  Density functional theory (DFT) studies of weakly interacting complexes have
recently focused on the importance of van der Waals dispersion forces whereas,
the role of exchange has received far less attention. Here, by exploiting the
subtle binding between water and a boron and nitrogen doped benzene derivative
(1,2-azaborine) we show how exact exchange can alter the binding conformation
within a complex. Benchmark values have been calculated for three orientations
of the water monomer on 1,2-azaborine from explicitly correlated quantum
chemical methods, and we have also used diffusion quantum Monte Carlo. For a
host of popular DFT exchange-correlation functionals we show that the lack of
exact exchange leads to the wrong lowest energy orientation of water on
1,2-azaborine. As such, we suggest that a high proportion of exact exchange and
the associated improvement in the electronic structure could be needed for the
accurate prediction of physisorption sites on doped surfaces and in complex
organic molecules. Meanwhile to predict correct absolute interaction energies
an accurate description of exchange needs to be augmented by dispersion
inclusive functionals, and certain non-local van der Waals functionals (optB88-
and optB86b-vdW) perform very well for absolute interaction energies. Through a
comparison with water on benzene and borazine (B$_3$N$_3$H$_6$) we show that
these results could have implications for the interaction of water with doped
graphene surfaces, and suggest a possible way of tuning the interaction energy.
