Charge density uniqueness

In DFT, the electronic density rather than the wavefiinction is tire basic variable. Flohenberg and Kohn showed [24] that all the observable ground-state properties of a system of interacting electrons moving in an external potential are uniquely dependent on the charge density p(r) that minimizes the system s total... 

The anions MeF6 and X approach each other closely to form the heptacoordinated complex MeF6X(n+1)", or separate from one another, according to the polarization potential of the outer-sphere cation (alkali metal cation -M+). This process is unique in that the mode frequencies of the complexes remain practically unchanged despite varying conditions. This particular stability of the complexes is due to the high charge density of Ta5+ and Nbs+. 

The most important parameters of the ionic atmosphere are the charge density Qv r) and the electrostatic potential /(r) at the various points. Each of these parameters is understood as the time-average value. These values depend only on distance r from the central ion, not on a direction in space. For such a system it is convenient to use a polar (spherical) coordinate system having its origin at the point where the central ion is located then each point can be described by a single and unique coordinate, r. 

Of46,135 reflections measured (29,973 with I > 2a(T)), only 156 reflections were missing to sin 9/A= 1.34 A-1 5102 reflections were unique of which 2681 had been measured more than nine times (symmetry equivalents plus multiple measurements). The merging R values were R1 = 0.037 and R2 = 0.024 for 4809 accepted means. Examination of the reflection statistics (Table 2) with respect to F2/charge density study. 

As noted by Bader, this expression is unique in relating a property of the electronic charge density to the local components of the total energy. 

In ionic block copolymers, micellization occurs in a solvent that is selective for one of the blocks, as for non-ionic block copolymers. However, the ionic character of the copolymer introduces a new parameter governing the structure and properties of micellar structures. In particular, the ionic strength plays an important role in the conformation of the copolymer, and the presence of a high charge density leads to some specific properties unique to ionic block copolymers. Many of the studies on ionic block copolymers have been undertaken with solvents selective for the ionic polyelectrolyte block, generally water or related solvents, such as water-methanol mixtures. However, it has been observed that it is often difficult to dissolve ionic hydrophilic-hydrophobic block copolymers in water. These dissolution problems are far more pronounced than for block copolymers in non-aqueous selective solvents, although they do not always reflect real insolubility. In many cases, dissolution can be achieved if a better solvent is used first and examples of the use of cosolvents are listed by Selb and Gallot (1985). 

Having resolved the molecular perception problem and achieved a unique representation of all atoms, bonds, and rings in the molecule, the second major step is the definition of the most useful measure for local similarity of atoms and atomic environment. For the purpose of COSMO/rag, we need to achieve the state that atoms are considered as most similar, if their partial molecular surfaces and surface polarities, i.e., polarization charge densities, are most similar. But since the latter is not known, at least for the new molecule under consideration, we have to ensure that the local geometries and the electronic effects of the surrounding atoms are most similar. Obviously, two similar atoms should at legist be identical with respect to their element and their hybridization. Turning this information into a unique real number, a similarity index of the lowest order (zeroth order) can be defined for each atom from the atom element numbers and... 

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