An acid may also form hydrogen bonds to its conjugate base.
A conjugate base is involved in the reaction.
It all depends on how basic the "conjugate base" of the acid is.
It cannot be deprotonated in solution, but the conjugate base with methyllithium is known.
Formally, a carbanion is the conjugate base of a carbon acid.
As usual, a weaker acid has a stronger conjugate base.
An acid and its conjugate base are opposite in strength.
Truly, only the very weakest of acids have strong conjugate bases.
A strong conjugate base will always attract a proton.
It is the conjugate base, not dmgH itself, that forms the complexes.