New lithium imide salts have been studied using computational chemistry methods. Intrinsic anion oxidation potentials and ion pair dissociation energies are presented for six lithium sulfonyl imides (R-O₂S-N-SO₂-R) and six lithium phosphoryl imides (R₂-OP-N-PO-R₂), as a function of -F, -CF₃, and -C≡N substitution. The modelled properties are used to estimate the electrochemical oxidation stability of the anions and the relative ease of charge carrier creation in lithium battery electrolytes. The results show that both properties are improved with cyano-substitution, which in part is corroborated when comparing with other classes of lithium salts. However, the comparison also shows ambiguous oxidation stability results for cyano-substituted reference salts of the type PF_x(CN)_6−x⁻ and BF_x(CN)_4−x⁻, using two different approaches – we present a tentative explanation for this. For the imide anions and PF₆⁻, the bond dissociation energy is introduced as a third property, to gauge the thermal stability of the imide anions. The results suggest that the C-S and C-P bonds are the most liable to break and that the thermal stability is inversely related to the ion pair dissociation energy.