  Knowledge of the molecular frontier levels' alignment in the ground state can
be used to predict the photocatalytic activity of an interface. The position of
the adsorbate's highest occupied molecular orbital (HOMO) levels relative to
the substrate's valence band maximum (VBM) in the interface describes the
favorability of photogenerated hole transfer from the VBM to the adsorbed
molecule. This is a key quantity for assessing and comparing H$_2$O
photooxidation activities on two prototypical photocatalytic TiO$_2$ surfaces:
anatase (A)-TiO$_2$(101) and rutile (R)-TiO$_2$(110). Using the projected
density of states (DOS) from state-of-the-art quasiparticle (QP) $G_0W_0$
calculations, we assess the relative photocatalytic activity of intact and
dissociated H$_2$O on coordinately unsaturated (Ti$_{\textit{cus}}$) sites of
idealized stoichiometric A-TiO$_2$(101)/R-TiO$_2$(110) and bridging O vacancies
(O$_{\textit{br}}^{\textit{vac}}$) of defective
A-TiO$_{2-x}$(101)/R-TiO$_{2-x}$(110) surfaces ($x=\frac{1}{4},\frac{1}{8}$)
for various coverages. Such a many-body treatment is necessary to correctly
describe the anisotropic screening of electron-electron interactions at a
photocatalytic interface, and hence obtain accurate interfacial level
alignments. The more favorable ground state HOMO level alignment for
A-TiO$_2$(101) may explain why the anatase polymorph shows higher
photocatalytic activities than the rutile polymorph. Our results indicate that
(1) hole trapping is more favored on A-TiO$_2$(101) than R-TiO$_2$(110) and (2)
HO@Ti$_{\textit{cus}}$ is more photocatalytically active than intact
H$_2$O@Ti$_{\textit{cus}}$.
