Quantum chemical calculations of equilibrium copper (I) isotope fractionations in ore-forming fluids

We calculated the equilibrium isotope fractionation of Cu (I) complexes in hydrothermal ore-forming fluids using quantum chemical calculations (based on the density functional theory and Hartree–Fock approximations) of molecular structures and vibrational frequencies to gain insights into the Cu isotope (63Cu, 65Cu) composition in natural systems. The calculated molecular structures of liquid — (copper chlorides and copper hydrosulfides) and vapor-phase (CuCl(H2O) and Cu3Cl3) Cu complexes are largely consistent with the experimental data. The predicted vibrational frequencies are dependent on the energy levels of theory and basis sets used in the calculations. The vibrational frequency shift due to isotopic substitution is most prominent in the stretching (for linear molecules such as CuCl) and bending (for [CuCl2]1− and [CuCl3]2−) modes of vibration. lculated reduced partition function ratio (i.e. 103 · ln(β65–63)) of each copper isotopomer depends on the Cu coordination environments and types of ligands. The Cu complexes with a longer bond length (e.g., Cu–Cl or Cu–S) and larger coordination number apparently have greater isotope fractionation among the monomer complexes. A significant copper isotope fractionation has been predicted for each Cu complex: Cu3Cl3 (vapor phases) contain the most enriched 65Cu isotopes, whereas [CuCl3]2− (liquid phase) is the most depleted. The calculated δ65Cu range [maximum δ65Cu for Cu3Cl3–minimum δ65Cu for [CuCl3]2−] increases with a decrease in the temperature; the ranges are 0.76–0.89‰ at 500 °C, 1.00–1.17‰ at 400 °C, 1.37–1.61‰ at 300 °C, 2.01–2.35‰ at 200 °C, and 2.50–2.92‰ at 150 °C. These ranges around 150–500 °C are somewhat larger than the observed isotopic compositions in sea-floor hydrothermal vents (approximately 0.8–1.3‰) and porphyry copper deposits (0.7‰). While detailed information about phase equilibria (stability fields) among both vapor and liquid copper complexes as function of composition, temperature and pressure should be known to better discuss the origin of the Cu isotope composition in natural systems, current theoretical prediction shows the effect of temperature could contribute to a variation in isotopic composition in the natural system. lculation indicates that temperature and types of ligands affect the copper isotope fractionation in the ore-forming fluids, and also imply that the liquid-vapor equilibrium (e.g., volcanic degassing) could lead to significant copper isotope fractionation. On the other hands, Cu isotope fractionations of [CuCl2]1− and [Cu(HS)2]1−, the major copper-bearing species in hydrothermal conditions, are rather similar; thus, the fractionation without a change in the oxidation states may not fully account for the natural isotopic variation unless the concentrations of both Cu3Cl3 and for [CuCl3]2− are significant in the hydrothermal fluids.