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When estimating the length for a one-dimensional particle-in-a-box model for a hydrocarbon (such as 1,3-butadiene), do we include the bond lengths between the (terminal) carbon and hydrogen atoms at the ends of the chain?

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    $\begingroup$ No, they are not in part of the double bond conjugation and so the $\pi$ electrons are not delocalised into these bonds (nor onto and CH bond). Only use delocalised electrons in particle in a box. $\endgroup$
    – porphyrin
    Oct 31, 2016 at 8:21

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As porphyrin said in his comment, the $\ce{C-H}$ bond is not part of the delocalized $\pi$ system that makes up the one dimensional box. This is partially because hydrogen does not have a p orbital to contribute to the system. The $\pi$ system that creates the box is the result of overlap between p orbitals found on adjacent carbon atoms, meaning that you would be able to approximate the length of the box by summing up the bond lengths between all adjacent carbons in the delocalized system. While resonance means that there are not actually alternating double and single bonds across the $\pi$ system, all of the $C-C$ bonds will be the same length, which should be close to the average of the bond lengths for the most stable resonance contributor.

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