Nature makes an astonishing array of complex terpenoid natural products from only a few simple achiral, acyclic precursors such as farnesyl pyrophosphate.1 Still, many details of terpenoid cyclization mechanisms are unknown. One outstanding issue is whether nonclassical carbocations are involved in these mechanisms,1, 2 and if so, then when, where, and why? During our ongoing theoretical studies on the mechanisms of terpenoid cyclizations, we encountered the unusual carbocation 1 (Figure 1).3, 4 In this complex cation, a formally tetracoordinate proton is seemingly suspended between two CC bonds on opposite sides of a cyclooctadiene ring.
Intrigued by this structure, we set out to explore simpler related species to see how common this structural motif might be. Initially we explored models based on 1,5-cyclooctadiene (2; Figure 2). Addition of a proton between its two CC bonds followed by geometry optimization (using either B3LYP/6-31+G(d,p) or MP2/6-31+G(d,p)) led to cation 3 (Figure 3).4 The geometry of cation 3, which is D2-symmetric, is quite similar to the core of 1.5 The central proton of 3 is shared evenly by all four “alkene” carbon atoms at a distance of 1.48 Å (B3LYP level) or 1.46 Å (MP2 level) from each;6 C⋅⋅⋅H distances in both cyclic7 and acyclic8 three-center, two-electron [C⋅⋅⋅H⋅⋅⋅C]+ cations are less, typically around 1.3 Å. The double bonds in 2 appear to be well-preorganized to chelate a proton and are lengthened upon doing so as they share their electron density with the sandwiched proton. Overall, cation 3 can be viewed as a hybrid of the resonance structures shown in Scheme 1, a very unusual flavor of nonclassical cation9 that boasts a five-center, four-electron bonding array.
Interestingly, both doubly allylic bonds (between carbon atoms marked with asterisks in Figure 2) of 2 are slightly lengthened upon addition of the proton, which indicates that they may help stabilize the four equivalent resonance structures shown in Scheme 1.10 If the limiting resonance structure, which is shown at the left of Scheme 2 and consists of a proton sandwiched between two butadienes, is a significant contributor, then we arrive at the very unusual resonance hybrid shown at the right of Scheme 2, a nine-center, eight-electron species.11, 12
Let us now consider the distribution of charge throughout the molecule. Computed atomic charges13 are shown in Figure 4 a and the electrostatic potential of 3,14 mapped onto a surface that approximates the van der Waals surface of this species, is shown in Figure 4 b. The central proton is the most positive atom in 3, but positive charge is still delocalized over the molecule. In addition, it appears that access to the central proton is somewhat limited. The computed chemical shift of the central proton is also quite unusual with δ=+13.45 ppm (GIAO/B3LYP/6-31+G(d,p) level) or δ=+13.33 ppm (GIAO/MP2/6-31+G(d,p) level).15, 16 These chemical shift values are quite unlike those observed experimentally and computationally for protons in stable three-center, two-electron [C⋅⋅⋅H⋅⋅⋅C]+ cations, which typically range from δ=−7 to −3 ppm.8, 17 Clearly, whereas the hydrogens in [C⋅⋅⋅H⋅⋅⋅C]+ cations are quite electron-rich (hydride-like), the hydrogen in cation 3 is quite electron-deficient.
One qualitative approach to constructing the molecular orbitals of the nine-center array in 3 is to build them from combinations of the π orbitals of butadiene and the s orbital of a proton. This leads to the orbitals shown at the center of Figure 4 c. This qualitative picture is also reflected in the Kohn–Sham orbitals18 from our B3 LYP/6-31+G(d,p) calculations which are shown on the outside of Figure 4 c. Wiberg bond indices13c for the C⋅⋅⋅H bonds, partial CC double bonds, and doubly allylic CC bonds are 0.21, 1.65, and 0.94, respectively, and these values are most consistent with the five-center, four-electron picture described above (see Scheme 1).
What are the limits on forming cations such as 3?12 Although cation 3 is highly delocalized, protonation of cyclooctadiene 2 on the “outside” actually leads to a more stable isomer, 4 (Figure 5).19a Structure 4 is approximately 40 kcal mol−1 lower in energy than 3 (39.6 and 40.3 kcal mol−1 at the B3LYP/6-31+G(d,p) and MP2/6-31+G(d,p) levels, respectively), perhaps, at least in part, because 4 allows an alternative nonclassical (three-center, two-electron) bonding array to form. The barrier for rearrangement of 3 to 4, via the transition-state structure shown in Figure 6,4b is computed to be 2.8 kcal mol−1 at the B3LYP/6-31+G(d,p) level and 8.5 kcal mol−1 at the MP2/6-31+G(d,p) level.19b Note that, as expected for a very exergonic reaction, this is an early transition state, dominated by shifting of the proton. Note also that one of the doubly allylic bonds lengthens, which is indicative of hyperconjugative stabilization of the positive charge that builds up in its vicinity as the proton moves away from its central position. Whether or not suitably substituted systems that favor “in-protonation” or protect such “in-protonated” structures can be contrived is an open question.20, 21
The propensities of other 1,5-cyclooctadiene isomers to form cations such as 3 were also explored.12 First, there is another conformer of (E,E)-2. This structure, shown at the top of Figure 7, is less stable than 2 by 6.5 kcal mol−1 at the B3LYP/6-31+G(d,p) level and 7.9 kcal mol−1 at the MP2/6-31+G(d,p) level, and its two CC bonds are parallel rather than “crossed” as they are in 2. This arrangement is also suitable for sandwiching a proton, and C2h-symmetric structure 5 is the energy-minimized structure of the resulting carbocation (Figure 8). Analogous delocalized cations could not, however, be located for E,Z and Z,Z isomers of 2 (Figure 7).22 This finding is consistent with the fact that the E,E isomers seem to be better preorganized to share a proton; that is, they have shorter distances between their double bonds.
In summary, we have described a new type of nonclassical carbocation with a tetracoordinate proton. While exotic in their appearance, such species might be formed from suitable cyclooctadienes or by rearrangements of other cations and may even play a role in some biosynthetic terpenoid cyclizations. We are exploring both of these possibilities.3 The prospect that such intermediates can lead to many different species through simple addition, rearrangement, or deprotonation reactions is particularly attractive from the perspective of reaction design.