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Title: Theoretical Electron Density Distributions for Fe- and Cu-Sulfide Earth Materials: A Connection between Bond Length, Bond Critical Point Properties, Local Energy Densities, and Bonded Interactions

Abstract

Bond critical point and local energy density properties together with net atomic charges were calculated for theoretical electron density distributions, F(r), generated for a variety of Fe and Cu metal-sulfide materials with high- and low-spin Fe atoms in octahedral coordination and high-spin Fe atoms in tetrahedral coordination. The electron density, F(rc), the Laplacian, 32F(rc), the local kinetic energy, G(rc), and the oxidation state of Fe increase as the local potential energy density, V(rc), the Fe-S bond lengths, and the coordination numbers of the Fe atoms decrease. The properties of the bonded interactions for the octahedrally coordinated low-spin Fe atoms for pyrite and marcasite are distinct from those for high-spin Fe atoms for troilite, smythite, and greigite. The Fe-S bond lengths are shorter and the values of F(rc) and 32F(rc) are larger for pyrite and marcasite, indicating that the accumulation and local concentration of F(r) in the internuclear region are greater than those involving the longer, high-spin Fe-S bonded interactions. The net atomic charges and the bonded radii calculated for the Fe and S atoms in pyrite and marcasite are also smaller than those for sulfides with high-spin octahedrally coordinated Fe atoms. Collectively, the Fe-S interactions are indicated to be intermediatemore » in character with the low-spin Fe-S interactions having greater shared character than the highspin interactions. The bond lengths observed for chalcopyrite together with the calculated bond critical point properties are consistent with the formula Cu+Fe3+S2. The bond length is shorter and the F(rc) value is larger for the FeS4 tetrahedron displayed by metastable greigite than those displayed by chalcopyrite and cubanite, consistent with a proposal that the Fe atom in greigite is tetravalent. S-S bond paths exist between each of the surface S atoms of adjacent slabs of FeS6 octahedra comprising the layer sulfide smythite, suggesting that the neutral Fe3S4 slabs are linked together and stabilized by the pathways of electron density comprising S-S bonded interactions. Such interactions not only exist between the S atoms for adjacent S8 rings in native sulfur, but their bond critical point properties are similar to those displayed by the metal sulfides.« less

Authors:
; ; ; ; ;
Publication Date:
Research Org.:
Pacific Northwest National Laboratory (PNNL), Richland, WA (US), Environmental Molecular Sciences Laboratory (EMSL)
Sponsoring Org.:
USDOE
OSTI Identifier:
902666
Report Number(s):
PNNL-SA-53778
4198; KP1704020; TRN: US200718%%48
DOE Contract Number:
AC05-76RL01830
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Physical Chemistry B, 111(8):1923-1931; Journal Volume: 111; Journal Issue: 8
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 58 GEOSCIENCES; IRON SULFIDES; SULFIDE MINERALS; COPPER SULFIDES; BOND LENGTHS; CHALCOPYRITE; ELECTRON DENSITY; ENERGY DENSITY; KINETIC ENERGY; MARCASITE; POTENTIAL ENERGY; PYRITE; TROILITE; Environmental Molecular Sciences Laboratory

