Where can I find a way to construct the hamiltonian of a water molecule bounded to a surface? More generally,how can one write the hamiltonian of an atom bounded to a surface?
There are lots of different models for water and its interactions, depending on what you want to do with them.
Here are some entry points:
They either contain an explicit Hamiltonian or refer to one.
Arnold gave links to some publications about water adsorption on surfaces described with atomistic modeling. However, there are simples models, with simple hamiltonians, from which you can derive plenty of cool properties of adsorption of atoms on surfaces. (Here, I interpret your “bounded” as indicating physisorption; chemical bonds would be another topic altogether.)
I hope you find these models interesting, as they describe a lot of the phenomenology of adsorption. I'd be happy to discuss follow-up questions!