Oxygen isotope exchange kinetics between H2O and H4SiO4 from ab initio calculations

Oxygen isotope exchange between H₂O and H₄SiO₄ was modeled with ab initio calculations on H₄SiO₄ + 7H₂O. Constrained optimizations were performed with the B3LYP/6-31+G(d,p) method to determine reactants, transition states, and intermediates. Long-range solvation was accounted for using self-consistent reaction field calculations. The mechanism for exchange involves two steps, a concerted proton transfer from H₄SiO₄ forming a 5-coordinated Si followed by a concerted proton transfer from the 5-coordinated Si forming another H₄SiO₄. The 5-coordinated Si intermediate is C2 symmetric. At 298K and with implicit solvation included, the Gibbs free energy of activation from transition state theory is 66 kJ/mol and the predicted rate constant is 16 s⁻¹. Equilibrium calculations between 298K and 673K yield α_H4SiO4-H2O that are uniformly less than, but similar to, α_qtz-H2O, and therefore α_qtz-H4SiO4 is expected to be relatively small in this temperature range.     

Theoretical exploration of the water exchange mechanism of the polyoxocation GaO4Al12(OH)24(H2O)12 in aqueous solution

Reaction pathways, solvent effects and energy barriers have been investigated for the water exchange of the polyoxocation GaO₄Al₁₂(OH)₂₄(H₂O)₁₂⁷⁺ (K-GaAl₁₂) in aqueous solution by means of supermolecule density functional theory calculations. In the proposed reaction pathway, the supermolecular reactant K-GaAl₁₂15H₂O first loses a water ligand to form an intermediate with a five-coordinated aluminum atom, and then the incoming water molecule in the second coordination sphere attacks the intermediate with a five-coordinated aluminum atom to produce the reaction product. Our calculated results indicate that the water exchange of K-GaAl₁₂ proceeds via a dissociative mechanism, and that the reverse reaction of Step II is the most favorable dissociative pathway, with a barrier height of 31.3 kJ mol⁻¹. The calculated transition-state rate for the favorable dissociative pathway is much larger than the experimental rate constant, but is close to the data calculated for Al₃₀ by molecular dynamics. The transmission coefficient was also predicted on the basis of both the calculated transition-state rate and the experimental rate. Our calculated results also indicate that both the explicit solvent effect and the bulk solvent effect have obvious effects on the barrier heights of the water exchange reaction of K-GaAl₁₂. By comparison, the water exchange mechanism for K-GaAl₁₂ was found to be more similar to that for mineral surfaces than that for monomeric aluminum species.     

Calorimetric measurements of fusion enthalpies for Ni2SiO4 and Co2SiO4 olivines and application to olivine-liquid partitioning

Calorimetric measurements of fusion enthalpies for Ni₂SiO₄ and Co₂SiO₄ olivines were carried out using a high-temperature calorimeter, and Ni and Co partitioning between olivine and silicate liquid was analyzed using the measured heats of fusion. The fusion enthalpy of Co₂SiO₄ olivine measured by transposed-temperature drop calorimetry was 103 ± 15 kJ/mol at melting point (1688 K). The fusion enthalpy of Ni₂SiO₄ olivine was calculated based on the enthalpies of liquids in the system An₅₀Di₅₀-Ni₂SiO₄ measured by transposed-temperature drop calorimetry at 1773 K, and was 221 ± 26 kJ/mol at its metastable melting point (1923 K). The fusion enthalpy of Ni₂SiO₄ is the largest among those of olivine group, this is caused by the large crystal field stabilization energy of six-coordinated Ni²⁺ in olivine. The larger fusion enthalpy of Ni₂SiO₄ can account for the large and variable partition coefficient of Ni between olivine and silicate liquid. Based on the comparison between partition coefficients calculated from thermodynamic data and those observed in partition experiments, it is considered that the magnitude of partition coefficients is primarily dependent on the heats of fusion of the components. Furthermore, the activity coefficients for Ni-, Co- and Mn-bearing components in magmatic liquid are nearly of the same magnitude.     

