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The mechanism of the (bis(phosphanylethyl)phosphane)Pt2+ catalyzed cyclo-isomerization reaction of 7-methyl-octa-1,6-diene to form 1-isopropylbicyclo[3.1.0]hexane was studied using computational methods. The cyclopropanation step was found to be the turnover-limiting step. The overall reaction proceeds via both a 5-exo and a 6-endo route. W conformations were shown to facilitate cyclopropanation, but do not have any influence on the rate of the 1,2-hydride shifts.
The conversion of squalene to hopene by squalene-hopene cyclase (SHC)1 represents one of the most impressive examples of a cyclo-isomerization reaction (eq. 1).2 It also highlights the general theme of utilizing poly-unsaturation to drive the synthesis of complex multicyclic products in terpene biosynthesis.3 The key transformation used in the construction of the terpenoids is the cation-olefin reaction, which, because of its ability to regenerate the cationic reactive intermediate, is perfectly suited to cascade polycyclization processes.4 In the biological context, the initiators of these reactions are typically Brønsted in nature, but metals can also be involved (e.g. Mg2+ for pyrophosphate ionization). Initiation and propagation is tightly controlled by the appropriate cyclase enzyme, with preorganization, cation-π, H-bonding etc., providing the stereo-, regio-, and chemoselectivity in these reactions.
Transition metal catalyzed cycloisomerization reactions are some of the most efficient methods for constructing polycyclic products,5 and like the enzymatic cases similarly utilize unsaturation to drive the production of polycyclic isomers. Judicious choice of metal catalyst (e.g. Ru,5 vs Pt6 vs Au7) enables different isomerization pathways to be exploited and unique products to be obtained. One unusual cycloisomerization pathway is the conversion of 1,6- and 1,7-dienes into bicyclopropane products8 by electrophilic phosphine ligated Pt(II) dications (e.g. eq 2).9,10 Like the enzymatic reactions, these processes are thought to proceed via ionic intermediates, though many of the mechanistic details underpinning the transformation are missing.
The illustrated cycloisomerization of β-citronellene to cis-thujane typifies a reaction that has a number of similarities to the biosynthesis of the thujane monoterpenes (Scheme 1).11 Starting from geranyl pyrophosphate, the pathways to the natural products are initiated by the generation of an allyl cation, which undergoes a cation-olefin cyclization to the terpinyl cation A, which after a 1,2-hydride shift and a second cation-olefin cyclization (transannular this time), provides the skeleton of the thujanes. A regiochemically parallel sequence of steps for the cycloisomerization of β-citronellene to cis-thujane was proposed for the Pt-catalyzed reaction (i.e. initial cyclohexyl ring formation followed by 1,2-hydride shift and transannular ring formation, Scheme 2).12,13 Also consistent with the data was a separate sequence of steps wherein the first C-C bond forming reaction generated the 5-membered ring, which after a 1,2-hydride shift and cyclopropanation, provided the bicyclopropane product.9,10 Since cationic intermediates corresponding to both an initiating 6-endo and 5-exo ring forming reaction could be trapped, it was not possible to differentiate between these two possible pathways. Since C-C bond formation had been shown to be rapid and reversible and 1,2-hydride shifts are typically fast, we postulated that the two pathways would ultimately be distinguished by the competitive rates of their cyclopropanation steps.
Although little is know about the details of the Pt-mediated cyclopropanation steps, the addition of a metal carbon bond to a fully formed, or incipient γ-carbocation has been previously studied for M= Ti,14 Fe,15 and Sn.16 In all three cases, the reactions are known to be stereospecific, and double invertive at each center (e.g. eq. 3),13 consistent with a reaction proceeding via a W-conformation (in red) that orients the two leaving groups.
In the present case, one could a priori see how the annulative reaction pathway (5-exo) could easily accommodate the W-conformer (Scheme 2), however, the conformation penalties and/or benefits imposed by confining the cation and the metal into a cyclohexane ring (6-endo) were less obvious.