Citation Formats

Gibbs, Gerald V., Cox, David F., Rosso, Kevin M., Ross, Nancy L., Downs, R. T., and Spackman, M. A. Theoretical Electron Density Distributions for Fe- and Cu-Sulfide Earth Materials: A Connection between Bond Length, Bond Critical Point Properties, Local Energy Densities, and Bonded Interactions. United States: N. p., 2007. Web. doi:10.1021/jp065086i.
Gibbs, Gerald V., Cox, David F., Rosso, Kevin M., Ross, Nancy L., Downs, R. T., & Spackman, M. A. Theoretical Electron Density Distributions for Fe- and Cu-Sulfide Earth Materials: A Connection between Bond Length, Bond Critical Point Properties, Local Energy Densities, and Bonded Interactions. United States. doi:10.1021/jp065086i.
Gibbs, Gerald V., Cox, David F., Rosso, Kevin M., Ross, Nancy L., Downs, R. T., and Spackman, M. A. Thu . "Theoretical Electron Density Distributions for Fe- and Cu-Sulfide Earth Materials: A Connection between Bond Length, Bond Critical Point Properties, Local Energy Densities, and Bonded Interactions". United States. doi:10.1021/jp065086i.
@article{osti_902666,
title = {Theoretical Electron Density Distributions for Fe- and Cu-Sulfide Earth Materials: A Connection between Bond Length, Bond Critical Point Properties, Local Energy Densities, and Bonded Interactions},
author = {Gibbs, Gerald V. and Cox, David F. and Rosso, Kevin M. and Ross, Nancy L. and Downs, R. T. and Spackman, M. A.},
abstractNote = {Bond critical point and local energy density properties together with net atomic charges were calculated for theoretical electron density distributions, F(r), generated for a variety of Fe and Cu metal-sulfide materials with high- and low-spin Fe atoms in octahedral coordination and high-spin Fe atoms in tetrahedral coordination. The electron density, F(rc), the Laplacian, 32F(rc), the local kinetic energy, G(rc), and the oxidation state of Fe increase as the local potential energy density, V(rc), the Fe-S bond lengths, and the coordination numbers of the Fe atoms decrease. The properties of the bonded interactions for the octahedrally coordinated low-spin Fe atoms for pyrite and marcasite are distinct from those for high-spin Fe atoms for troilite, smythite, and greigite. The Fe-S bond lengths are shorter and the values of F(rc) and 32F(rc) are larger for pyrite and marcasite, indicating that the accumulation and local concentration of F(r) in the internuclear region are greater than those involving the longer, high-spin Fe-S bonded interactions. The net atomic charges and the bonded radii calculated for the Fe and S atoms in pyrite and marcasite are also smaller than those for sulfides with high-spin octahedrally coordinated Fe atoms. Collectively, the Fe-S interactions are indicated to be intermediate in character with the low-spin Fe-S interactions having greater shared character than the highspin interactions. The bond lengths observed for chalcopyrite together with the calculated bond critical point properties are consistent with the formula Cu+Fe3+S2. The bond length is shorter and the F(rc) value is larger for the FeS4 tetrahedron displayed by metastable greigite than those displayed by chalcopyrite and cubanite, consistent with a proposal that the Fe atom in greigite is tetravalent. S-S bond paths exist between each of the surface S atoms of adjacent slabs of FeS6 octahedra comprising the layer sulfide smythite, suggesting that the neutral Fe3S4 slabs are linked together and stabilized by the pathways of electron density comprising S-S bonded interactions. Such interactions not only exist between the S atoms for adjacent S8 rings in native sulfur, but their bond critical point properties are similar to those displayed by the metal sulfides.},
doi = {10.1021/jp065086i},
journal = {Journal of Physical Chemistry B, 111(8):1923-1931},
number = 8,
volume = 111,
place = {United States},
year = {Thu Mar 01 00:00:00 EST 2007},
month = {Thu Mar 01 00:00:00 EST 2007}
}
  • Bond critical point, bcp, and local energy density properties for the electron density, ED, distributions, calculated with first principle quantum mechanical methods for divalent transition metal Mn-, Co- and Fe-containing silicates and oxides are compared with experimental model ED properties for tephroite, Mn 2SiO 4, fayalite, Fe 2SiO 4 and Co 2SiO 4 olivine, each determined with high energy synchrotron single crystal X-ray diffraction data. Trends observed between the experimental bond lengths, R(M-O), (M = Mn, Fe, Co), and the calculated bcp properties are comparable with those observed for non-transition M-O bonded interactions. The bcp, local total energy density, H(rmore » c), and bond length trends determined for the Mn-O, Co-O and Fe-O interactions are virtually identical. A comparison is also made with model experimental bcp properties determined for several Mn-O, Fe-O and Co-O bonded interactions for organometallic complexes and several oxides. Despite the complexities of the structures of the organometallic complexes, the agreement between the calculated and the model experimental bcp properties is good in several cases. The G(r c)/p(r c) vs. R(M-O) trends established for non-transition metal M-O bonded interactions hold for the given transition metal M O bonded interactions with the G(r c)/p(r c) ratio increasing in value as H(r c) becomes progressively more negative in value and the shared character of the interaction increases. As observed for the non-transition metal M-O bonded interactions, the Laplacian, (nabla) 2p(r c), increases in value as p(r c) increases and as H(r c) decreases. The Mn-O, Fe-O, and Co-O bonded interactions are indicated to be of intermediate character with a substantial component of closed-shell character compared with Fe-S and Ni-S bonded interactions which show greater shared character based on the |V(r c)|/G(r c) bond character indicator. The atomic charges conferred on the transition metal atoms for the three olivines decrease with increasing atomic number from Mn to Fe to Co.« less
