I am actually quite proud of our tight binding parameterisation for water. In many ways our "TB water" is better than "DFT water". Our diffusivity is closer to experiment by a factor of two and, unlike in DFT, our ice floats!
While we initially developed the PITB theory to study transition metal oxides (particularly stoichiometric and non stoichiometric oxides of zirconium and titanium) , it occurred to me that we could also study "hydrogen oxide". In fact the oxygen–oxygen bond length in water and ice is about the same as in zirconia, and to me the hydrogen bond is really a covalent bond with a proton interposed (off centre and slightly non linear). A number of clever undergraduate students helped me in this, especially Catherine Walsh and Jeff Armstrong, and we published our first findings in 2011 . Then a very clever and dedicated PhD student named Terence Sheppard embarked on a massive undertaking to find a transferable parameter set to describe carbon, oxygen and hydrogen in small organic molecules  and in water . He succeeded after much trial and tribulation (and sadly he left physics). We were working on a large project in catalysis and our collaborators in physical chemistry were working on benzyl acetone. So Terence succeeded in simulating the "enolisation" of that molecule. His movie is next:
Enolisation of benzyl acetone
Terence set up a molecular dynamics simulation in which the molecule is solvated in water, one of whose molecules has one extra proton: that is, a "hydronium" molecule, H3O+. Enolisation is the addition of a proton to a C=O group to convert it to a C–O–H group. You can see in this movie that the proton (hydrogen atom) transfers from one water molecule to another and is finally transferred to the solvated molecule. Terence has cleverly coloured the oxygen blue in any water molecule that is currently holding the extra proton.
Later, Sasha Lozovoi, extended the model to include parameters for titanium dioxide . The essential two points are:
Water and anatase TiO2
This movie made by Sasha shows water molecules adsorbed onto the surface of a nanocrystal of anatase. The point above about transferability applies here, while for clarity only, Sasha has coloured the oxygen atoms belonging to water in a slightly darker blue.
Water on (001) rutile TiO2
In this movie, Sasha shows a layer of water on the (001) surface of rutile. A big debate exists around whether water will dissociate spontaneously on the oxide surface. Generally we do not find dissociation, which is consistent with observation; however dissociation has been found in DFT simulations.
Tigany Zarouk has now extended the TB model to including metallic titanium, and Sasha is currently studying the behaviour of water on Ti as part of our "quantum corrosion" project.
Meanwhile we were very lucky to have Sebastian (Seb) Budd researching his MSci project in the group in 2020. Since the enolisation shows the transfer of a proton between water molecules, which is equivalent to the diffusion of the hydronium, Seb chose to study the Grotthuss process using our TB water. Here are a couple of his movies, which you will also find at our quantum corrosion web site.
This shows the proton transfer, or Grotthuss process. The point is that the H3O+ species will migrate through water at some rate depending on temperature; and this amounts to an electrical current since the hydronium ion is charged. However it is the hydrogen which is migrating, not the oxygen. Seb indicates this by colouring the oxygen blue in that water molecule that is currently carrying the extra proton.
As expected in such a process and is well known in kinetic Monte-Carlo simulations of vacancy migration the most common jump is that which returns the system to the previous state (for example, if an atom jumps into a vacant site, the most common next step is for it to jump back again). This is called "flickering". The same happens in the Grotthuss process and here you see the proton flickering between two water molecules. This is quite a long lived object and it is called a "Zundel ion", H5O2+
We are currently continuing from where Seb left off to try and calculate the proton diffusivity quantitatively and to assess the role of quantum tunelling on the rate coefficient. Watch this space…!