We report analytical expressions for the dimethylsulfoxide (DMSO)-Li + and DMSO-I - potential energy hypersurfaces. Quantum chemically calculated energies were fitted to polynomial functions of different number of parameters. These calculations are augmented by calculations of the electrostatic potential in the vicinity of DMSO. Global geometry optimizations and calculations of ion-induced frequency shifts have been performed. We find that at its global energy minima, Li + in the DMSO-Li + complex is bound to the oxygen atom with an energy of about 2.6eV while I - in the vicinity is bound between the two methyl groups in a shallow energy minimum with about 0.6eV.