Pushing the limits of concertedness. A waltz of wandering carbocations

Abstract

Among the array of complex terpene-forming carbocation cyclization/rearrangement reactions, the so-called "triple shift" reactions are among the most unexpected. Such reactions involve the asynchronous combination of three 1,n-shifts into a concerted process, e.g., a 1,2-alkyl shift followed by a 1,3-hydride shift followed by a second 1,2-alkyl shift. This type of reaction so far has been proposed to occur during the biosynthesis of diterpenes and the sidechains of sterols. Here we describe efforts to push the limits of concertedness in this type of carbocation reaction by designing, and characterizing with quantum chemical computations, systems that could couple additional 1,n-shift events to a triple shift leading, in principle to quadruple, pentuple, etc. shifts. While our designs did not lead to clear-cut examples of quadruple, etc. shifts, they did lead to reactions with surprisingly flat energy surfaces where more than five chemical events connect reactants and plausible products. Ab initio molecular dynamics simulations demonstrate that the formal minima on these surfaces interchange on short timescales, both with each other and with additional unexpected structures, allowing us a glimpse into a very complex manifold that allows ready access to great structural diversity.

Fig. 1. Top left: a two-step reaction. Top right: conversion of a 2-step reaction into a concerted reaction with 2 asynchronous chemical events. Bottom: potential extension to a concerted reaction with even more asynchronous events.

Fig. 2. Triple shift reaction reported by Hong and Tantillo (System-A). Relative free energies (in kcal mol^–1 computed at 298 K and 1 atm) are calculated with respect to 1 at the B3LYP/6-31+G(d,p) level (see Fig. 1 in ref. 42 for more details).

Fig. 3. Top: regular trajectory, starting from the TS towards reactants and then from the TS towards products (type I). Middle: trajectories that recross in one direction (types II–III). Bottom: trajectories that recross in both directions (type IV). Numbering (1 and 2) is used to distinguish halves of a complete trajectory.

Fig. 4. Comparison of the three systems examined. Relative free energies of the stationary points (B3LYP/6-31+G(d,p)) are noted in kcal mol^–1. Dashed lines are qualitative representations of the IRCs generated from TS-1-4-Me and TS-2-4*-H. For system C we have included a representation of the plane formed by C3, C4 and C8 in 1-H, 2-H and 4*-H with selected distances and angles, with the purpose of highlighting their geometric features, which are characteristic of non-classical carbocations (for further discussion on this topic see ESI†).–

Fig. 5. Top: evolution of the C3–C8 bond distance from –300 fs to 300 fs. Middle-up: evolution of the C3–C4 bond distance from –300 fs to 300 fs. Middle-down: evolution of the C4–C8 bond distance from –300 fs to 300 fs. Bottom: evolution of the C3–H18 (black) and C4–H18 (grey) bond distances from –300 fs to 300 fs. In all cases, only data from those trajectories that did not recross is shown.

Fig. 6. Evolution of C3–H18 (black) and C4–H18 (grey) distances along the analyzed trajectories. Top: full time-frame. Bottom: –300 to 300 fs time-frame.

Fig. 7. Product distribution at 1000 fs (inner circle) and 2000 fs (outer circle). Structures in black at the inner circle disappear in the larger trajectories (at 2000 fs) and structures in black in the outer circle are not found at 1000 fs. Structures in other colors are found in trajectories at both time steps. Structures shown are not necessarily PES minima.

Fig. 8. Reaction paths followed by trajectories, depicted as sequences of structures with a defined connectivity. Structures in black correspond to those that appear in Fig. 7 (we use the prefix Str on their names to avoid confusion with other numbers used in the representation). Below each of those, a number in blue indicates how many times this structure appears at exactly the 1000 fs time step of a trajectory, and a number in red how many times it does so at 2000 fs. With dashed squares, we have highlighted those structures most frequently encountered, while we have used solid squares to indicate tertiary carbocations (perhaps surprisingly, they are not among those structures most frequently encountered at either 1000 or 2000 fs). All black structures in the scheme were used as starting points of geometry optimizations. For those where the optimization preserved connectivity (they are actual minima on the potential energy surface), their energies relative to 1-H are noted between parentheses. The numbers in blue on the structures represent the methyl groups that keep their structural integrity along the trajectory.