Ab initio valence force field calculations for quartz

We have derived valence force constants for the tetrahedral SiO₄ unit and the inter-tetrahedral SiOSi linkage from previous ab initio molecular orbital calculations on H₄SiO₄ and H₆Si₂O₇ using a split-valence polarized Gaussian basis set (6-31G^*), and used these to calculate the infrared and Raman active vibrational modes of α-quartz. The calculation gives frequencies approximately 15% greater than experiment, as expected from harmonic force constants obtained at this level of Hartree-Fock theory, but the calculation gives the correct distribution of modes within each frequency range. Calculated 28–30 Si and 16–18 O isotope shifts and pressure shifts to 6 GPa are also in reasonable agreement with experiment. We have also used our ab initio force field to calculate the vibrational spectrum for β-quartz. The results suggest either that inclusion of a torsional force constant is important for determining the stability of this high temperature polymorph, or that the β-quartz has a disordered structure with lower symmetry (P6₂) domains, as suggested by earlier diffraction studies.     

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.     

硼酸盐矿物中硼氧原子簇的分子轨道理论计算：6—31G＊的结果

本文利用6-31G*基组的分子轨道理论从头计算法对[BO_3],[BO_4],[OB_2]等三个硼氧多面体进行平衡几何构型和振动光谱频率的计算,并与早先的6-31G结果进行了比较,说明在分子轨道理论从头计算法中扩大使用的基组对计算结果的改进有着明显的作用。     

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.     

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).     

Molecular modeling of Al and benzene interactions with Suwannee fulvic acid

The effects that Al³⁺ and benzene interactions exhibit on a model fulvic acid were investigated. Energy minimizations of the structures mimicking the interactions of Al³⁺-Suwannee fulvic acid (SFA), benzene-SFA and Al³⁺-benzene-SFA were run with a solvation sphere of 60 H₂O molecules with the semi-empirical methods PM3 and PM5. The semi-empirical method PM3 was run with Gaussian 98 and CAChe Workstation Pro 6.1.1 to compare the results of the energy minimization algorithms in the two programs. PM5 calculations were run with CAChe Workstation Pro 6.1.1. Molecular dynamics (MD) simulations were run in Cerius² (Accelrys Inc., San Diego, CA) using the Universal Force Field (UFF) 1.02 [Rappé A. K., Casewit C., Colwell K., Goddard W., and Skiff W. (1992) UFF, a full periodic-table force-field for molecular mechanics and molecular dynamics simulations. J. Am. Chem. Soc.114(25), 10024-10035] and COMPASS force field [Sun H. (1998) COMPASS: an ab initio force-field optimized for condensed-phase applications—overview with details on alkane and benzene compounds. J. Phys. Chem. B102, 7338-7364]. Single point calculations were run on the minimized structures at the B3LYP/6-31G(d) level to obtain more accurate estimates of the energy on the minimized structures derived from the PM3, PM5, and UFF methods and to normalize energies to the same reference state. This methodology was used as the standard of comparison for all the models to assess whether or not a given configuration was reasonably stable.The PM3/G03 energy minimizations predicted the lowest B3LYP/6-31G(d) potential energies of the methodologies examined in this study. Thus, this method is considered the most reliable of those tested. The PM3/G03 method predicted that there would be aromatic-aromatic interactions between benzene and SFA. The presence of Al³⁺ was predicted not to interfere with aromatic-aromatic interactions between benzene and SFA, but benzene may influence the location of metal complexation to SFA.     

A theoretical study of bond distances,X-ray spectra and electron density distributions in borate polyhedra

The borate polyhedra BO ₃ ^3? , B(OH)₃, BO ₄ ^5? , and B(OH) ₄ ^? are studied using the ab initio and multiple scattering Xα quantum mechanical methods. The ab initio self-consistent-field (SCF) molecular orbital (MO) method, at the minimum basis set level, predicts equilibrium B-O distances within 0.04 Å of their average values in solids so long as the polyhedron charge is small. Orbital energies from double zeta basis set ab initio calculations and analogies with isoelectric compounds are used to assign the X-ray spectra of BO ₃ ^3? and to predict the valence region spectra of BO ₄ ^5? . Contour maps of the difference between molecular and superimposed free atom electron densities show charge buildup along the B-O bond which is only slightly smaller than that observed in CO ₃ ^2? .     

