The structures and consecutive energies and enthalpies of dissociation reactions were studied theoretically for cations of the general formula H3+Arn(H-2)(m) (n = 0, 6; m = 0, 6; and, n + m = 6). It was found that the extent of modification of the core cation by particular ligands is the main reason for differences between properties of pure and mixed complexes. Since this modification is caused by the core-ligand interactions, the differences in the nature of interactions for binding of argon or molecular hydrogen to the H-3(+) cation are addressed. The vibrational frequencies for the H-3(+) modes were studied as a source of information concerning the environment of the core ion.