Calculation of equilibrium stable isotope partition function ratios for aqueous zinc complexes and metallic zinc

Abstract The goal of this study is to determine reduced partition function ratios for a variety of species of zinc, both as a metal and in aqueous solutions in order to calculate equilibrium stable isotope partitioning. We present calculations of the magnitude of Zn stable-isotope fractionation ( 66,67,68 Zn/ 64 Zn) between aqueous species and metallic zinc using measured vibrational spectra (fit from neutron scattering studies of metallic zinc) and a variety of electronic structure models. The results show that the reduced metal, Zn(0), will be light in equilibrium with oxidized Zn(II) aqueous species, with the best estimates for the Zn(II)–Zn(0) fractionation between hexaquo species and metallic zinc being Δ 66/64 Zn aq-metal ∼ 1.6‰ at 25 °C, and Δ 66/64 Zn aq-metal ∼ 0.8‰ between the tetrachloro zinc complex and metallic zinc at 25 °C using B3LYP/aug-cc-pVDZ level of theory and basis set. To examine the behavior of zinc in various aqueous solution chemistries, models for Zn(II) complex speciation were used to determine which species are thermodynamically favorable and abundant under a variety of different conditions relevant to natural waters, experimental and industrial solutions. The optimal molecular geometries for [Zn(H 2 O) 6 ] 2+ , [Zn(H 2 O) 6 ]·SO 4 , [ZnCl 4 ] 2− and [Zn(H 2 O) 3 (C 3 H 5 O(COO) 3 )] − complexes in various states of solvation, protonation and coordination were calculated at various levels of electronic structure theory and basis set size. Isotopic reduced partition function ratios were calculated from frequency analyses of these optimized structures. Increasing the basis set size typically led to a decrease in the calculated reduced partition function ratios of ∼0.5‰ with values approaching a plateau using the aug-cc-pVDZ basis set or larger. The widest range of species were studied at the B3LYP/LAN2DZ/6-31G ∗ level of theory and basis-set size for comparison. Aqueous zinc complexes where oxygen is bound to the metal center tended to have the largest reduced partition function ratios, with estimated fractionations ranging from 2.2 to 2.9‰ ( 66 Zn/ 64 Zn) at 25 °C relative to metallic zinc. The tetrahedrally coordinated tetrachloro zinc complex, where zinc is bound exclusively to chloride, had the lowest reduced partition function ratio for a Zn(II) species (Δ 66/64 Zn aq-metal ∼ 1–1.3‰ at 25 °C). Increasing the number of waters in the second shell of solvation of the above complexes led to variable results, most commonly leading to a decrease of ∼0.2 to 0.3‰ in calculated Δ 66/64 Zn aq-metal at 25 °C. These estimates are useful in the interpretation of observed fractionations during the electrochemical deposition of zinc, where aqueous-metal fractionations of up to 5.5‰ are observed. The models show these are not caused by an equilibrium fractionation process. These results suggest that the redox cycle of zinc during industrial processing may be responsible for isotopically distinct reservoirs of zinc observed in polluted environments. The leaching of metallic zinc or zinc tailings from industrial sites could lead to the observed heavy signature in river systems, the magnitude of which will be reliant on the source material and the aqueous species that form.