Reduced Partition Function Ratios Research Articles

Reduced partition function ratios of hydrogen species adsorbed on platinum cluster Pt19 studied by density functional theory

ABSTRACTGeometry optimization and estimation of H/D reduced partition function ratios (RPFRs) of Pt19–H, Pt19–H+, Pt19–H2, and Pt19–H2+ models of hydrogen species adsorbed on surfaces of metallic platinum particles, were carried out based on the density functional theory. Two types of optimized structures were obtained for Pt19–H and Pt19–H+, and three for Pt19–H2 and Pt19–H2+. Stabilization energy consideration suggested that the most probable structure for Pt19–H and Pt19–H+ is the one in which H/H+ is bonded to a Pt atom, and that for Pt19–H2 and Pt19–H2+ is the one in which two H/H+s are bonded to two adjacent Pt atoms with no direct bonding between the two H/H+s. The value of RPFR obtained for those structures ranged from 3.9303 to 4.4014 at 25 °C. Interaction between two adjacent H–Pt bonds seems to slightly enhance the mutual RPFR values.

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; 1s.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).

Equilibrium zinc isotope fractionation in Zn-bearing minerals from first-principles calculations

Isotopic composition analysis contributes significantly to the investigation of the biogeochemical cycle of zinc with its economical, environmental and health implications. Interpretation of isotopic measurements is however hindered by the lack of a set of equilibrium isotopic fractionation factors between Zn-bearing minerals. In this study, equilibrium mass-dependent Zn isotope fractionation factors in Zn-bearing minerals are determined from first-principles calculations within the density functional theory (DFT) scheme. A wide range of minerals belonging to sulfide, carbonate, oxide, silicate, sulfate and arsenate mineral groups are modelled to account for the natural diversity of Zn crystal-chemical environment. Calculated reduced partition function ratios (β-factors) span a range smaller than 2‰ at 22°C. All studied secondary minerals (adamite, gahnite, gunningite, hemimorphite, hydrozincite, zincite) but zinc carbonate (smithsonite) are isotopically heavier than zinc sulfide minerals (sphalerite and wurtzite) from which they could form through supergene processes. Zinc–aluminium spinel and zinc silicate are the isotopically heaviest minerals. The investigation of the crystal-chemical parameters at the origin of differences in isotopic properties shows an excellent linear correlation between lnβ and Zn interatomic force constants. β-factors are also observed to increase when the Zn-first neighbour bond lengths decrease and charges on atoms involved in the bonding increase and vice versa. These findings are in line with the observation of heavy isotope enrichment in systems having the largest bond strength.

Theoretical calculation of oxygen equilibrium isotope fractionation factors involving various NOy molecules, [rad]OH, and H2O and its implications for isotope variations in atmospheric nitrate

The oxygen stable isotope composition (δ18O) of nitrogen oxides [NOx=nitric oxide (NO)+nitrogen dioxide (NO2)] and their oxidation products (NOy=NOx+nitric acid (HNO3)+particulate nitrate (p-NO3−)+nitrate radical (NO3)+dinitrogen pentoxide (N2O5)+nitrous acid (HONO)+…) have been shown to be a useful tool for inferring the proportion of NOx that is oxidized by ozone (O3). However, isotopic fractionation processes may have an influence on δ18O of various NOy molecules and other atmospheric O-bearing molecules pertinent to NOx oxidation chemistry. Here we have evaluated the impacts of O isotopic exchange involving NOy molecules, the hydroxyl radical (OH), and water (H2O) using reduced partition function ratios (xβ) calculated by hybrid density functional theory. Assuming atmospheric isotopic equilibrium is achieved between NO and NO2 during the daytime, and NO2, NO3, and N2O5 during the nighttime, δ18O–δ15N compositions were predicted for the major atmospheric nitrate formation pathways using our calculated exchange fractionation factors and isotopic mass-balance. Our equilibrium model predicts that various atmospheric nitrate formation pathways, including NO2+OH→HNO3, N2O5+H2O+surface→2HNO3, and NO3+R→HNO3+R will yield distinctive δ18O–δ15N compositions. Our calculated δ18O–δ15N compositions match well with previous atmospheric nitrate measurements, and will potentially help better understand the role oxidation chemistry plays on the N and O isotopic composition of atmospheric nitrate.

