Periodic Hartree-Fock study of minerals: Tetracoordinated silica polymorphs

Periodic Hartree-Fock STO-3G calculations have been performed on several tetracoordinated silica polymorphs: low and high quartz, low and idealized high cristobalite and prototype tridymite. The optimized structural parameters are in overall good agreement with experimental data. In the particular case of -quartz, the SiO₄ tetrahedra are found to be irregular. The optimized values of the two different SiO bond lengths are respectively 1.608 Å and 1.613 Å. The potential energy versus tilt angle curves suggest a picture of the high temperature phases in terms of delocalized oxygen atoms which is consistent with a disordered structure. Finally, the bonding in silica polymorphs is discussed from electron density maps and Mulliken population analysis.     

An ab initio study of the O-H stretching frequency in tremolite

We have carried out a series of ab initio molecular orbital calculations for a cluster designed to model the OH site environment in tremolite to investigate the forces affecting the O-H stretch frequency in the crystal. The results of our calculations suggest that there are repulsive interactions between the hydrogen atom and silicon and oxygen atoms in the silicate ring adjacent to the OH site in tremolite. From our model calculations, we predict that the O-H stretching frequency of tremolite should first increase, then decrease, with applied pressure. This may affect the variation in H/D fractionation factors involving tremolite and other amphiboles with depth.     

Crossover of cation partitioning in olivines: a combination of ab initio and Monte Carlo study

We report studies based on a combination of ab initio electronic structure and Monte Carlo (MC) technique on the problem of cation partitioning among inequivalent octahedral sites, M1 and M2 in mixed olivines containing Mg²⁺ and Fe²⁺ ions. Our MC scheme uses interactions derived out of ab initio, density functional calculations carried out on measured crystal structure data. Our results show that there is no reversal of the preference of Fe for M1 over M2 as a function of temperature. Our findings do not agree with the experimental findings of Redfern et al. (Phys Chem Miner 27:630–637, 2000), but are in agreement with those of Heinemann et al. (Eur J Mineral 18:673–689, 2006) and Morozov et al. (Eur J Mineral 17:495–500, 2005).     

High-pressure stability, structure and compressibility of Cmcm -MgAl2O4: an ab initio study

 Quantum-mechanical solid-state calculations have been performed on the highest-pressure polymorph of magnesium aluminate (CaTi₂O₄-type structure, Cmcm space group), as well as on the low-pressure (Fd3ˉm) spinel phase and on MgO and Al₂O₃. An ab initio all-electron periodic scheme with localized basis functions (Gaussian-type atomic orbitals) has been used, employing density-functional-theory Hamiltonians based on LDA and B3LYP functionals. Least-enthalpy structure optimizations in the pressure range 0 to 60 GPa have allowed us to predict: (1) the full crystal structure, the pV equation of state and the compressibility of Cmcm-MgAl₂O₄ as a function of pressure; (2) the phase diagram of the MgO–Al₂O₃–MgAl₂O₄ system (with exclusion of CaFe₂O₄-type Pmcn-MgAl₂O₄), and the equilibrium pressures for the reactions of formation/decomposition of the Fd3ˉm and Cmcm polymorphs of MgAl₂O₄ from the MgO + Al₂O₃ assemblage. Cmcm-MgAl₂O₄ is predicted to form at 39 and 57 GPa by LDA and B3LYP calculations, with K ₀=248 (K′=3.3) and 222 GPa (K′=3.8), respectively. Results are compared to experimental data, where available, and the performance of different DFT functionals is discussed. Received: 31 January 2001 / Accepted: 16 May 2001     

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.     

