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1.
Minimum energy geometries and electron density distributions, ϱ(r), for ∼40 polyatomic oxide molecules containing first and second row M-cations have been calculated at the Hartree-Fock level with a 6-311++G** basis set. The nature of the bonded interactions
in these molecules is examined in terms of the relative electronegativities, χ
M
, of the M-cations and the properties of the electron density distribution, ϱ(r
c
), evaluated at the bond critical points, r
c
, along each MO bond. As ϱ(r
c
) and the Laplacian of ϱ(r
c
) increase, χ
M
increases indicating an increase in the covalent character of the bonded interactions between M and O. The ratios of the curvatures of ϱ(r
c
) indicate that the NO bond is predominantly covalent, that the CO and SO bonds are of intermediate type and that the remaining
MO bonds are indicated to be predominantly ionic in character. A comparison of the critical point properties of ϱ(r
c
) and χ
M
indicates that the minimum energy MO bond length is an important determinate of the properties of ϱ(r
c
) and the character of the MO bonds.
On the other hand, values of the local energy density, H(r
c
), indicate that the LiO, BeO, NaO, MgO and AlO bonds are predominantly ionic and that the BO, CO, NO, SiO, PO and SO bonds
are predominantly covalent in character. The χ
M
-values provided by the properties of ϱ(r
c
) indicate that the covalent component of a bond increases with decreasing bond length, coordination number and increasing
bond strength. Each MO bond seems to represent a unique entity and to possess a distinct set of ϱ(r
c
) properties, the distinction being greater for the more electronegative cations.
The bonded radius of the oxide ion, r
b
(O), and the χ
M
-values determined from ϱ(r
c
) correlate with values determined from promolecule electron density distributions. In addition, r
b
(O) and χ
M
-values determined from experimental electron density distributions for crystals correlate with values determined from procrystal
electron density distributions. The number of critical points and bond paths are modeled rather faithfully by procrystal and
promolecule electron density distributions, despite the neglect of the binding forces in their constructions.
Received: October 15, 1996/Revised, accepted: February 10, 1997 相似文献
2.
S. Feth G. V. Gibbs M. B. Boisen Jr. F. C. Hill 《Physics and Chemistry of Minerals》1998,25(3):234-241
Bond critical point properties calculated for the MN bonds in a number of geometry optimized nitride molecules containing first- and second-row M cations are compared with those calculated for a number of oxide molecules. As reported for the oxides, the value of the
electron density, ρ(r
c
), at the bond critical points, r
c
, increases with decreasing bond length while for the more electronegative cations, the local energy density, H(r
c
) decreases nonlinearly in value as the relative electronegativities of the M-cations, χ
M
, tend to increase. In the majority of cases, χM, |λ1|/λ3 and ∇2ρ(r
c
) increase with decreasing minimum energy bond lengths. The bond lengths adopted by the molecules are indicated to be an important
determinant of the critical point properties of the electron density distributions. The relative electronegativities derived
from the electron density distributions of the nitrides agree with those derived for the oxides and Pauling’s electronegativities
to within ∼5%, on average.
Received: 3 February 1997 / Revised, accepted: 11 July 1997 相似文献
3.
For the fibrous zeolites natrolite, Na2[Al2Si3O10]·2H2O, mesolite, Na2Ca2[Al2Si3O10]3·8H2O, and scolecite, Ca[Al2Si3O10]·3H2O, with topologically identical aluminosilicate framework structures, accurate single-crystal X-ray diffraction data have
been analyzed by least-squares refinements using generalized scattering factor (GSF) models. The final agreement indices were
R(F ) = 0.0061, 0.0165, and 0.0073, respectively. Ensuing calculations of static deformation [Δρ(r)], and total, [ρ(r)], model electron density distributions served to study chemical bonding, in particular by topological electron density analyses
yielding bond critical point (bcp) properties and in situ cation electronegativities. The results for 32 SiO, 24 AlO, 14 CaO,
and 12 NaO unique bonds are compiled and analyzed in terms of both mean values and correlations between bond lengths, bonded
oxygen radii, bcp densities, curvatures at the bcps, and electronegativities. Comparison with recent literature data obtained
from both experimental electron density studies on minerals and model calculations for geometry-optimized molecules shows
that the majority of the present findings conforms well with chemical expectation and with the trends observed from molecular
modeling. For the SiO bond, the shared interaction is indicated to increase with decreasing bond length, whereas the AlO bond
is of distinctly more polar nature, as is the NaO bond compared to CaO. Also, the observed ranges of the Si and Al in situ
electronegativities and their mean electronegativities agree well with both Pauling's values and model calculation results,
and statistically significant correlations are obtained which are consistent with trends described for oxide and nitride molecules.
