The structure, bonding and vibrational properties of the mixed LiLnX(4) (Ln = La, Dy; X = F, Cl, Br, I) rare earth/alkali halide complexes were studied using various quantum chemical methods (HF, MP2 and the Becke3-Lee-Yang-Parr exchange-correlation density functional) in conjunction with polarized triple-zeta valence basis sets and quasi-relativistic effective core potentials for the heavy atoms. Our comparative study indicated the superiority of MP2 theory while the HF and B3-LYP methods as well as less sophisticated basis sets failed for the correct energetic relations. In particular, f polarization functions on Li and X proved to be important for the Li X interaction in the complexes. From the three characteristic structures of such complexes, possessing 1-(C-3v), 2- (C-2v), Or 3-fold coordination (C-3v) between the alkali metal and the bridging halide atoms, the bi- and tridentate forms are located considerably lower on the potential energy surface then the monodentate isomer. Therefore only the bi- and tridentate isomers have chemical relevance. The monodentate isomer is only a high-lying local minimum in the case of X = F. For X Cl, Pr, and I this structure is found to be a second-order saddle point. The bidentate structure was found to be the global minimum for the systems with X = F, Cl, and Br. However, the relative stability with respect to the tridentate structure is very small (1-5 kJ/mol) for the heavier halide derivatives and the relative order is reversed in the case of the iodides. The energy difference between the three structures and the dissociation energy decrease in the row F to I. The ionic bonding in the complexes was characterized by natural charges and a topological analysis of the electron density distribution according to Bader's theorem. Variation of the geometrical and bonding characteristics between the lanthanum and dysprosium complexes reflects the effect of "lanthanide contraction". The calculated vibrational data indicate that infrared spectroscopy may be an effective tool for experimental investigation and characterization of LiLnX(4) molecules.