Preferential formation of ^(13)C–^(18)O bonds in carbonate minerals, estimated using first-principles lattice dynamics

Equilibrium constants for internal isotopic exchange reactions of the type: Ca^(12)C^(18)O^(16)O_2+Ca^(13)C^(16)O_3 ↔ Ca^(13)C^(18)O^(16)O_2+Ca^(12)C^(16)O_3 for individual CO_3^(2−) groups in the carbonate minerals calcite (CaCO_3), aragonite (CaCO_3), dolomite (CaMg(CO_3)_2), magnesite (MgCO_3), witherite (BaCO_3), and nahcolite (NaHCO_3) are calculated using first-principles lattice dynamics. Calculations rely on density functional perturbation theory (DFPT) with norm-conserving planewave pseudopotentials to determine the vibrational frequencies of isotopically substituted crystals. Our results predict an ∼0.4‰ excess of ^(13)C^(18)O^(16)O_2^(2-) groups in all studied carbonate minerals at room-temperature equilibrium, relative to what would be expected in a stochastic mixture of carbonate isotopologues with the same bulk ^(13)C/^(12)C, ^(18)O/^(16)O, and ^(17)O/^(16)O ratios. The amount of excess ^(13)C^(18)O^(16)O^(2-)_2 decreases with increasing temperature of equilibration, from 0.5‰ at 0 °C to