There is a fascinating Accounts of Chemical Research
Myths about the Proton. The Nature of H+ in Condensed Media
Christopher A. Reed
Here are a few highlights.
H+ must be solvated and is nearly always di-ordinate, i.e. "bonded" to two units. H3O+ is a rarely seen.
"In contrast to the typical asymmetric H-bond found in proteins (N–H···O) or ice (O–H···O), the short, strong, low-barrier (SSLB) H-bonds found in proton disolvates, such as H(OEt2)2+ and H5O2+, deserve much wider recognition.''This is particularly interesting because quantum nuclear effects are important in these SSLBs.
A poorly understood feature of the IR spectra of proton disolvates in condensed phases is that IR bands associated with groups adjacent to H+, such as νCO in H(Et2O)2+ or νCO and δCOH in H(CH3OH)8+,(50) lose much of their intensity or disappear entirely.(51)So is it Zundel or Eigen? Neither, in wet organic solvents:
Contrary to general expectation and data from gas phase experiments, neither the trihydrated Eigen ion, H3O+·(H2O)3, nor the tetrahydrated Zundel ion, H5O2+·(H2O)4, is a good representation of H+ when acids ionize in wet organic solvents, .... Rather, the core ion structure is H7O3+ ....
The H7O3+ ion has its own unique and distinctive IR spectrum that allows it to be distinguished from alternate formulations of the same stoichiometry, namely, H3O+·2H2O and H5O2+·H2O.(58) It has its own particular brand of low-barrier H-bonding involving the 5-atom O–H–O–H–O core and it has somewhat longer O···O separations than in the H5O2+ ion.What happens in water? The picture is below.
What is particularly interesting is the "continuous broad absorption" (cab) shown in blue. This is very unusual for a chemical IR spectra. Reed says "Theory has not reproduced the cba, but it appears to be the signature of delocalized protons whose motion is faster than the IR time scale."
I don't quite follow this argument. The protons are delocalised within the flat potential of the SSLB H-bond, but there is a well defined zero-point energy associated with this. The issue may be more how does this quantum state couple to other fluctuations in the system.
There is a 2011 theory paper by Xu, Zhang, and Voth [unreferenced by Reed] that does claim to explain the "continuous broad absorption". Also Slovenian work highlighted in my post Hydrogen bonds fluctuate like crazy, should be relevant. The key physics may be that for O-O distances of about 2.5-2.6 A the O-H stretch frequency varies between 1500 and 2500 cm-1. Thus even small fluctuations in O-O produce a large line width.
Repeating the experiments in heavy water or deuterated acids would put more constraints on possible explanations since quantum effects in H-bonding are particularly sensitive to isotope substitution and the relevant O-O bond lengths.
[I am just finishing a paper on this subject (see my Antwerp talk for a preview)].