The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling

The magnesium isotope compositions of sedimentary carbonates are widely used to investigate the geochemical cycling of this element in seawater. Density Functional Theory techniques and experimental data from this study and literature on Mg isotope fractionation between sedimentary minerals and fluids have been used to derive equilibrium fractionation factors and to quantify the impact of aqueous magnesium speciation on the isotopic composition of its aquo ion and Mg in the precipitated carbonates. Although aqueous Mg2+ undergoes hydrolysis to a lesser extent than divalent transition metals, it nevertheless forms relatively strong complexes with inorganic and organic ligands including bicarbonate/carbonate, sulfate and carboxylate. Furthermore, aqueous Mg2+ undergoes a significant contraction of its coordination sphere when it reacts with bicarbonate and carbonate ions to form the MgHCO3+ and MgCO3° complexes which favors the preferential partitioning of heavy Mg into these species. Calculated values of the reduced partition function ratios for Mg2+(aq) and Mg2+ bound to a number of inorganic and organic ligands show a strong enrichment of 26Mg in MgCO3°, MgHCO3+ and MgSO4° compared to Mg2+ (i.e. 1000lnβ26/24MgCO3°-1000lnβ26/24Mg2+=5.2 at 25°C), and either a significant enrichment (Mg(oxalate)2−, Mg(oxalate)22−, Mg(citrate)−) or depletion (Mg(EDTA)2−, Mg(citrate)24−) of 26Mg in Mg-carboxylate complexes compared to Mg2+. Analysis of experiments from this study and the literature on Mg isotope fractionation between aqueous solution and Mg carbonate and hydroxide minerals validate the reduced partition functions for Mg2+, Mg bicarbonate/carbonate and carboxylate couples generated in the present work and confirms the significant impact of carbonate and carboxylic ligands on the isotope composition of precipitated Mg-bearing minerals. This study thereby provides new insights into the parameters controlling the isotope composition of aqueous Mg2+in natural fluids as well as improved tools to reconstruct paleo-environmental conditions from the magnesium isotope compositions recorded in carbonate sediments.

Isotope fractionation of Si in protonation/deprotonation reaction of silicic acid: A new pH proxy

Isotopic fractionation of Si in protonation/deprotonation reactions of monomeric silicic acids was theoretically and experimentally studied. The reduced partition function ratio for Si (as 1000 lnβ) complexes was theoretically estimated by ab initio methods. Three permil of isotope fractionation was estimated to be possible for the 28Si-30Si isotope pair. This prediction was experimentally demonstrated by multi-collector inductively coupled plasma mass spectrometer measurements of Si-bearing aqueous solutions, for which equilibrated Si(OH)4 and SiO(OH)3− were separated using an anionic exchange column. The results create a new possibility for the application of Si isotopes as proxies for paleo-pH in the 9<pH<12 range.

Theoretical calculation of nitrogen isotope equilibrium exchange fractionation factors for various NOy molecules

The nitrogen stable isotope ratio (15N/14N) of nitrogen oxides (NOx=NO+NO2) and its oxidation products (NOy=NOx+PAN (peroxyacetyl nitrate=C2H3NO5)+HNO3+NO3+HONO+N2O5+⋯+particulate nitrates) has been suggested as a tool for partitioning NOx sources; however, the impact of nitrogen (N) equilibrium isotopic fractionation on 15N/14N ratios during the conversion of NOx to NOy must also be considered, but few fractionation factors for these processes have been determined. To address this limitation, computational quantum chemistry calculations of harmonic frequencies, reduced partition function ratios (15β), and N equilibrium isotope exchange fractionation factors (αA/B) were performed for various gaseous and aqueous NOy molecules in the rigid rotor and harmonic oscillator approximations using the B3LYP and EDF2 density functional methods for the mono-substitution of 15N. The calculated harmonic frequencies, 15β, and αA/B are in good agreement with available experimental measurements, suggesting the potential to use computational methods to calculate αA/B values for N isotope exchange processes that are difficult to measure experimentally. Additionally, the effects of solvation (water) on 15β and αA/B were evaluated using the IEF-PCM model, and resulted in lower 15β and αA/B values likely due to the stabilization of the NOy molecules from dispersion interactions with water. Overall, our calculated 15β and αA/B values are accurate in the rigid rotor and harmonic oscillator approximations and will allow for the estimation of αA/B involving various NOy molecules. These calculated αA/B values may help to explain the trends observed in the N stable isotope ratio of NOy molecules in the atmosphere.

