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Verification of the Validity of the CNTBands Tool

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1	-	According to experimental data the band gap of semiconducting nanotube is inversely proportional to its radius. The simple [http://prl.aps.org/abstract/PRL/v68/i5/p631_1 analytical model] also explained in solution for [/site/wiki/529/CNTBands_Problems__Solutions.pdf homework Problem 3] indicates that the dependence is	+	According to experimental data the band gap of semiconducting nanotube is inversely proportional to its radius. The simple [http://prl.aps.org/abstract/PRL/v68/i5/p631_1 analytical model] also explained in solution for [/site/wiki/529/CNTBands_Problems__Solutions.pdf homework Problem 3] indicates that the prefactor '''''V''''' in this dependence is the absolute value of the nearest neighbor tight-binding element in the pi-orbital approximation
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3	$E_{g}=\frac{V}{R}$
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5	-	~~if the~~ CNT radius ~~is measured in the units of carbon-carbon bond length.~~ '''''V''''' is the ~~absolute value~~ of ~~the nearest neighbor tight~~-~~binding element in the pi-orbital approximation~~. If '''''R''''' is ~~measured~~ in nanometers,	+	Here CNT radius '''''R''''' is measured in the units of carbon-carbon bond length. If '''''R''''' is expressed in nanometers,
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7	$E_{g}=0.142\frac{V}{R}$
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9	The plot below, which collects data from pi-orbital tight-binding simulations from ''CNTBands'' (dark-blue circles) demonstrates that this is indeed the case. The solid red line is the inverse dependence given by the equation above.
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11	[[Image(CNTBandgap_vs_Radius.png)]]