  Room temperature ionic liquids play an important role in many technological
applications and a detailed understanding of their frontier molecular orbitals
is required to optimize interfacial barriers, reactivity and stability with
respect to electron injection and removal. In this work, we calculate
quasiparticle energy levels of ionic liquids using first-principles many-body
perturbation theory within the GW approximation and compare our results to
various mean-field approaches, including semilocal and hybrid
density-functional theory and Hartree-Fock. We find that the mean-field results
depend qualitatively and quantitatively on the treatment of
exchange-correlation effects, while GW calculations produce results that are in
excellent agreement with experimental photoelectron spectra of gas phase ion
pairs and ionic liquids. These results establish the GW approach as a valuable
tool for understanding the electronic structures of ionic liquids.
