Mean charge density

This is why I and some others have been agitating about the recent reports, starting in Nature magazine in September 1999, that atomic orbitals had been directly observed. This is simply impossible unless one is using the word "orbital" rather perversely to mean charge density (Scerri, 2000). 

Figure 4. Linear correlation of In vs. mean charge density of oxygen atoms, < (0)MNDO, for LiCLCCHx Fy pc + y = 3/ DMSO. ...

The charge density obtained using the theoretical procedures can be usefully compared with that from X-ray diffraction by several means. Charge density maps either in total or in deformation provide the obvious tools to evaluate how well the two models agree. Crystal95 [39] offers routines to calculate... 

Consider a sphere centered on an ion k with radius r. The areic charge density at the surface of the sphere is calculated on the basis of the mean charge density ... 

Figure 17.3 Linear correlation of ln(fC/i) vs mean charge density of oxygen atoms,

For most metal-oxide interfaces, however, the Fermi level does not coincide with Ezcp- A charge transfer takes place, which aligns the chemical potentials, and induces an interfadal dipole potential, which bends the bands. It is possible to estimate the self-consistent charge density in the vicinity of the interface, within a Thomas-Fermi approximation, if the MIGS density at mid-gap is taken equal to a single exponential function Af( zcp,z) = noexp(—z//p). The potential V z) due to the mean charge density p(z) is related to p(z) by Poisson s equation ... 

The most elementary mean-field models of electronic structure introduce a potential that an electron at r would experience if it were interacting with a spatially averaged electrostatic charge density arising from the N- 1 remaining electrons ... 

Most TB approaches are not charge self-consistent. This means that they do not ensure that the charge derived from the wavefiinctions yields the effective potential assumed in their calculation. Some methods have been developed which yield charge densities consistent with the electronic potential [14, H and 16]. 

The elements of the F matr ix depend on either the charge densities q or the bond orders p, which in turn depend on the elements of the F matrix. This circular dependence means that we must start with some initial F matrix, calculate eigenvectors, use the eigenvectors to calculate q and p, which lead to new elements in the F matr ix, calculate new eigenvectors leading to a new F matrix, and so on, until repeated iteration brings about no change in the results. The job now is to fill in the elements of the F matr ix. 

Pc- (c) Dipole density p. (d) Water contribution to the surface potential x calculated from the charge density Pc by means of Eq. (1). All data are taken from a 150 ps simulation of 252 water molecules between two mercury phases with (111) surface structure using Ewald summation in two dimensions for the long-range interactions. 

This valence bond description leads to an interesting conclusion. Because the transition state occurs at the point where the initial and final state VB configurations cross, the transition state receives equal contributions from each. This is so whether the transition state is early or late. Thus, the nucleophile Y and the leaving group X possess about equal charge densities in the transition state. This conclusion means that an early transition state is not (in this sense) reactantlike , for a reactantlike transition state should have most of the charge on Y. Similarly, a late transition state is not necessarily productlike. This view is at variance with other interpretations. 

In this expression, Wp is the weight of particles titrated (g), Cb and Vb are the concentration of the base (i.e., titrant) and the volume of the base at equivalence point. The surface charge density can be calculated for the particles having a known diameter by means of the following expression ... 

---