Hydrogen bonds are incredibly important for understanding the properties of water and for a wide range of biomolecular structures and processes. Without them you would be dead!
Unlike most chemical bonds, hydrogen bonds can range significantly in length, strength, and vibrational frequency. The graph below from a Science paper The Quantum structure of the Intermolecular Proton bond.
shows how the vibrational frequency of an asymmetric A-O-H...O-B bond varies with the proton affinity difference between A and B. Note the substantial softening as things get more symmetrical.
The figure below from another paper shows how the frequency softening is correlated with the bond length.
I am particularly interested in this because I want to know these effects depend on
- breakdown of the Born-Oppenheimer approximation
- the partially covalent character of hydrogen bonds
and whether a simple model Hamiltonian with two diabatic states and one vibrational mode treated exactly (see this earlier post) can capture the essential details and the trends above.