Theoretical estimates of equilibrium sulfur isotope effects in aqueous sulfur systems: Highlighting the role of isomers in the sulfite and sulfoxylate systems

We present theoretical calculations for all three isotope ratios of sulfur (33S/32S, 34S/32S, 36S/32S) at the B3LYP/6-31+G(d,p) level of theory for aqueous sulfur compounds modeled in 30-40H2O clusters spanning the range of sulfur oxidation state (Sn, n = −2 to +6) for estimating equilibrium fractionation factors in aqueous systems. Computed 34β values based on major isotope (34S/32S) reduced partition function ratios (RPFRs) scale to a first order with sulfur oxidation state and coordination, where 34β generally increase with higher oxidation state and increasing coordination of the sulfur atom. Exponents defining mass dependent relationships based on β values (x/34κ = ln(xβ)/ln(34β), x = 33 or 36) conform to tight ranges over a wide range of temperature for all aqueous compounds (33/34κ ≈ 0.5148-0.5159, 36/34κ ≈ 1.89-1.90 from T ⩾ 0 °C). The exponents converge near a singular value for all compounds at the high temperature limit (33/34κT→∞ = 0.51587 ± 0.00003 and 36/34κT→∞ = 1.8905 ± 0.0002; 1 s.d. of all computed compounds), and typically follow trends based on oxidation state and coordination similar to those seen in 34β values at lower temperatures. Theoretical equilibrium fractionation factors computed from these β-values are compared to experimental constraints for HSO3−T(aq)/SO2(g, aq), SO2(aq)/SO2(g), H2S(aq)/H2S(g), H2S(aq)/HS−(aq), SO42−(aq)/H2ST(aq), S2O32−(aq) (intramolecular), and S2O32−(aq)/H2ST(aq), and generally agree within a reasonable estimation of uncertainties. We make predictions of fractionation factors where other constraints are unavailable. Isotope partitioning of the isomers of protonated compounds in the sulfite and sulfoxylate systems depend strongly on whether protons are bound to either sulfur or oxygen atoms. The magnitude of the HSO3−T/SO32− major isotope (34S/32S) fractionation factor is predicted to increase with temperature from 0 to 70 °C due to the combined effects of the large magnitude (HS)O3−/SO32− fractionation factor (1000ln34α(HS)bisulfite-sulfite = 19.9‰, 25 °C) relative to the (HO)SO2−/SO32− fractionation factor (1000ln34α(HO)bisulfite-sulfite = −2.2‰, 25 °C), and the increased stability of the (HS)O3− isomer with increasing temperature. We argue that isomerization phenomenon should be considered in models of the sulfur cycle, including models that describe the overall sulfur isotope fractionations associated with microbial metabolism (e.g., microbial sulfate reduction).