Article pubs.acs.org/JPCA
Changes in Charge Distribution, Molecular Volume, Accessible Surface Area and Electronic Structure along the Reaction Coordinate for a Carbocationic Triple Shift Rearrangement of Relevance to Diterpene Biosynthesis Young J. Hong,‡ Robert Ponec,†,* and Dean J. Tantillo‡,* ‡
Department of Chemistry, University of California−Davis, 1 Shields Avenue, Davis, California, United States Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic v.v.i., Prague 6, Suchdol 2, 165 02, Czech Republic
†
S Supporting Information *
ABSTRACT: The nature of the recently described “triple shift” rearrangement of a biologically relevant carbocation (computed in the absence of a surrounding enzyme) is characterized by examining the evolution of charge distribution, molecular volume, accessible surface area, and multicenter bonding indices along its reaction coordinate. Implications for interaction of the rearranging carbocation with a terpene synthase active site are discussed.
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Synchronous is applied to describe the order of “events” or “subevents” in a concerted reaction; if these events occur to the same extent at most points along a reaction coordinate, then they occur synchronously, and if not, they occur asynchronously. Note that this term is used herein with regard to the extent of geometric changes, not explicitly with respect to time, although the latter is possible if dynamics simulations are undertaken.1,2,7 An event is defined as a chemical change (change in electronic structure) that one might reasonably expect to correspond to a concerted reaction on its own. A subevent is defined as an instance of bond-making or bond-breaking (or a significant conformational change), several of which may together constitute an event. We acknowledge that there is some room for ambiguity in the application of these terms, so we recommend that events and subevents for any reactions whose synchronicity is discussed be clearly defined. Events and subevents for the triple shift reaction shown in Scheme 1 are listed in Table 1. Energetics and Geometric Asynchronicity. A plot of the intrinsic reaction coordinate (IRC)5a,8 for the triple shift reaction is shown in Figure 1. Although the computed reaction coordinate contains several shoulders, the path from reactant to product is smooth and free of intermediates.9 Despite the fact that several bond-making and bond-breaking events are merged into a concerted process, the barrier is also not predicted to be high2,10only approximately 15 kcal/mol. Secondary carbocation structures that have been proposed previously to be intermediates (B and D; Scheme 1) do appear along the reaction coordinate (Figure 1), but are not minima. Clearly the three alkyl- or H-shift events that occur during this reaction occur asynchronously. A [1,2] sigmatropic alkyl shift of C12 from C13 to C16 occurs first. Then a hydrogen atom on C12 shifts
INTRODUCTION The study of the mechanisms of concerted reactions (i.e., reactions with no intermediate minima on their potential energy surfaces (PES))1 in which several bond-making/breaking events occur asynchronously has a long (and often contentious) history.2 Recently, it has been proposed that a variety of such processes occur during terpene-forming carbocation reactions reactions in which carbocations are formed in the active sites of enzymes and allowed to react through cyclizations and rearrangements to produce natural products with complex carbocyclic skeletons.3 In these concerted but asynchronous processes, [1,2] sigmatropic alkyl shifts, alkene−carbocation cyclizations (or their reverse), sigmatropic and nonpericyclic hydride shifts, intramolecular proton transfers, addition of external nucleophiles to carbocation centers, and deprotonation of C−H bonds α or β to carbocation centers are combined.4 While many such examples of this type of reaction have been described,4 perhaps the most dramatic is the “triple shift” shown in Scheme 1 (a combination of a [1,2] alkyl shift, a 1,3-hydride shift and another [1,2] alkyl shift), a reaction that may occur during the biosynthesis of kaurene, atiserene, and related diterpenes.5 These diterpenes are produced by various plants as biosynthetic precursors for a range of natural products with diverse biological and ecological functions.5 Herein we describe how charge distribution, molecular volume, solvent accessible surface area, and multicenter bonding change along the reaction coordinate for this “triple shift” reaction, and highlight potential implications of these changes for controlling the product distributions of these reactions.6
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RESULTS AND DISCUSSION Terminology. There has been, from time to time, some confusion in the literature regarding terminology related to synchronicity. Herein the following definitions are used.1,2 Concerted indicates a single-step reaction, with a single transition state structure and no intermediate minima on its PES. © 2012 American Chemical Society
Received: May 15, 2012 Revised: August 10, 2012 Published: August 11, 2012 8902
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Scheme 1. Triple Shift Rearrangement. Structure Labels and Atom Numbers Correspond to Those Used in ref 5a To Facilitate Comparison with Previous Work
Table 1. Events and Subevents for the Triple Shift Reaction (Scheme 1)
Figure 1. IRC plot (energy vs reaction coordinate) for the conversion of C2 to E (B3LYP/6-31+G(d,p); energies do not include zero point energy corrections (adapted from Figure 4 in ref 5a. Copyright American Chemical Society). Colors correspond (approximately) to events listed in Table 1 (borders between colors assigned based on C12−H distances in Figure 2).
