Density-of-coordination

Kursanov et al. (85) investigated the effect of substituents on the n electron density of coordinated arenes. Two series of compounds were examined in this study (I) /j -arene-Cr(CO)3 (II) A -arene-Cr(CO)2P(Ph)s. As for all other r complexes, an upheld shift of the carbon nuclei of the n ligand was detected on complexation. In addition, qualitatively similar orders of shielding were noted in the complexed and uncomplexed benzenes. In particular, C(2,4) of the coordinated arene were observed to have the analagous functions of the corresponding atoms in the uncomplexed speices. C(3) (meta), however, in the n... 

In the case of a reduced density-matrix description of the system dynamics, the reduced probability density of coordinate Ri is given by... 

Figure A3.13.9. Probability density of a microcanonical distribution of the CH cliromophore in CHF within the multiplet with cliromophore quantum nmnber V= 6 (A. g = V+ 1 = 7). Representations in configuration space of stretching and bending (Q coordinates (see text following (equation (A3.13.62)1 and figure A3.13.10). Left-hand side typical member of the microcanonical ensemble of the multiplet with V= 6...

We are using the term space as defined by one or more coordinates that are not necessarily the a , y, z Cartesian coordinates of space as it is ordinarily defined. We shall refer to 1-space, 2-space, etc. where the number of dimensions of the space is the number of coordinates, possibly an n-space for a many dimensional space. The p and v axes are the coordinates of the density-frequency space, which is a 2-space. 

Pd(II) compounds coordinate to alkenes to form rr-complexes. Roughly, a decrease in the electron density of alkenes by coordination to electrophilic Pd(II) permits attack by various nucleophiles on the coordinated alkenes. In contrast, electrophilic attack is commonly observed with uncomplexed alkenes. The attack of nucleophiles with concomitant formation of a carbon-palladium r-bond 1 is called the palladation of alkenes. This reaction is similar to the mercuration reaction. However, unlike the mercuration products, which are stable and isolable, the product 1 of the palladation is usually unstable and undergoes rapid decomposition. The palladation reaction is followed by two reactions. The elimination of H—Pd—Cl from 1 to form vinyl compounds 2 is one reaction path, resulting in nucleophilic substitution of the olefinic proton. When the displacement of the Pd in 1 with another nucleophile takes place, the nucleophilic addition of alkenes occurs to give 3. Depending on the reactants and conditions, either nucleophilic substitution of alkenes or nucleophilic addition to alkenes takes place. 

Linear polyethylene (high density) was introduced in the late 1950s, with the development of coordination catalysts. Chlorosulfonation of these base resins gave products that were superior to the eadier, low density types in both chemical resistance and mechanical properties and with distinct advantages in mbber processibiUty (6,7). 

The worked out soi ption-photometric method of NIS determination calls preliminary sorption concentration of NIS microamounts from aqueous solutions on silica L5/40. The concentrate obtained is put in a solution with precise concentration of bromthymol-blue (BTB) anionic dye and BaCl, excess. As a result the ionic associate 1 1 is formed and is kept comparatively strongly on a surface. The BTB excess remains in an aqueous phase and it is easy to determinate it photometrically. The linear dependence of optical density of BTB solutions after soi ption on NIS concentration in an interval ITO - 2,5T0 M is observed. The indirect way of the given method is caused by the fact the calibration plot does not come from a zero point of coordinates, and NIS zero concentration corresponds to initial BTB concentration in a solution. 

A functional is defined in mathematics as a function of a function. In Density Functional Theory, functionals are fiinaions of the electron density (itself a function of coordinates in teal space). 

As a result of the systematic application of coordination-chemistry principles, dozens of previously unsuspected stnicture types have been synthesized in which polyhedral boranes or their anions can be considered to act as ligands which donate electron density to metal centres, thereby forming novel metallaboranc elusters, ". Some 40 metals have been found to act as acceptors in this way (see also p. 178). The ideas have been particularly helpful m emphasizing the close interconnection between several previously separated branches of chemistry, notably boron hydride clu.ster chemistry, metallaboranc and metallacarbaborane chemistry (pp. 189-95). organometallic chemistry and metal-metal cluster chemistry. All are now seen to be parts of a coherent whole. 

To look ahead a little, there are properties that depend on the choice of coordinate system the electric dipole moment of a charged species is origin-dependent in a well-understood way. But not the charge density or the electronic energy Quantities that have the same value in any coordinate system are sometimes referred to as invariants, a term borrowed from the theory of relativity. 

It is worthwhile to consider the same theorem in terms of coordinate space instead of occupation number space. Thus, we may envision an ensemble of systems whose states are X>, and whose distribution probabilities among these states are w(X). We define the density operator... 

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