S_N2 Reaction: Stereochemistry

Recall that an S_N2 reaction follows a concerted mechanism, where the nucleophilic attack and the departure of the leaving group occur simultaneously. 

High electron density around the leaving group blocks the frontside of the substrate, which forces the nucleophile to initiate a backside attack.

As the HOMO of the nucleophile effectively overlaps with the LUMO of the electrophile, a new bond begins to form, and simultaneously, the bond between the electrophile and the leaving group weakens.

Concurrently, the angle between the substituents and the leaving group reduces from 109.5° to 90°, and the geometry of the carbon atom changes from tetrahedral — in the substrate — to trigonal bipyramidal, in the pentacoordinate transition state. 

However, to retain the tetravalency of carbon, the leaving group departs the transition state, and the geometry of carbon becomes tetrahedral once again. 

In the product, the substituents on carbon have turned inside out, resulting in an inverted tetrahedron — similar to an umbrella that flips in strong wind. Also, the nucleophile is placed directly opposite to the original position of the leaving group.

In an achiral substrate, due to the plane of sym