Ab initio molecular orbital calculations for boron isotope fractionations on boric acids and borates

Ab initio quantum chemistry calculations have been performed on the isotopic exchange reaction between B(OH)₃ and B(OH)₄⁻. Several calculation methods have been carefully compared and evaluated. The “water-droplet” method is chosen to investigate this isotope exchange reaction using cluster models with up to 34 water molecules surrounding the solute. HF/6-31G* level calculations coupled with a 0.920 scaling factor are used for the frequency calculations. A larger K value (1.027) is obtained from this study compared to the commonly used 1.0194 (Kakihana et al., 1977).The fractionations for several boric acid polymers and boron minerals are also studied. Our results suggest that assuming the BO₄ bonding in B(OH)₄⁻ is identical to that in borosilicates is wrong. Tetrahedral boron in silicates has a significantly smaller reduced isotopic partition function ratio (RPFR) and hence will be much isotopically lighter than in B(OH)₄⁻.The new theoretical curve of pH vs. δ¹¹B composition of B(OH)₄⁻ using our calculated 1.027 can be used to predict pH values for equilibrium cases such as incorporation into inorganic calcite. We also find that the shape of this curve is very sensitive to both K and pK_a value, giving the possibility of also predicting salinity from the different shapes of the curve.     

Ab initio calculation of interatomic force constants in H6Si2O7 and the bulk modulus of α quartz and α cristobalite

Ab initio force constants calculated for Si-O stretch and Si...Si non-bonded interactions in H₆Si₂O₇ are found comparable with experimental values derived from the lattice dynamics of α quartz. The bulk moduli of α quartz and α cristobalite are calculated using the molecular Si...Si force constant and assuming rigid regular SiO₄ tetrahedra. In the case (α quartz) where data are available the calculation agrees well with experiment.     

Ab initio studies of structural instabilities in magnesium silicate perovskite

Density-functional simulations are used to calculate structural properties and high-symmetry phonons of the hypothetical cubic phase, the stable orthorhombic phase and an intermediate tetragonal phase of magnesium silicate perovskite. We show that the structure of the stable phase is well described by freezing a small number of phonons into the cubic phase. We use the frequencies of these modes to estimate transition temperatures for cubic → tetragonal and tetragonal → orthorhombic phase transitions. Unstable modes are investigated further to find that the coupling with the strain suggests that phonons give a better representation than rigid unit modes. The phonons of an intermediate tetragonal phase were found to be stable except for two rotational modes. The eigenvectors of the most unstable mode of each of the cubic and tetragonal phases account for all the positional parameters of the orthorhombic phase. The phase boundary for the orthorhombic-tetragonal transition intersects possible mantle geotherms, suggesting that the tetragonal phase may be present in the lower mantle.     

Ab initio study of the high-pressure behavior of CaSiO3 perovskite

Using density functional simulations, within the generalized gradient approximation and projector-augmented wave method, we study structures and energetics of CaSiO₃ perovskite in the pressure range of the Earths lower mantle (0–150 GPa). At zero Kelvin temperature the cubic CaSiO₃ perovskite structure is unstable in the whole pressure range, at low pressures the orthorhombic (Pnam) structure is preferred. At 14.2 GPa there is a phase transition to the tetragonal (I4/mcm) phase. The CaIrO₃-type structure is not stable for CaSiO₃. Our results also rule out the possibility of decomposition into oxides.

Ab initio study of MgSiO3 C2/c enstatite

We have used a newly developed ab initio constant-pressure molecular dynamics with variable cell shape technique to investigate the zero temperature behaviour of high pressure clinoenstatite (MgSiO₃-C2/c) from 0 up to 30 GPa. The optimum structure at 8 GPa, as well as structural trends under pressure, compare very well with experimental data. At this pressure, we find noticeable “fluctuations” in the chain configuration which suggests the structure is on the verge of a mechanical instability. Two distinct compressive behaviours then appear: one below and another above 8 GPa. This phenomenon may be related to the observed transition to a lower symmetry P2₁/c phase which involves a reconfiguration of the silicate chains, and suggests that the C2/c structure at low pressures found here, may be an artifact of the dynamical algorithm which preserves space group in the absence of symmetry breaking fluctuations. Comparison with calculations in other magnesium silicate phases, indicates that the size and shape of the silicate units (isolated and/or linked tetrahedra and octahedra) are generally well described by the local density approximation; however, the weaker linkages provided by the O-Mg-O bonds, are not as well described. This trend suggests that, as in the recently studied case of H₂O-ice, the structural properties of more inhomogeneous systems, like enstatite, may be improved by using gradientcorrected density functionals.     