Received: 10 May 1999 / Revised, accepted: 14 September 1999 相似文献
4.
The maximum entropy method (MEM) is used here to get an insight into the electron density [ρ(r)] of phengites 2M
1 and 3T, paying special attention to the M1-formally empty site and charge distribution. Room temperature single crystal X-ray diffraction
data have been used as experimental input for MEM. The results obtained by MEM have been compared with those from conventional
structure refinement which, in turn, has provided the prior-electron density to start the entropy maximization process. MEM
reveals a comparatively non-committal approach, able to produce information related to the M1-site fractional occupancy, and
yields results consistent with those from the difference Fourier synthesis, but free of the uncertainties due to the abrupt
truncation of the series. The charge distribution is investigated by means of the notion of ‘‘site basin’’, i.e., those site-centered
volumes delimited by a surface such as ∇ρ·n = 0. In particular, we observe: (1) the overall partitioning of the basin total charge between cation and anion sites, and
the interlayer site charge seems to depend on sample composition, and (2) the apical-oxygen plane total basin charge and hydroxyl
basin charge are presumably related to the polytype. The MEM-determined electron density does not allow full exploration of
the critical points for very complex structures as micas, insofar as conventional room temperature experimental diffraction
data are used. 相似文献
5.
R. T. Downs G. V. Gibbs M. B. Boisen Jr K. M. Rosso 《Physics and Chemistry of Minerals》2002,29(5):369-385
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 相似文献
6.
G. V. Gibbs F. C. Hill M. B. Boisen R. T. Downs 《Physics and Chemistry of Minerals》1998,25(8):585-590
The strength of a bond, defined as p=s/r, where s is the Pauling bond strength and r is the row number of an M cation bonded to an oxide anion, is related to a build-up of electron density along the MO bonds in a relatively large number of oxide and hydroxyacid molecules, three oxide minerals and three molecular crystals.
As p increases, the value of the electron density is observed to increase at the bond critical points with the lengths of the
bonds shortening and the electronegativities of the M cations bonded to the oxide anion increasing. The assertion that the covalency of a bond is intrinsically connected to its
bond strength is supported by the electron density distribution and its bond critical point properties. A connection also
exists between the properties of the electron density distributions and the connectivity of the bond strength network formed
by the bonded atoms of a structure.
Received: 20 August 1997 / Revised, accepted: 3 November 1997 相似文献
7.
R. Bianchi A. Forni F. Cámara R. Oberti H. Ohashi 《Physics and Chemistry of Minerals》2007,34(8):519-527
The synthetic LiGaSi2O6 clinopyroxene is monoclinic C2/c at room-T. Its experimental electron density, ρ(r), has been derived starting from accurate room-T single-crystal diffraction data. Topological analysis confirms an intermediate ionic-covalent character for Si–O bonding,
as found by previous electron-density studies on other silicates such as diopside, coesite and stishovite. The non-bridging
Si–O bonds have more covalent character than the bridging ones. The Ga–O bonds have different bonding characters, the Ga–O2
bond being more covalent than the two Ga–O1 bonds. Li–O bonds are classified as pure closed-shell ionic interactions. Similar
to spodumene (LiAlSi2O6), Li has sixfold coordination, but the bond critical points associated to the two longest bonds are characterized by very
low electron density values. Similar to what previously found in spodumene and diopside, O···O interactions were detected
from the topological analysis of ρ(r), and indicate a cooperative interaction among the lone pairs of neighbouring oxygen atoms. In particular, this kind of interaction
has been obtained for the O1···O1 edge shared between two Ga octahedra. Integration over the atomic basins gives net charges
of −1.39(10), 2.82(10), 1.91(10) and 0.82(8) e for O (averaged), Si, Ga and Li atoms, respectively. Periodic Hartree–Fock
and DFT calculations confirm the results obtained by multipole refinement of the experimental data. Moreover, the theoretical
topological properties of the electron density distribution on the Si2O6 group are very similar to those calculated for spodumene.
Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. 相似文献
8.
