Determining conditions that drive carbonate formation is important for many phenomena such as paleoindicators for mineral deposition, the carbon cycle, biomineralization, and industrial applications such as scale inhibition and manufacturing of cement and concrete. Magnesium and incorporated water have been observed to play critical roles in nonclassical crystallization pathways of calcium carbonate, the dominant carbonate found in nature, through promoting formation of low energy metastable intermediates such as monohydrocalcite (CaCO3 center dot H2O), ikaite (CaCO3 center dot 6H(2)O), and amorphous calcium carbonate (CaCO3 center dot H2O). The impact of Mg on the thermodynamics and water binding ability of these hydrated intermediates is challenging to measure and is not understood at the molecular level. In this work, density-functional theory and ab initio thermodynamics are used to quantify the impact of Mg on structure, thermodynamics, and water binding energies of the crystalline hydrated Ca carbonates as a function of temperature in aqueous and ultrahigh vacuum conditions, as well as CO2-rich environments relevant to carbon sequestration. For monohydrocalcite, Mg incorporation is found to destabilize the structure despite a dramatic increase in the water binding energy, thus confirming that Mg promotes monohydrocalcite formation kinetically rather than thermodynamically. For ikaite, however, Mg promotes its formation both kinetically and thermodynamically, expanding the stability region for ikaite in cold water.