Surface complexation of arsenic(V) to iron(III) (hydr)oxides: structural mechanism from ab initio molecular geometries and EXAFS spectroscopy

Arsenic(V), as the arsenate (AsO₄)³⁻ ion and its conjugate acids, is strongly sorbed to iron(III) oxides (α-Fe₂O₃), oxide hydroxides (α-,γ-FeOOH) and poorly crystalline ferrihydrite (hydrous ferric oxide). The mechanism by which arsenate complexes with iron oxide hydroxide surfaces is not fully understood. There is clear evidence for inner sphere complexation but the nature of the surface complexes is controversial. Possible surface complexes between AsO₄ tetrahedra and surface FeO₆ polyhedra include bidentate corner-sharing (²C), bidentate edge-sharing (²E) and monodentate corner-sharing (¹V). We predicted the relative energies and geometries of AsO₄-FeOOH surface complexes using density functional theory calculations on analogue Fe₂(OH)₂(H₂O)_nAsO₂(OH)₂³⁺ and Fe₂(OH)₂(H₂O)_nAsO₄⁺ clusters. The bidentate corner-sharing complex is predicted to be substantially (55 kJ/mole) more favored energetically over the hypothetical edge-sharing bidentate complex. The monodentate corner-sharing (¹V) complex is very unstable. We measured EXAFS spectra of 0.3 wt. % (AsO₄)³⁻ sorbed to hematite (α-Fe₂O₃), goethite(α-FeOOH), lepidocrocite(γ-FeOOH) and ferrihydrite and fit the EXAFS directly with multiple scattering. The phase-shift-corrected Fourier transforms of the EXAFS spectra show peaks near 2.85 and 3.26 Å that have been attributed by previous investigators to result from ²E and ²C complexes. However, we show that the peak near 2.85 Å appears to result from As-O-O-As multiple scattering and not from As-Fe backscatter. The observed 3.26 Å As-Fe distance agrees with that predicted for the bidentate corner-sharing surface (²C) complex. We find no evidence for monodentate (¹V) complexes; this agrees with the predicted high energies of such complexes.     

Thermodynamics and phonon dispersion of pyrope and grossular silicate garnets from ab initio simulations

The phonon dispersion and thermodynamic properties of pyrope (\(\hbox {Mg}_3\hbox {Al}_2\hbox {Si}_3\hbox {O}_{12}\)) and grossular (\(\hbox {Ca}_3\hbox {Al}_2\hbox {Si}_3\hbox {O}_{12}\) ) have been computed by using an ab initio quantum mechanical approach, an all-electron variational Gaussian-type basis set and the B3LYP hybrid functional, as implemented in the Crystal program. Dispersion effects in the phonon bands have been simulated by using supercells of increasing size, containing 80, 160, 320, 640, 1280 and 2160 atoms, corresponding to 1, 2, 4, 8, 16 and 27 \(\mathbf {k}\) points in the first Brillouin zone. Phonon band structures, density of states and corresponding inelastic neutron scattering spectra are reported. Full convergence of the various thermodynamic properties, in particular entropy (S) and specific heat at constant volume (\(C_\mathrm{{V}}\)), with the number of \(\mathbf {k}\) points is achieved with 27 \(\mathbf {k}\) points. The very regular behavior of the S(T) and \(C_\mathrm{{V}}(T)\) curves as a function of the number of \(\mathbf {k}\) points, determined by high numerical stability of the code, permits extrapolation to an infinite number of \(\mathbf {k}\) points. The limiting value differs from the 27-\(\mathbf {k}\) case by only 0.40 % at 100 K for S (the difference decreasing to 0.11 % at 1000 K) and by 0.29 % (0.05 % at 1000 K) for \(C_\mathrm{{V}}\). The agreement with the experimental data is rather satisfactory. We also address the problem of the relative entropy of pyrope and grossular, a still debated question. Our lattice dynamical calculations correctly describe the larger entropy of pyrope than grossular by taking into account merely vibrational contributions and without invoking “static disorder” of the Mg ions in dodecahedral sites. However, as the computed entropy difference is found to be larger than the experimental one by a factor of 2–3, present calculations cannot exclude possible thermally induced structural changes, which could lead to further conformational contributions to the entropy.     

The vibrational frequencies of forsterite Mg2SiO4: an all-electron ab initio study with the CRYSTAL code

The vibrational spectrum of Mg₂SiO₄ olivine was calculated at the Γ point by using the periodic ab initio CRYSTAL program. An all electron localized Gaussian-type basis set and the B3LYP Hamiltonian were employed. The full set of frequencies (35 IR active, 36 Raman active, 10 “silent” modes) was computed and compared to experimental data from different sources (four for IR and four for Raman). A generally good agreement is observed with experiment (the mean absolute difference ranging from 7 to 10 cm⁻¹ for the various sets), when some of the experimental frequencies, whose attribution is uncertain or appears to be affected by large errors, are not taken into account. A small number of observed peaks are not consistent with calculated frequencies, and a few theoretical peaks do not correspond to measured values. The implications are discussed in detail. The full set of modes are characterized using different tools, namely isotopic substitution, direct inspection of the eigenvectors and graphical representation, so as to obtain a consistent mode assignment.     