G. V. Gibbs N. L. Ross D. F. Cox K. M. Rosso B. B. Iversen M. A. Spackman 《Physics and Chemistry of Minerals》2014,41(1):17-25
The power law regression equation, <R(M–O)> = 1.46(<ρ(r c)>/r)?0.19, relating the average experimental bond lengths, <R(M–O)>, to the average accumulation of the electron density at the bond critical point, <ρ(r c)>, between bonded pairs of metal and oxygen atoms (r is the row number of the M atom), determined at ambient conditions for oxide crystals, is similar to the regression equation R(M–O) = 1.41(ρ(r c)/r)?0.21 determined for three perovskite crystals at pressures as high as 80 GPa. The pair are also comparable with the equation <R(M–O)> = 1.43(<s>/r)?0.21 determined for oxide crystals at ambient conditions and <R(M–O)> = 1.39(<s>/r)?0.22 determined for geometry-optimized hydroxyacid molecules that relate the geometry-optimized bond lengths to the average Pauling bond strength, <s>, for the M–O bonded interactions. On the basis of the correspondence between the equations relating <ρ(r c)> and <s> with bond length, it seems plausible that the Pauling bond strength might serve a rough estimate of the accumulation of the electron density between M–O bonded pairs of atoms. Similar expressions, relating bond length and bond strength hold for fluoride, nitride and sulfide molecules and crystals. The similarity of the expressions for the crystals and molecules is compelling evidence that molecular and crystalline M–O bonded interactions are intrinsically related. The value of <ρ(r c)> = r[(1.41)/<R(M–O)>]4.76 determined for the average bond length for a given coordination polyhedron closely matches the Pauling’s electrostatic bond strength reaching each the coordinating anions of the coordinated polyhedron. Despite the relative simplicity of the expression, it appears to be more general in its application in that it holds for the bulk of the M–O bonded pairs of atoms of the periodic table. 相似文献
9.
The experimental multipole electron density, ρ(r), of diopside was derived from high-resolution single-crystal diffraction at room temperature. Its topological analysis revealed
predominantly ionic Si–O bonding, as found in electron density studies of other silicates. In particular, the non-bridging
Si–O bonds are slightly less ionic in character than the bridging Si–O bonds. The Ca–O and Mg–O bonds are classified as pure
closed-shell ionic interactions. An analysis of –∇2ρ(r) showed the presence of maxima around the oxygen atoms, associated to lone pairs domains that are involved in bonds with
the surrounding ions. Calculation of atomic basins gave net charges of –1.56(12), 3.11(17), 1.79(13) and 1.88(18) e for O
(averaged), Si, Ca and Mg atoms, respectively. O···O interactions between the O atoms at the vertices of the SiO4 tetrahedron were also detected from the topological analysis of ρ(r), and indicate a cooperative interaction among the lone pairs of neighbouring oxygen atoms. All these results were also confirmed
by periodic restricted Hartree–Fock (RHF) calculations.
Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users. 相似文献
10.
Bond critical point properties of electron density distributions calculated for representative Si5O16 moieties of the structure of coesite are compared with those observed and calculated for the bulk crystal. The values calculated
for the moieties agree with those observed to within ∼5%, on average, whereas those calculated for the crystal agree to within
∼10%. As the SiOSi angles increase and the SiO bonds shorten, there is a progressive build-up in the calculated electron density
along the bonds. This is accompanied by an increase in both the curvatures of the electron density, both perpendicular and
parallel to each bond, and the Laplacian of the electron density distribution at the bond critical points. The cross sections
of the bonds at the critical points become more circular as the angle approaches 180o. Also, the bonded radius of the oxide
anion decreases about twice as much as that of the Si cation as the SiO bond length decreases and the fraction of s-character of the bond is indicated to increase. A knowledge of electron density distributions is central to our understanding
of the forces that govern the structure, properties, solid state reactions, surface reactions and phase transformations of
minerals. The software (CRYSTAL95 and TOPOND) used in this study to calculate the bond critical properties of the electron
density and Laplacian distributions is bound to promote a deeper understanding of crystal chemistry and properties.
Received: 23 February 1998 / Revised, accepted: 16 July 1998 相似文献
11.
G. V. Gibbs A. F. Wallace R. T. Downs N. L. Ross D. F. Cox K. M. Rosso 《Physics and Chemistry of Minerals》2011,38(4):267-291
Electron density distributions, bond paths, Laplacian and local-energy density properties have been calculated for a number
of As4S
n
(n = 3, 4 and 5) thioarsenide molecular crystals. On the basis of the distributions, the intramolecular As–S and As–As interactions
classify as shared bonded interactions, and the intermolecular As–S, As–As and S–S interactions classify as closed-shell van
der Waals (vdW) bonded interactions. The bulk of the intermolecular As–S bond paths link regions of locally concentrated electron
density (Lewis-base regions) with aligned regions of locally depleted electron density (Lewis-acid regions) on adjacent molecules.