Ab initio calculation of the carbon isotope signatures of amino acids

Carbon isotope compositions for the 20 standard amino acids are calculated using high-level molecular orbital and density functional theory methods. In agreement with measurements of the isotopic compositions of amino acids in a cyanobacterium [Macko, S.A., Fogel, M.L., Hare, P.E., Hoering, T.C., 1987. Isotope fractionation of nitrogen and carbon in the synthesis of amino acids by microorganisms. Chemical Geology 65, 79–92] the calculations give heavy signatures for aspartic acid + asparagine, serine, glutamine + glutamic acid and light signatures for leucine and isoleucine. The relative intramolecular enrichment of ¹³C in carboxyl groups is often much less than measured [Abelson, P.H., Hoering, T.C., 1961. Carbon isotope fractionation in formation of amino acids by photosynthetic organisms. Proceedings of the National Academy of Sciences, USA 47, 623–632]. Fractionations predicted from density functional calculations often differ by several per mil from those predicted from molecular orbital calculations.     

Ab initio thermochemistry of some geochemically relevant molecules in the system Cr-O-H-Cl

A complete theoretical model chemistry algorithm (TMCA) for the prediction of thermodynamic properties of geochemically relevant gaseous and aqueous complexes, based on molecular quantum mechanics, is presented and discussed. Cr species are selected as a case study due to the high nuclear mass and the complex electronic structure of this transition metal. The various derived magnitudes are internally consistent and sufficiently accurate to warrant comparison with the existing (and often conflictual) experimental data and literature estimates. The TMCA is based on density functional theory (DFT) B3LYP/6-31G(d,p) gas phase computations followed by computation of solvation effects by the integral polarized continuum model approach at HF/STO-3G level. Energy corrections due to relativistic effects and electron-electron correlation are accounted for by a newly developed periodic function based on computed ionization potentials and electron affinity of the central metal. Electrostatic entropy contributions to the bulk solvation entropy are accounted for by a Born-model equation based on the electrostatic component of the Integral Equation Formalism—Polarized Continuum Model (IEFPCM) coupling work. As an ancillary result, the TMCA model confirms the validity of the absolute solvation energy terms of the aqueous proton. The TMCA model is of general validity and could be eventually adopted as a standard procedure in the ab initio assessment of gas-phase and aqueous-phase energetics of geochemically relevant species.     

Ab initio potentials for the calculation of the dynamical and elastic properties of α-quartz

Ab initio LDF theory has been used to derive interatomic potentials for the Si-O and O-O interaction in α-quartz. The potentials have been used to study the lattice dynamical properties of α-quartz from 1 atm to 12.5 Gpa pressure. The results are compared with other calculated and experimentally derived potentials.     

Ab initio investigation into the elasticity of ultrahigh-pressure phases of SiO2

In this study, we report the elastic properties of three ultrahigh-pressure phases of SiO₂: pyrite, cotunnite and Fe₂P types between 300 and 1,500 GPa calculated by means of the density functional ab initio method. It is generally thought that materials tend to be more compact and isotropic with increasing pressure. These three ultrahigh-pressure phases of silica are mechanically stable in the investigated pressure range according to the Born criteria, while the cotunnite and Fe₂P types are unstable at lower pressure. The elastic azimuthal anisotropy of these ultrahigh-pressure phases of silica shows that all the structures counterintuitively have considerable anisotropies even at multimegabar pressures. Among the three investigated structures, the cotunnite type of SiO₂ is the most elastically anisotropic phase due to a soft compression along the b axis combined with a large distortion of the polyhedrons that make the structure. This might also be related to its thermodynamic unfavorability compared to the Fe₂P type under extreme pressure condition. The bond property analyses clearly show that the Si–O bond remains an ionic-covalent mixed bond even at multimegabar pressures with an invariable ionicity with pressure. This argument can explain the monotonously pressure dependence of the elastic anisotropy in the case of pyrite, while the changes in the velocity distribution patterns out of the thermodynamic instability range largely contribute to those of the cotunnite and Fe₂P types.     

Ab initio elasticity of FeS2 pyrite from 0 to 135 GPa

Polynomial expressions for the elastic tensor coefficients, the bulk, the shear and Young’s moduli, the speed of sound for longitudinal and transverse waves, the equation of state and the x coordinate of the sulfur atom in pyrite are reported based on ab initio calculations in the range of 0–135 GPa. Comparison with published experimental data indicates good agreement for the equation of state and for values at 0 GPa as well as reasonable agreement for first derivatives. All modeling and interpretation was performed with Materials Toolkit v.2.0 and all ab initio computations with VASP.     

