(a) Give an orbital representation for an SN 2 reaction with ( S )-RCHDX and : Nu^-, if in the t

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(a) Give an orbital representation for an SN 2 reaction with...

(a) Give an orbital representation for an $\mathrm{S}_{\mathrm{N}} 2$ reaction with ( $S$ )-RCHDX and : $\mathrm{Nu}^{-}$, if in the transition state the $\mathrm{C}$ on which displacement occurs uses $s p^2$ hybrid orbitals. (b) How does this representation explain (i) inversion, (ii) the order of reactivity $3^n>2^a>1^{-n}$ ? (a) See Fig. 7-1. (b) (i) The reaction is initiated by the nucleophile beginning to overlap with the tail of the $s p^3$ hybrid orbital holding $\mathrm{X}$. In order for the tail to become the head, the configuration must change; inversion occurs. (ii) As H's on the attacked C are replaced by R's, the TS becomes more crowded and has a higher enthalpy. With a $3^{\circ} \mathrm{RX}$, there is a higher $\Delta H^{\ddagger}$ and a lower rate.

(a) Give an orbital representation for an $\mathrm{S}_{\mathrm{N}} 2$ reaction with ( $S$ )-RCHDX and : $\mathrm{Nu}^{-}$, if in the transition state the $\mathrm{C}$ on which displacement occurs uses $s p^2$ hybrid orbitals. (b) How does this representation explain (i) inversion, (ii) the order of reactivity $3^n>2^a>1^{-n}$ ?
(a) See Fig. 7-1.
(b) (i) The reaction is initiated by the nucleophile beginning to overlap with the tail of the $s p^3$ hybrid orbital holding $\mathrm{X}$. In order for the tail to become the head, the configuration must change; inversion occurs. (ii) As H's on the attacked C are replaced by R's, the TS becomes more crowded and has a higher enthalpy. With a $3^{\circ} \mathrm{RX}$, there is a higher $\Delta H^{\ddagger}$ and a lower rate.

Key Concepts

S_N2 Reaction Mechanism

The S_N2 mechanism is a bimolecular nucleophilic substitution in which the nucleophile attacks the substrate in a single, concerted step. During this process, the bond between the carbon and the leaving group breaks at the same time that a new bond between the carbon and the nucleophile is being formed. This synchronous bond-making and bond-breaking process is characterized by a well?defined transition state that features simultaneous partial bonds to both the incoming nucleophile and the leaving group.

Molecular Orbital Considerations

From an orbital perspective, the S_N2 reaction involves the interaction of the highest occupied molecular orbital (HOMO) of the nucleophile with the lowest unoccupied molecular orbital (LUMO) of the substrate, which is typically an antibonding orbital associated with the carbon–leaving group bond. This orbital overlap is crucial for initiating the nucleophilic attack and facilitating the transition state formation. The quality and symmetry of the interacting orbitals determine the efficiency of the electron density flow, which in turn affects the reaction rate and outcome.

Transition State and Hybridization

In the S_N2 reaction’s transition state, the carbon center undergoing substitution adopts a geometry that is intermediate between the tetrahedral configuration of the ground state and a planar sp^2-like configuration. This change in hybridization is a response to the simultaneous formation and cleavage of bonds, resulting in a transient geometry where the molecular orbitals are reorganized. The sp^2 orbital framework in the transition state represents the rehybridization necessary to accommodate the incoming nucleophile and the departing leaving group, while also providing a pathway for inversion of configuration.

Stereochemical Inversion

Stereochemical inversion in S_N2 reactions, often referred to as the Walden inversion, occurs because the nucleophile attacks the substrate from the side opposite the leaving group. As the nucleophile begins overlap with the orbital containing the leaving group’s electron density, the geometry demands a reorganization of the substituents around the central carbon. This reorientation results in the inversion of the stereochemistry at the reaction center, a hallmark of the S_N2 mechanism.

Steric Hindrance and Reactivity

The reactivity order observed in S_N2 reactions is strongly influenced by steric hindrance around the electrophilic carbon. As bulky substituents replace smaller ones, the transition state becomes increasingly crowded, raising its energy and thereby the activation barrier. This steric effect translates into a slower reaction rate for more substituted (e.g., tertiary) centers compared to less crowded (e.g., primary) centers. Greater congestion in the transition state ultimately leads to lower reactivity as the nucleophile finds it more difficult to effectively attack the substrate.

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