The complexation of different simple anions (F−, Cl−, BF4 − and ClO4 −) with a neutral cryptand, with neutral BN dipoles as functional units, and modifications thereof has been studied using ab initio Hartree–Fock calculations. F− is the most strongly preferred anion for all cryptand versions, except for the largest cavity cryptand for which Cl− is preferred. The formed complexes in general show very low lithium ion affinities, much lower than those for anions such as PF6 − and TFSI (by up to 50%). The lowest lithium affinity is obtained for the combination of the smallest cryptand and the F− anion. Implications of using these cryptands in polymer electrolytes are discussed.