Is there a molecule that can donate a hydrogen to a hydrogen bond but not accept one? It would seem that since the donated hydrogen needs to be bonded to an electronegative atom, that electronegative atom will always have lone pairs available to accept a hydrogen bond.
For example, in ethanol, the H in the OH can participate in hydrogen bonding since the the O is electronegative. Then the oxygen with its two lone pairs can also accept hydrogen bonds.
In reverse, things like diethyl ether can accept but not donate hydrogens because the oxygen is surrounded by carbons, not hydrogen.
Are there any exceptions to this apparent rule?