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note
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2 molecule is adopted here as the chemical potential of the reservoir.
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22
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12844260396
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note
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There is a slight difference in length ( less than 0.01 Å ) between the two types of Si-O bonds in α-quartz. More importantly, local atomic arrangements ( e.g., distance to a back O atom ) in the long bond and the short bond sides differ significantly.
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23
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12844282098
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note
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++ are different to each other, there remains an ambiguity as to determine the occupancy levels. We have examined the deep level positions of a variety of geometries with +2, +1.5, +1, +0.5, 0 charged states, and found the ambiguity causes the error of the occupancy level less than 0.5 eV. The negative U character holds even with this numerical ambiguity.
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