Density Functional Theory Calculations of H/D Isotope Effects on Polymer Electrolyte Membrane Fuel Cell Operations

Abstract To elucidate hydrogen isotope effects observed between fuel and exhaust hydrogen gases during polymer electrolyte membrane fuel cell operations, H-to-D reduced partition function ratios (RPFRs) for the hydrogen species in the Pt catalyst phase of the anode and the electrolyte membrane phase of the fuel cell were evaluated by density functional theory calculations on model species of the two phases. The evaluation yielded 3.2365 as the value of the equilibrium constant of the hydrogen isotope exchange reaction between the two phases at 39 °C, which was close to the experimentally estimated value of 3.46–3.99 at the same temperature. It was indicated that H+ ions on the Pt catalyst surface of the anode and H species in the electrolyte membrane phase were isotopically in equilibrium with one another during fuel cell operations.

Equilibrium magnesium isotope fractionation between aqueous Mg2+ and carbonate minerals: Insights from path integral molecular dynamics

The theoretical determination of the isotopic fractionation between an aqueous solution and a mineral is of utmost importance in Earth sciences. While for crystals, it is well established that equilibrium isotopic fractionation factors can be calculated using a statistical thermodynamic approach based on the vibrational properties, several theoretical methods are currently used to model ions in aqueous solution. In this work, we present a systematic study to determine the reduced partition function ratio (β-factor) of aqueous Mg2+ using several levels of theory within the simulations. In particular, using an empirical force field, we compare and discuss the performance of the exact results obtained from path integral molecular dynamics (PIMD) simulations, with respect to the more traditional methods based on vibrational properties and the cluster approximation. The results show the importance of including configurational disorder for the estimation of the equilibrium isotope fractionation factor. We also show that using the vibrational frequencies computed from snapshots taken from equilibrated classical molecular dynamics represents a good approximation for the study of aqueous ions.Based on these conclusions, the β-factor of aqueous Mg2+ have been estimated from a Car–Parrinello molecular dynamics (CPMD) simulation with an ab initio force field, and combined with the β-factors of carbonate minerals (magnesite, dolomite, calcite and aragonite). Mg β-factor of Mg-bearing aragonite, calculated here for the first time, displays a lower value than the three other carbonate minerals. This is explained by a strong distortion of the cationic site leading to a decrease of the coordination number during Ca–Mg substitution. Overall, the equilibrium magnesium isotope fractionation factors between aqueous Mg2+ and carbonate minerals that derive from this methodological study support the previous theoretical results obtained from embedded cluster models.

Influence of Mg&amp;lt;sup&amp;gt;2+&amp;lt;/sup&amp;gt;, Fe&amp;lt;sup&amp;gt;2+&amp;lt;/sup&amp;gt; and Zn&amp;lt;sup&amp;gt;2+&amp;lt;/sup&amp;gt; Cations on &amp;lt;sup&amp;gt;13&amp;lt;/sup&amp;gt;C-&amp;lt;sup&amp;gt;18&amp;lt;/sup&amp;gt;O Bonds in Precipitated Aragonite, Calcite and Dolomite: An &amp;lt;i&amp;gt;ab Initio&amp;lt;/i&amp;gt; Study

