A theoretical study has been carried out on model systems to study a recently reported, (Nature, 2011, 473, 109) biosynthetic, [4 + 2] cycloaddition catalyzed by a stand-alone enzyme (the cyclase SpnF). It was suggested in this paper that SpnF is the first known example of a Diels–Alderase (DA). In the present study, for a model system of the substrate a transition structure was found with density functional calculations (DFT). In addition, the intrinsic reaction coordinate calculations indicated that the transition structure is that of a concerted, but highly asynchronous, DA reaction. Based on the DFT and Møller–Plesset second order calculations the activation energy was estimated to be about 15 kcal mol−1. The results of a natural population analysis indicated that there is significant charge transfer in the transition state, and it is proposed that possibly the enzyme plays a dual role of not only folding the substrate into the proper conformation for the DA reaction to occur, but also lowering its activation energy by stabilization of the highly polarized transition structure.

The biogenic origins of complex cyclic terpenes derive from the interplay of enzymes and the intrinsic reactivity of carbocation species at major branch-points along intramolecular cyclization pathways to ultimately determine the distribution of terpene skeletal types in nature. Solanaceous plants biosynthesize chemical defense compounds, largely derived from the eremophilane and spirovetivane-type sesquiterpenes. These hydrocarbon skeletons share a common biogenic origin, stemming from alternative Wagner–Meerwein rearrangements of the eudesm-5-yl carbocation during the cyclization of farnesyl pyrophosphate (FPP) catalyzed by sesquiterpene synthases. While the spirojatamane skeleton shares the same carbocation intermediate, this class of sesquiterpenes has not been reported in the Solanaceae and is exceedingly rare in nature. To investigate the physical basis for alternative rearrangements of the eudesm-5-yl carbocation, we carried out quantum mechanics (QM) analyses to calculate the allowable conformations, energies, and transition states linking conformers of the eudesm-5-yl carbocation to the eremophilene, spirovetivane, and spirojatamane skeletons. Additionally, we conducted parallel investigations on simplified decalin carbocation systems to examine the contribution of ring substituents to allowable conformations and rearrangement pathways. Our study reveals that ring substituents expand the conformational space accessible to the eudesm-5-yl carbocation while sterically blocking rearrangements in certain contexts. From our analysis, we define a conformational threshold for each possible rearrangement based on dihedral angles describing transition state geometry. Further, our calculations indicate that methylene migration rearrangements leading to spiro compounds are thermodynamically dominant in the eudesm-5-yl and simpler decalin carabocation systems. Interestingly, the theoretical abundance of sesquiterpene skeletal types arising from the intrinsic reactivity of the eudesm-5-yl carbocation stands in sharp contrast to their currently known natural abundance. The implications of these results for the catalytic tragectories catalyzed by sesquiterpene synthases are discussed.

The long-standing question of what is the nature of the cyclization of squalene to form tetracyclic and pentacyclic triterpenes has been addressed computationally. Using the DFT method with an intrinsic reaction coordinate calculation, we find that the first three rings of protonated squalene were formed without the intermediacy of mono- or bicyclic carbocations. The cyclization, calculated in the gas phase, proceeds in a highly asynchronous, concerted reaction to yield the tricyclic, tertiary carbocation with a 5-membered C ring. The fourth double bond of squalene is not properly oriented for the ring expansion of the C ring in concert with the formation of the 5-membered ring.

A theoretical study has been carried out on model systems to study a recently reported, (Nature, 2011, 473, 109) biosynthetic, [4 + 2] cycloaddition catalyzed by a stand-alone enzyme (the cyclase SpnF). It was suggested in this paper that SpnF is the first known example of a Diels–Alderase (DA). In the present study, for a model system of the substrate a transition structure was found with density functional calculations (DFT). In addition, the intrinsic reaction coordinate calculations indicated that the transition structure is that of a concerted, but highly asynchronous, DA reaction. Based on the DFT and Møller–Plesset second order calculations the activation energy was estimated to be about 15 kcal mol−1. The results of a natural population analysis indicated that there is significant charge transfer in the transition state, and it is proposed that possibly the enzyme plays a dual role of not only folding the substrate into the proper conformation for the DA reaction to occur, but also lowering its activation energy by stabilization of the highly polarized transition structure.