Computational methods have recently been used successfully to study related reactions such as Pd promoted sigmatropic shifts17 and Pd catalysed allylic rearrangements.18 To gain insight into the sequence of steps describing the two pathways and additionally provide the first computational evaluation of the double invertive cyclopropanation reaction, we initiated a DFT study on the comparative reaction surfaces. The model complex chosen for evaluation utilized the triphos ligand stripped of its phenyl substituents.19
Calculations have been performed using GAUSSIAN 0320. Ground state structures were optimized in the gas phase using the RB3LYP hybrid functional21,22 in combination with the 6−31+G** basis set. Pt was modeled using the SDDALL basis set, which includes effective core potentials.23 This combination of functional and basis set has been shown to give good agreement with both structure and vibrational frequencies for Pd and Pt complexes.24 Transition states were located using QST2, QST3 or TS methods.25 Frequency calculations were carried out in the gas phase to confirm the presence of transition states and minima, as well as to establish free energy, enthalpy and entropy values. Except for structure 9, which was found to feature one negligible imaginary frequency at 5.15i cm−1, all structures are confirmed minima or transition states, respectively. Transition states connecting 6 and 12 and those between 6 and 13 were confirmed by IRC calculations. In the case of the other transition states the motion associated with the imaginary frequencies supported their nature.
Molecular orbitals were visualized using Molekel.26
Intermediates and transition states were identified for both the 5-exo and the 6-endo pathways resulting in the formation of the bicyclic product 13 (Scheme 2). Scheme 3 depicts all intermediates found for the 5-exo and 6-endo pathways. In some cases conformers of the intermediates were found and they are distinguished by the alphabetical labels. For clarity not all conformers are indicated in Scheme 3, only some of those pertaining to 1, where the diene is coordinated to the catalyst. In both pathways, depending on the initial conformation of the coordinated diene, multiple routes to the γ-carbocation were found. The energy profiles of the intermediates and the transition states connecting them are given in Fig. 1; in this case the most significant conformers are included. The atom labelings for both pathways are shown in Fig. 2.
Although extended conformers were “normal” with regards to their Pt-η2-alkene bonding, more curled conformers minimized to unusual structures wherein the Pt had slipped towards the terminus (C1) and generated positive character at C2,27,28 which was further stabilized by the pendant alkene.29 This latter interaction spread the charge over several centers (including C7)30 and significantly distorted the Pt-C and C-C bonds. In three of the four cyclization conformers (1a, 1c and 1d), this arrangement led to alkene slipped minima (2, 7 and 8) (Scheme 4).
The boat-like pre-cyclization conformers (1a, 1b, Scheme 3), smoothly traversed into the 5-exo reaction surface. Intermediate 2 completes the cyclization by fully adding the alkene to generate 3, which has a cis arrangement of substituents on the cyclopentane ring (Scheme 4). The orientation positioning the two alkenes in a gauche relationship, 1b, does not minimize to a non-classical structure but instead completes the cyclization to 4 with a trans arrangement of groups. We speculate that these boat-like structures do not follow the 6-endo mode since this pathway would form boat products.31,32
When the pre-cyclization conformers are chair-like (1c and 1d, Scheme 3), these lead to similarly chair-like non-classical alkene structures (7 and 8, Scheme 4). Compound 8 efficiently completes a 5-exo cyclization with a low activation barrier to a conformer of 4 (~1.6 kcal/mol), but it is also able to execute a higher energy 6-endo cyclization to form 10 (~12.8 kcal/mol). Noteworthy in the conversion of 8 to 10 is the motion that couples the 1,2-shift of the Pt from the terminal carbon to the internal carbon and the reciprocating 2,1-shift of the stabilizing alkene from the internal to the terminal position. This provides a mechanism for migrating the alkene to the terminus while minimizing positive charge build up on the least substituted carbon center.