The influence of metal cations on 13C-18O bonds in carbonates is still under debate. This paper used ab initio method to investigate this kind of influence of Mg2+, Fe2+ and Zn2+ cations on 13C-18O bonds in precipitated aragonite, calcite and dolomite. The polynomials of Δ47 and reduced partition function ratios (RPFRs) for 13/12C, 14/12C and 18/16O of these minerals were given within temperatures ranging from 260 to 1500 K. We found that these cations significantly decreased the Δ47 values at the level of 10-3 - 10-2 per mil, comparing with pure crystals; and that if the Δ47 values were used to reconstruct the temperatures Ts, the deviation of T was about 7.2°C for, for instance, zinc-enriched aragonite, as discussed in our paper. It was suggested that due to such influence, researchers would better use a proper thermometer according to the main impurity metal cations in carbonates. We also found that according to the probability theory, the theoretical value of the influence of phosphoric acid on Δ47 of CO2 degassed from different carbonates was zero.

First-principles study of sulfur isotope fractionation in sulfides

Isotope fractionation parameters for sulfur have been calculated using first-principles methods based on density-functional perturbation theory for sphalerite, galena, alabandite, greenockite and cinnabar in the temperature range of 0–1000°C. For comparison, the 10 3 lnα value between sphalerite and galena, which appears to be well determined, is also calculated, and a good agreement between this calculation and other results is found. The calculations show that the order of heavy isotope enrichment is sphalerite > cinnabar > greenockite > alabandite > galena. The reduced partition function ratios of 33 S/ 32 S, 36 S/ 32 S in the temperature range of 0–1000°C are also calculated, and there exists a fixed proportion relation between sulfur isotope 32 S, 33 S, 34 S and 36 S in the calculated five sulfides, which can be expressed as δ 34 S = 1:940 δ 33 S and δ 36 S = 1.891 δ 34 S , in agreement with previously published relationships.

Reduced partition function ratios of iron and oxygen in goethite

First-principles calculations based on the density functional theory (DFT) with or without the addition of a Hubbard U correction, are performed on goethite in order to determine the iron and oxygen reduced partition function ratios (β-factors). The calculated iron phonon density of states (pDOS), force constant and β-factor are compared with reevaluated experimental β-factors obtained from Nuclear Resonant Inelastic X-ray Scattering (NRIXS) measurements. The reappraisal of old experimental data is motivated by the erroneous previous interpretation of the low- and high-energy ends of the NRIXS spectrum of goethite and jarosite samples (Dauphas et al., 2012). Here the NRIXS data are analyzed using the SciPhon software that corrects for non-constant baseline. New NRIXS measurements also demonstrate the reproducibility of the results. Unlike for hematite and pyrite, a significant discrepancy remains between DFT, NRIXS and the existing Mössbauer-derived data. Calculations suggest a slight overestimation of the NRIXS signal possibly related to the baseline definition. The intrinsic features of the samples studied by NRIXS and Mössbauer spectroscopy may also contribute to the discrepancy (e.g., internal structural and/or chemical defects, microstructure, surface contribution). As for oxygen, DFT results indicate that goethite and hematite have similar β-factors, which suggests almost no fractionation between the two minerals at equilibrium.

Theoretical calculations of Cd isotope fractionation in hydrothermal fluids

Abstract This study reports a systematic approach of quantum chemical calculations (density functional theory) of cadmium isotope reduced partition function ratios to understand the fractionation properties of Cd species in hydrothermal fluids, including cadmium hydrate, chloride, hydroxide, nitrate, hydrosulfide complexes. The optimized structures and the calculated vibrational frequencies of the selected Cd complexes by B3LYP method are consistent with the experimental data. The reduced partition function ratios 103ln (β114–110) of the Cd complexes were calculated with varying temperatures from 0 °C to 400 °C or 500 °C, which are from 0.680‰ to 2.098‰ at 50 °C. The isotope fractionation between different Cd species seems to be small, and there exists a trend of heavy Cd isotope enrichment as cadmium hydroxides > cadmium nitrates > cadmium hydrates > cadmium chlorides > cadmium hydrosulfide, according to the calculated reduced partition function ratios 103ln (β114–110) by this study. This suggests that Cd hydroxide complexes and hydrosulfide complexes may produce larger fractionation than others, which even reaches + 1.641‰ between Cd(OH)Cl and CdHS+ at 25 °C. As the major Cd-bearing species in hydrothermal conditions, CdOH(H2O)5+ and CdCl(H2O)5+, the fractionation factor α is found to be + 0.120‰ at 150 °C. These theoretical calculations provide insight into Cd isotope behavior in solution conditions, especially in hydrothermal fluids.

