The infrared and Raman spectra of CaCO3 calcite substituted with 80% O-18 have been recorded. A detailed mode assignment is proposed for all the observed bands, including combinations and overtones. These data are used to propose a simplified model of the vibrational density of states (VDOS) from which the specific heat, the entropy, and the high-temperature equation of state are calculated. Excellent agreement between calculated and measured values of the thermodynamic properties is obtained when measured vibrational mode anharmonicity is included in the calculations. The model can be used to infer the properties of calcite at high pressures (less than or equal to 3 Gpa) and temperatures (less than or equal to 1200 K). The observed frequency shifts induced by O-18 substitution in both IR and Raman spectra are used to construct the VDOS of (CaCO3)-O-18 calcite. The reduced partition function of calcite is then calculated and the effects of anharmonicity are discussed. Finally the effect of pressure on the reduced partition function is calculated and is shown to be appreciable even at high temperatures.