A comparison of procrystal and ab initio model representations of the electron-density distributions of minerals

 The procrystal calculation of the electron density is a very rapid procedure that offers a quick way to analyze various bonding properties of a crystal. This study explores the extent to which the positions, number, and properties of bond-critical points determined from the procrystal representations of the electron density for minerals are similar to those of first-principles ab initio model distributions. The purpose of the study is to determine the limits imposed upon interpretation of the procrystal electron density. Procrystal calculations of the electron density for more than 300 MO bonds in crystals were compared with those previously calculated using CRYSTAL98 and TOPOND software. For every bond-critical point found in the ab initio calculations, an equivalent one was also found in the procrystal model, with similar magnitudes of electron density, and at similar positions along the bonds. The curvatures of the electron densities obtained from the ab initio and the procrystal distributions are highly correlated. It is concluded that the procrystal distributions are capable of providing good estimates of the bonded radii of the atoms and the properties of the electron-density distributions at the bond-critical points. Because the procrystal model is so fast to compute, it is especially useful in addressing the question as to whether a pair of atoms is bonded or not. If the Bader criteria for bonding are accepted, then the successful generation of the bond-critical points by the procrystal model demonstrates that bonding is an atomic feature. The main difference between the critical-point properties of the procrystal and the ab initio model is that the curvature in the electron density perpendicular to the bond path of the ab initio model is sharper than for the procrystal model. This is interpreted as indicating that the electrons that migrate into a bond originate from its sides, and not from the regions closer to the nuclei. This observation also suggests that ab initio optimization routines could see an improvement in speed if the parameters relating to the angular components of atomic wave functions were to vary before the radial components. Received: 6 August 2001 / Accepted: 21 November 2001     

Elastic properties of six silicate garnet end members from accurate ab initio simulations

The elastic properties of six silicate garnet end members, among the most important rock-forming minerals, are investigated here for the first time via accurate ab initio theoretical simulations. The Crystal program is used, which works within periodic boundary conditions and allows for all-electron basis sets to be adopted. From the computed elastic tensor, Christoffel’s equation is solved along a set of crystallographic directions in order to fully characterize the seismic wave velocity anisotropy in such materials. Polycrystalline isotropic aggregate elastic properties are derived from the computed single-crystal data via the Voigt-Reuss-Hill averaging procedure. Transferability of the elastic properties from end members to their solid solutions with different chemical compositions is also addressed.     

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.     

Determination of the origin and magnitude of Al/Si ordering enthalpy in framework aluminosilicates from ab initio calculations

Ab initio total energy calculations based on a new optimised oxygen pseudopotential has been used to determine the enthalpy of disorder for the exchange of Al and Si in tetrahedral coordination in simple derivative aluminosilicate structures based on the high temperature tridymite structure. The problem has been studied as a function of defect interaction, and defect concentration, and the results indicate that the energy for Al/Al neighbouring tetrahedra can be assigned primarily to two effects, the first, a coulombic effect, associated with the disturbed charge distribution, and the second associated with the strain related to misfit due to the very different dimensions of the Si and Al containing tetrahedra. In practice each of these effects contributes approximately 0.2 eV per Al−Al neighbour to the overal disorder enthalpy. These simple results were obtained after a careful study of possible chemical interaction between adjacent Al/Si containing tetrahedra which showed that chemical interaction was effectively absent. Since individual Al/Si tetrahedra proved to be discrete entities that are individually heavily screened by the shared oxygens it follows that coulombic and strain effects in disorder effectively account for the whole of the disorder enthalpy. The complete set of results have been used to establish new criteria for the structure and disorder enthalpies of the feldspar group of minerals and their long period derivatives. Received: October 7, 1996 / Revised, accepted: March 17, 1997     

