Quantum chemical calculations on large supermolecular carbonate-water and carbonate mineral clusters are used to predict equilibrium constants for C-13,C-12-isotope-exchange reactions between CO2(g), aqueous carbonate species, and the common carbonate minerals. For the aqueous species, we evaluate the influence of the size and conformational variability of the solvation shell, the exchange-correlation functional, and the basis set. The choice of exchange-correlation functional (PBE vs B3LYP), the basis set (6-31G* vs aug-cc-pVDZ), and solvation shell size (first shell only vs first shell and a partial second shell) each produce changes of similar to 5-10 per mil in the reduced partition function ratio. Conformational variability gives rise to a standard error of similar to 0.5 per mil using similar to 10 solute-solvent conformations. The best results are obtained with the B3LYP/aug-cc-pVDZ combination, but because the improvements in the basis set and exchange correlation functional drive the reduced partition function ratios in opposite directions, reasonably good results are also obtained with the PBE/6-31G* combination. To construct molecular clusters representative of mineral environments, a new method is introduced on the basis of conservation of Pauling bond strength. Using these clusters as models for minerals, calculations of mineral-gas and mineral-aqueous carbon-isotope fractionation factors, are in good agreement with experimental measurements. Carbon-isotope fractionation factors for gas, aqueous, and mineral phases are thus integrated into a single theoretical/computational framework.