Simplified vibrational densities of states for five different carbonates are constructed using measured IR and Raman spectra. From the spectroscopic models we calculate thermodynamic and thermoelastic properties of magnesite, calcite, aragonite, dolomite, and siderite. The effects of temperature and pressure on the vibrational frequencies are explicitly introduced into the computations. These spectroscopic models provide high level agreement with the measured values of entropy and heat capacity (within +/- 2%), with the exception of aragonite (within +/- 5% above 600 K) due to its breakdown to calcite: For the molar volumes the agreement is within +/- 0.5 %. The Gibbs free energies of each mineral are then computed in order to obtain pressure and temperature equilibrium conditions for different chemical reactions involving carbonates. Comparing the predicted phase diagrams with those experimentally determined provides an additional constraint on the validity of spectroscopic models and in the values of formation enthalpies.