The dwarf nova MN Dra: Periodic processes at various phases of the supercycle

We analyze photometry of the dwarf nova MN Dra carried out using various instruments at four observatories on 18 nights between May 20 and June 28, 2009. The observations cover a variety of activity states of the system: a superoutburst, three normal outbursts, and quiescence. Analysis of the system’s light curve during the superoutburst decline reveals positive superhumps that recur, on average, with a period of 0.105 days and are due to the direct apsidal precession of the accretion disk. These are observed until the end of the superoutburst, but their period decreases at a rate of −24.5 × 10⁻⁵ of the period per period. Both the positive-superhump period and its derivative are in good agreement with estimates made during previous superoutbursts. At the brightness minimum and in normal outbursts, MN Dra displays brightness variations with a period of 0.096 days, whose amplitude is much larger during the brightness minimum (0.8 ^m –1.5 ^m ) than during normal outbursts (0.1 ^m –0.2 ^m ). We suggest that these brightness variations could be negative superhumps due to nodal precession of the oblique accretion disk.     

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.     

Dissolution mechanisms of water in depolymerized silicate melts: Constraints from H and Si NMR spectroscopy and ab initio calculations

Dissolution of water in magmas significantly affects phase relations and physical properties. To shed new light on the this issue, we have applied ¹H and ²⁹Si nuclear magnetic resonance (NMR) spectroscopic techniques to hydrous silicate glasses (quenched melts) in the CaO-MgO-SiO₂ (CMS), Na₂O-SiO₂, Na₂O-CaO-SiO₂ and Li₂O-SiO₂ systems. We have also carried out ab initio molecular orbital calculations on representative clusters to gain insight into the experimental results.The most prominent result is the identification of a major peak at ∼1.1 to 1.7 ppm in the ¹H MAS NMR spectra for all the hydrous CMS glasses. On the basis of experimental NMR data for crystalline phases and ab initio calculation results, this peak can be unambiguously attributed to (Ca,Mg)OH groups. Such OH groups, like free oxygens, are only linked to metal cations, but not part of the silicate network, and are thus referred to as free hydroxyls in the paper. This represents the first direct evidence for a substantial proportion (∼13∼29%) of the dissolved water as free hydroxyl groups in quenched hydrous silicate melts. We have found that free hydroxyls are favored by (1) more depolymerized melts and (2) network-modifying cations of higher field strength (Z/R²: Z: charge, R: cation-oxygen bond length) in the order Mg > Ca > Na. Their formation is expected to cause an increase in the melt polymerization, contrary to the effect of SiOH formation. The ²⁹Si MAS NMR results are consistent with such an interpretation. This water dissolution mechanism could be particularly important for ultramafic and mafic magmas.The ¹H MAS NMR spectra for glasses of all the studied compositions contain peaks in the 4 to 17 ppm region, attributable to SiOH of a range of strength of hydrogen bonding and molecular H₂O. The relative population of SiOH with strong hydrogen bonding grows with decreasing field strength of the network-modifying cations. Ab initio calculations confirmed that this trend largely reflects hydrogen bonding with nonbridging oxygens.     

Correlations between 11B NMR parameters and structural characters in borate and borosilicate minerals investigated by high-resolution MAS NMR and ab initio calculations

Borates consisting of diverse fundamental building blocks (FBB) formed from complex polymerization of planar triangular [Bϕ₃] groups and tetrahedral [Bϕ₄] groups, where ϕ = O and OH, provide an excellent opportunity for investigation of correlations between the NMR parameters and local structures. However, previous studies suggested that the ¹¹B NMR parameters in borates are insensitive to local structural environments other than the B coordination number, in contrast to those documented for ²⁹Si, ²³Na and ²⁷Al in silicates, and no correlation between ¹¹B chemical shifts and the sum of bond valences has been established for borate minerals with hydroxyl groups or molecular water in the structures. In this study, high-resolution NMR spectra have been acquired at the ultra high field of 21 T as well as at 14 T for selected borate and borosilicate minerals, and have been used to extract high-precision NMR parameters by using combined ab initio theoretical calculations and spectral simulations. These new NMR parameters reveal subtle correlations with various structural characters, especially the effects of the ¹¹B chemical shifts from the bridging oxygen atom(s), site symmetry, symmetry of FBB, the sum of bond valences, as well as the next-nearest-neighbor cations and hydrogen bonding. Also, these results provide new insights into the shielding mechanism for ¹¹B in borate and borosilicate minerals. In particular, this study demonstrates that the small variation in ¹¹B chemical shifts can still be used to probe the local structural environments and that the established correlations can be used to investigate the structural details in borates and amorphous materials.     