Once these intermediate conformers were reached we assume rapid interconversion via low energy processes (ring flips, etc). The barriers for these cyclizations are considerably below the later ones indicating that the competing pathways are not being differentiated in the first C–C bond-forming cyclization.
The next step in both pathways is a 1,2-hydride shift that moves the positive charge from a carbon outside the ring to a ring contained one, forming 5 and 11. The barriers calculated for this process are low ranging from 2.5 to 10.1 kcal mol−1. Yet again the differences between the 5-exo and 6-endo pathways are insufficient to differentiate the two pathways. The tertiary carbocations 5 and 11 are estimated to be very close in energy and it may be assumed that both are accessed in the course of the reaction.
The carbocations 5 and 11 have bond angles and lengths associated with classical carbocations. In the course of seeking routes to cyclopropanation two further readily accessible intermediates, 6 and 12, were discovered. Key dimensions are given in Table 1. The conformation of these intermediates is discussed further below but it is apparent from, for example, the closing of the C1-C2-C6 angle that they may well lie on the pathway to formation of the three membered cyclopropane ring. Activation barriers to their formation lie in the range 1.4 to 5.5 kcal mol−1.
Given the similarity of their structures, it came as no surprise that in searching for the ring closure pathway, two transition states were identified connecting 6 to 12. One involved no additional species whereas the other had a molecule of ethene associated with the Pt (introduced to simulate an associative pathway for cyclopropanation). Corresponding geometric parameters can be found in Table 2. Comparison of the free energies of the two possible transition states (Figure 3) revealed that the values are extremely similar.
In the final step of the reaction, in both routes, the organic moiety is lost from the Pt catalyst to form the cyclopropane ring. Both dissociative and associative mechanisms were considered. In modeling the associative transition state a molecule of ethene was used as the displacing ligand instead of the diene starting material for computational expediency.
In the case of the 6-endo pathway, the breaking Pt-C bond in the transition state was slightly shorter than the distance between the metal centre and the incoming alkene (Fig. 4). The opposite, however, was found for the 5-exo pathway. Also, in the case of the 6-endo pathway the distances between the metal centre and the incoming/leaving groups were generally longer than for the 5-exo pathway. However, the cyclopropanation was more advanced for the 6-endo pathway as evidenced by that transition state showing the shorter C1-C6 distance (Table 3). Furthermore, the ethene C-C bond lengths in the transition states are 1.35 Å (6-endo) and 1.35 Å (5-exo), confirming an interaction between the metal centre and the alkene.
Consideration of the corresponding activation barriers for the cyclopropanation step (Fig. 5) reveals that cyclopropanation is the rate determining step for both pathways.33 The presence of ethene reduces the free energy of the cyclopropanation transition state in the gas phase. The structure of the associative cyclopropanation transition state (from 6) is shown in Fig. 6 and has the trigonal bipyramidal conformation generally assumed for substitution of Pt(II) complexes.34
The similarity of the two competing associative transition state energies does not allow the two pathways to be energetically differentiated, though the preceding low energy steps do have their own preferred pathways. Furthermore, comparison between the activation energies for the cyclopropanation step (circa 28 kcal mol−1) and the interconversion between 6 and 12 (circa 11−13 kcal mol−1, respectively), reveals, that interconversion between 6 and 12 is far more likely than cyclopropanation. This, therefore, suggests that regardless of which regio-direction the first cyclization takes (6-endo vs. 5-exo), a late stage pathway exists for inter-converting the competing reaction surfaces. In that sense the two pathways are not actually competing, and the question of which mechanism to product becomes moot; both mechanisms lead to product via a common intermediate.
The above discussion of the 6-endo pathway versus 5-exo pathway should thus be supplanted and the question reformulated as to whether the annulative or transannular arrangement is more favorable for cyclopropanation. Since 12 is 2 kcal/mol higher than 6 and their ΔG‡ are the same, this would point to a slight preference for the transannular situation. One could reasonably also conclude that they are nearly identical and neither is especially advantageous.
