- the stability of H5O2+ in liquid water, [the Zundel cation]
- that such complexes involving shared protons via hydrogen bonding have a
**giant electric polarisability**, several orders of magnitude larger than typical molecules.

Both ideas remain controversial. A consequence of the second is that the coupling of electric field fluctuations associated with the solvent of the complex will result in a large range of vibrational energies, leading to the continuous absorption.

Later I will discuss the relative merits of Zundel's explanation. Here I just want to focus on understanding the essential physics behind the claimed giant polarisability. The key paper appears to be a 1972 JACS

Extremely high polarizability of hydrogen bonds

R. Janoschek , E. G. Weidemann , H. Pfeiffer , G. Zundel

[The essential physics seems to be in a 1970 paper I don't have electronic access to].

If one considers the one-dimensional potential for proton transfer within a Zundel cation with O-O distance of 2.5 Angstroms it looks like the double well potential below.

The two lowest vibrational eigenstates are separated in energy by a small tunnel splitting omega of the order of 10-100 cm-1. These two states can be viewed as symmetric and anti-symmetric combinations of oscillator states approximately localised in the two wells. The transition dipole moment p between these two states is approximately the well separation [here roughly 0.5 Angstroms (times of the proton charge)].

At zero temperature the electric polarisability is approximately, p^2/omega. Omega is at least an order of magnitude smaller than a typical bond stretching frequency and p^2 can be an order of magnitude larger than for a typical covalent bond.

Hence, the polarisability can be orders of magnitude larger than that for a typical molecule.

A few consequences of this picture are that the polarisability will vary significantly with

Extremely high polarizability of hydrogen bonds

R. Janoschek , E. G. Weidemann , H. Pfeiffer , G. Zundel

[The essential physics seems to be in a 1970 paper I don't have electronic access to].

If one considers the one-dimensional potential for proton transfer within a Zundel cation with O-O distance of 2.5 Angstroms it looks like the double well potential below.

The two lowest vibrational eigenstates are separated in energy by a small tunnel splitting omega of the order of 10-100 cm-1. These two states can be viewed as symmetric and anti-symmetric combinations of oscillator states approximately localised in the two wells. The transition dipole moment p between these two states is approximately the well separation [here roughly 0.5 Angstroms (times of the proton charge)].

At zero temperature the electric polarisability is approximately, p^2/omega. Omega is at least an order of magnitude smaller than a typical bond stretching frequency and p^2 can be an order of magnitude larger than for a typical covalent bond.

Hence, the polarisability can be orders of magnitude larger than that for a typical molecule.

A few consequences of this picture are that the polarisability will vary significantly with

- isotopic [H/D] substitution
- temperature (on the scale of the tunnel splitting)
- the donor acceptor distance.

It is interesting.

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