Here I give a few of my own biased tentative thoughts. Comments and suggestions would be very welcome.

Over the past decade there have been

*several significant advances*that are relevant to understanding nuclear quantum effects in water. It was only by writing this summary that I realised just how tangible and significant these advances are. I am not sure other fields I am familiar with have experienced comparable advances.

**Experiment.**

Deep inelastic neutron scattering reveals the momentum distribution of protons, and can be compared to path integral simulations, as described here. Furthermore, this has illuminated competing quantum effects, as described here.

**Quantum chemistry.**

New accurate intermolecular potential energy surfaces and force fields, such as MB-pol.

**Computational.**

Path integral simulations. Besides significant increases in computational power [Moore's law] making simulation of much larger systems and better "statistics" possible, there have been significant methodological advances, such as Ring Polymer Molecular Dynamics, and PIGLET.

**New concepts and organising principles.**

*Competing quantum effects*associated with the zero-point energy of O-H stretching and bending modes. The competition is particularly subtle in water, to the point that it can change the sign of isotope effects.

Dynamical properties such as proton transport being dominated by

*extremely rare events*, associated with short hydrogen bonds.

**Simple models.**

The coarse-grained monatomic Water (mW) model captures many anomalies of classical water, showing their origin is in the tetrahedral bonding. A diabatic state model captures essential features of the potential energy surface of single hydrogen bonds, particularly the variation with the distance between oxygen atoms. The model does describes competing quantum effects.

These advances present some

*significant opportunities and challenges.*

**Experiment.**

Resolving the ambiguity associated with interpreting the deep inelastic neutron scattering experiments. Going from the data to robust (i.e. non-controversial) spatial probability distributions for protons, particularly ones involving proton delocalisation would be nice.

**Simulation.**

The path integral simulations will only be as good at the potential energy surfaces that they use. For example, recent work shows how calculated isotope effects vary significantly with the DFT functional that is used. This is because the potential energy surface, particularly with respect to the proton transfer co-ordinate, is quite sensitive to the oxygen atom separation, and to the level of quantum chemical theory. This becomes particularly important for properties that are determined by rare events [i.e. thermal and quantum fluctuations to short hydrogen bonds].

**Simple models.**

Monatomic Water (mW) is completely classical. It would be nice to have a quantum generalisation that can describe how the water phase diagram changes with isotope (H/D substitution). Note there is already a problem because mW is so coarse-grained that it does not contain the O-H stretch. On the other hand, mW does describe the librational modes, and these do make a significant contribution to quantum nuclear effects in water, as described here.

I welcome suggestions and comments.

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