Concerted cycloaddition of perezone (1)

The folded conformers of perezone which are the precursors of pipitzols, present two easily differentiable arrangements according to the face of the quinone on which the side chain approaches, and each of them presents two possible orientations of the double bond; this is whether the side chain approaches exo (1-a and 1-c,Fig. 2) or endo (1-b and 1-d). It is important to notice that to date only compounds originating from the exo approach have been isolated from the plant and obtained by synthesis.[¹-⁴,¹⁶,¹⁸] Deuterium labeling experimentation on perezone´s C14 methyl group (structure 1-d, Fig. 1), demonstrated complete preservation of deuterium on methyl C14 of the endo adduct, thus assuring the concerted mechanism nature.[¹⁶,²¹,²²]

Fig. 2 Transition states in the formation of the four isomeric pipitzols 1-a - 2-d. 

With the available conformers and the structure of the two isolable diasteromeric pipitzols, the search for the transition states associated with the four possible approaches was undertaken. (See Table S3) All four transition states are characterizable and are presented in Fig. 3.

Fig. 3 Geometries of the transition-states A, B and C, D of the cycloaddition path to produce α- and β- pipitzols, respectively. 

The mere existence of a transition state formally concludes the problem of the existence of the folded conformers of perezone as in this case, it has allowed the characterization of the four transition states associated with the formation of the four possible pipitzol diastaroisomers. On a surface of any nature, (potential energy in this case, and electron density or coulombic potential as an example), the existence of a point of (3, -1) curvature, (associable with a transition state) in which two curvatures are negative and one positive, the energy reaches a maximum within the plane defined by the corresponding axes and a minimum along the third axis which, is perpendicular to the previous plane. The existence of a transition state is a necessary and sufficient condition for the associated minima and maxima to exist, regardless of its vibrational nature.

The forming sigma bond distances and the pyramidization (() of the involved carbon atoms are presented in Table 1. In the transition state that leads to the formation of exo-β-pipitzol, the C2-C12 bond distance is the largest in all cases (see entry C, Table 1), while C6-C13 is the shortest. A larger bond could diminish the angular strain and allow for a more synchronous approximation of the two olefin carbon atoms towards the quinone center, affecting the experimented vibrational degrees of freedom. This can be understood in terms of the greater participation of the second bond in the stability (or the shorter length of the C6-C13 bond).

Table 2 shows the energy parameters for the formation of the four possible products of cycloaddition using tetralin as an implicit solvent.[¹] In terms of the stability of the adducts, the transition states that lead to the exo isomers are ca. 6.0 kcal/mol more stable than the endo ones, being enthalpy as the major contributor term. The angular strain on endo products, causes a stability loss reflected mainly on the enthalpic term, with values matching the T(S term (T = 480 K), while for the exo products the T(S term represents 40 % of the enthalpy value. Lastly, the exo adduct derived (- and β-pipitzols are 10.8 and 11.8 kcal/mol more stable with respect to their parent conformer.

Data presented in Fig. 4, allowed us to quickly conclude on why, neither (- nor β- adducts generated by the side chain endo approximation have ever been observed. The activation energy for the former is 6.5 kcal/mol while for the latter is 6.3 kcal/mol higher with respect to the corresponding transition states for the formation of exo products. The formation of β-pipitzol requires overpassing an activation energy barrier of (G^≠ = 37.4 kcal/mol, while for α-pipitzol this energy is of 38.3 kcal/mol. Therefore, a resulting energy difference of ((G^≠= 0.8 kcal/mol led to an approximate proportion of 70/30. [²³]

Fig. 4 Intramolecular [5+2] cycloaddition paths of perezone to produce (- and (-pipitzols at M06-2X/6-311++G(2d,2p) level of theory in tetralin as implicit solvent. 

