The Nature of the Hydrogen Bond: Models and Theories

D-H...:A H-bonded interactions (D and :A = H-bond donor and acceptor) display a wide interval of binding energies, E(HB), from less than one to 45 kcal/mol which, unlike normal chemical bonds, feature properties that do not simply depend on D and :A but display large variations even for a same donor-acceptor couple. For example, weak HO-H...OH2 bonds in neutral water [E(HB) ~ 5 kcal/mol; d(O...O) ~ 2.70-2.75 Å] change, in acidic and basic medium, to very strong [H2O...H...OH2]+ or [HO...H...OH]- bonds having E(HB) ~ 26-31 kcal/mol and d(O...O) ~ 2.38-2.42 Å. These impressive differences appear to depend on two independent factors: (i) H-bonds are the stronger the more electronegative the donor (D) and acceptor (:A) atoms are, implying that any (D,A) couple defines its own H-bond electronegativity class, EC(D,A); (ii) For a same EC(D,A), H-bonds are the stronger the more similar the proton affinities of D and A are, a fact easily expressible in terms of the PA/pKa equalization principle [1-3] for which really strong H-bonds can be observed only when the differences ΔPA = PA(D-) - PA(:A) or ΔpKa = pKa(D-H) - pKa(A-H+) tend to zero (PA being the gas-phase proton affinity and pKa the acid-base dissociation constant in water). Molecular arrangements able to reach this condition of PA/pKa matching have been classified as the four strong chemical leitmotifs [4,5]. These properties are at variance with all other types of chemical bond and can be imputed to the dual nature of the H-bond, which is not really ‘a bond’ but rather ‘two bonds’ formed by a same central proton with the two lone pairs located on the so-called donor and acceptor atoms. In a similar way, the H-bond energy, E(HB), is not the D-H...:A dissociation energy, but rather the smaller of the two bond-dissociation energies, D°(D-H) and D°(H-A). If one is stronger, the other is weaker so that strong H-bonds are those where ΔD° = D°(D-H) - D°(H-A) = 0 and n(D-H) = n(H-A) = 1/2 (n = bond number). The dual H-bond model leads to some important consequences: (1) All H-bond properties are controlled by two driving variables to be identified in the two proton affinities, pa(D-) and pa(:A), or better in their linear combinations: H-Bond Properties = F {[Σpa = pa(D-) + pa(:A)]; [Δpa = pa(D-) - pa(:A)]} (2) In symmetric [X...H...X]+ and [X...H...X] bonds, Δpa = 0 by definition and EHB reaches a maximum typical of each EC(X,X). It can be shown that this E(HB),MAX is proportional to 1/2D°(X-H) and is a linear function of χ(X), the electronegativity of X. (3) All bonds of a same EC(D,A) have energies E(HB) = EHB,MAX exp[-k (dD...A -dD...A,min)], where dD...A,min is the minimum D...A distance associated with E(HB),MAX. (4) For a given EC(D,A), Σpa is constant and H-bond properties depend only on the Δpa difference (pa equalization principle). When Δpa is expressed in terms of ΔpKa, H-bond energies can be appreciated by a simple tool, the pKa slide rule, which collects, in form of a bar chart, the pKa of the most common H-bond donors and acceptors (see also the poster communication “The pKa Slide Rule as a Tool for Predicting Hydrogen Bond Strengths”)