Thermodynamic properties of H4SiO4 in the ideal gas state as evaluated from experimental data

Solid phases of silicon dioxide react with water vapor with the formation of hydroxides and oxyhydroxides of silica. Recent transpiration and mass-spectrometric studies convincingly demonstrate that H₄SiO₄ is the predominant form of silica in vapor phase at water pressure in excess of 10⁻² MPa. Available literature transpiration and solubility data for the reactions of solid SiO₂ phases and low-density water, extending from 424 to 1661 K, are employed for the determination of Δ_fG⁰, Δ_fH⁰ and S⁰ of H₄SiO₄ in the ideal gas state at 298.15 K, 0.1 MPa. In total, there are 102 data points from seven literature sources. The resulting values of the thermodynamic functions of H₄SiO₄(g) are: Δ_fG⁰ = −1238.51 ± 3.0 kJ mol⁻¹, Δ_fH⁰ = −1340.68 ± 3.5 kJ mol⁻¹ and S⁰ = 347.78 ± 6.2 J K⁻¹ mol⁻¹. These values agree quantitatively with one set of ab initio calculations. The relatively large uncertainties are mainly due to conflicting data for H₄SiO₄(g) from various sources, and new determinations of would be helpful. The thermodynamic properties of this species, H₄SiO₄(g), are necessary for realistic modeling of silica transport in a low-density water phase. Applications of this analysis may include the processes of silicates condensation in the primordial solar nebula, the precipitation of silica in steam-rich geothermal systems and the corrosion of SiO₂-containing alloys and ceramics in moist environments.     

Activation volumes for oxygen exchange between the GaO4Al12(OH)24(H2O)127+(aq) (GaAl12) polyoxocation and aqueous solution from variable pressure O NMR spectroscopy

Activation volumes for exchange of oxygen between bulk aqueous solution and sites in the GaO₄Al₁₂(OH)₂₄(H₂O)₁₂⁷⁺(aq) (GaAl₁₂) complex were measured by variable-pressure ¹⁷O NMR techniques. Near 322 K, rates of exchange for the less labile set of bridging hydroxyls in the GaAl₁₂ decrease by a factor of about two with increasing pressure from 0.1 to 350 MPa. These data indicate a substantially positive activation volume of ΔV^‡ = +7 ± 1 cm³/mol, which is the first activation volume measured for a bridging hydroxyl in a polynuclear complex. This result suggests significant bond-lengthening in the activation step. Electrostriction effects should be small because exchange occurs via a pH-independent path under the experimental conditions. The second, more labile set of bridging hydroxyls exchange too rapidly for the variable-pressure techniques employed here. The exchange of bound-water molecules on the GaAl₁₂ was observed at P = 350 MPa using the ¹⁷O-NMR line-broadening technique. Comparison with previous measurements at 0.1 MPa indicates decreasing line width from 0.1 to 350 MPa for temperatures at which exchange dominates, yielding an activation volume of ΔV^‡ = +3(± 1) cm³/mol. This activation volume is smaller than the value for the Al(H₂O)₆³⁺ complex, suggesting that water exchange on the larger GaAl₁₂ complex has less dissociative character although the average charge density is lower.     

Hydrogen isotopic fractionation in lipid biosynthesis by H2-consuming Desulfobacterium autotrophicum

We report hydrogen isotopic fractionations between water and fatty acids of the sulfate-reducing bacterium Desulfobacterium autotrophicum. Pure cultures were grown in waters with deuterium (D) contents that were systematically varied near the level of natural abundance (−37‰ ? δD ? 993‰). H₂ of constant hydrogen isotope (D/H) ratio was supplied to the cultures. The D/H ratios of water, H₂, and specific fatty acids were measured by isotope-ratio mass spectrometry. The results demonstrate that D. autotrophicum catalyzes hydrogen isotopic exchange between water and H₂, and this reaction is conclusively shown to approach isotopic equilibrium. In addition, variation in the D/H ratio of growth water accounts for all variation in the hydrogen isotopic composition of fatty acids. The D/H ratios of fatty acids from cultures grown on H₂/CO₂ are compared with those from a separate set of cultures grown on D-enriched formate, an alternative electron donor. This comparison rules out H₂ as a significant source of fatty acid hydrogen. Grown on either H₂/CO₂ or formate, D. autotrophicum produces fatty acids in which all hydrogen originates from water. For specific fatty acids, biosynthetic fractionation factors are mostly in the range 0.60 ? α_FA-water ? 0.70; the 18:0 fatty acid exhibits a lower fractionation factor of 0.52. The data show that α_FA-water generally increases with length of the carbon chain from C₁₄ to C₁₇ among both saturated and unsaturated fatty acids. These results indicate a net fractionation associated with fatty acid biosynthesis in D. autotrophicum that is slightly smaller than in another H₂-consuming bacterium (Sporomusa sp.), but much greater than in most photoautotrophs.     

