Question

The reaction(s) in which inversion of configuration occur(s) is(are) 

 

Hint:

{Mitsunobu} \(=\) activated alcohol \(\mathrm{S_N2}\) \(⇒\) inversion.
{Neighboring-group participation} (acyloxonium/thiiranium/halonium) often leads to backside opening \(⇒\) inversion at the attacked carbon.
{Rearrangements} like Hofmann and Baeyer–Villiger are concerted migrations \(⇒\) {retention} of configuration at the migrating center.

Answer 1

Step 1: Option (A) — Mitsunobu reaction.
Ph₃P/DEAD with a carboxylic acid converts an alcohol R^*–OH into the corresponding ester R^*–O₂CR' via an S_N2 displacement of the O–PPh₃ activated intermediate. The chiral center at carbon undergoes a single backside attack ⇒ Walden inversion.
Step 2: Option (B) — Anchimeric assistance (acyloxonium) under heat.
On heating, the neighboring acetate participates to form a cyclic acyloxonium intermediate; subsequent intramolecular/backside attack (or acetate capture) occurs S_N2-like. The carbon bearing the leaving group is attacked from the opposite face ⇒ inversion at that stereocenter. (This is the classic neighboring-group participation in constrained bicyclic/allylic systems.)
Step 3: Option (C) — Hofmann rearrangement.
NaOBr converts an amide to a C_-1 shorter amine via N-bromoamide, rearrangement, and isocyanate. Stereochemical information at a migrating alpha-carbon (if present) is retained through the concerted migration; no inversion is involved.
Step 4: Option (D) — Baeyer–Villiger oxidation.
Peracid inserts an oxygen adjacent to a carbonyl with migration of one substituent. The migrating stereocenter (if any) migrates with retention (concerted rearrangement), not inversion.
Therefore, only (A) and (B) involve inversion of configuration.