# SN2 - Second-order Nucleophilic Substitution

## HOMO/LUMO Interactions in $SN2$ Reactions

Fig.1
Orbitals of the C-L bond.

In an $SN2$ reaction, an occupied n orbital of the nucleophile (HOMO = highest occupied moecular orbital; lone electron pair) interacts with the unoccupied, antibonding σ* orbital of the substrate's C-L bond (LUMO = lowest unoccupied molecular orbital). As a result, a new bonding, as well as a new antibonding molecular orbital are developed. The bonding molecular orbital has a lower energy level than the initial n orbital of the nucleophile does. As only the two electrons of the nucleophile have to be distributed among the new molecular orbitals, the antibonding molecular orbital is not occupied. Therefore, the system is stabilized by the HOMO/LUMO interaction. Thus, the HOMO/LUMO interaction leads to a bonding interaction between the substrate and the nucleophile. If the nucleophile's n orbital interacts with the bonding, occupied σ orbital of the C-L bond, the new antibonding molecular orbital would also have to be occupied. The system would then not be stabilized by this HOMO/HOMO interaction. Thus, the HOMO/HOMO interaction does not lead to a bonding interaction between the substrate and the nucleophile.

Fig.2
HOMO/HOMO and HOMO/LUMO interactions in an $SN2$ reaction.

Left (II): Not-stabilizing HOMO/HOMO (n/σ) interaction. Right (I): Stailizing HOMO/LUMO (n/σ*) interaction.

The strength of the HOMO/LUMO interaction depends considerably on the direction from which the nucleophile approaches the substrate. Three borderline cases are conceivable:

Fig.3
Borderline cases of the nucleophile approach's direction.
• The nucleophile attacks the substrate along the C-L bonding axis from the opposite side of L. This is a back-side attack.
• The nucleophile approaches the substrate along the C-L bonding axis from the side on which L is found. This is called front-side attack.
• The nucleophile approaches the substrate perpendicularly to the C-L bonding axis. This is a side attack.

### Back-side attack

In a back-side attack of the nucleophile on the substrate, the following orbital interaction is possible.

Fig.4
HOMO/LUMO interaction (n/σ*) in the back-side attack.

As one can see in the illustration above, the back-side attack enables the overlapping of the nucleophilie's HOMO (n orbital, lone electron pair) with the substrate's LUMO (C-L σ*), in particular with the larger lobe of the substrat's LUMO. If the nucleophile does not approach the substrate exactly along the C-L bonding axis, the HOMO/LUMO interaction is weaker. To make a long story short, the back-side attack leads to a strong bonding HOMO/LUMO interaction between the nucleophile and the substrate. Therefore, the back-side attack actually occurs in the $SN2$ reaction.

### Front-side and side attack

Fig.5
HOMO/LUMO interaction (n/σ*) in the side attack.

Due to the steric hindrance between the nucleophile and the leaving group, a front-side attack that occurs right along the C-L bonding axis is particularly unfavourable. A side attack also has several disadvantages.

• In the side attack, the minor overlapping of the nucleophile's LUMO with the smaller orbital lobes of the substrate's LUMO (σ*), which are located between the carbon and the leaving group, leads to a weaker interaction than in the back-side attack.
• In the side attack, one lobe of the nucleophile's HOMO overlaps with two small lobes of the substrates LUMO (σ*). These small lobes of the LUMO have opposite signs in the wavefunction, as the LUMO possesses a nodal plane between the carbon and the leaving goup. Consequently, the overlapping of the nucleophile's HOMO with one of the small substrate's LUMO lobes causes a bonding interaction, while the overlapping with the other small LUMO lobe leads to an antibonding interaction. In summary it may be said, the HOMO/LUMO interactions in the side attack do not produce bonding interactions between the substrate and the nucleophile.

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