The paths are comparable with intermolecular paths reported for several other molecular crystals that link aligned Lewis base
and acid regions in a key–lock fashion, interactions that classified as long-range Lewis acid–base-directed vdW interactions.
As the bulk of the intermolecular As–S bond paths (~70%) link Lewis acid–base regions on adjacent molecules, it appears that
molecules adopt an arrangement that maximizes the number of As–S Lewis acid–base intermolecular bonded interactions. The maximization
of the number of Lewis acid–base interactions appears to be connected with the close-packed array adopted by molecules: distorted
cubic close-packed arrays are adopted for alacránite, pararealgar, uzonite, realgar and β-AsS and the distorted hexagonal
close-packed arrays adopted by α- and β-dimorphite. A growth mechanism is proposed for thioarsenide molecular crystals from
aqueous species that maximizes the number of long-range Lewis acid–base vdW As–S bonded interactions with the resulting directed
bond paths structuralizing the molecules as a molecular crystal. 相似文献
12.
Jason B. Burt Nancy L. Ross G. V. Gibbs George R. Rossman Kevin M. Rosso 《Physics and Chemistry of Minerals》2007,34(5):295-306
Potential protonation sites for, kyanite, sillimanite, and andalusite, located in a mapping of the (3, −3) critical points
displayed by their L(r) = −∇2ρ(r) distributions, are compared with polarized single-crystal FTIR spectra of kyanite and sillimanite determined earlier and
with andalusite measured in this study. For andalusite, seven peaks were observed when the electric vector, E, is parallel to [100]: four intense ones at 3,440, 3,460, 3,526, and 3,597 cm−1 and three weaker ones at 3,480, 3,520, and 3,653 cm−1. Six peaks, three intense ones at 3,440, 3,460, and 3,526 cm−1 and three weaker ones at 3,480, 3,520, and 3,653 cm−1 when E parallels [010]. No peaks were observed when E is parallel to [001]. The concentration of water in andalusite varies between 110 and 168 ppm by weight % H2O. Polarized FTIR spectra indicate that the OH vector is parallel to (001) in andalusite and sillimanite and
in kyanite. Examination of the L(r) (3, −3) critical points in comparison with the polarized FTIR indicates that H prefers to bond to the oxygen atoms O1 and
O2 in andalusite and O2 and O4 in sillimanite which correspond to the underbonded oxygen atoms and those with the largest
L(r) maxima. In kyanite, comparison of the FTIR spectrum and the critical points indicates that H will preferentially bond to
the two 4-coordinated O2 and O6 atoms. 相似文献
13.
Planewave pseudopotential calculations of supercell total energies were used as bases for first-principles calculations of
the CaCO3–MgCO3 and CdCO3–MgCO3 phase diagrams. Calculated phase diagrams are in qualitative to semiquantitative agreement with experiment. Two unobserved
phases, Cd3Mg (CO3)4 and CdMg3(CO3)4, are predicted. No new phases are predicted in the CaCO3–MgCO3 system, but a low-lying metastable Ca3Mg(CO3)4 state, analogous to the Cd3Mg(CO3)4 phase is predicted. All of the predicted lowest-lying metastable states, except for huntite CaMg3(CO3)4, have dolomite-related structures, i.e. they are layer structures in which A
m
B
n
cation layers lie perpendicular to the rhombohedral [111] vector.
Received: 6 May 2002 / Accepted: 23 October 2002
Acknowledgements This work was partially supported by NSF contract DMR-0080766 and NIST. 相似文献
14.
An analysis of SOHO/LASCO C3 data shows that there are discontinuities in the radial profiles of the plasma density within limited regions in front of
each of ten coronal mass ejections, which represent shocks. The shock velocities in various events reach V ≈ 800–2500 km/s. A comparison of the dependence of the AlfvenicMach numberM
A
on the shock strength ρ
2/ρ
1 detected at distancesR > 10R⊙ from the center of the Sun with calculations carried out using ideal magnetic hydrodynamics shows that the effective ratio
of specific heats γ describing processes inside the shock front varies from 2 to 5/3 (ρ
1 and ρ
2 are the densities in front of and behind the shock, and R⊙ is the solar radius). This corresponds to an effective number of degrees of freedom between two and three. A similar dependenceMA(ρ
2
/ρ
1) was found for near-Earth bow shocks and interplanetary collisionless shocks. These features support the hypothesis that
the studied discontinuities preceding coronal mass ejections are collisionless shocks. 相似文献
15.
