First order variation in charge

In considering the analytical realization of the present model, the case of the first order in charge expansion of the differential electronegativity and total energy E is firstly treated (Putz, 2006). 

Within the same approach the absolute hardness of (4.254) can be as well evaluated to give its density functional, yielding the form  

Nevertheless, having computed Zd as (4.258) it is useful in writing the total energy expansion accordingly  

Note that although the physical functional dependence of x d is of iV as resulting from (4.258), the iV-dependence of Zd in Eq. (4.260) was emphasized in order to be consistent with the mathematical expression of dE in the view of further integration between the related limits. Nevertheless, 

There is now easy to recognize that the absolute EN (4.253) will be particularized by the appropriate integration of Eq. (4.260) when Eq. (4.258) is considered, giving the density functional (Putz, 2006)  

---

Second Order Variation in Charge—First Order in... 

Pure A is charged to the reactor at 400 kPa and 330 °K. The reaction is first-order in species A. The variation of the reaction rate constant with v temperature is given below. 

In order to examine the workings of oxidation and reduction, the first order of business is to determine the oxidation number. The oxidation number is essentially what we have called charge so far. Up to now we have simply looked up the charge in a table, but now we have a slightly different set of rules for determining the oxidation number, as there is some variation not predicted by tables. 

---