Activation enthalpy favors the formation of stable exo adducts, since angular strain is larger in endo adducts. Selectivity towards exo adducts can be explained in terms of steric compression. Careful observation of the endo adducts allows to identify a severe deformation in the environment at C12 carbon. The steric demand that the five-membered ring closure requires is responsible for hindering the endo isomers formation. These isomers have not been observed, not even by heating methods in which the vibrationally excited states would be feasible, as it has been proposed as mechanisms without the existence of folded conformers.[²⁴]

The sigma bond formation process is asynchronous since the C2-C12 bond is shorter than the C6-C13 one and the stability of C13 is attributable to its tertiary carbocation character. Nevertheless, the pyramidization degree is larger on C6 than C2, as it is with the C13 and C12 pair, probably originated from the intense angular tension upon the formation of the second bond and the bicycle closure.

The stability of C13 is originated as well by the hyperconjugation arising from two vicinal hydrogen atoms oriented in such a way that σ_C-H is held perpendicular to the carbon atom plane. The hyperconjugation contribution to stability is not ideal since C13 has a certain degree of pyramidization.

The approximation of the lateral chain towards the quinone group is defined by the dihedral angle C1-C2-C8-C18, with values of 98.1°and 52.0º for the transition states of exo adducts A and C (which lead to the formation of (- and β-pipitzol), respectively and the endo adducts with values of 129.4° and 122.4° for B and D, respectively (Table 1). The lateral chain folding entails the consecutive gauche conformation along that segment, with an ideal dihedral angle of 60º. In this regard, the endo transition states show an intense twisting concerning exo ones. The C2-C8-C10-C12 dihedral angle has values of 30.8° and 30.5º for A and C, respectively and 24.5° and 12.4º for endo B and D transition states, respectively. Nevertheless, the C8-C10-C11-C12 segment has a more relaxed geometry in transition state A of 56.6º, while the same segment in transition state C shows a high degree of eclipsed conformation with a value of 3.9º. The same segment on B and D transition states show dihedral angles of 19.9° and 30.2° revealing the angular tension generated on these systems. Finally, the endo and exo orientations are described by the C10-C11-C12-C13 dihedral angle which has values of 152.5°, 133.4°, 157.6° and 160.5º for A, C, B and D transition states, respectively.

Topological analysis of the electron density

According to Professor Houk intermolecular interactions as well as deformations experimented by the reacting fragments in transition states determine both the favored products and the activation energies.[²⁵] Since the fragments involved in the formation of pipitzols belong to the same molecule, carrying out deformation energy analysis is not possible. Instead, it was decided to obtain atomic properties under the framework of Bader’s Quantum Theory of Atoms in Molecules (QTAIM).[²⁶,²⁷]

Table 3 shows the energetic differences corresponding to the evolution of 4 fragments of perezone: (F1) the quinoid ring, (F2) the isopropenyl group (F3) the alkyl chain bonding the first two, and (F4) the methyl group. The process comprises the change of the reagents to the corresponding transition states. This data indicates the isopropenyl group is responsible for the increase in energy required to reach the transition states of the 4 isomers. Charge transfer to the quinoid ring and pyramidalization accounts for the destabilization. The reduction in stability of F2 is compensated by the quinoid ring, which is increasingly stabilized when F2 approximates in endo fashion. The exo configuration, observed experimentally, is explained by the contributions of F3, since the steric compression which deforms the fragment is decisive as for the exo conformers, F3 is strongly stabilizing with contributions of -11.67 and -11.60 kcal/mol for the α- and β conformers respectively. The α-endo conformer is destabilizing with a contribution of 6.33 kcal/mol (18.00 kcal/mol overall with respect to the α-exo isomer). β-endo contribution of -2.64 kcal/mol is only slightly stabilizing. Hence, the steric compression of the lateral chain is decisive for the stereoselectivity of the exo isomers over the endo.

