Water-trapping of unstable carbocations taking place into the inverted region of the Marcus equation. First experimental and computational evidence

About the Existence of Organic Oxonium Ions as Mechanistic Intermediates in Water Solution

“…This assumption is, however, set against the indivisible quantum nature of the electron. Thus, in the case of diabatic inner-shell reactions, the SET process (electron jumping) occurs at the cross point of the R and P parabolas, which represents the transition state (TS) of the reaction. , Therefore, accordingly to the MT, the activation free energy (Δ G ≠ ) for SET reactions in polar solvents is a nonlinear function of the free energy of reaction (Δ G ) and the barrier height for Δ G = 0, called the intrinsic reaction barrier (Λ), as shown by eq . − The Λ value is related to the most popular reorganization energy (λ) by the expression: Λ = λ/4. − Others and we have used eq successfully for the computation of reaction barriers for the hydration of several carbocations. − For adiabatic reactions, the TS are tunneled and the reaction profile is different (red line in Figure ). The adiabaticity of a reaction is measured by the overlapping (coupling) Hamiltonian ( H ) between the IS and FS at the TS (Figure ).…”

“…For related reactions involving thermodynamically less-stable carbocations (e.g., norbornyl bridgehead carbocations), even lower Δ G ≠ barriers (ca. 0.02 kcal/mol) were calculated by using eq for the global hydration reaction . Contrarily, in the case of more stable carbocations, such as benzylic-like carbocations, significantly higher barriers were experimentally determined (2.15–13.08 kcal/mol) .…”

The Mechanism of Hydrolysis of Aryldiazonium Ions Revisited: Marcus Theory vs. Canonical Variational Transition State Theory

“…The Marcus theory, which was originally conceived for treating kinetic data of single‐electron‐transfer (SET) reactions in solution, is able to predict nonlinear structure–reactivity relationships between the free energy of activation (Δ G ≠ ) and the overall free‐energy change (Δ G ) for said reactions 11,13. This theory is, therefore, very different to the general chemical intuition based on “linear free‐energy relationships” (LFERs), which all involve the proportionality between Δ G and Δ G ≠ 16.…”

“…Later, the Marcus theory was refined and extended to obtain rate data for a variety of organic reactions, including hydrogen‐transfer reactions,18 proton‐transfer reactions,19 methyl‐transfer reactions,20,21 ambident reactivity22 and also water‐trapping reactions of aryl‐substituted carbocations (stable carbocations with free energies of hydration Δ G w > –10 kcal mol –1 ) 12,23. We have recently demonstrated for the first time that there is no linear relationship between Δ G w ≠ and Δ G w in the case of the very exergonic (Δ G w < –40 kcal mol –1 ) hydration reactions of unstable 1‐norbornyl cations 13…”

“…On the other hand, we believe that the computation of Δ E ≠ values for the S N 1 and S N 2 reactions using an alternative theoretical approach, such as the Marcus equation,11,12 could afford new criteria that could be used to distinguish between the two controversial mechanisms (S N 1 and S N 2) proposed for this reaction. In this regard, we have a positive experience in using the Marcus theory, having demonstrated that the reactivity of very unstable 1‐norbornyl cations in water solution, with free energies of hydration Δ G w < –40 kcal mol –1 , can be explained in a straightforward manner by using this theory 13…”