Using a variety of density functional theory (DFT) methods, we present a systematic computational screening effort to analyze the chemical and radiation stability for a large number of anions and cations that constitute room-temperature ionic liquids (RTILs). We compute various electronic properties such as the HOMO–LUMO gap, the ionization potential, and the electron affinities for a large library of ions (42 cations and 42 anions). The theoretical analysis provides the most comprehensive characterization of the chemical and radiation stability of individual ions in RTILs to date. Our calculations reveal that cation stability is closely related to constituent alkyl chain length and branching, whereas the anion stability is mostly dictated by ion size and electronegativity. Furthermore, these calculations show that the ωB97XD functional is the most internally consistent for predicting the chemical and radiation stability. These calculations establish a chemical stability database and a theoretical procedure for further experimental and computational studies of RTILs.