Effects of speciation on equilibrium fractionations and rates of oxygen isotope exchange between (PO4)aq and H2O

The effects of phosphate speciation on both rates of isotopic exchange and oxygen isotope equilibrium fractionation factors between aqueous phosphate and water were examined over the temperature range 70 to 180°C. Exchange between phosphate and water is much faster at low pH than at high pH, an observation that is similar to what has been observed in the analogous sulfate-water system. Oxygen isotope fractionations between protonated species like H₃PO₄ and H₂PO₄⁻ that are dominant at relatively low pH and species like PO₄³⁻ and ion pairs like KHPO₄⁻ that are dominant at relatively high pH, range between 5 and 8‰ at the temperatures of the experiments. In aqueous phosphate systems at equilibrium, ¹⁸O/¹⁶O ratios increase with increasing degree of protonation of phosphate. This effect can be explained in part by the relative magnitudes of the dissociation constants of the protonated species. Under equilibrium conditions, carbonate in solution or in solid phases concentrates ¹⁸O relative to orthophosphate in solution or in solid phases at all temperatures, supporting the traditional view that biogenic phosphate is precipitated in near oxygen isotope equilibrium with body/ambient aqueous fluids with no attendant vital effects.     

Polymerization of silicate and aluminate tetrahedra in glasses,melts and aqueous solutions—II. The network modifying effects of Mg2+ , K+, Na+, Li+, H+, OH−, F−, Cl−, H2O,CO2 and H3O+ on silicate polymers

The effect of the group IA and VIIA ions, as well as Mg²⁺, and the molecules H₂O, CO₂, H₃O⁺ and OH^? on the energy of the Si-O bond in a H₆Si₂O₇ cluster has been calculated using semiempirical molecular orbital calculations (CNDO/2). Three types of elementary processes, i.e. substitution, addition, and polymerization reactions have been used to interpret data on the dynamic viscosity, surface tension and surface charge, hydrolytic weakening, diffusivity, conductivity, freezing point depression, and degree of polymerization of silicates in melts, glasses, and aqueous solutions. As a test of our calculational procedure, observed X-ray emission spectra of binary alkali silicate glasses were compared with calculated electronic spectra. The well known bondlength variations between the bridging bond [Si-O(br)] and the non-bridging bond [Si-O(nbr)] in alkali silicates are shown to be due to the propagation of oscillating bond-energy patterns through the silica framework. A kinetic interpretation of some results of our calculations is given in terms of the Bell-Evans-Polanyi reaction principle.     

Calculated phase equilibria in K2O-FeO-MgO-Al2O3-SiO2-H2O for sapphirine-quartz-bearing mineral assemblages

Sapphirine, coexisting with quartz, is an indicator mineral for ultrahigh‐temperature metamorphism in aluminous rock compositions. Here a new activity‐composition model for sapphirine is combined with the internally consistent thermodynamic dataset used by THERMOCALC, for calculations primarily in K₂O‐FeO‐MgO‐Al₂O₃‐SiO₂‐H₂O (KFMASH). A discrepancy between published experimentally derived FMAS grids and our calculations is understood with reference to H₂O. Published FMAS grids effectively represent constant a_H2O sections, thereby limiting their detailed use for the interpretation of mineral reaction textures in compositions with differing H₂O. For the calculated KFMASH univariant reaction grid, sapphirine + quartz assemblages occur at P–T in excess of 6–7 kbar and 1005 °C. Sapphirine compositions and composition ranges are consistent with natural examples. However, as many univariant equilibria are typically not ‘seen’ by a specific bulk composition, the univariant reaction grid may reveal little about the detailed topology of multi‐variant equilibria, and therefore is of limited use for interpreting the P–T evolution of mineral assemblages and reaction sequences. Calculated pseudosections, which quantify bulk composition and multi‐variant equilibria, predict experimentally determined KFMASH mineral assemblages with consistent topology, and also indicate that sapphirine stabilizes at increasingly higher pressure and temperature as X_Mg increases. Although coexisting sapphirine and quartz can occur in relatively iron‐rich rocks if the bulk chemistry is sufficiently aluminous, the P–T window of stability shrinks with decreasing X_Mg. An array of mineral assemblages and mineral reaction sequences from natural sapphirine + quartz and other rocks from Enderby Land, Antarctica, are reproducible with calculated pseudosections. That consistent phase diagram calculations involving sapphirine can be performed allows for a more thorough assessment of the metamorphic evolution of high‐temperature granulite facies terranes than was previously possible. The establishment of a a‐x model for sapphirine provides the basis for expansion to larger, more geologically realistic chemical systems (e.g. involving Fe³⁺).     

