What is a hydrogen bond? Mutually consistent theoretical and experimental criteria for characterizing H-bonding interactions
by Frank Weinhold and Roger Klein
It contains the following wonderful paragraph
The definitions of H-bonding to be found in current textbooks (or indeed those of the past half-century) employ near-identical verbiage to express concurrence with the classical electrostatic viewpoint, viz. “a special type of dipole–dipole force” 10, “particularly strong dipole–dipole forces” 11, “an extreme form of dipole–dipole interaction” 12, “unique dipole–dipole attractions” 13, “a sort of super dipole–dipole force”14, and the like. Popular molecular mechanics (MM) and molecular dynamics (MD) potentials 15 exhibit similarly unanimous adherence to classical electrostatic functional forms to ‘simulate’ H-bonding, thereby defining how this phenomenon has been represented to MM/MD users since the 1960s. In the face of such unanimity, the title question may seem to have been long since settled!The authors calculate the dipole-dipole interaction for twenty different hydrogen bonded complexes and find there is no correlation (chi less than 0.1!) with the actual binding energies. In contrast there are strong correlations with quantum signatures such as the intermolecular bond order and the "ionic-covalent resonance" character of the ground state wavefunction.
[Aside: this is essentially the same quantum physics as in my recent paper on H-bonding].
They also give a nice explanation of why simple classical electrostatic calculations sometimes give approximately the right binding energies for the wrong reasons. At the equilibrium geometry the classical electrostatic interaction energy is of the order of a few kcal/mol. These calculations neglect the significant steric repulsion energy (a quantum effect) which in reality is overcome by the strong (quantum) attractive interaction associated with "ionic-covalent resonance".