# SN2 - Second-order Nucleophilic Substitution

## The Transition State of $SN2$ Reactions

The stereochemically unambiguous result of $SN2$ reactions - that is, the complete inversion of configuration of the reaction center - proves that the structure differs considerably from that of $SN1$ reactions. According to the $SN2$ reaction's kinetics, the substrate (electrophile), as well as the nucleophile, participate in the transition state. Obviously, the nucleophile attacks the substrate from the opposite side of the leaving group, as complete inversion takes place. In the transition state, the nucleofuge-carbon bond is partially cleaved, while the nucleophile-carbon bond is partially formed, and the remaining three substituents are arranged trigonal planar around the central carbon. The central carbon is $sp2$-hybridized, whereat the p orbital is used for the partial nucleofuge- and nucleophile-carbon bond. As a result of the transition state structure, the movement of the remaining three substituents is comparable to an umbrella's inversion in a windstorm. This inversion is called Walden inversion, named after Paul Walden (1863-1957).

Fig.1
Transition state and energy diagram of an $SN2$ reaction: Chloroform hydrolysis.

Due to their extremely short lifetime, transition states cannot be measured directly. They represent an energy maximum on the reaction coordinate. Their lifetime does not last any longer than one molecular vibration, which is approximately 10-12 s. In bimolecular reactions, such as in an $SN2$ reaction, the transition state represents one specific orientiation of the reactants. That is, compared to the beginning of the reaction, the formerly infinite number of arrangements in space that the reactants might assume is reduced to only one. Thus, their entropy decreases. The entropy of activation ΔS is therefore negative. The higher the amount of (negative) activation entropy is, the higher the free energy of activation ΔG = ΔH - TΔS is, as well.

Entropy of activation
ΔS = (entropy of the transition state) - (entropy of the starting products).
Free energy of activation
ΔG = ΔH - TΔS.
Fig.2
Mountain pass model of a reaction coordinate.

The reaction coordinate, the transition state's energy and its entropy may be illustrated by a mountain pass model. Each point on the mountain's surface represents a specific atom's spatial arrangement and the system's energy. The starting products are located at the bottom of the mountain, while the products are located at the bottom on the opposite side. In order to be converted into the products, the starting products have to cross over the mountain. The easiest way over the mountain, which also requires the least amount of energy, is the mountain pass. In the model, the mountain pass represents the transition state of the reaction. The reaction coordinate is the direct connection of starting products, transition state (mountain pass), and products on the mountain's surface (the red line in the illustration). A mountain pass that is relatively broad in cross direction represents a reaction with a lower free energy of activation ΔG than a narrow mountain pass does. Why? A broader mountain pass means that more spatial arrangements of atoms with equal or almost equal energy are availabe in, or near, the transition state. Therefore, the transition state's entropy S, and thus the activation entropy of the reaction ΔS, is all the more higher, the broader the mountain pass is. Consequently, the broader the mountain pass is, the lower the free energy of activation ΔG is, as well.

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