Energy and Structural Consequences in Real Systems

We shall now look at a number of thermodynamic and structural variations in transition-metal compounds which owe their origins, at least in part, to the properties of open d shells. 

The enthalpies of hydration plotted in this figure refer to the process in Eq. (8.8). 

On the left, the divalent metal ion is spherical with a J-electron configuration which is amply described as d . On the right, the metal is engaged in six octahedrally disposed bonds and its J-electron configuration is best recorded as The electronic contributions to the hydration process refer, as usual, to the formation of the bonds and the attraction of electrons to the central metal, to the 

Within the hydration process in Eqn. (8.8), a spherical ion becomes a (hydrated) octahedral ion, [M(H20)6]. Part of the Coulomb energy of the free ion concerns repulsion and exchange terms within the d configuration. This is replaced by equivalent repulsion and exchange terms within the configuration. Let us estimate the trends in these quantities separately. 

Coulomb and exchange integrals arise in connection with the two-electron Coulomb operator eVri2. Coulomb integrals take the form  

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