  • Generalized X-ray scattering factor model experimental electron density distributions and bond critical point, bcp, properties generated in recent studies for the earth materials stishovite, forsterite, fayalite and cuprite with high energy single crystal synchrotron X-ray diffraction data and those generated with high resolution diffraction data for coesite and senarmonite were found to be adequate and in relatively good agreement, ~5% on average, with those calculated with quantum chemical methods with relatively robust basis sets. High resolution low energy single crystal diffraction data, recorded for the molecular sieve AlPO4-15, were also found to yield model electron density distribution values at themore » bcp points for the AlO and PO bonded interactions that are in relatively good to moderately good agreement with the theoretical values, but the Laplacian values of the distribution at the points for the two bonded interactions were found to be in relatively poor agreement. In several cases, experimental bcp properties, generated with conventional low energy X-ray diffraction data for several rock forming minerals, were found overall to be in poorer agreement with the theoretical properties. The overall agreement between theoretical bcp properties generated with computational quantum methods and experimental properties generated with synchrotron high energy radiation not only provides a basis for using computational strategies for studying and modeling structures and their electron density distributions, but it also provides a basis for improving our understanding of the crystal chemistry and bonded interactions for earth materials. Theoretical bond critical point properties generated with computational quantum methods are believed to rival the accuracy of those determined experimentally. As such the calculations provide a powerful and efficient method for evaluating electron density distributions and the bonded interactions for a wide range of earth materials.« less
  • For a variety of molecules and Earth materials, the theoretical local kinetic energy density, G(rc), increases and the local potential energy density, V(rc), decreases as the MO bond lengths (M = first and second row metal atoms) decrease and electron density, ρ(rc), is localized at the bond critical points, rc. Despite claims that the ratio, G(rc)/ρ(rc), classifies bonded interactions as shared covalent when less than unity and closed shell ionic when greater than unity, the ratio was found to increase from 0.5 to 2.5 a.u. as the local electronic energy density H(rc) = G(rc) + V(rc) decreases and becomes progressivelymore » more negative. In any event, the ratio is indicated to be a measure of the character for a given M-O bond, the greater the ratio, the larger the value of ρ(rc), the smaller the coordination number of the M atom and the more covalent the bond. H(rc)/ρ(rc) vs. G(rc)/ρ(rc) scatter diagrams categorize the M-O bond data into domains with the H(rc)/ρ(rc) ratio tending to increase as the electronegativity of the M atoms increase. Estimated values of G(rc) and V(rc), using an expression based on gradient corrected electron gas theory, are in good agreement with theoretical values, particularly for bonded interactions involving second row M atoms. The agreement is poorer for the more covalent C-O and N-O bonds.« less
  • The empirical bond strength of the SiO bond correlates with the value of the electron density at the bond critical point calculated for a large number of silicates and observed for the silica polymorphs stishovite and coesite. The greater the bond strength, the greater the localization of the electron density at the critical point, the shorter the bond, and the greater the covalent character of the bonded interaction. Bond strength and resonance bond number are considered to represent similar properties of the electronic structure of the bond.
  • A classification of the HF bonded interactions comprising a large number of molecules has been proposed by Espinosa et al. [J. Chem. Phys. 117, 5529 (2002)] based on the ratio |V(rc)|/G(rc) where |V(rc)| is the magnitude of the local potential energy density and G(rc) is the local kinetic density evaluated at the bond critical points, rc. A calculation of the ratio for the MO bonded interactions comprising a relatively large number of molecules and earth materials, together with the constraints imposed by the values of Ñ2ρ(rc) and the local electronic energy density H(rc) = G(rc) + V(rc) in the HFmore » study, yielded the same classification for the oxides as found for the fluorides. This is true despite the different trends of the bond critical point and local energy properties with the bond length displayed by the HF and MO bonded interactions. LiO, NaO and MgO bonded interactions classify as closed shell ionic bonds, BeO, AlO, SiO, BO and PO bonded interactions classify as bonds of intermediate character and NO bonded interactions classify as shared covalent bonds. CO and SO bonded interactions classify as both intermediate and covalent bonded interactions. The CO triple bonded interaction classifies as a bond of intermediate character and the CO single bonded interaction classifies as a covalent bond whereas their H(rc) value indicates that they are both covalent bonds. The |V(rc)|/G(rc) ratios for the BeO, AlO and SiO bonded interactions indicate that they have a substantial component of ionic character despite their classification as bonds of intermediate character. The trend between |V(rc)|/G(rc) and the character of the bonded interaction is consistent with trends expected from electronegativity considerations. The connection between the net charges and the experimental SiO bond length evaluated for the Si and O atoms comprising two orthosilicates are examined in terms of the |V(rc)|/G(rc) values.« less