Results are presented from ab initio calculations on several mixed alkali halide dimers made up of Li, Na, F, and Cl. All of the dimers are investigated at the restricted Hartree-Fock level to provide ab initio estimates of geometries, vibrational frequencies, and binding energies. The dimer LiNaF2 is then treated using a variety of basis sets at the Hartree-Fock level, as well as at correlated levels (second-order Moller-Plesset and coupled-cluster singles and doubles) to examine the sensitivity of the calculations to use of higher levels of theory. The results are then compared to the experimental data available for the LiNaF2 molecule, previous theoretical results for the monomers, and recent semiempirical calculations on the mixed dimers.