(as a hydride) to C13, an event that occurs along the portion of the IRC near to the computed transition state structure. The third event, a [1,2] sigmatropic alkyl shift of C13 from C16 to C12, occurs along the downward slope from the transition state structure to the product, E.
Changes in specific interatomic distances along the IRC are shown in Figure 2. The first alkyl shift event involves breaking the C12−C13 bond (green) and forming the C12−C16 bond (orange); as the former of these two distances increases, the 8903
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Figure 2. Plot of selected interatomic distances vs reaction coordinate for the conversion of C2 to E. Colors correspond (approximately) to events listed in Table 1.
latter decreases, indicating that the bond-making and bondbreaking subevents within the alkyl shift event themselves occur synchronously. Note that the C12−C13 bond distance peaks before the overall transition state structure is reached. The 1,3-hydride shift event involves lengthening the C12−H bond (dark blue) and shortening the C13−H bond (light blue); these two bond length changes also mirror each other, but occur further along the reaction coordinate than the two comprising the first alkyl shift event, with the two distances being equal to each other near the transition state structure. The final alkyl shift event involves breaking of the C13−C16 bond (red) and formation of the C12−C13 bond (green), which was broken in the first alkyl shift event. Here, as the C13−C16 distance increases, the C12−C13 distance decreases. Note, however, that the C12− C13 distance also decreased temporarily during the 1,3-hydride shift event, that is, between the two alkyl shift events, so as to allow the hydride to transfer between C12 and C13. Note also that the final C12−C16 distance is slightly longer than its lowest value, consistent with a slight build-up of double bond character for this bond as C13 migrates over it (a similar increase in double bond character occurs for the C13−C16 bond during the initial alkyl shift event). Overall, the three shifting events occur asynchronously, although not completely separately, with respect to each other, although the bond-making and bond-breaking subevents comprising them occur synchronously. Molecular Shape. Several reports have discussed the changes in substrate molecular volume that occur during terpene synthase promoted carbocation rearrangements.11 In general, it appears that molecular volume decreases during such reactions, since acyclic reactants are converted to cyclic (or polycyclic) products; that is, new C−C σ-bonds are formed, which bring atoms closer together, making structures more compact.11 This sort of volume reduction may help product release, since a smaller product would be more loosely bound than a larger reactant that binds to the same active site (assuming that the shape of the active site does not change much in response), but may also allow for formation of byproducts as a carbocation cascade approaches its conclusion.11 The triple shift reaction does not involve a net increase in C−C σ-bonds or rings, however. Nonetheless, overall the molecular volume does decrease from the beginning to the end of this reaction (which is only part of a larger carbocation cascade);5 apparently the [2.2.2] bicycle in the final carbocation is more compact than the [3.2.1] bicycle in the starting carbocation (see Figures 3 and 4). As shown in Figure 3, this change in volume is not monotonic, however. A significant dip in volume is observed at the conclusion of the 1,3-hydride shift/initiation of the second [1,2] sigmatropic alkyl shift
Figure 3. Molecular volume and solvent accessible surface area (SASA) for selected points along the IRC (structures corresponding to points are shown in Figure 4). Colors correspond (approximately) to events listed in Table 1.
