  Electronic level alignment at the interface between an adsorbed molecular
layer and a semiconducting substrate determines the activity and efficiency of
many photocatalytic materials. Standard density functional theory (DFT) based
methods have proven unable to provide a quantitative description of this level
alignment. This requires a proper treatment of the anisotropic screening,
necessitating the use of quasiparticle (QP) techniques. However, the
computational complexity of QP algorithms has meant a quantitative description
of interfacial levels has remained elusive. We provide a systematic study of a
prototypical interface, bare and methanol covered rutile TiO$_2$(110) surfaces,
to determine the type of many-body theory required to obtain an accurate
description of the level alignment. This is accomplished via a direct
comparison with metastable impact electron spectroscopy (MIES), ultraviolet
photoelectron spectroscopy (UPS) and two-photon photoemission (2PP) spectra. We
consider GGA DFT, hybrid DFT and $G_0W_0$, $\mathrm{scQP}GW1$,
$\mathrm{scQP}GW_0$, and $\mathrm{scQP}GW$ QP calculations. Our results
demonstrate that $G_0W_0$, or our recently introduced $\mathrm{scQP}GW1$
approach, are required to obtain the correct alignment of both highest occupied
and lowest unoccupied interfacial molecular levels (HOMO/LUMO). These
calculations set a new standard in the interpretation of electronic structure
probe experiments of complex organic molecule-semiconductor interfaces.
