  Titanium dioxide (TiO$_2$) plays a central role in the study of artificial
photosynthesis, owing to its ability to perform photocatalytic water splitting.
Despite over four decades of intense research efforts in this area, there is
still some debate over the nature of the first water monolayer on the
technologically-relevant anatase TiO$_2$ (101) surface. In this work we use
first-principles calculations to reverse-engineer the experimental
high-resolution X-ray photoelectron spectra measured for this surface in [Walle
et al., J. Phys. Chem. C 115, 9545 (2011)], and find evidence supporting the
existence of a mix of dissociated and molecular water in the first monolayer.
Using both semilocal and hybrid functional calculations we revise the current
understanding of the adsorption energetics by showing that the energetic cost
of water dissociation is reduced via the formation of a hydrogen-bonded
hydroxyl-water complex. We also show that such a complex can provide an
explanation of an unusual superstructure observed in high-resolution scanning
tunneling microscopy experiments.
