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How the cyclization can take place as there is no other functional group than $\ce{NO2}?$

1‐(2‐methylbutyl)‐2‐nitrocyclohexane to 2‐ethyl‐2‐methyl‐octahydroindole

One way that I can think of is photochemical bromination which occurs selectively at tertiary center which then can be promoted to give cation in polar medium. Nitro group on being reduced to amino group will attack on carbocation, thus closing the ring.

The problem here is that there are three tertiary centers and radical close to functional group will be more stable than the one at the far tertiary center on side chain.

How would you handle this conversion?

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The Hofmann-Loeffler-Freytag reaction as suggested by @user55119 in the comments above is the way to go.

First you need to reduce your nitro group. The reduction of alkyl nitro compounds is less simple than aromatic nitro groups and lower yielding in general. I would suggest the use of Al/Hg amalgam.

Acetylate the resulting amine.

N-chlorinate the amide - trichloroisocyanuric acid is good for this conditions

Irradiate the chlorinated amide to form the [5] ring similar to this example Baldwin gelsimicine synthesis

Finally hydrolyse off the acetyl group with cHCl.

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