Ab Initio Prediction of H-bond Energies and/or Geometries

D-H...:A H-bonded interactions (D and :A = H-bond donor and acceptor) display a wide interval of binding energies, E(HB), ranging from less than one to more than 30 kcal/mol (45 kcal/mol if [F...H...F] bonds are considered) because of two independent factors: (i) H-bonds are the stronger the more electronegative the donor (D) and acceptor (:A) atoms are [1]; (ii) for a same D-A couple [or H-bond electronegativity class, 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 [2-4] for which really strong H-bonds can be observed only when the differences DPA = PA(D-) – PA(:A) or DpKa = pKa(D-H) - pKa(A-H+) tend to zero (PA being the gas-phase proton affinity and pKa the co-logarithm of the corresponding acid-base dissociation constant in water). These properties are at variance with all other types of chemical bond and derive from 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. These considerations emphasize the role played by PA/pKa equalization in strengthening the H-bond, a hypothesis often invoked but never fully verified in the past which is now reconsidered in this Communication by a new instrument, the pKa slide rule. This is a bar-chart reporting, in separate scales, the pKa’s of the D-H proton donors and :A proton acceptors most frequently involved in D-H...:A bond formation (103 entries over the -14<pKa<53 range). Allowing the two scales to shift so to bring into coincidence the donor and acceptor molecules, the ruler permits graphical evaluation of DpKa and then empirical appreciation of D-H...:A bond strengths according to the pKa equalization principle. Systematic screening of two classical databases (NIST gas-phase enthalpies and CSD geometries) was carried out for all the most important X-H...X H-bonds having DpKa = 0, leading to the assessment of the maximum energies, E(HB),MAX, and the shortest D...A distances, dD...A,min, for the most important electronegativity classes. Comparison of data has led to formulate the general equation (1) E(HB) = E(HB),MAX exp[-k (dD...A -dD...A,min)], which permits easy prediction of energies given the geometries, and viceversa. The combined use of the pKa slide rule and eq (1) will be illustrated in a number of practical applications.