exclusive fvo-oxymercuration. In this reaction, the ratio between the isomers depends on the nature of the fvo-substituent (R1) and tro/o-substituent (R2) (Equation (36)). The presence of electron-withdrawing fvo-substituents always leads to a much greater selectivity in favor of 94a-d over 95a-d.116 117 As indicated by extensive theoretical calculations, the charge distribution in the transition states governs the selectivity of these reactions.118... 

Several issues remain to be addressed. The effect of the mutual penetration of the electron distributions should be analyzed, while the use of theoretical densities on isolated molecules does not take into account the induced polarization of the molecular charge distribution in a crystal. In the calculations by Coombes et al. (1996), the effect of electron correlation on the isolated molecule density is approximately accounted for by a scaling of the electrostatic contributions by a factor of 0.9. Some of these effects are in opposite directions and may roughly cancel. As pointed out by Price and coworkers, lattice energy calculations based on the average static structure ignore the dynamical aspects of the molecular crystal. However, the necessity to include electrostatic interactions in lattice energy calculations of molecular crystals is evident and has been established unequivocally. 

The electron density distribution of a known surface structure can be calculated from first-principles. Thus, the He diffraction data can be compared with theoretical results, in particular, to verify different structural models. Hamann (1981) performed first-principles calculations of the charge-density distributions of the GaAs(llO) surface, for both relaxed and unrelaxed configurations. The He diffraction data are in excellent agreement with the calculated charge-density distributions of the relaxed GaAs(llO) surface, and are clearly distinguished from the unrelaxed ones (Hamann, 1981). 

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