An algorithm for calculating rotation-vibrational energy levels and wave functions for AB-CD tetra-atomic systems is presented. By transforming the wave equation into a large sparse eigenvalue problem, we can take advantage of the implicitly restarted Lanczos method developed by Sorensen and co-workers. The algorithm has been applied to calculations of the lowest 40 bound states of (HF)(2), (DF)(2) and HF . DF with even and odd parities. The lowest 40 energies and corresponding wave functions for (HF)(2) with J = 0 and even parity can be calculated in 10.5 minutes on 126 processors of a CRAY T3E. The resulting energy levels are found to be in excellent agreement with the previously reported values of Zhang, et al. [J. Chem. Phys. 102, 2315 (1995)].