(see also point 92 in Figure 4). Not surprisingly, the molecular volume increases then decreases during each of the two alkyl shift events (although the change is greater for the second alkyl shift), as the migrating CH2 group for each is connected to the rest of the carbon framework by two long partial C−C bonds while at and near the midpoint of its shifting motion (e.g., point 43 and point 116 in Figure 4). Solvent accessible surface area (SASA) for selected structures along the IRC is also shown in Figure 3. Overall, changes to this quantity are much less dramatic than those to molecular volume. However, the accessibility of each specific carbon atom involved in the triple shift process changes significantly (Figure 5). For example, during the first alkyl shift, C12 moves from a relatively exposed position to a more congested area, and then during the second alkyl shift, C12 becomes an even less accessible bridgehead carbon. C13 experiences the same kind of changes, but in the opposite sense. C16, is essentially buried throughout the triple shift process, but its small changes in SASA do reflect the changes to molecular geometry that occur, with the accessibility of this atom increasing during the alkyl shift events. The accessibility of each of these atoms is relevant to both their ability to interact with active site residues if the triple shift occurs during the enzyme catalyzed production of kaurene, atiserene, and related diterpenes4,5a,12 and the likelihood that they may be attacked by nucleophiles.4,5a,13 Charge Distribution. The charge distribution in the rearranging carbocation also varies throughout the triple shift (Figure 6). The most positive region of the carbocation for any point along the reaction coordinate encompasses not only the carbon atom that formally bears the positive charge, but also the groups that are hyperconjugated to it.4,14 For example, as the first alkyl shift begins, the methyl and methylene groups attached to C16 are most positive (based on computed electrostatic potential). As this event proceeds, these groups become less positive, while the groups attached to C13 become more so. Analogous changes occur 8904
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Figure 4. Selected points along the IRC,5a with associated relative energies (kcal/mol) in parentheses.
it is useful to examine so-called bond indices for points along the reaction coordinate. These indices allow electronic information hidden in a complex wave function to be described in the language of bonds, bond orders, etc., the way that most chemists think of molecular structure. The most simple indices are the 2-center indices, exemplified by Wiberg and Wiberg−Mayer indices,15 whose values provide insight into the “extent“ of bonding interactions localized between pairs of atoms. The values for molecules close to equilibrium geometries, for example, often coincide closely with classical bond multiplicities.16,17 Consequently, monitoring of the variation in 2-center indices along an IRC provides a straightforward means of obtaining insight into the electronic reorganization occuring during a reaction. Key C−C 2-center indices for the triple shift are shown in Figure 7. The C12−C13 2-center index first decreases as this bond breaks in the first alkyl shift event, then it remains low until the C12−C13 bond reforms during the final alkyl shift event. The C12−C16 2-center index increases during the first alkyl shift event as expected and then remains high during the remaining events. The behavior of the C13−C16 2-center index mirrors this, since this bond is not broken until the final alkyl shift event. These changes in bond order track with changes in bond lengths (Figure 2). The 2-center C−H indices for the bonds that break and form as the hydrogen shifts also correspond nicely to changes in bond lengths (compare Figure 8 and Figure 2). While the 2-center indices provide a useful description of the coupled breaking and formation of bonds throughout the triple
Figure 5. SASA calculated for carbon atoms directly involved in bondmaking and bond-breaking (structures corresponding to points are shown in Figure 4). Colors correspond (approximately) to events listed in Table 1.
during the other two events of the triple shift. Again, these changes are relevant to the ability of particular substructures to participate in interactions (C−H···π or other types of cation···π)12 with residues in an active site that might facilitate or repress the triple shift. Electronic Structure. Geometric structure and electronic structure for molecules are intimately connected. The discussion above was focused on geometric structure, but how does the electronic structure of a triple shifting carbocation evolve along the reaction coordinate? Are the three events coupled by electronic delocalization or are they essentially separate (asynchronous) in that regard as well? To answer such a question 8905
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Figure 6. Electrostatic potential surfaces (range is 0.09 [red] to 0.18 au [blue, most positive]) for structures shown in Figure 4.