A comparison of isotope fractionation of carbon and hydrogen from paddy field rice roots and soil bacterial enrichments during CO2/H2 methanogenesis

To better understand the isotope biogeochemistry of paddy field CH₄, we investigated carbon and hydrogen isotope fractionation during CO₂ reduction by a methanogenic community enriched from California paddy field soil and rice plants. Results from analyses of terminal restriction fragment length polymorphism (T-RFLP) and sequences of the archaeal small-subunit (SSU) rRNA-encoding genes (rDNA) showed a difference in methanogenic community structure between the soil (dominated by Methanobacteriaceae) and roots (dominated by Methanospirillaceae) which was essentially the same for sampling dates 15 and 99 days after flooding (DAF). CO₂/H₂ methanogenesis by these microbial communities produced CH₄ with different isotope ratios and fractionation factors (α factors). The carbon isotope α factors in an open system with a continuous supply of 0.5% H₂ were 1.050 ± 0.002 and 1.057 ± 0.001 for soil and root enrichment cultures at 15 DAF, and 1.052 ± 0.0.002 and 1.059 ± 0.002 for soil and root enrichment cultures at 99 DAF, respectively. These α factors are similar to, but distinct from values previously obtained from cultures of mesophilic methanogens and are larger than calculated values (1.045) for paddy soil. Fractionation of hydrogen isotopes was also studied in a closed system under 80% H₂. The difference in α factors between soil and root enrichment cultures remained clear. The hydrogen isotope fractionations between culture water and the product CH₄ were −327 ± 14‰ and −319 ± 18‰ for soil enrichments, and −389 ± 17‰ and −382 ± 21‰ for root enrichments at 15 DAF and 99 DAF, respectively.     

Kinetics of H2-O2-H2O redox equilibria and formation of metastable H2O2 under low temperature hydrothermal conditions

Hydrothermal experiments were conducted to evaluate the kinetics of H_2(aq) oxidation in the homogeneous H₂-O₂-H₂O system at conditions reflecting subsurface/near-seafloor hydrothermal environments (55-250 °C and 242-497 bar). The kinetics of the water-forming reaction that controls the fundamental equilibrium between dissolved H_2(aq) and O_2(aq), are expected to impose significant constraints on the redox gradients that develop when mixing occurs between oxygenated seawater and high-temperature anoxic vent fluid at near-seafloor conditions. Experimental data indicate that, indeed, the kinetics of H_2(aq)-O_2(aq) equilibrium become slower with decreasing temperature, allowing excess H_2(aq) to remain in solution. Sluggish reaction rates of H_2(aq) oxidation suggest that active microbial populations in near-seafloor and subsurface environments could potentially utilize both H_2(aq) and O_2(aq), even at temperatures lower than 40 °C due to H_2(aq) persistence in the seawater/vent fluid mixtures. For these H₂-O₂ disequilibrium conditions, redox gradients along the seawater/hydrothermal fluid mixing interface are not sharp and microbially-mediated H_2(aq) oxidation coupled with a lack of other electron acceptors (e.g. nitrate) could provide an important energy source available at low-temperature diffuse flow vent sites.More importantly, when H_2(aq)-O_2(aq) disequilibrium conditions apply, formation of metastable hydrogen peroxide is observed. The yield of H₂O_2(aq) synthesis appears to be enhanced under conditions of elevated H_2(aq)/O_2(aq) molar ratios that correspond to abundant H_2(aq) concentrations. Formation of metastable H₂O₂ is expected to affect the distribution of dissolved organic carbon (DOC) owing to the existence of an additional strong oxidizing agent. Oxidation of magnetite and/or Fe⁺⁺ by hydrogen peroxide could also induce formation of metastable hydroxyl radicals (•OH) through Fenton-type reactions, further broadening the implications of hydrogen peroxide in hydrothermal environments.     

