For almost seventy years chemists have wondered about the molecular origin of the large - some- times very large - difference in the ionization constants of polyvalent acids and bases.

For instance, the first and second hydrogen-ion association constants of malonic acid are K₁ = 4.9 x 10⁵ and K₂ = 6.7 x 10² (in liter/mol), respectively. The ratio of these two constants is a measure of the correlation between the two protons occupying the two carboxylic sites (sec section 2).

What is the molecular interpretation of these strong correlations? Most theories have focused on electrostatic interactions to explain these correlations. This is, of course, true in general since the origin of almost all intermolecular interactions that determine the correlations is electrostatic. However, one can make a clear-cut theoretical distinction between (1) direct proton-proton interactions; (2) indirect proton-proton correlation mediated by the solvent; (3) indirect proton-proton correlation mediated by the dicarboxylic acid, and (4) solvation effects on the dicarboxylic acid.

Qualitatively the four components of the correlation can be visualized as follows. First, suppose that the two protons are adsorbed on a rigid adsorbent-molecule in vaccum. Then the correlation between the protons is due to direct electrostatic interactions between the proton charges. If the same system is immersed in a solvent, then the solvent will modify the electrostatic interaction. This is generally taken into account by introduction a dielectric constant that modifies the Coulombic interactions between the two protons.  In general, such correlations mediated by the solvent cannot be accounted for by a single parameter such as macroscopic the dielectric constant. 

Suppose next that the adsorbent molecule is not rigid but flexible (as are all the polyvalent acids and bases). Then, if we are in vaccum, the adsorption of one proton will change the distribution of the configurations of the adsorbent molecule. This change will, in turn, contribute to the correlation between the two protons.

Finally, immersing the flexible adsorbent molecule in a solvent give rises to solvation effects that are coupled to the configurational changes. Thus, the adsorption of a proton affects the configuration of the adsorbent molecule. This, in turn affects the solvation of the adsorbent molecule, and hence the correlation between the two protons.