Calculations Predict That Heavy-Atom Tunneling Dominates Möbius Bond Shifting in [12]- and [16]Annulene

Abstract

The contribution of heavy-atom tunneling to reactions of [12]- and [16]­annulene was probed using small-curvature tunneling rate calculations. At the CCSD­(T)/cc-pVDZ//M06-2X/cc-pVDZ level, tunneling is predicted to account for more than 50% of the rate for Möbius bond shifting and ca. 35% of the rate for electrocyclization in [12]­annulene, and over 80% of the rate for Möbius bond shifting in [16]­annulene, at temperatures at which these reactions have been observed experimentally.

Heavy‐Atom Tunneling in Organic Reactions

“…In turn, lowering the barrier causes it to become narrower, as indicated by the dotted line in Figure ; at a point 5.0 kcal mol −1 above the reactant, the barrier for hexatriene is 5.1 bohr amu 1/2 wide, compared to 4.1 bohr amu 1/2 for [12]annulene. The temperature at which the tunneling‐inclusive rate constant is predicted to be 3×10 −5 s −1 is 272 K for hexatriene, compared to circa 185 K for [12]annulene …”

Heavy‐Atom Tunneling in Organic Reactions

“…At À40 8 8C, the endothermic p-BS step is computed (SCT) to be dominated by tunneling (56 %). [30] Using the Bell formula as described by Greer and Doubleday [14] (v°= 720 cm À1 ), the tunneling fraction is 64 %, in moderate agreement with the SCT value.T he k CVT/SCT at this temperature is 2.5 10 À5 s À1 ,w ithin an order of magnitude of the experimental value.F urthermore,t he exothermic electrocyclization step 10 b!11 has abarrier that is just slightly wider than that for 9!10 a.A tÀ40 8 8C, tunneling is predicted by SCT calculations to account for 35 %ofthe ring-closure step (32 % using the Bell formula). Thus,this is amulti-step mechanism in which carbon tunneling plays as ignificant role for two steps.…”

“…[29b] This discrepancy of about 3.5 kcal mol À1 between computed and experimental barriers can be an indicator of tunneling. As in the case of planar p-BS,t he computed rate constants indicated > 99 %t unneling at temperatures below 120 K. [30] At 220 K( experimental T), the tunneling contribution was still 86 %. However,a lthough the corresponding k CVT/SCT for 7b!8b is very large (1.2 10 5 s À1 ), the effective rate constant k eff is about seven orders of magnitude lower (2.5 10 À2 s À1 ) due to the conformational equilibrium occurring before the p-BS event (Scheme 5).…”

“…Thus,this is amulti-step mechanism in which carbon tunneling plays as ignificant role for two steps. [30] Collectively,a ll the annulene p-BS reactions considered here are dominated by heavy-atom tunneling at temperatures at which they have been observed to occur. Thep ercentage contribution of tunneling differs based on the conformational motions necessary to attain ag eometry where BS can occur.…”

“…Due to the smaller distance between the reacting carbons of the hexatriene unit in [12]annulene compared to that in the parent hexatriene,t he cyclization barrier is lower for [12]annulene;1 3kcal mol À1 vs.2 0kcal mol À1 .I nt urn, lowering the barrier causes it to become narrower,a si ndicated by the dotted line in Figure 8; at ap oint 5.0 kcal mol À1 above the reactant, the barrier for hexatriene is 5.1 bohr amu 1/2 wide, compared to 4.1 bohr amu 1/2 for [12]annulene.T he temperature at which the tunneling-inclusive rate constant is predicted to be 3 10 À5 s À1 is 272 Kf or hexatriene, [18] compared to circa 185 Kfor [12]annulene. [30] Computed barrier shapes for several symmetric reactions are shown in Figure 9. Tw oo ft he reactions-planar p-BS in heptalene (4)and 7a ([16]annulene)-are not fast at very low temperatures such as 10 K. Only at higher temperatures (for example,80Kfor 7a)dothe rate constants exceed 1 10 À5 s À1 due to the need for vibrational activation to boost the system to ap oint where the barrier width is less than about 4bohr amu 1/2 .…”