Solution mechanisms of silicate in aqueous fluid and H2O in coexisting silicate melts determined in-situ at high pressure and high temperature

The structure of H₂O-saturated silicate melts, coexisting silicate-saturated aqueous solutions, and supercritical silicate liquids in the system Na₂O·4SiO₂–H₂O has been characterized with the sample at high temperature and pressure in a hydrothermal diamond anvil cell (HDAC). Structural information was obtained with confocal microRaman and with FTIR microscopy. Fluids and melts were examined along pressure-temperature trajectories defined by the isochores of H₂O at nominal densities, ρ_fluid, (from EOS of pure H₂O) of 0.90 and 0.78 g/cm³. With ρ_fluid = 0.78 g/cm³, water-saturated melt and silicate-saturated aqueous fluid coexist to the highest temperature (800 °C) and pressure (677 MPa), whereas with ρ_fluid = 0.90 g/cm³, a homogeneous single-phase liquid phase exists through the temperature and pressure range (25–800 °C, 0.1–1033 MPa). Less than 5 vol% quartz precipitates near 650 °C in both experimental series, thus driving Na/Si-ratios of melt + fluid phase assemblages to higher values than that of the Na₂O·4SiO₂ starting material.Molecular H₂O (H₂O°) and structurally bonded OH groups were observed in coexisting melts and fluids as well as in supercritical liquids. Their OH/(H₂O)-ratio is positively correlated with temperature. The OH/(H₂O)° in melts is greater than in coexisting fluids. Structural units of Q³, Q², Q¹, and Q⁰ type are observed in all phases under all conditions. An expression of the form, 12Q³ + 13H₂O2Q² + 6Q¹ + 4Q⁰, describes the equilibrium among those structural units. This equilibrium shifts to the right with increasing pressure and temperature with a ΔH of the reaction near 425 kJ/mol.     

Oxygen isotope exchange rate between dissolved sulfate and water at hydrothermal temperatures

Oxygen isotope exchange rate between dissolved sulfate and water was experimentally determined at 100, 200 and 300°C. The isotope exchange rate is strongly dependent on temperature and pH of the solution. Combining the temperature and pH dependence of the reaction rate, the exchange reaction was estimated to be first-order with respect to sulfate. The logarithm of apparent rate constant of exchange reaction at a given temperature is a function of the pH calculated at the experimental temperatures. From the pH dependence of the apparent rate constant, it was deduced that the isotope exchange reaction between dissolved sulfate and water proceeds through collision between H₂SO⁰₄ and H₂O at low pH, and between HSO^?₄ and H₂O at intermediate pH. The isotope exchange rate obtained indicates that oxygen isotope geothermometry utilizing the studied isotope exchange is suitable for temperature estimation of geothermal reservoirs. The extrapolated half-life of this reaction to oceanic temperature is about 10⁹ years, implying that exchange between oceanic sulfate and water cannot control the oxygen isotope ratio of oceanic sulfates.     

Effect of oxygen fugacity on the H2O storage capacity of forsterite in the carbon-saturated systems

High pressure experiments have been performed in the systems Mg₂SiO₄-C-O-H and Mg₂SiO₄-K₂CO₃-C at 6.3 GPa and 1200 to 1600 °C using a split-sphere multi-anvil apparatus. In the Mg₂SiO₄-C-O-H system the composition of fluid was modeled by adding different amounts of water and stearic acid. The fO₂ was controlled by the Mo-MoO₂ or Fe-FeO oxygen buffers. Several experiments in the Mg₂SiO₄-C-O-H system and all experiments in the Mg₂SiO₄-K₂CO₃-C system have been conducted without buffering the fO₂. Forsterite in the system Mg₂SiO₄-K₂CO₃-C does not reveal OH absorption bands in the IR spectra, while forsterite coexisting with carbon-bearing fluid and silicate melt at logfO₂ from FMQ-2 to FMQ-5 (from 2 to 5 log units below fayalite-magnetite-quartz oxygen buffer) contains 800-1850 wt. ppm H₂O. The maximum concentrations were detected at 1400 °C and FMQ-3.5. We observed an increase in the solidus temperature in the system Mg₂SiO₄-C-O-H from 1200 to above 1600 °C with log fO₂ decreasing from FMQ-2 to FMQ-5. The increase of the solidus temperature and the broadening of the stability field of the H₂O-H₂-CH₄ subsolidus fluid phase at 1400-1600 °C explain the high H₂O storage capacity of forsterite relative to that crystallized from carbon-free, oxidized, hydrous, silicic melt. At temperatures above 1400 °C liquidus forsterite precipitated along with diamond from oxidized (FMQ-1) carbonate-silicate melt and from silicate melt dissolving the moderately reduced C-O-H fluid (from FMQ-2 to FMQ-3.5). Formation of diamond was not detected under ultra-reduced conditions (FMQ-5) at 1200-1600 °C. Olivine co-precipitating with diamond from dry carbonate-silicate or hydrous-silicic fluid/melt can provide information on the H₂O contents and speciation of the diamond-forming media in the mantle. The conditions for minimum post-crystallization alteration of olivine and its hydrogen content are discussed.     

