In this manuscript we report high-level ab initio (RI-MP2(full)/6-31++G**) and DFT (B3LYP/ 6-31++G** and MPWB1K/6-31++G**) calculations on complexes between the bis(arene)chromium complex (eta6-C6H6)(eta6C6F6)Cr(0) (1) and cations/anions. This interesting molecule 1, which is synthetically available, exhibits a dual binding mode to anions and cations, with interaction energies similar to those previously reported for benzene with cations and hexafluorobenzene with anions. In addition, the simultaneous interaction with cations and anions is also studied.