Overall ΔG‡ between the lowest energy intermediate, 7, and the cyclopropanation transition state is 31 kcal/mol, rather larger than suggested by the experimental conditions.35,36 This breaks down to an activation enthalpy of 18 kcal/mol and an activation entropy of −47 cal/K/mol. The large negative ΔS‡ is a consequence of the associative transition state. Gas phase calculations are not really appropriate for modeling reactions in solution where there is a change in the number of moles between reactant and product, because they over estimate translational and rotational entropy.37 On the other hand ΔH‡ which does not include entropy effects will underestimate ΔG‡ for an associative reaction. The values of 18 and 31 may be regarded as lower and upper estimates for the free energy of activation for this reaction. Thus the proposed mechanism is compatible with the experimental reaction conditions.
The two intermediates 6 and 12 were found to play a decisive role in the cyclopropanation step of this reaction. Both feature a W conformation, which has been observed in numerous non-cationic cyclopropanation reactions.14 Key structural parameters for 6 and 12 are given in Table 1 together with those for the product 13. Of particular note are the short C1-C6 distance and the small C1-C2-C6 angles of the carbocations, identifying 6 and 12 as non-classical structures. In this particular case this arrangement allows overlap between the empty p orbital on the carbocation, which forms a stroke of the W, and the bonding Pt-C orbital (Figs. 7 and and8).8). Furthermore, a W conformation features least steric hindrance (Fig. 7). Both of these factors should facilitate C-C bond formation. Indeed, visualization of the HOMO, as well as NBO analysis (Table 4) of intermediates 6 and 12 confirm that cyclopropanation is considerably advanced in W structures compared to different conformers. Generally speaking, the Pt-C1 occupancy is smaller for W shaped structures (mirrored by an increase in Pt-C1 bond length), whereas the p-orbital occupancy is greater than in non-W shaped analogues. In addition the interaction energy for W structures arising from donation of electron density from the Pt-C orbital into the empty p orbital on C6 via the back lobe of the Pt-C1 bond, an interaction known as homohyperconjugation or percaudal (“through the tail”) conjugation,38 is considerably greater. This is reflected by the considerably shorter C1-C6 bond length in W conformers (up to 0.36 Å).
The question that naturally arises is whether hyperconjugation is restricted to Pt (metal) systems or whether these may occur in any W conformation. In order to assess this, Pt(triphos) was replaced by H and the intermediates were reoptimized. Fig. 9 shows the minimum energy structures, 14 and 15, found for the 6-endo and 5-exo pathways respectively. The conformations of 14 and 15 are generally speaking similar to the metal analogues, 12 and 6. In a like manner to the Pt systems the protonated structures 14 and 15 adopt a W structure.
Table 5 compares structural parameters of the protonated intermediates with the Pt analogues. The C1-C6 distances and the C1-C2-C6 angles, as well as a corresponding NBO analysis, suggest that a percaudal interaction is present in protonated structures, but comparison of Pt and protonated systems (Table 5), reveals that hyperconjugation is less pronounced in the protonated analogues. The difference between C1-C6 distances in W and non-W shaped structures is 1.8 times larger in the Pt systems (ΔC1-C6(Pt) = 0.36 Å) compared to the protonated ones (ΔC1-C6(H) = 0.20 Å). (Table 3). This is reinforced by the corresponding interaction energies, namely that between the Pt-C1 bonding orbital and the empty orbital on C6. Furthermore, non-W structures of Pt and non-metal systems are extremely similar in terms of geometrical parameters, whereas these deviate substantially in the case of W systems. In particular, the C1-C6 distances of the W-shaped Pt systems are appreciably shorter (between 0.14 Å and 0.29 Å) than those of the protonated analogues. In the case of W-structures, the C1-C2-C6 angle is appreciably smaller for the Pt system than the corresponding protonated analogue indicating that the percaudal interaction is weaker in the protonated systems. (ΔC1-C2-C6(5exo) = 7.9°, ΔC1-C2-C6(6endo) = 18.2°). This reflects the above mentioned finding that the C1-C6 distances are shorter for the Pt analogues.