Ab initio calculations of the Fe(II) and Fe(III) isotopic effects in citrates,nicotianamine, and phytosiderophore,and new Fe isotopic measurements in higher plants

Iron is one of the most abundant transition metal in higher plants and variations in its isotopic compositions can be used to trace its utilization. In order to better understand the effect of plant-induced isotopic fractionation on the global Fe cycling, we have estimated by quantum chemical calculations the magnitude of the isotopic fractionation between different Fe species relevant to the transport and storage of Fe in higher plants: Fe(II)-citrate, Fe(III)-citrate, Fe(II)-nicotianamine, and Fe(III)-phytosiderophore. The ab initio calculations show firstly, that Fe(II)-nicotianamine is ～3‰ (⁵⁶Fe/⁵⁴Fe) isotopically lighter than Fe(III)-phytosiderophore; secondly, even in the absence of redox changes of Fe, change in the speciation alone can create up to ～1.5‰ isotopic fractionation. For example, Fe(III)-phytosiderophore is up to 1.5‰ heavier than Fe(III)-citrate₂ and Fe(II)-nicotianamine is up to 1‰ heavier than Fe(II)-citrate. In addition, in order to better understand the Fe isotopic fractionation between different plant components, we have analyzed the iron isotopic composition of different organs (roots, seeds, germinated seeds, leaves and stems) from six species of higher plants: the dicot lentil (Lens culinaris), and the graminaceous monocots Virginia wild rye (Elymus virginicus), Johnsongrass (Sorghum halepense), Kentucky bluegrass (Poa pratensis), river oat (Uniola latifolia), and Indian goosegrass (Eleusine indica). The calculations may explain that the roots of strategy-II plants (Fe(III)-phytosiderophore) are isotopically heavier (by about 1‰ for the δ⁵⁶Fe) than the upper parts of the plants (Fe transported as Fe(III)-citrate in the xylem or Fe(II)-nicotianamine in the phloem). In addition, we suggest that the isotopic variations observed between younger and older leaves could be explained by mixing of Fe received from the xylem and the phloem.     

Ab initio calculations of 17O and nT NMR parameters (nT=31P, 29Si) in H3 TOTH3 dimers and T 3O9 trimeric rings

NMR shieldings (σ) and electric field gradients (eq) are calculated using ab initio methods at the O and T nuclei (where T=P, Si) in two different types of molecules-TH₃ dimers, i.e. H₃SiOSiH₃ and H₃POPH ₃ ²⁺ , and TO₄ trimeric rings, i.e., Si₃O ₉ ^6- and P₃O ₉ ^3- , which serve as models for assessing the effects of polymerization, bond length and bond angle variation on the NMR properties of polymerized silicates and phosphates. In agreement with earlier ab initio studies on H₃SiOSiH₃ we confirm that σ(²⁹Si), σ(³¹P), σ(¹⁷O) and eq(¹⁷O) all decrease as θ(SiOSi) decreases in the range from 180° to 100°. However, correction for artifacts due to distant core electrons leads to a considerably reduced value for the anisotropy in σ ^O, bringing it into better agreement with estimated experimental values. The qualitative change in σ(²⁹Si) with θ(SiOSi) can be understood on the basis of changes in the energies of the highest energy occupied MO's and consequent variations in their contributions to the paramagnetic part of the shielding. For H₃POPH ₃ ²⁺ we calculate a larger value of eq^O than for the analog Si compound but the same type of variation of σ(¹⁷O) with θ(TOT). The change in σ(³¹P) with θ(POP) is, however, calculated to be much smaller than in the Si case and a maximum is predicted for intermediate angles. For the trimeric rings we obtain energy optimized geometries in good agreement with x-ray structural data, with T-O terminal distances systematically shorter than the T-O bridging distances. Calculated σ(T) anisotropies are also in good agreement with experiment and can be simply related to the calculated structure. After correction for distant core effects we obtain a change in σ(³¹P) between PO ₄ ^3- and P₃O ₉ ^3- in reasonable agreement with experiment.     