Figure 7. 2-Center C−C bond indices for selected points along the IRC. Colors correspond (approximately) to events listed in Table 1.
Figure 8. 2-Center C−H bond indices for selected points along the IRC. Colors correspond (approximately) to events listed in Table 1. 8906
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would expect to be transition state structures for these shifts if they were not combined into the triple shift. Interestingly, 4-center delocalization, which peaks in the vicinity of the transition state structure, was also detected for the hydride shift event (Figure 10). Although the hydride shifts between C12 and C13, it appears that C16 is also involved in the delocalization. In structures resembling B and D (Scheme 1), hyperconjugation between the C12−C16 bond and C13, and the C13−C16 bond and C12, respectively, is expected (see Figure 9), providing a means for coupling C16 to the C12,C13,H array. Perhaps the most important message from Figure 10 is that the sign of the 4-center index is negative, which is consistent with stabilizing 4-center 4-electron bonding, reminiscent of aromatic transition state structures for allowed 4-electron pericyclic reactions, which involve Möbius orbital arrays (e.g., conrotatory 4-electron electrocyclizations).19
shift (see also Figure 2), the fact that several bonds are broken and formed during the triple shift, and that carbocations tend to delocalize their electron density and charge, indicates that more extensive delocalization may be involved. This can be assessed using multicenter bond indices (MCI).18 MCI values for arrays of up to six atoms that might reasonably be expected to be involved in bond-making and bond-breaking were computed (see Computational Methods and Supporting Information for details), but no significant multicenter bonding was observed for arrays of more than four atoms. 3-Center bonding was detected for two fragments (C12,C13,H and C12,C16,C13; Figure 9), with maximum values values close
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CONCLUSIONS The triple shift reaction analyzed herein is complex, but its key features are revealed by the various quantities computed herein. Standard geometric parametersbond lengths, angles, etc.are consistent with the three shifting events occurring almost, but not quite, separately; that is, they occur asynchronously. Molecular volume decreases overall and dips at the beginning and end of the third shifting event, a change in molecular shape that might be expected to lead to looser binding with a terpene synthase active site. Although overall accessible surface area does not change much throughout this reaction, access to particular carbons of the molecular framework varies significantly, allowing certain groups to be exposed to an active site environment only at certain points along the reaction coordinate. The distribution of positive charge in the rearranging carbocation also changes significantly, and the maps we provide show regions most likely to participate in C−H/cation−π/lone pair interactions with an active site. Multicenter bond indices reveal the extent of different types of delocalization along the reaction coordinate, highlighting not only the 2-center and 3-center delocalization expected, but also the less obvious contribution from 4-center delocalization, which is associated with aromatic stabilization in a Möbius orbital array.
Figure 9. 3-Center bond indices for selected points along the IRC. Colors correspond (approximately) to events listed in Table 1.
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COMPUTATIONAL METHODS Cartesian coordinates for all structures and intrinsic reaction coordinate (IRC) calculations8 were reported previously in ref 5a. All of these calculations were performed with Gaussian 03.20 All geometries were optimized using the B3LYP/6-31+G(d,p) method,21 and all stationary points were characterized by frequency calculations. Molecular volume was calculated using the volume method implemented in Gaussian 09.22 SASA was calculated using the GETAREA method implemented in the Fantom program.23 SASA was calculated for non-hydrogen atoms using a water probe with a 1.4 Å radius. Structural drawings were produced using Ball & Stick.24 Multicenter bond indices were heuristically proposed by several independent groups as a generalization of the earlier concept of 2-center Wiberg or Wiberg−Mayer indices defined as biatomic terms from the partitioning of the identity 1.15−18
Figure 10. 4-Center bond indices for selected points along the IRC. Colors correspond (approximately) to events listed in Table 1.
Tr(PS)2 = 2N =
to 1. The positive sign of these indices is consistent with 3-center 2-electron bonding, as expected for the cationic sigmatropic and hydride shifts. The maxima of the 3-center indices correspond to structures along the reaction coordinate resembling species one
∑ WA + ∑ WAB A
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