Calculation of Si NMR shifts of silicate complexes with carbohydrates, amino acids, and muhicarboxylic acids: potential role in biological silica utilization

The existence of ether or ester-like complexes of silicate with organic compounds has long been debated in the literature on biological utilization of silicon. Comparison of theoretically calculated ²⁹Si NMR chemical shifts for such complexes with experimentally measured values in biological systems could provide a diagnostic tool for identifying which, if any of these molecules exist under physiological conditions. Results are presented here for ab initio molecular orbital calculations of ²⁹Si NMR shifts and formation energies of silicate complexes with polyalcohols, sugar-acids, pyranose sugars, amino acids and multicarboxylic acids. The effects of functional group and molecular structure including ligand size, denticity, ring size, silicon polymerization and coordination number on calculated ²⁹Si shifts were considered. The potential role of such compounds in biological silica utilization pathways is discussed.²⁹Si NMR shifts and energies were calculated at the HF/6-311+G(2d,p)//HF/6-31G* level. The main result is that only five-membered rings containing penta- and hexa-coordinated Si can explain experimentally observed resonances at ∼ −101 and −141 ppm. Further, the heptet observed in ¹H-²⁹Si coupled spectra can only be explained by structures where Si bonds to oxygens atoms in H-C-O-Si linkages with six symmetrically equivalent H atoms.While compounds containing quadra-coordinated silicon may exist in intracellular silicon storage pools within diatoms, calculated reaction energies suggest that the organism has no thermodynamic advantage in taking up extracellular organ-silicate compounds, instead of silicic acid, from the ambient aqueous environment. Hyper-coordinated complexes are deemed unlikely for transport and storage, though they may exist as transient reactive intermediates or activated complexes during enzymatically- catalyzed silica polymerization, as known previously from sol-gel silica synthesis studies.     

Experimental and theoretical vibrational spectroscopy studies of acetohydroxamic acid and desferrioxamine B in aqueous solution: Effects of pH and iron complexation

The deprotonation and iron complexation of the hydroxamate siderophore, desferrioxamine B (desB), and a model hydroxamate ligand, acetohydroxamic acid (aHa), were studied using infrared, resonance Raman and UV-vis spectroscopy. The experimental spectra were interpreted by a comparison with DFT calculated spectra of aHa (partly hydrated) and desB (reactive groups of unhydrated molecule) at the B3LYP/6-31G* level of theory. The ab initio models include three water molecules surrounding the deprotonation site of aHa to account for partial hydration. Experiments and calculations were also conducted in D₂O to verify spectral assignments. These studies of aHa suggest that the cis-keto-aHa is the dominant form, and its deprotonation occurs at the oxime oxygen atom in aqueous solutions. The stable form of iron-complexed aHa is identified as Fe(aHa)₃ for a wide range of pH conditions. The spectral information of aHa and an ab initio model of desB were used to interpret the chemical state of different functional groups in desB. Vibrational spectra of desB indicate that the oxime and amide carbonyl groups can be identified unambiguously. Vibrational spectral analysis of the oxime carbonyl after deprotonation and iron complexation of desB indicates that the conformational changes between anion and the iron-complexed anion are small. Enhanced electron delocalization in the oxime group of Fe-desB when compared to that of Fe(aHa)₃ may be responsible for higher stability constant of the former.     

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.     

