Pearson model

The two-parameter models of Miedema (Section 2.6) and Pearson (this section) are both based on the idea of electronegativity and its equalization on bond formation but each interprets the positive contribution to AH in a different way in the Miedema model it means equalizing the electron density at the surface of the atom, while in the Pearson model it is called chemical hardness and also expresses resistance against charge transfer. 

In the Pearson model the electronegativity x is the first derivative of the energy E with respect to the amount of electronic charge on the atom the chemical hardness rj is the second derivative, both at constant internuclear distance and nuclear charge ... 

The quantitative concepts in the Pearson model coincide with previous intuitive ideas on electronegativity and hardness ... 

The Pearson model may be extended to include the Madelung potential ions feel the charges in their environment. The Coulomb contribution affects the electronegativity of an atom by the charges q that surround it at distances R ... 

The formalism of the phlogiston model, if it existed, would follow closely that of the Pearson model, with differences being in the extension with interstitials, the Madelung potential, and a second electronegativity parameter to include the homopolar bond. 

The phlogiston parameters and rj of all the elements could be derived from the ionization energy and the electron affinity as in the Pearson model, but they also can be determined by fitting the theoretical function of the bond energy with experimentally observed values as in the Miedema model. Given the bond length Rq the parameter x and rj for every element can be derived with a least-squares fit. The existence of any compound, its bond energy, and polarity can be simply estimated with these parameters. 

However, one just notes that the assumptions made claims that all pairs electronegativity-hardness, either for atoms or molecules, are correlated by the same factor 9. Therefore, this treatment seems that doesn t properly correlate the average electronegativity X with the average of the chemical hardness t] without such universal proportionality. Further expansions of this Parr-Pearson model were made (Nalewajski, 1998), but the difficulties concerning the inherent correlation between X and T] still remain. 

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