The interaction of alkali metals-specifically, lithium-with polycyclic aromatic hydrocarbons (PAHs) was studied using a variety of electronic structure methods. Electron transfer from lithium to a PAH depends on the size and structure of the PAH and the electronic structure method used. In some cases, we observe an artificial transfer when using density functional theory (DFT) due to the self-interaction error, whereas Hartree-Fock underestimates the amount of charge transfer due to overlocalization. Our results have interesting implications for the validity of DFT calculations on the alkali metal-PAH interaction in Li batteries, hydrogen storage devices, and alkali-metal-doped superconductors.