Ionic Binding Energies, Ionization Potentials, and Electron Affinity

7 Ionic Binding Energies, Ionization Potentials, and Electron Affinity 

The density description focused attention on the total ionic energy E(Z, N) and led to the Z-1/3 expansion (48), when combined with the 1/Z series (43). Two further developments of E(Z, N) will be recorded here, following the work 

But now it has been shown [cf. equation (30) above] that the binding energies of atoms are closely related to the electrostatic potential created at the nucleus by the electronic charge cloud. If we assume the unperturbed charge cloud to be that of a neutral atom (Z-1, Z— 1), then its interaction with the nucleus is increased by a factor Z/Z— 1 on adding a proton and this strongly suggests that one should form the quantity (Z,Z—1)-(Z/Z— l)i (Z—1,Z— 1). One obtains from the 1/Z expansion 

However, the movement of n protons, for n 1, will usually be a very substantial perturbation and the convergence must be expected to become poorer. A modification of the above formulae (66) and (67) has been proposed.24 

The analysis of Lawes et al. of the results of Table 3 above led to the result that the first- and second-order terms explicitly displayed above could give an accurate representation of Table 3, but now at constant atomic number Z. Furthermore, they noticed that there was a close relation between the derivatives(3 /9JV) n-z and (d2E/dN2) n-z. The obvious interest from the studies of Pyper and Grant prompted Lawes et al. to study further the relation of the above treatment of E(Z, N) to the Hartree-Fock studies. 

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