锚固力作用下的边坡临界滑动场法研究与应用

极限平衡方法计算锚固力作用下边坡稳定性时,通常将锚固力作为集中力处理,得到的滑面正应力和条间力分布曲线极不合理。除此之外,若按常规方法处理锚固力的作用,采用临界滑动场法分析锚固边坡稳定性时,搜索的滑动面会产生突变。为克服以上固有缺点,将半无限体受法向力作用的弹性力学解答近似作为锚固力在边坡体内产生的附加应力等效模型,并在此基础上建立了锚固力作用下的边坡临界滑动场计算方法,且通过算例分析表明了这种集中力近似等效处理方式的合理性,进一步丰富了锚固边坡稳定性分析方法。算例分析与工程应用表明,锚固力的作用会改变边坡临界滑动面位置,该方法能够搜索到锚固力作用下的合理临界滑动面,且滑面正应力和条间力分布曲线也较合理,相应的安全系数也较可靠。同时,该法能够全面评价边坡的整体和局部稳定性,可为实际边坡工程提供欠稳定区域的空间分布情况,使其得到有效的治理。     

Ab initio quantum chemical investigation of arsenic sulfide molecular diversity from As4S6 and As4

The structural diversity of arsenic sulfide molecules in compositions between As₄S₆ and As₄ was investigated using ab initio quantum chemical calculations. The As₄S₆ molecule consists of four trigonal pyramid coordinations of As atoms bonding to three S atoms. In the As₄S₅ composition, only one type of molecular configuration corresponds to an uzonite-type molecule. In the As₄S₄ composition, two molecular configurations exist with realgar-type and pararealgar-type molecules. Three molecular configurations are in the As₄S₃ composition. The first configuration comprises trigonal pyramidal As atom coordinations of two types: bonding to two S atoms and one As atom, and bonding to one S atom and two As atoms. The second is the molecular configuration of dimorphite. The third comprises trigonal pyramidal As atom coordinations of two types: bonding to three As atoms, and bonding to one As atom and two S atoms. The As₄S₂ composition allows molecular configurations of two types. One is comprised of trigonal pyramidal As atom configurations of one type bonding to two As atoms and one S atom. The other comprises trigonal pyramidal As atom coordinations of three types: bonding to two S atoms and one As atoms, bonding to one S atom and two As atoms, and bonding to three As atoms. The As₄S molecule has trigonal pyramidal As atom coordinations of two types: bonding to one S atom and two As atoms, and bonding to three As atoms. The As₄S composition permits only one molecular configuration, which suggests that the mineral duranusite comprises the As₄S molecular geometry. In all, ten molecular configurations are predicted in the molecular hierarchy of the arsenic sulfide binary system. The simulated Raman spectral profiles are helpful in searching for undiscovered arsenic sulfide minerals.     

Equilibrium H/H fractionations in organic molecules: I. Experimental calibration of ab initio calculations

Carbon-bound hydrogen in sedimentary organic matter can undergo exchange over geologic timescales, altering its isotopic composition. Studies investigating the natural abundance distribution of ¹H and ²H in such molecules must account for this exchange, which in turn requires quantitative knowledge regarding the endpoint of exchange, i.e., the equilibrium isotopic fractionation factor (α_eq). To date, relevant data have been lacking for molecules larger than methane. Here we describe an experimental method to measure α_eq for C-bound H positions adjacent to carbonyl group (H_α) in ketones. H at these positions equilibrates on a timescale of days as a result of keto-enol tautomerism, allowing equilibrium ²H/¹H distributions to be indirectly measured. Molecular vibrations for the same ketone molecules are then computed using Density Functional Theory at the B3LYP/6-311G** level and used to calculate α_eq values for H_α. Comparison of experimental and computational results for six different straight and branched ketones yields a temperature-dependent linear calibration curve with slope = 1.081−0.00376T and intercept = 8.404−0.387T, where T is temperature in degrees Celsius. Since the dominant systematic error in the calculation (omission of anharmonicity) is of the same size for ketones and C-bound H in most other linear compounds, we propose that this calibration can be applied to analogous calculations for a wide variety of organic molecules with linear carbon skeletons for temperatures below 100 °C. In a companion paper (Wang et al., 2009) we use this new calibration dataset to calculate the temperature-dependent equilibrium isotopic fractionation factors for a range of linear hydrocarbons, alcohols, ethers, ketones, esters and acids.     