Nano Cavity Induced Isotope Separation of Zinc: Density Functional Theoretical Modeling

Density functional theoretical calculation was performed to understand the isotopic fraction of zinc in the nano cavity of different crown ethers and crown ethers anchored on solid resin matrix. The structure, energetic, thermodynamics, and vibration IR spectra were also evaluated. The gas phase binding energy of Zn2+ with crown ether of varied cavity can be correlated with NPA charge transfer but no such correlation is obtained with the fraction of electron transfer, ΔN. The reduced partition function ratio (RPFR) of complexes of Zn2+ ion with different solvents, crown ethers, and grafted crown ethers was also computed to predict the isotope separation factor of the Zn2+ ion. The present study reveals that with increasing cavity size of the crown ether the RPFR was found to be decreased leading to a high value of isotope separation factor as observed in the experiments. An attempt was made to correlate the calculated RPFR and separation factor with binding energy of different zinc-crown ether systems. Fu...

Density functional theory estimation of isotope fractionation of Fe, Ni, Cu, and Zn among species relevant to geochemical and biological environments

This paper reports the values of reduced partition function ratios (as 1000lnβ) for Fe, Ni, Cu, and Zn bound to a number of inorganic and organic ligands. We used Density Functional Techniques to update the existing data and calculate lnβ for new ligands. This work allows for the mass-dependent isotope fractionation to be predicted for various inorganic (hydrated cation, hydroxide, chloride, sulfate, sulfide, phosphate) and organic (citrate, amino acid) complexes of Fe, Ni, Cu, and Zn. Isotope fractionation among coexisting complexes of these metals was evaluated from the lnβ values in a variety of geochemical and biological environments. The results provide a framework for interpretation of isotope fractionation observed in seawater and chemical sediments, in the roots and aerial parts of plants, and among the organs and body fluids of mammals.

Estimation of Reduced Partition Function Ratios of Lithium-Graphite Intercalation Compounds by Density Functional Theory

The reduced partition function ratio (RPFR) of lithium in lithium-graphite intercalation compounds (Li-GICs) was evaluated at the UB3LYP=6-311G(d) level of theory. The partition functions were written in the usual rigid-rotor harmonic oscillator approximation.With a C24H12coronene molecule as the model of graphene, lithium-coronene sandwich, and club sandwich compounds were considered as models of Li-GICs. The estimated value of the6Li-to-7Li RPFR was 1.0402 at 25 °C, which yielded 1.034 as the value of the equilibrium constant, K, of the lithium isotope exchange reaction between a lithium ion in an ethylene carbonate=ethylmethyl carbonate mixed solvent and a lithium atom in interlayer space of graphite. The estimated value of K was larger than the experimental value of 1.025. The unsatisfactory agreement between the estimated and experimental K values suggested that larger molecules should be used as models of graphene and that the vibrational anharmonicity should also be taken into consideration.

Position-Specific and Clumped Stable Isotope Studies: Comparison of the Urey and Path-Integral Approaches for Carbon Dioxide, Nitrous Oxide, Methane, and Propane

We combine path-integral Monte Carlo methods with high-quality potential energy surfaces to compute equilibrium isotope effects in a variety of systems relevant to 'clumped' isotope analysis and isotope geochemistry, including CO2, N2O, methane, and propane. Through a systematic study of heavy-atom isotope-exchange reactions, we quantify and analyze errors that arise in the widely used Urey model for predicting equilibrium constants of isotope-exchange reactions using reduced partition function ratios. These results illustrate that the Urey model relies on a nontrivial cancellation of errors that can shift the apparent equilibrium temperature by as much as 35 K for a given distribution of isotopologues. The calculations reported here provide the same level of precision as the best existing analytical instrumentation, resolving the relative enrichment of certain isotopologues to as little as 0.01‰. These findings demonstrate path-integral methods to be a rigorous and viable alternative to more approximate methods for heavy-atom geochemical applications.