Last, but not least, it is noteworthy to mention that the only geometric parameters that change significantly on going from a non-W structure to a W structure are the C1-C6 bond length, and the C1-C2-C6 bond angles (Table 3). This is a strong indication that homohyperconjugation and no other interaction are responsible for the facilitated C-C bond formation.
It is also possible that a percaudal interaction also plays a role in the 1,2-hydride shifts, either by destabilizing the ground state (donation of electron density from the bonding Pt-C2 into the antibonding C6-H orbital) or by stabilizing the transition state. No correlation could be found (neither in the starting material nor in the transition state) between a W conformation and the activation energies, geometric parameters or orbital occupancies associated with the 1,2-hydride shift.
In light of the fact that a W structure is required for a facile cyclopropanation, one may question the need of intermediate 12, since structure 11, the preceding intermediate, actually features the required conformation. A cyclopropanation transition state which directly connected 11 with the desired products therefore would render the interconversion from 11 to 12, which was associated with a 5.40 kcal mol−1 activation barrier unnecessary.
A corresponding transition state, which features a W structure, was located for 11 → 13 + 1 with a structure similar to the ethene free structure, 12 → 13 + 1. The most important geometric parameters are listed in Table 6 along with the corresponding data from 10. As can be seen from Table 6 the two transition states 11 → 13 + 1 and 12 → 13 + 1 have very similar geometric parameters. However, closer analysis of the data suggests that 10 cyclopropanates more readily than 11 (shorter C1-C6 bond length, smaller Pt-C occupancy and longer Pt-C bond length etc. in the case of 12 → 13 + 1). Indeed, the free energy, ΔG298, of the reaction 11 → 13 + 1 is 1.31 kcal mol−1 higher than the route 12 → 13 + 1. Hence, as the cyclopropanation reaction was found to be the rate determining step, the pathway involving the unconventional intermediate 12 is more likely to occur.
Similar to the 6-endo case, direct cyclopropanation from the W structure 5 may occur, avoiding 6. However, the activation barrier for conversion of 5 into 6 is only 1.43 kcal mol−1 and the geometric features of the two intermediates are nearly identical. Thus, no appreciable advantage of direct cyclopropanation from 5 is expected.
The computational studies provide strong supporting evidence that the cyclopropanation step is rate determining in the production of 13, as has been proposed. However, contrary to what was expected, the cyclopropanation transition states for the 5-exo and 6-endo pathways have very similar free energy values (ΔG298 = 0.12 kcal mol−1). In addition, the difference in the free energies of activation, ΔG‡298, between the 5-exo and 6-endo pathway for the cyclopropanation step is only 1.86 kcal mol−1. Figure 10 shows the energy surface for some of the key transformations which gives an effective visualization of a slightly rumpled energy surface before the final transformation. It has also been demonstrated that interconversion between the two channels via 6 and 12 (and via 4b and 10 through 8) is more facile than cyclopropanation thus all pathways to the two interconverting intermediates are possible and all intermediates are likely to be sampled.
A W-conformation is vital for cyclopropanation, but does not play a decisive role in the case of the 1,2-hydride shift. Percaudal interactions are not restricted to Pt (or other metals, as were reported in the literature), but are present also in protonated systems but to a significantly lesser extent. It is therefore likely that homohyperconjugation occurs in every W system but the degree to which it facilitates ring closure will vary. In the reaction examined here, there appears to be little to discriminate between annulative or transannular cyclpropanation.
MRG wishes to thank the National Institutes of General Medicine for generous support (GM-60578). JCG and FB thank St. Hugh's College, Oxford for support.
Cartesian coordinates for intermediates and transition states. Ball and stick diagrams of optimized structures. Imaginary frequencies.
Zero point energy corrections, entropy corrections (298°K), ΔE(SCF), ΔH(298°K), ΔG(298°K).