G2 theory calculations on [H3SiO4]−, [H4]SiO4], [H3AlO4]2−, [H4AlO4]− and [H5AlO4]: Basis set and electron correlation effects on molecular structures,atomic charges,infrared spectra,and potential energies

G2 theory calculations were performed on [H₃SiO₄]^?, H₄SiO₄, [H₃AlO₄]^2?, [H₄AlO₄]^?, and [H₅AlO₄]. Molecular structures, atomic charges, and infrared spectra at the HF/6-31G^* and MP2/6-31G^* levels are compared. The influence of polarization and diffuse functions on the structure of [H₃SiO₄]^? is also examined. Basis set and electron correlation effects on potential energies are assessed by comparing various levels of theory. Proton affinities of these gas-phase molecules and related mineral surface species are predicted based on corrections for cluster-size effects.     

The stability of CaCO3·6H2O (ikaite)

Experimental runs were made in cold-seal pressure vessels using synthetic CaCO₈·6H₂O, calcite and aragonite as starting materials. The reaction CaCO₃·6H₂O (ikaite) ? CaCO₃ (calcite I) + 6H₂O was reversed across its metastable extension into the aragonite stability field and the phase boundary is defined by brackets at 4.14kb, 14.3°C and 2.96 kb, ?3.0°C. An invariant point for CaCO₃·6H₂O, calcite I, aragonite and water thus occurs at about 3.02 kb and ?2.0°C. No other reaction could be reversed. Calculations based on the equilibrium phase boundary between calcite and ikaite and the available thermochemical data for calcite and water yield the stadard free energy of formation, standard enthalpy of formation and third law entropy of CaCO₃·6H₂O at 25°C and 1 bar total pressure; ?607.3 kcal/mole, ?705.8 kcal/mole, and 88.4 cal/deg mole, respectively.     

Calorimetric study of olivine solid solutions in the system Mg2SiO4-Fe2SiO4

Solution enthalpies of synthetic olivine solid solutions in the system Mg₂SiO₄-Fe₂SiO₄ have been measured in molten 2PbO·B₂O₃ at 979 K. The enthalpy data show that olivine solid solutions have a positive enthalpy of mixing and the deviation from ideality is approximated as symmetric with respect to composition, in contrast to the previous study. Applying the symmetric regular solution model to the present enthalpy data, the interaction parameter of ethalpy (W_H) is estimated to be 5.3±1.7 kJ/mol (one cation site basis). Using this W_h and the published data on excess free energy of mixing, the nonideal parameter of entropy (W_s) of olivine solid solutions is estimated as 0.6±1.5 J/mol·K.     