Reduced Partition Function Ratio in the Frequency Complex Plane: A Mathematical Approach

This paper gives a mathematical approach to calculate the fractionation factor of isotopes in a general cluster (also known as super-molecule), which composes of necessary chemical effect within three bonds outside the interested atom(s). The cluster might have imaginary frequencies after being optimized in quantum softwares. The approach includes the contribution of the difference, which is resulted from the substitution of heavy and light isotopes in the cluster, of vibrations of imaginary frequencies to give precise prediction of isotope fractionation factor. We call the new mathematical approximation “reduced partition function ratio in the frequency complex plane (RPFRC)”. If there is no imaginary frequency for a cluster, RPFRC is simplified to be Urey (1947) or Bigeleisen and Mayer (1947) formula. Final results of this new algorithm are in good agreement with those in earlier studies.

Equilibrium isotopic fractionation of copper during oxidation/reduction, aqueous complexation and ore-forming processes: Predictions from hybrid density functional theory

Copper exists as two isotopes: 65Cu (∼30.85%) and 63Cu (∼69.15%). The isotopic composition of copper in secondary minerals, surface waters and oxic groundwaters is 1–12‰ heavier than that of copper in primary sulfides. Changes in oxidation state and complexation should yield substantial isotopic fractionation between copper species but it is unclear to what extent the observed Cu isotopic variations reflect equilibrium fractionation. Here, I calculate the reduced partition function ratios for chalcopyrite (CuFeS2), cuprite (Cu2O), tenorite (CuO) and aqueous Cu+, Cu+2 complexes using periodic and molecular hybrid density functional theory to predict the equilibrium isotopic fractionation of Cu resulting from oxidation of Cu+ to Cu+2 and by complexation of dissolved Cu. Among the various copper(II) complexes in aqueous environments, there is a significant (1.3‰) range in the reduced partition function ratios. Oxidation and congruent dissolution of chalcopyrite (CuFeS2) to dissolved Cu+2 (as Cu(H2O)5+2) yields 65–63δ(Cu+2–CuFeS2)=3.1‰ at 25°C; however, chalcopyrite oxidation/dissolution is incongruent so that the observed isotopic fractionation will be less. Secondary precipitation of cuprite (Cu2O) would yield further enrichment of dissolved 65Cu since 65–63δ(Cu+2–Cu2O) is 1.2‰ at 25°C. However, precipitation of tenorite (CuO) will favor the heavy isotope by +1.0‰ making dissolved Cu isotopically lighter. These are upper-limit estimates for equilibrium fractionation. Therefore, the extremely large (9‰) fractionations between dissolved Cu+2 (or Cu+2 minerals) and primary Cu+ sulfides observed in supergene environments must reflect Rayleigh (open-system) or kinetic fractionation. Finally the previously proposed (Asael et al., 2009) use of δ65Cu in chalcopyrite to estimate the oxidation state of fluids that transported Cu in stratiform sediment-hosted copper deposits is refined.

Oxygen and Hydrogen Isotopic Preference in Hydration Spheres of Magnesium and Calcium Ions

Molecular orbital calculations were performed to estimate the 18O/16O and D/H isotopic reduced partition function ratios (rpfrs) of water molecules around magnesium and calcium ions. As model for water molecules in the ith hydration sphere of the cation in aqueous solutions containing that cation, we considered water molecules in the ith hydration sphere that were surrounded by water molecules in the (i+1)th hydration sphere in clusters, M2+(H2O)n (M = Mg or Ca; n up to 100). The calculations indicated that the decreasing order of the 18O preference over 16O in the primary hydration sphere is Mg2+ &gt; Ca2+ &gt; bulk water. That is, water molecules in the primary hydration spheres of the Mg2+ and Ca2+ ions are expected to be enriched in the heavier isotope of oxygen relative to water molecules in bulk, and the degree of the enrichment is larger for the Mg2+ ion than for the Ca2+ ion. No such preference was observed for hydrogen isotopes in any hydration sphere or for oxygen isotopes in the secondary and outer hydration spheres.