Table 3 Change in Potential Energy related to four fragments of perezone. Values in kcal/mol. (F indicates fragment) 

	∆ε‡F1	∆ε‡F2	∆ε‡F3	∆ε‡F4	∆ε‡
A α-Exo	-19.54	69.82	-11.67	-8.84	29.77
B α-Endo	-25.67	64.83	6.33	-6.65	38.85
C β-Exo	-19.57	70.15	-11.60	-9.24	29.74
D β -Endo	-25.10	72.22	-2.64	-6.36	38.12

Experimentally, the formation of (-pipitzol is similar to the formation of the β-isomer, in that the two adducts are obtained in the same proportion. The contributions to free energy show this behavior has its origin in the activation enthalpy, since in all cases the activation entropy maintains similar values and points towards the decrease of the well-known degrees of freedom common to cycloaddition reactions. Additionally, entropy is highly relevant for (-isomers with respect to β-isomers.

To study the influence of the steric clash as the energy barrier of the compounds studied here, a calculation of the non-covalent interactions (NCI) based on the reduced density gradient s(r) was performed.

The reduced density gradient s(r) is a dimensionless quantity especially suited to identify noncovalent interactions that show the inhomogeneity of the electronic density. The capability of s(r) to recognize chemical hallmarks is reflected by the positions of its critical points (CP). The CP in s(r) is located at critical points in the electron density (∇ρ(r)=0), and at points where a complex balance between ρ(r) and von Weizsäcker kinetic exists.[²⁸] The latter are blind to QTAIM theory and correspond to intramolecular weak interactions. In this approach, the classification of the NCI is done in terms of the maximum variations in the contributions to the Laplacian, along with the axes, corresponding to the eigenvalues (λi) of the electron-density Hessian matrix. The sign of λ2 enables us to distinguish between the different types of weak interactions, attractive and repulsive (such as steric repulsions), while the electron density lets us assess the interaction strength. To gain a deeper understanding of factors controlling the selectivity trends, we performed an analysis of NCI in TSs based on the study of the density reduced gradient.

Firstly, we considered the endo-exo selectivity in the thermal reaction to prove if the steric compression of the lateral chain is decisive for the stereoselectivity of the exo isomers over the endo, as is suggested by the atomic properties calculated using QTAIM.

Fig. 5 collects NCI surfaces of TSA, TSB, TSC, and TSD. We can observe a complicated group of NCI surfaces, where bicolored isosurfaces appear reflecting stabilizing features counter-balanced by destabilizing interactions due to steric crowding. Due to this complexity, it is not possible to point out that NCI is the cause of the observed selectivity. Therefore, we have performed an integration of the electronic density in NCI. The integration of the electronic density in volume elements, defined by sign(λ2)ρ ranges, has been proved to be a useful tool for the estimation of the strength of the NCI. [²⁹] We performed the integration of ρ in two ranges, corresponding to attractive (-0.05 ≤ sign(λ2)ρ ≤ 0.00) and the repulsive ones (0.00 ≤ sign(λ2)ρ ≤ 0.05). The results are depicted in Table 4.

Fig. 5 Low gradient isosurfaces (s=0.5 u.a.) for the TS’s in the thermal reaction. 

Analyzing the integral values for TSA and TSB in Table 4, it is clear that the attractive and repulsive NCI seems to govern the endo-exo selectivity. TSA presents the higher value of attractive NCI where the difference relative to TSB is equal to 0.04 u.a. On the other hand, the repulsive NCI integrals in the TSB are slightly higher than in the TSA case by 0.02 u.a. Therefore, we can conclude that both sorts of interaction lead the exo approximation as the preferred one. That is, in the exo TS the attractive NCI are maximized whereas the repulsive ones are slightly alleviated.

In the β-pipitzol case, the density integral values show that TSC present less steric repulsion than TSD with a difference of 0.06 u.a., whereas the value of the attractive density integral are the same. Therefore, these results allowed us to conclude that the exo preference in this instance is explained by the less steric hindrance in the exo approximation.