Actual charge density

Figure 6.8. Approximate charge density prior to bonding in overlapping atomic orbitals that form <7-type molecular orbitals in ML6 (a) (b) eg, (c) e g. The actual charge density in the molecule...

In the Landau theory (6), the change <5 > in the actual charge density as one moves away from the phase transition point is expanded in terms of a... 

The tangent curve follows the amplitude of the 1/r Coulomb potential, which reflects the actual charge density, except when r —> 0. 

An improvement of Slater s screening rules would be to make the screening potential consistent with the actual charge density of the occupied orbitals. The English physicist Douglas R. Hartree advanced and developed this idea. 

We can use Eq. [94] to obtain a condition under which the Debye-Hiickel equation may be reliably applied to a planar system. As the ratio of the apparent charge density to the actual charge density approaches unity, the ADH surface potential approaches the PB (and DH) value. If we solve Eq. [94] for the ratio cja/cjo and, using Eqs. [27] and [11], insert this into the value of the surface potential given by Eq. [28], we obtain the expressions... 

By comparing the actual charge density to the apparent charge density in Fq. [94], we can define the fraction of surface charge neutralized by counterions, /iieutj according to the apparent Debye-Hiickel solution, as... 

The fact that the apparent linear charge density is lower than the actual charge density can be seen as confirmation that PB theory does predict some sort of counterion condensation. We mention that because the ADH method results from a (linear) DH interpretation of the (nonlinear) PB equation, it also has a (rather tenuous) mathematical connection to Manning s coimterion condensation theory, which also makes use of the DH solution. " From either Eq. [192] or Eq. [263], the fraction of linear charge density neutralized can be written as (ignoring a contribution from Q... 

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