Purely ionic and molecular orbital modelings of the bonding in mineral crystal structures

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Virginia Polytechnic Institute and State University

The modified electron gas (MEG) model has been used to generate ionic model CaCO₃ crystals in the calcite, aragonite, diopside, and perovskite structure types. For calcite and aragonite, the model predicts shorter CO bonds and larger bulk moduli than observed. Modeling of the thermochemistry of CaCO₃ does not reproduce the observed thermochemistry even qualitatively. The model predicts that the hypothetical diopside structure type is the most stable form CaCO₃ among the four structure types. These discrepancies may illustrate the significance of CO bond covalency in determining the physico-chemical properties of CaCO₃.

The MEG model has also been used to generate model alkali halide crystals in the sphalerite, rocksalt, and CsCl types in an exploration of the reliability of the radius ratio rule. The MEG model predicts the correct cation coordination numbers for 13 of 16 alkali halides, whereas the radius ratio rule predicts the correct coordination numbers in at most 9 of the same 16 alkali halides. Analyses of the model crystal structures suggests that energy minimization is more important than packing efficiency in determining the most stable structures for ionic crystals.

The molecular orbital (MO) model has been used to determine minimum-energy geometries and electron density distributions in sulfate hydroxyacid molecules. These molecules have been used to model the bonding in sulfate crystals. SO bond lengths calculated for H₂SO₄ and H₂S₂O₇ correlate linearly with fractional s-characters of the bonds, as in sulfate crystals. With increasing S coordination number, the bonded radii of S and O, as determined from electron density maps, increase at the same rate, contrary to the common assumption of constant anion H₂S₂O₇ shows a relatively large change in energy as its SOS angle is deformed from its minimum-energy value (125.6°) to l80°, in conformity with the small variation among observed SOS angles. In contrast, SiOSi and POP angles show relatively wide variations in crystals and molecules. This suggests that polysulfates may be less amenable than polysilicates or polyphosphates to polymorphism or glass formation. Other properties of H₂SO₄ are also calculated and compared with experimental observations and previous calculations.