Thermodynamics of Metal Carbonates and Bicarbonates and Their Hydrates for Mg, Ca, Fe, and Cd Relevant to Mineral Energetics.

The heats of formation of the carbonate, bicarbonate, and bicarbonate/hydroxide metal complexes, including hydrates of Mg, Ca, Fe, and Cd, and the oxides, dichlorides, and dihydroxides are predicted from atomization energies using correlated molecular orbital theory at the CCSD(T) level extrapolated to the complete basis set limit following the Feller-Peterson-Dixon (FPD) approach. Using the calculated gas phase values and the available experimental solid-state values, we predicted the cohesive energies of selective minerals. The gas phase decomposition energies of MO, CO, and HO follow the order Mg ≈ Ca > Cd ≈ Fe and correlate with the hardness of the metal +2 ions. Gas phase hydration energies show that the order is Mg > Fe > Ca ≈ Cd. There are a number of bulk hydrated Mg and Ca complexes that occur as minerals but there are few if any for Fe and Cd, suggesting that a number of factors are important in determining the stability of the bulk mineral hydrates. The FPD heats of formation were used to benchmark a range of density functional theory exchange-correlation functionals, including those commonly used in solid-state mineral calculations. None of the functionals provided chemical accuracy agreement (±1 kcal/mol) with the FPD results. The best agreement to the FPD results is predicted for ωB97X and ωB97X-D functionals with an average unsigned error of 10 kcal/mol. The worst functionals are PW91, BP86, and PBE with average unsigned errors of 32-36 kcal/mol.