The hydrogen bonding puzzle

Chemistry is local. For example, the energy and length of a C-C or O-H bond varies little between molecules. It does not matter whether the C-C bond is in ethanol or in a huge protein. (See also an earlier post on transition metal complexes within proteins). One of the great strengths of valence bond theory is that (unlike molecular orbital theory and standard implementations of density functional theory) it captures this local perspective, as emphasized by Sason Shaik.

However, a significant exception to this purely local picture for chemical bonding is provided by hydrogen bonding. We can denote a hydrogen bond by D-H...A where D and A are the donor and acceptor, respectively. The H-bond puzzle is discussed extensively in the 2009 book, The Nature of the Hydrogen Bond by Gastone Gilli and Paola Gilli  (and also in an article from 2000). Here is a paraphrase from page 62 of the book:

"the unique feature of the H-bond is that bonds made by the same donor-acceptor pair may display an extremely wide range of energies and geometries. This extreme variability is well represented by the R1-O-H....:O-R2 bonds that, according to the choice of R1 and R2, can span d(O...O) values from 2.38 to 3.00 Angstroms and d(H...O) ones from 1.20 to 2.00 A, while the bonding energy collapses from 25-30 kcal/mol (~1.0 eV) to less than 1 kcal/mol (~0.04 eV).