Molecular orbital calculations of vibrations in three-membered aluminosilicate rings

Ab initio, molecular orbital calculations at the 3–21G^* level were carried out on H₆Si₃O₉, [H₆Si₂AlO₂]^1?, [H₆SiAl₂O₉]^2?, and [H₆A1₃O₉]^3? cyclic molecules in order to determine their structures and vibrational frequencies. These three-membered rings were found to have minima in their potential energy surfaces indicating stability of the species. The H₆Si₃O₉ ring was found to be slightly non-planar, but the [H₆SiAl₂O₉]^2? and [H₆Al₃3O₉]^3? configurations are more planar. Vibrational frequencies of the Raman-active, bridging oxygen “breathing” modes increase with Si⁴⁺ content. Galeener's (1982a, b) assignment of the D₂ peak (606 cm^?1) in the Raman spectrum of vitreous silica to an oxygen breathing mode in rings of three SiO₄ tetrahedra is reconfirmed. Correlation of the ring breathing mode frequencies as a function of (AI/AI + Si) with Raman peaks in the SiO₂-NaAlSiO₄ system is high. Three-membered aluminosilicate rings are likely to exist and give rise to Raman peaks between 540 and 600 cm_?1 in fully-polymerized aluminosilicate glasses.     

Molecular orbital models of aqueous aluminum-acetate complexes

Molecular orbital calculations with HF/3-21G^∗∗, HF/6-311+G^∗∗, and MP2/6-311+G^∗∗ basis sets (HF = Hartree-Fock approximation; MP2 = 2nd-order Møller-Plesset perturbation theory) have been performed on molecular clusters in the system acetate-aluminum-water. The results model the structures, energetics, and vibrational spectra of Al³⁺ and Al³⁺-acetate complexes in the aqueous phase. An octahedral to tetrahedral coordination change is predicted in the species Al³⁺ (OH)_m⁻ · n (H₂O) [where m + n = 6) as m increases from two to three. Calculated reaction energetics for aqueous Al³⁺-acetate complexation compare favorably with experimental enthalpies. In addition, the possible existence of more than one configuration for each Al` -acetate species was investigated. Theoretical vibrational spectra of the Al³⁺-acetate complexes provide predictions for the identification of Al³⁺-acetate species in aqueous solutions.     

Ab initio crystal structure and elasticity of tuite, γ-Ca<Subscript>3</Subscript>(PO<Subscript>4</Subscript>)<Subscript>2</Subscript>, with implications for trace element partitioning in the lower mantle

Tuite forms by the breakdown of apatite at high pressure and is thus expected to play a role in extending the phosphorus cycle beyond the stability field of apatite and into the lower mantle. With its large, high-coordination cation sites, tuite is thought to be able to dissolve large quantities of incompatible elements such as rare earth elements, Sr, Th, and U, and is potentially an important mantle reservoir for these elements. In this paper, ab initio calculations of the structure and elasticity of tuite to lower mantle pressure are presented and used to probe trace element incorporation. The calculated zero-pressure volumes of the M1 and M2 cation sites were 50.23 and 36.61 Å³, while the corresponding bulk moduli K ₀ are 116.1 and 94.2 GPa, significantly lower than the 234.1 GPa calculated for the M site of CaSiO₃ perovskite (cpv), another likely host for incompatible elements in the mantle. The partitioning of impurities between tuite and cpv is investigated using a lattice strain model, parameterized by the ab initio calculations, to calculate isovalent substitution energies across a range of pressures and impurity sizes. Additionally, energies of strontium and barium defects in tuite are compared with those of equivalent defects in cpv, and it is found that both elements will partition strongly from cpv into tuite.     

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     

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 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.     

