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Stishovite is a notable exception. Here each Si is octahedrally coordinated to six O neighbors, with each O atom bonded to three Si neighbors. We have not considered such structures in this work.
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0011462961
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The bridging O atoms exposed by the (100) surface bridge a surface Si with a subsurface Si. On the (101) surface, such atoms bridge two surface Si atoms. We have done some preliminary investigations on ODH mechanisms involving the bridging O atoms. This involves a temporary breaking of the bridge and reconnecting, which result in large structural relaxations several layers below the surface. Therefore, studying reaction mechanisms properly with such bridging O atoms would require a much thicker slab model (i.e., increased number of atomic layers), thereby implying considerably more computational effort than we could afford. Instead, we focused on a complete catalytic cycle involving the O atoms of the surface OH groups, which involves much less structural relaxation in the subsurface layers.
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A more accurate slab representation would have been to include the bottom O layer and cap the O atoms with H, as was done for the top surface. We did perform one such a calculation for the relaxed surface structure, and compared the relative positions for the top two Si layers, the top bridging O layer, and the top hydroxyl layer with the corresponding atoms in Fig. 2(c). The maximum positional deviation was less than 0.1 Å, and all the respective bond lengths and angles were within a few percent agreement. With the expanded slab, we also computed reaction heat and the activation barriers for the O-insertion step and the first ethane insertion step of the ODH cycle in absence of surface P (the first two steps of Fig. 7). The computed heats and barriers were within 3-5 kcal/mol of the results presented in Sec. IV. This appears to indicate that the bottom-layer O atoms play only a minor role in the surface structure and the reaction energetics presented in this work.
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0011517090
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note
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3 parameters used in this work is 33.5 kcal/mol.
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-
-
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79
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0011514781
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note
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The surface relaxation into a quartz-like phase is not due to the thinness of the simulation slab, as we explicitly verified using an eight-layer slab model and fixing the bottom two layers.
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-
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80
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0011465783
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note
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2 and ethane molecules, thereby rendering release of ethylene and water energetically expensive. Similar problems can also occur with a threefold-coordinated P, as discussed later in Ref. 79.
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81
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0011517091
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note
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5 bond sticking out of the surface and, P is known to like both valences: 5+ and 3+. However, the transition state for this reaction involves a threefold-coordinated, but a four-valent P with a double-bonded O, which leads to an energy barrier of ∼100 kcal/mol. Therefore, redox reactions with P appear unfavorable in the ODH cycle.
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82
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0011428689
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note
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2. Therefore, O migration cannot be ruled out as all alternative mechanism for the initial formation of peroxide bonds.
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83
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0011415372
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note
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58 kcal/mol is somewhat larger than the "typical" chemical activation energies which generally range from 20 to 50 kcal/mol. Reactions with energies below about 20 kcal/mol proceed readily at low temperatures and may be typified by biological processes. Reactions with activation energies greater than 50 kcal/mol are typically high temperature gas phase reactions such as combustion. Our experimental conditions are at the lower end of "high temperature." If we raise the reactor temperature by 50-100 °C, gas phase homogeneous reactions become significant. The computed energy of 58 kcal/mol appears consistent with this experimental observation, i.e., 58 kcal/mol, and 650 °C are both on the low end of "high temperature."
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