Valence charge distribution

In principle, the electronic quadrupole can also be extracted from the calculated valence charge distribution. This is a tensor quantity and its components are defined by the matrix... 

IV) Functions, called augmenting functions (AF), which are needed to describe small residual distortions of the valence charge distribution on formation of the molecule. 

Tytko KH, Mehmke J, Fischer S (1999) Bonding and Charge Distribution in Isopolyox-ometalate Ions and Relevant Oxides - A Bond Valence Approach. 93 125-317... 

Within the computational scheme described in the course of this work, the available information about the atomic substructure (core+valence) can be taken into account explicitly. In the simplest possible calculation, a fragment of atomic cores is used, and a MaxEnt distribution for valence electrons is computed by modulation of a uniform prior prejudice. As we have shown in the noise-free calculations on l-alanine described in Section 3.1.1, the method will yield a better representation of bonding and non-bonding valence charge concentration regions, but bias will still be present because of Fourier truncation ripples and aliasing errors ... 

Qa and Qc are the charges obtained from the multipolar expansion of the interacting A and C molecular charge distributions, NyAL and NyAL being their respective number of valence electrons. Wa and Wc are the A and C atoms effective van der Waals radii. Kac is a proportionality factor tabulated upon the atomic numbers of the A and C atoms, a is a constant fixed to 12.35. The same treatment is applied to the others terms of the repulsion energy. 

Charge distributions and bonding in compounds of Cd and Hg in the solid and gaseous states can be studied by the well-established X-ray photoelectron spectrometry (XPS) and ultraviolet photoelectron spectrometry (UPS), respectively. With XPS, inner-shell electrons are removed which are indirectly influenced by the bonding, i.e., distribution of the valence electrons. UPS sees this electron distribution directly, since it measures the residual kinetic energies of electrons removed from the valence shells of the atoms, or, better, from the outer occupied orbitals of the molecules. The most detailed information accessible by UPS is obtained on gases, and it is thus applied here to volatile compounds, i.e., to the halides mainly of Hg and to organometallic compounds. 

Figure 2.1. illustrates these differences for the 2s NAOs of Li-, Li°, and Li+, showing the strong decrease in the radius of this valence orbital as the net charge increases. It is evident that an attempt to describe, e.g., the valence electron distribution of Li+ in terms of the fixed 2s AO of Li (or Li-) would incur a large error,... 

The second term in equation (9) is the usual electrostatic term. Here vA is the valency of the unit and e is the elementary charge, and ip(z) is the electrostatic potential. This second term is the well-known contribution accounted for in the classical Poisson-Boltzmann (Gouy -Chapman) equation that describes the electric double layer. The electrostatic potential can be computed from the charge distribution, as explained below. 

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