Kinetics and Mechanism of Trithionate and Tetrathionate Oxidation at Low pH by Hydroxyl Radicals

The oxidation kinetics of trithionate (S₃O₆^2- ) and tetrathionate (S₄O ₆ ^2- ) with hydroxyl radicals (OH^*) have been investigated in systems analogous to acid mine drainage (AMD) environments. The discovery of hydroxyl radical (OH^*) formation on pyrite surfaces (Borda et al., 2003) suggests hydroxyl radicals may affect the oxidation kinetics of intermediate sulfur species such as tetrathionate. Cyclic voltammetry experiments in acidic solutions indicate that the reaction of S₄O ₆ ^2- with OH^* goes through an unknown intermediate, tentatively assigned as S₃O ₄ ^n- . An outer-sphere electron transfer mechanism for the reaction of S₄O ₆ ^2- with OH^* to form S₃O ₄ ^n- is proposed based on experimental results. Oxidation rates for trithionate and tetrathionate in the presence of Fenton's reagent (which forms hydroxyl radicals) are too fast to be directly measured using UV-Vis spectrophotometry, electrochemical, or stop-flow spectrophotometry methods. Competitive reaction kinetics within the context of the Haber—Weiss mechanism suggests that the rate constant for the oxidation of trithionate and tetrathionate with OH^* is in excess of 10⁸ M^-1 sec^-1.     

The oxidation states of copper and iron in mineral sulfides, and the oxides formed on initial exposure of chalcopyrite and bornite to air

Metal L_2,3, sulfur K and oxygen K near-edge X-ray absorption fine structure (NEXAFS) spectra for chalcopyrite, bornite, chalcocite, covellite, pyrrhotite and pyrite have been determined from single-piece natural mineral specimens in order to assess claims that chalcopyrite should be regarded as Cu^IIFe^IIS₂ rather than Cu^IFe^IIIS₂, and that copper oxide species are the principal initial oxidation products on chalcopyrite and bornite exposed to air. Spectra were obtained using both fluorescence and electron yields to obtain information representative of the bulk as well as the surface. Where appropriate, NEXAFS spectra have been interpreted by comparison with the densities of unfilled states and simulated spectra derived from ab initio calculations using primarily the FEFF8 code and to a lesser extent WIEN2k. Metal 2p and S 2p photoelectron spectra excited by monochromatised Al K_α X-rays were determined for each of the surfaces characterised by NEXAFS spectroscopy. The X-ray excited Cu LMM Auger spectrum was also determined for each copper-containing sulfide. FEFF8 calculations were able to simulate the experimental NEXAFS spectra quite well in most cases. For covellite and chalcocite, it was found that FEFF8 did not provide a good simulation of the Cu L₃-edge spectra, but WIEN2k simulations were in close agreement with the experimental spectra. Largely on the basis of these simulations, it was concluded that there was no convincing evidence for chalcopyrite to be represented as Cu^IIFe^IIS₂, and no strong argument for some of the Cu in either bornite or covellite to be regarded as Cu(II). The ab initio calculations for chalcopyrite and bornite indicated that the density of Cu d-states immediately above the Fermi level was sufficient to account for the Cu L₃-edge absorption spectrum, however these incompletely filled Cu d-states should not be interpreted as indicating some Cu(II) in the sulfide structure. It was also concluded that the X-ray absorption spectra were quite consistent with the initial oxidation products on chalcopyrite and bornite surfaces being iron oxide species, and inconsistent with the concomitant formation of copper-oxygen species.     