Correlations between 29Si, 17O and 1H NMR properties and local structures in silicates: an ab initio calculation

In order to gain insight into the correlations between ²⁹Si, ¹⁷O and ¹H NMR properties (chemical shift and quadrupolar coupling parameters) and local structures in silicates, ab initio self-consistent field Hartree-Fock molecular orbital calculations have been carried out on silicate clusters of various polymerizations and intertetrahedral (Si-O-Si) angles. These include Si(OH)₄ monomers (isolated as well as interacting), Si₂O(OH)₆ dimers (C₂ symmetry) with the Si-O-Si angle fixed at 5° intervals from 120° to 180°, Si₃O₂(OH)₈ linear trimers (C₂ symmetry) with varying Si-O-Si angles, Si₃O₃(OH)₆ three-membered rings (D₃ and C₁ symmetries), Si₄O₄(OH)₈ four-membered ring (C₄ symmetry) and Si₈O₁₂(OH)₈ octamer (D₄ symmetry). The calculated ²⁹Si, ¹⁷O and ¹H isotropic chemical shifts (δ_i ^Si, δ_i ^O and δ_i ^H) for these clusters are all close to experimental NMR data for similar local structures in crystalline silicates. The calculated ¹⁷O quadrupolar coupling constants (QCC) of the bridging oxygens (Si-O-Si) are also in good agreement with experimental data. The calculated ¹⁷O QCC of silanols (Si-O-H) are much larger than those of the bridging oxygens, but unfortunately there are no experimental data for similar groups in well-characterized crystalline phases for comparison. There is a good correlation between δ_i ^Si and the mean Si-O-Si angle for both Q ¹ and Q ², where Q ⁿ denotes Si with n other tetrahedral Si next-nearest neighbors. Both the δ _i ^O and the ¹⁷O electric field gradient asymmetry parameter, η of the bridging oxygens have been found to depend strongly on the O site symmetry, in addition to the Si-O-Si angle. On the other hand, the ¹⁷O QCC seems to be influenced little by structural parameters other than the Si-O-Si angle, and is thus expected to be the most reliable ¹⁷O NMR parameter that can be used to decipher Si-O-Si angle distribution information. Both the ¹⁷O QCC and the ²H QCC of silanols decrease with decreasing length of hydrogen bond to a second O atom (Si-O-H···O), and the δ _i ^H increase with the same parameter. Received: 18 July 1997 / Revised, accepted: 23 February 1998     

Prediction of CH4 and CO2 hydrate phase equilibrium and cage occupancy from ab initio intermolecular potentials

Presented is an improved model for the prediction of phase equilibria and cage occupancy of CH₄ and CO₂ hydrate in aqueous systems. Different from most hydrate models that employ Kihara potential or Lennard-Jones potential with parameters derived from experimental phase equilibrium data of hydrates, we use atomic site-site potentials to account for the angle-dependent molecular interactions with parameters directly from ab initio calculation results. Because of this treatment, our model can predict the phase equilibria of CH₄ hydrate and CO₂ hydrate in binary systems over a wide temperature-pressure range (from 243-318 K, and from 10-3000 bar for CH₄ hydrate; from 253-293 K, and from 5-2000 bar for CO₂ hydrate) with accuracy close to experiment. The average deviation of this model from experimental data is less than 3% in pressures for a given temperature. This accuracy is similar to previous models for pressures below 500 bar, but is more accurate than previous models at higher pressures. This model is also capable of predicting the cage occupancy and hydration number for CH₄ hydrate and CO₂ hydrate without fitting any experimental data. The success of this study validates the predictability of ab initio intermolecular potentials for thermodynamic properties.