Ab initio calculated geometries and charge distributions for H4SiO4 and H6Si2O7 compared with experimental values for silicates and siloxanes

Ab initio STO-3G molecular orbital theory has been used to calculate energy-optimized Si-O bond lengths and angles for molecular orthosilicic and pyrosilicic acids. The resulting bond length for orthosilicic acid and the nonbridging bonds for pyrosilicic acid compare well with Si-OH bonds observed for a number of hydrated silicate minerals. Minimum energy Si-O bond lengths to the bridging oxygen of the pyrosilicic molecule show a close correspondence with bridging bond length data observed for the silica polymorphs and for gas phase and molecular crystal siloxanes when plotted against the SiOSi angle. In addition, the calculations show that the mean Si-O bond length of a silicate tetrahedron increases slightly as the SiOSi angle narrows. The close correspondence between the Si-O bond length and angle variations calculated for pyrosilicic acid and those observed for the silica polymorphs and siloxanes substantiates the suggestion that local bonding forces in solids are not very different from those in molecules and clusters consisting of the same atoms with the same coordination numbers. An extended basis calculation for H₄SiO₄ implies that there are about 0.6 electrons in the 3d-orbitals on Si. An analysis of bond overlap populations obtained from STO-3G* calculations for H₆Si₂O₇ indicates that Si-O bond length and SiOSi angle correlations may be ascribed to changes in the hybridization state of the bridging oxygen and (d – p) π-bonding involving all five of the 3d AO's of Si and the lone-pair AO's of the oxygen. Theoretical density difference maps calculated for H₆Si₂O₇ show a build-up of charge density between Si and O, with the peak-height charge densities of the nonbridging bonds exceeding those of the bridging bonds by about 0.05 e Å^?3. In addition, atomic charges (+1.3 and ?0.65) calculated for Si and O in a SiO₂ moiety of the low quartz structure conform reasonably well with the electroneutrality postulate and with experimental charges obtained from monopole and radial refinements of diffraction data recorded for low quartz and coesite.     

Lattice dynamical calculations of anisotropic temperature factors of atoms in quartz,and the structure of β-quartz

Temperature factors for oxygen and silicon atoms in β-quartz were calculated on a Born-von Karman lattice dynamical model of an ordered structure. The calculated thermal ellipsoids were in excellent agreements with those of the previous structure refinements of the order model, for both magnitudes and orientations of the principal axes. The temperature factors are contributed mainly by the soft optic modes in Γ-M and the lowest-lying acoustic modes along Γ-A, which are also strongly temperature-dependent. The cusp-shaped temperature dependence of mean square displacements, 〈u²〉, of oxygen atom, observed previously around the α-β transition, are resulted from the softening of these modes. The temperature-dependent modes in Γ-A were also found to cause diffuse scattering extending along ±c^* of the fourth hexagon of the hk0 reciprocal lattice plane. The negative expansion known in β-quartz were interpreted in terms of asymmetrical forces exerting on oxygen atoms in Si-O-Si bending modes. In β-quartz, librational motions of oxygen atoms around Si-Si lines with large amplitudes, whose center is just on the β-position of high symmetry, must be possible under the condition that bending tetrahedral O-Si-O angles is energetically more favourable than compressing or stretching Si-O bonds.     

First-principles calculations of equilibrium fractionation of O and Si isotopes in quartz,albite, anorthite,and zircon

In this study, we used first-principles calculations based on density functional theory to investigate silicon and oxygen isotope fractionation factors among the most abundant major silicate minerals in granites, i.e., quartz and plagioclase (including albite and anorthite), and an important accessory mineral zircon. Combined with previous results of minerals commonly occurring in the crust and upper mantle (orthoenstatite, clinoenstatite, garnet, and olivine), our study reveals that the Si isotope fractionations in minerals are strongly correlated with SiO₄ tetrahedron volume (or average Si–O bond length). The ³⁰Si enrichment order follows the sequence of quartz > albite > anorthite > olivine ≈ zircon > enstatite > diopside, and the ¹⁸O enrichment follows the order of quartz > albite > anorthite > enstatite > zircon > olivine. Our calculation predicts that measurable fractionation of Si isotopes can occur among crustal silicate minerals during high-temperature geochemical processes. This work also allows us to evaluate Si isotope fractionation between minerals and silicate melts with variable compositions. Trajectory for δ³⁰Si variation during fractional crystallization of silicate minerals was simulated with our calculated Si isotope fractionation factors between minerals and melts, suggesting the important roles of fractional crystallization to cause Si isotopic variations during magmatic differentiation. Our study also predicts that δ³⁰Si data of ferroan anorthosites of the Moon can be explained by crystallization and aggregation of anorthite during lunar magma ocean processes. Finally, O and Si isotope fractionation factors between zircon and melts were estimated based on our calculation, which can be used to quantitatively account for O and Si isotope composition of zircons crystallized during magma differentiation.