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note
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If a carbon atom with three nearest neighbours is bonded to a carbon atom with four nearest neighbours, the potential energy formula of Tersoff interpolates the bond properties so that they are intermediate between those of a single and double bond. In doing so the binding energy is overestimated and artificial configurations can be favored. Brenner pointed out that a double bond admixture due to π overlap cannot occur and that such a bond is better described as a single bond plus a radical orbital. He introduced a correction for this specific case, which was determined by fitting the vacancy formation energies in diamond and graphite.
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Tersoff as well as Brenner used in their formulas for the pair interactions a cutoff function simply taken as (see Refs. 20 and 21) (Equation Presented) which has a continuous value and derivative for all bond lengths r, and goes from 1 to 0 in a small range around (R + S)/2
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Tersoff as well as Brenner used in their formulas for the pair interactions a cutoff function simply taken as (see Refs. 20 and 21) (Equation Presented) which has a continuous value and derivative for all bond lengths r, and goes from 1 to 0 in a small range around (R + S)/2.
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