First-principles study of (MgH2SiO4)? n (Mg2SiO4) hydrous olivine structures. I. Crystal structure modelling of hydrous olivine Hy-2 a (MgH2SiO4) ? 3(Mg2SiO4)

 Recently, the Hy-2a hydrous olivine (MgH₂ SiO₄)·3(Mg₂SiO₄) occurring as nanometre-sized inclusions in mantle olivines has been found by TEM, and has been suggested to be a new DHMS phase (Khisina et al. 2001). A model of the crystal structure of Hy-2a has been proposed as a 2a-superstructure of olivine with one Me²⁺ -vacant octahedral layer in the (1 0 0) plane per Hy-2a unit cell (Khisina and Wirth 2002). In the present study the crystal structure of Hy-2a hydrous olivine is optimized by ab initio calculations. The aims of this study are: (1) verification of the suggested models of Hy-2a hydrous olivine structure; (2) calculation of the most stable configurations for Hy-2a structure with minimum static lattice energy, by assuming a possible formation of Me²⁺ vacancies in either M1 or M2 octahedral sites; (3) determination of the position of protons and hydrogen bonds in the Hy-2a structure. Several different possible configurations of the Hy-2a structure are optimized. The results support the idea of a stable olivine structure with ordered planar-segregated OH-bearing defects oriented parallel to (1 0 0). The data obtained indicate a preferred stability of the Hy-2a structure with the protons associated with M1 vacancies and bonded with O1 and O2 oxygen sites. The relative energy values of the optimized Hy-2a structure configurations correlate as a rule with the average shifts of atoms from their positions in pure forsterite structure. Received: 7 February 2002 / Accepted: 23 October 2002     

Theoretical investigation of iron isotope fractionation between Fe(H2O)6 and Fe(H2O)6: Implications for iron stable isotope geochemistry

The magnitude of equilibrium iron isotope fractionation between Fe(H₂O)₆³⁺ and Fe(H₂O)₆²⁺ is calculated using density functional theory (DFT) and compared to prior theoretical and experimental results. DFT is a quantum chemical approach that permits a priori estimation of all vibrational modes and frequencies of these complexes and the effects of isotopic substitution. This information is used to calculate reduced partition function ratios of the complexes (10³ · ln(β)), and hence, the equilibrium isotope fractionation factor (10³ · ln(α)). Solvent effects are considered using the polarization continuum model (PCM). DFT calculations predict fractionations of several per mil in ⁵⁶Fe/⁵⁴Fe favoring partitioning of heavy isotopes in the ferric complex. Quantitatively, 10³ · ln(α) predicted at 22°C, ∼ 3 ‰, agrees with experimental determinations but is roughly half the size predicted by prior theoretical results using the Modified Urey-Bradley Force Field (MUBFF) model. Similar comparisons are seen at other temperatures. MUBFF makes a number of simplifying assumptions about molecular geometry and requires as input IR spectroscopic data. The difference between DFT and MUBFF results is primarily due to the difference between the DFT-predicted frequency for the ν₄ mode (O-Fe-O deformation) of Fe(H₂O)₆³⁺ and spectroscopic determinations of this frequency used as input for MUBFF models (185-190 cm⁻¹ vs. 304 cm⁻¹, respectively). Hence, DFT-PCM estimates of 10³ · ln(β) for this complex are ∼ 20% smaller than MUBFF estimates. The DFT derived values can be used to refine predictions of equilibrium fractionation between ferric minerals and dissolved ferric iron, important for the interpretation of Fe isotope variations in ancient sediments. Our findings increase confidence in experimental determinations of the Fe(H₂O)₆³⁺ − Fe(H₂O)₆²⁺ fractionation factor and demonstrate the utility of DFT for applications in “heavy” stable isotope geochemistry.     

Density functional studies of the structural characteristics, Al NMR chemical shifts and water-exchange reactions of Al30O8(OH)56(H2O)26(Al30) in aqueous solution

In this paper, the structure of the Al₃₀O₈(OH)₅₆(H₂O)₂₆¹⁸⁺(Al₃₀) polyoxocation in aqueous solution is investigated, including an exploration of its water-exchange reaction using a supramolecular model. Thirty-one solvent water molecules were explicitly included in the supramolecular model to approximate the influence of the solvent. The calculated results indicated that both the gas-phase and the supramolecular models could correctly reproduce the structure of the Al₃₀ polyoxocation, but the supramolecular model described the structure more accurately. Using the supramolecular model, we calculated the ²⁷Al NMR chemical shifts of various aluminum atoms using HF and GIAO methods, and they compared well to the chemical shifts determined experimentally. The water-exchange reaction of the Al₃₀ polyoxocation could not be simulated with the gas phase model because of a proton-transfer reaction that is induced by the highly positive charge of the Al₃₀ polyoxocation. However, the inclusion of an explicit second solvation sphere lowered the acidity of the coordinated water molecules and allowed simulation of the water exchange reaction.