Water and methanol are common solvents used in liquid chromatographic (LC) separations. It is highly desirable to model .the interactions of these solvents in order to better understand the nature of analyte solvation and its effect on retention. Therefore, structure and frequencies of complexes of these solvent molecules have been studied from a theoretical perspective as a first step in this direction. Specifically, cluster structures have been optimized at the RHF and MP2 levels in various flexible basis sets and with the counterpoise correction for basis set superposition error, and trends in the structure and binding energies of several clusters are described. Good agreement wasobtained for the water dimer with the experimental value for the binding energy of D20 using MP2 energies from 6-3 11G**/6-3 l+G** basis sets in conjunction with counterpoise optimizations and full counterpoise corrections. In this investigation harmonic frequencies have been calculated and corrected for the effects of anharmonicity by several methods, two of which are original. The first new method fits a Morse potential function to the energy computed along each normal mode. A second new method is based on fitting a quartic polynomial to energies computed along each normal mode. In cases where the quartic potential function is not very different from the harmonic well, a second order perturbation formula provides a reasonable approximation to the anharmonic vibrational frequencies. When the quartic potential is very far from the harmonic potential, a variational treatment of the vibrations is required. We find that the Morse method delivers reasonable estimates of frequencies of anharmonic motions at lower cost than multi-point potential mapping/multiple geometry optimization/Taylor series methods, and is more successful at predicting intermolecular frequencies than the anharmonic VSCF methods found in GAMESS software. Variational calculations using the quartic polynomials produce estimates of frequencies comparable to the more costly VSCF method. Both the Morse method and polynomial method are very fast computationally relative to these and other methods found in the literature.