Ab initio 6-31G** electronic structure calculations have been used to determine the minimum energy geometries and vibrational frequencies of molecular clusters of water and carbon dioxide. Application of statistical thermodynamics leads to theoretical equilibrium constants for gas phase dimerization of water and the formation of an adduct of carbon dioxide with water. The low energy vibrations of the clusters lead to much larger contributions to the vibrational partitioning of the energy than do the fundamental vibrations of the monomeric species. A new "Harmonic-Morse" formula is derived to estimate anharmonicity from optimized harmonic frequencies and two additional values on the potential surface for each vibration. These ab initio calculations of equilibrium constants are very close to recent measurements and fall within the range of values obtained by other methods. This no-parameter treatment gives excellent agreement for the equilibrium of H2O-CO2 near the supercritical fluid range of CO2 and suggests that a "Theory of Significant Clusters" may be extended to a model of supercritical fluids which includes the effects of anharmonicity.