I am in a working group on Quantum effects in water. The workshop runs for 4 weeks. There will be about 12 working groups. Each is meant to produce a ten page review that will be then be combined into a review article, co-authored by all the participants.

Today we discussed a possible classification of different quantum effects.

They are manifested in H/D [hydrogen/deuterium] isotope substitution experiments.

For equilibrium properties these isotope effects would be non-existent if the nuclear dynamics is treated classically. This is because at the level of the Born-Oppenheimer approximation the potential energy surface for H and D is identical.

For dynamical properties such as the water self-diffusion constant there is a trivial classical effect from the scaling of vibrational frequencies with H/D substitution.

As I mentioned before, most quantum nuclear effects are associated with vibrational zero-point energy. But, there are effects associated with tunnelling and quantum delocalisation such as a in high pressure phases of ice such as ice X.

Here is one possible classification.

**Trivial effects.**

These arise simply because the H/D substitution changes vibrational frequencies by a scaling factor of sqrt(2)=1.414. An example, is the large difference between the specific heat of heavy and regular water. This simply arises because the thermal population of the vibrational excited states changes because of the change in hbar omega/k_B T. One would observe such a change in almost any solid or liquid.

**Significant or non-trivial effects.**

Examples are the pH of heavy water, and liquid-vapour isotopic fractionation ratio. The non-trivial dependence of this on temperature [taken from this paper] is shown below. It is intimately connected with competing quantum effects.

**Anomalous effects.**

These have the

**opposite sign**to what one expects and sees in simple solids and liquids. For example,

the volume expansion from solid H20 and D2O, is the opposite to the contraction that occurs in most solids, as described here.

It would nice to make these classifications a bit sharper.

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