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Why must the alkyl halide be sp3 hybridized with respect to the carbon connected to the halogen for the alkylation to occur?

Why, for example, can't we use acetylide with a bromine substituted for hydrogen on one side in conjunction with aluminum tribromide to alkylate benzene?

If anything this seems to be more favorable as an sp carbocation is likely less stable than an sp3 carbocation.

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    $\begingroup$ You can do this. As @jerepierre has noted the intermediates involved are higher in energy and consequently more reactive once generated. But under controlled conditions the reaction does work. You just need to use a stronger lewis acid than an aluminum trihalide. Google "Friedel Crafts alkenylation". $\endgroup$
    – ron
    Commented Jan 31, 2015 at 17:34

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If anything this seems to be more favorable as an sp carbocation is likely less stable than an sp3 carbocation.

That's the problem, sp2 and sp hybridized carbocations are less stable than sp3. Those carbocations are difficult to form and will likely undergo rearrangement faster than attack of the aromatic ring.

Modern organic synthesis has much better ways of making sp-sp2 and sp2-sp2 carbon-carbon bonds by palladium catalyzed cross-coupling.

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    $\begingroup$ Here's another way to look at it. The Friedel-Crafts alkylation reaction may be an electrophylic substitution with respect to the aromatic compounds, but it is a nucleophilic substitution with respect to the alkyl halide ($\text{S}_{\text{N}}2$ for primary and $\text{S}_{\text{N}}1$ for secondary and tertiary halides), although the leaving group needs to be activated so the reaction can occur in nonpolar solution. Alkenyl and alkynyl halides do not work in FC reactions because they cannot be $\text{S}_{\text{N}}1$ substrates. $\endgroup$
    – Ben Norris
    Commented Jan 31, 2015 at 15:12

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