Proton-bound homodimers: how are the binding energies related to proton affinities?

High-level quantum chemical calculations [G3(MP2)-RAD//MP2/6-31+G(d,p)] have been employed to investigate the relationship between the binding energy (BE) of a substrate (X) and its protonated form [H-X]+ with the proton affinity (PA) of the substrate (X) in several series of protonated homodimers ([X...H-X]+). We find that for each series of closely related substrates, the binding energy (BE) is correlated with the proton affinity (PA) in an approximately quadratic manner. Thus, for a given series, the BE initially increases in magnitude with increasing PA, reaches a point of maximum binding, and then becomes smaller as the PA increases further. This behavior can be attributed to the competing effects of the exothermic partial protonation of the substrate and the endothermic partial deprotonation of the protonated substrate. As the PA increases, protonation of X contributes to increased binding but the penalty for partial deprotonation of [H-X]+ also increases. Once the PA becomes sufficiently high, the penalty for the partial deprotonation of [H-X]+ dominates, leading to maximum binding occurring at intermediate PA.