再论花岗岩按照Sr-Yb的分类:标志

2006年作者曾经按照Sr=400×10~(-6)和Yb=2×10~(-6)作为标志将花岗岩分为埃达克岩、喜马拉雅型花岗岩、浙闽型花岗岩和广西型花岗岩,在浙闽型中又分出南岭型(Sr100×10~(-6)和Yb2×10~(-6)),于是花岗岩被分为5类。Sr=400×10~(-6)和Yb=2×10~(-6)是根据阿留申群岛中的Adak岛的资料得出来的。本文统计了全球花岗岩6000多个数据(其中,埃达克型花岗岩为2810个,喜马拉雅型花岗岩636个,浙闽型花岗岩1183个,南岭型花岗岩1518个,广西型花岗岩142个,总共6289个),统计的结果,各类花岗岩的地球化学特征大致如下:(1)埃达克型花岗岩富Al_2O_3和Sr,贫Y和Yb,具较高和变化的铕异常,绝大多数样品的Sr300×10~(-6),Yb2.5×10~(-6)(当Sr=400×10~(-6)～600×10~(-6)时Yb值最大,Sr超过600×10~(-6),Yb降低至2×10~(-6)),Al_2O_3在14%～18%之间,Eu/Eu~*大多在0.6～1.2范围;(2)喜马拉雅型花岗岩贫Sr和Yb,具中等的Al_2O_3和变化的Eu/Eu~*,Sr300×10~(-6)和Yb2×10~(-6)(少数Sr300×10~(-6)),Al_2O_3为13%～17%,Eu/Eu~*为0.2～1.0;(3)浙闽型花岗岩贫Sr富Yb,Sr在40×10~(-6)～400×10~(-6)之间,Yb1.5×10~(-6),Al_2O_3和Eu/Eu~*的变化类似喜马拉雅型花岗岩,Al_2O_3为12%～17%,Eu/Eu~*为0.4～1.0;(4)南岭型花岗岩以很低的Sr、Al_2O_3和Eu/Eu~*以及很高的Yb而不同于上述各类花岗岩,通常Yb1.5×10~(-6),Sr100×10~(-6)(Yb变化大,绝大多数2×10~(-6);当Yb在2×10~(-6)～8×10~(-6)时,部分样品Sr可100×10~(-6),但很少200×10~(-6));Al_2O_314%,集中在11%～13%之间,Eu/Eu~*0.7,大多0.4;Yb越大,Sr越低,负铕异常越明显。文中讨论了花岗岩Sr-Yb分类的意义,指出本分类适用于产于大陆和海洋的绝大多数中酸性岩浆岩(可能不适用于一部分特别富铁和钾的花岗岩,如具有高Sr和Yb特征的广西型花岗岩)。不同类型的花岗岩主要反映了源区压力的不同,而源区成分、温度、部分熔融程度、水和挥发分的加入以及岩浆混合等的影响可能是次要的。文中指出,该分类的依据、其实质,是熔体与残留相平衡的理论。与浙闽型花岗岩平衡的残留相是斜长石,与喜马拉雅型花岗岩平衡的是斜长石+石榴石,与埃达克型花岗岩平衡的是石榴石,与南岭型花岗岩平衡的是富钙的斜长石。文中指出,加强实验岩石学研究,将年代学和地球化学研究密切结合起来是深化花岗岩研究的关键。     

Theoretical reaction pathways for the formation of [Si(OH)5]1− and the deprotonation of orthosilicic acid in basic solution

Ab initio, molecular orbital calculations at the 6-31G¹ level including second-order Møller-Plesset electron correlation predict that the species [Si(OH)₅]¹⁻ is dynamically stable in a distorted trigonal bipyramid configuration. Reaction pathways for Si(OH)₄ + (OH)⁻ → [Si(OH)₅]¹⁻ → [(OH)₃SiO]¹⁻—H₂O are also calculated. The first reaction represents the formation of pentacoordinate Si from orthosilicic acid and hydroxide. The activation energy for adding a fifth Si-(OH)⁻ bond to the Si(OH)₄ molecule is ≈0.1 eV /molec (≈10kJ/mol). The second reaction is the deprotonation of the Si(OH)₄ which forms as a hydroxyl group leaves the [Si(OH)₅]¹⁻ molecule. Removal of a bond from this complex requires 0.9 eV/molecule (≈85 kJ/mol). Lengthening the Si—OH₂ distance results in the isolated molecules [(OH)₃SiO]¹⁻ + H₂O. This represents dehydration of the deprotonated orthosilicic acid.[Si(OH)₅]¹⁻ and [(OH)₃SiO]¹⁻- H₂O have the same energetic stability within the accuracy of these calculations. The potential energies of the isolated molecular systems [(OH)₃SiO]¹⁻+ H₂O and Si(OH)₄ + (OH)⁻ are considerably higher. These results suggest that [Si(OH)₅]¹⁻ may be a stable species or reaction intermediate in dissolution of silicate minerals in basic aqueous solutions.