Valence charges

This ionic potential is periodic. A translation of r to r + R can be acconnnodated by simply reordering the sunnnation. Since the valence charge density is also periodic, the total potential is periodic as the Hartree and exchange-correlation potentials are fiinctions of the charge density. In this situation, it can be shown that the wavefiinctions for crystalline matter can be written as... 

Reciprocal lattice vectors are usefiil in defining periodic fimctions. For example, the valence charge density, p (r), can be expressed as... 

Since and depend only on die valence charge densities, they can be detennined once the valence pseudo- wavefiinctions are known. Because the pseudo-wavefiinctions are nodeless, the resulting pseudopotential is well defined despite the last temi in equation Al.3.78. Once the pseudopotential has been constructed from the atom, it can be transferred to the condensed matter system of interest. For example, the ionic pseudopotential defined by equation Al.3.78 from an atomistic calculation can be transferred to condensed matter phases without any significant loss of accuracy. 

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... 

Extra radial flexibility has been proved necessary in order to model the valence charge density of metal atoms, in minerals [6,11], and coordination complexes [5], and similar evidence of the inability of single-exponential deformation functions to account for all the information present in the observations have also been found in studies of organic [12, 13] and inorganic [14] molecular crystals. 

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 ... 

Chen, R., Trucano, P. and Stewart, R.F. (1977) The valence-charge density of graphite, Acta Cryst., A33, 823-828. 

IVCT = inter valence charge-transfer LMCT = ligand-to-metal charge-transfer MLCT = metal-to-ligand charge-transfer MRI = magnetic resonance imaging... 

Valence (charge) of metal ion = 2aii atoms (bond valence)... 

In the context of the spherical shell model for nearly-free electrons, assuming that Au, Sc, and Ti contribute with 1,3,5 delocalized valence electrons, respectively, it appears that AueSc+ and Au5Ti+ are magic clusters with 8 valence electrons. However, for the other TM impurities, delocalization of valence charge is restricted to the 4s electrons if this model is forced to explain the observed drops of intensity, at n=5 and 7. We obtain the experimental magic numbers ° of Au TM+ clusters without resorting to the empirical shell-model of delocalized electrons. 

The key features of both catalytic cycles are similar. Alkene coordination to the metal followed by insertion to yield an alkyl-metal complex and CO insertion to yield an acyl-metal complex are common to both catalytic cycles. The oxidative addition of hydrogen followed by reductive elimination of the aldehyde regenerates the catalyst (Scheme 2 and middle section of Scheme 1). The most distinct departure in the catalytic cycle for cobalt is the alternate possibility of a dinuclear elimination occurring by the in-termolecular reaction of the acylcobalt intermediate with hydridotetracarbonylcobalt to generate the aldehyde and the cobalt(0) dimer.11,12 In the cobalt catalytic cycle, therefore, the valence charges can be from +1 to 0 or +1 to +3, while the valence charges in the rhodium cycles are from +1 to +3. 

Homonymous ions of deviating valency (charge) may also be formed in some processes of chemisorption they will then be formed on or near the surface but may subsequently diffuse into the interior of the crystal lattice. 

With this example of data from the dimetallofullerene Sc2 C84, the efficacy of combining x-ray absorption and charge-transfer atomic multiplet calculations in investigating the valency, charge transfer and cage-metal interaction of more complex, hybridised systems such as Sc2 C84 has been demonstrated. Based on the valence sensitivity of the measurement, we are confident in overruling... 

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