Theoretical estimates of equilibrium chromium-isotope fractionations

Equilibrium Cr-isotope (53Cr/52Cr) fractionations are calculated using published vibrational spectra and both empirical and ab initio force-field models. Reduced partition function ratios for chromium isotope exchange, in terms of 1000×ln(β53–52), are calculated for a number of simple complexes, crystals, and the Cr(CO)6 molecule. Large (>1‰) fractionations are predicted between coexisting species with different oxidation states or bond partners. The highly oxidized [Cr6+O4]2− anion will tend to have higher 53Cr/52Cr than coexisting compounds containing Cr3+ or Cr0 at equilibrium. Substances containing chromium bonded to strongly bonding ligands like CO will have higher 53Cr/52Cr than compounds with weaker bonds, like [CrCl6]3−. Substances with short Cr-ligand bonds (Cr–C in Cr(CO)6, Cr–O in [Cr(H2O)6]3+ or [CrO4]2−) will also tend have higher 53Cr/52Cr than substances with longer Cr-ligand bonds ([Cr(NH3)6]3+, [CrCl6]3−, and Cr-metal). These systematics are similar to those found in an earlier study on Fe-isotope fractionation (Geochim. Cosmochim. Acta 65 (2001) 2487). lculated equilibrium fractionation between Cr6+ in [CrO4]2− and Cr3+ in either [Cr(H2O)6]3+ or Cr2O3 agrees qualitatively with the fractionation observed during experimental (probably kinetic) reduction of [CrO4]2− in solution (Science 295 (2002) 2060), although the calculated fractionation (∼6–7‰ at 298 K) does appear to be significantly larger than the experimental fractionation (3.3–3.5‰). Our model results suggest that natural inorganic Cr-isotope fractionation at the earthʹs surface may be driven largely by reduction and oxidation processes.