H. Graetsch 《Physics and Chemistry of Minerals》2001,28(5):313-321
The crystal structure of intermediate incommensurate tridymite was refined at 150 °C from powder data. Upon cooling from
above 220 °C, the basic structure with space group symmetry C2221 is gradually distorted from orthorhombic to monoclinic symmetry. With decreasing temperature, the monoclinic angle γ smoothly
opens up to 90.3°, while a displacive modulation with temperature-dependent wavelength develops. The 3 + 1 dimensional superspace
group of the incommensurate phase is C1121(αβ0). The modulation mainly consists of two sinusoidal transverse displacement waves for the silicon atoms coupled to rotations
of the rigid SiO4/2 tetrahedra. The wave vector is r=0.1192(1)a* − 0.0043(1)b* at 150 °C. Below 150 °C tridymite discontinuously transforms to another orthorhombic phase and the modulation partially
locks in at the wave vector r
1=1/3a*. Simultaneously, an additional incommensurate modulation with r
2= 0.0395(1)b* − 0.3882(1)c* is formed. The two-dimensional modulation does not vary significantly with the temperature.
Received: 13 September 2000 / Accepted: 29 January 2001 相似文献
16.
J. S. Nicoll G. V. Gibbs M. B. Boisen Jr. R. T. Downs K. L. Bartelmehs 《Physics and Chemistry of Minerals》1994,20(8):617-624
Molecular orbital calculations completed on fluoride molecules containing first and second row cations have generated bond lengths, R, that match those observed for coordinated polyhedra in crystals to within ～0.04 Å, on average. The calculated bond lengths and those observed for fluoride crystals can be ranked with the expression R=Kp ?0.22, where p=s/r, s is the Pauling strength of the bond, r is the row number of the cation and K=1.34. The exponent -0.22 (≈ -2/9) is the same as that observed for oxide, nitride and sulfide molecules and crystals. Bonded radii for the fluoride anion, obtained from theoretical electron density maps, increase linearly with bond length. Those calculated for the cations as well as for the fluoride anion match calculated promolecule radii to within ～0.03 Å, on average, suggesting that the electron density distributions in the vicinity of the minima along the bond paths possess a significant atomic component despite bond type. Bonded radii for Si and O ions provided by experimental electron density maps measured for the oxides coesite, danburite and stishovite match those calculated for a series of monosilicic acid molecules. The resulting radii increase with bond length and coordination number with the radius of the oxide ion increasing at a faster rate than that of the Si cation. The oxide ion within danburite exhibits several distinct radii, ranging between 0.9 and 1.2 Å, rather than a single radius with each exhibiting a different radius along each of the nonequivalent bonds with B, Si and Ca. Promolecule radii calculated for the coordinated polyhedra in danburite match procrystal radii obtained in a structure analysis to within 0.002 Å. The close agreement between these two sets of radii and experimentally determined bonded radii lends credence to Slater's statement that the difference between the electron density distribution observed for a crystal and that calculated for a procrystal (IAM) model of the crystal “would be small and subtle, and very hard to determine by examination of the total charge density.” 相似文献
17.
The charge density and bond character of the rutile-type structure of SiO2 (stishovite) under compression to 30 GPa were investigated by X-ray diffraction study using synchrotron radiation and AgKα rotating anode X-ray generator through a newly devised diamond-anvil cell. The valence electron density was determined by
least-squares refinement including the κ parameter and the electron population in the X-ray atomic scattering parameters.
The oxygen κ-parameter of SiO2 is 0.94 under ambient conditions and 1.11 at 29.1 GPa and the silicon valence changes from +2.12(8) at ambient pressure to
+2.26(15) at 29.1 GPa. These values indicate that the electron distributions are more localized with increasing pressure.
The difference Fourier map shows the deformation of the valence electron distribution and the bonding electron population
in residual electron densities. The bonding electron observed from the X-ray diffraction study is interpreted by molecular
orbital calculations. The deformation of SiO6octahedra and the bonding electron density of stishovite structures are elucidated from the overlapping electron orbits. The
O–O distances of shared and unshared edge of SiO6 octahedra change with the cation ionicity. The repulsive force between the two cations in the adjacent octahedron makes its
shared edge shorter. The pressure changes of the apical and equatorial Si–O interatomic distances are explained by the electron
density of state (DOS) of Si and electron configuration.
Received: 7 January 2002 / Accepted: 6 May 2002 相似文献
18.
