The participation of the deep mantle in the global carbon cycle and its ability to sequester carbon over billion-year time scales depends upon the mineralogical host for carbon. Density-functional theory calculations for MgCO(3)-magnesite and structures with tetrahedrally coordinated carbon reveal the stability of magnesite up to similar to 80 GPa, with a bulk modulus of 110 ( +/- 2) GPa. Magnesite undergoes a structural transition to a pyroxene-like structure at similar to 80 100 GPa, with a density increase of 4.5 - 7.1%. Combined with thermodynamic models for the MgSiO(3) - MgCO(3) system, the inter-solubility of MgCO(3) with MgSiO(3) orthoenstatite and perovskite constrains the carbon content in the silicates to an upper bound of 4 and 20 ppm ( wt), respectively. The carbon content in lower mantle silicates is estimated to be no more than 1% of the mantle's total carbon budget for degassed regions, such that in even the mantle's most depleted regions, most carbon must be stored in carbonates or diamond.