In order to characterize the pressure-induced decomposition of ringwoodite (γ-Mg2SiO4), the topological analysis of the electron density ρ(r), based upon the theory of atoms in molecules (AIM) developed by Bader in the framework of the catastrophe theory, has been
performed. Calculations have been carried out by means of the ab initio CRYSTAL09 code at the HF/DFT level, using Hamiltonians
based on the Becke- LYP scheme containing hybrid Hartree–Fock/density functional exchange–correlation terms. The equation
of state at 0 K has been constructed for the three phases involved in the post-spinel phase transition (ringwoodite → Mg-perovskite + periclase)
occurring at the transition zone–lower mantel boundary. The topological results show that the decomposition of the ringwoodite
at high pressures is caused by a conflict catastrophe. Furthermore, topological evidences of the central role played by the
oxygen atoms to facilitate the pressure-induced ringwoodite decomposition and the subsequent phase transition have been noticed. 相似文献
19.
A. Kirfel T. Lippmann P. Blaha K. Schwarz D. F. Cox K. M. Rosso G. V. Gibbs 《Physics and Chemistry of Minerals》2005,32(4):301-313
A generalized X-ray scattering factor model experimental electron density distribution has been generated for the orthosilicate forsterite, using an essentially extinction and absorption free set of single crystal diffraction data recorded with intense, high energy synchrotron X-ray radiation (E=100.6 keV). A refinement of the model converged with an R(F)=0.0061. An evaluation of the bond critical point, bcp, properties of the distribution at the (3, –1) stationary points for the SiO and MgO bonded interactions, yielded values that agree typically within ~5%, on average, with theoretical values generated with quantum chemical computational strategies, using relatively robust basis sets. On the basis of this result, the modeling of the experimental distribution is considered to be adequate. As the bcp properties increase in magnitude, the MgO and SiO bonds decrease in length as calculated for a number of rock forming silicates. As asserted by Coppens (X-ray charge densities and chemical bonding. Oxford University Press, Oxford, 1997), large negative 2(rc) values, characteristic of shared interactions involving first row atoms, may not be characteristic of closed shell covalent bonded interactions involving second row Si, P and S atoms bonded to O. This study adds new evidence to the overall relatively good agreement between theoretical bcp properties generated with computational quantum strategies, on the one hand, and experimental properties generated with single crystal high energy synchrotron diffraction data on the other. The similarity of results not only provides a basis for using computational strategies for studying and modeling structures, defects and the reactivity of representative structures, but it also provides a basis for improving our understanding of the crystal chemistry of earth materials and the character of the SiO bonded interaction. 相似文献
20.
B. Cesare 《Contributions to Mineralogy and Petrology》1995,122(1-2):25-33
Equilibrium C–O–H fluid speciation calculations predict that graphite will precipitate from initially graphite saturated
fluid inclusions during cooling and exhumation of metamorphic rocks. In the case that no mass is gained or lost by the inclusions,
the original X
O ratio [O/(O+H)] of the fluid phase must be maintained. Given this closed system constraint, the down-temperature progress
of graphite precipitation can easily be monitored as a function of the varible X
O, and produces some effects that are of significance to fluid inclusion studies: 1. Variation of the H2O : CO2 : CH4 relationship in the graphite-saturated COH fluid, namely increase of X
H2
O and decrease of the carbonic fraction; 2. Decrease of fluid density due to precipitation of graphite, which is denser than
the residual fluid; 3. Alteration of the CO2 : CH4 ratio of the fluid, depending on the initial O : H ratio of the fluid: for X
O>1/3, fluids increase their CO2 : CH4 ratio with decreasing temperature, and vice-versa. This implies that the CO2 : CH4 ratio measured at room T will not represent the trapping value, which is in any case closer to unity. As a consequence of density reduction, isochores
extrapolated from densities observed at room temperature do not pass through the pressure-temperature conditions at which
the inclusion was trapped, with pressure underestimates of up to 2 kbar. Actual P-T trapping conditions are located along the equilibrium “bulk isochore” (curve of constant-X
O, constant-volume) of the fluid. Alteration of the CO2 : CH4 ratio is a mechanism by which a CO2-rich or CH4-rich carbonic phase can be formed from aqueous fluids that are slightly off the neutral X
O=1/3 value. Subsequent segregation of this phase from the aqueous counterpart may account for the formation of pure CO2 and CH4 fluids in the upper crust.
Received: 15 March 1995 / Accepted: 1 June 1995 相似文献