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Cite This: J. Org. Chem. 2018, 83, 5724−5730

Biosynthesis and Conformational Properties of the Irregular Sesquiterpenoids Isothapsadiene and β‑Isothapsenol Laurence G. Cool,*,† Karl E. Vermillion,§ Gary R. Takeoka,† Selina C. Wang,∥ and Dean J. Tantillo*,‡ †

United States Department of Agriculture, Agricultural Research Service, 800 Buchanan Street, Albany, California 94710, United States § United States Department of Agriculture, Agricultural Research Service, 1815 North University Street, Peoria, Illinois 61604, United States ∥ Olive Center and Department of Food Science and Technology, University of California−Davis, Davis, California 95616, United States ‡ Department of Chemistry, University of California−Davis, Davis, California 95616, United States S Supporting Information *

ABSTRACT: A carbocation cyclization/rearrangement mechanism for the biosynthesis of isothapsadiene and βisothapsenol is shown to be energetically viable on the basis of density functional theory (DFT) calculations. In addition, for both isothapsadiene and β-isothapsenol, variable-temperature NMR experiments reveal two equilibrium conformers that undergo hindered exchange. The identities of these conformers, which are related by a chair-flip, are confirmed by DFT calculations on their structures, energies, 1H and 13C chemical shifts, and interconversion pathways.

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INTRODUCTION The irregular sesquiterpenoids isothapsadiene (1) and βisothapsenol (2) (Scheme 1) were isolated from the root oil of Ligusticum grayi (Coult. & Rose), a member of the carrot family (Apiaceae), along with many related sesquiterpenoids.1 Mechanistic pathways for the formation of the irregular sesquiterpenoids from L. grayi were proposed;1 that for 1 and 2 is reproduced in Scheme 1. The observed broadening of many of the 13C NMR signals of 1 and 2 suggested that they exist as a mixture of conformational isomers that undergo hindered exchange at ambient temperature.1 In the low-temperature 13C NMR spectrum of 1, 30 signals appeared, confirming the existence of two conformers in a ratio of about 3:1; the NOESY spectrum permitted determination of the conformations of the major and minor conformers.1 Herein we describe density functional theory (DFT) calculations on the carbocation cyclization/rearrangement cascade2,3 leading to the isothapsane skeleton. We also describe additional NMR experiments, coupled with DFT calculations,4,5 that confirm the identities of the interconverting conformers of 1 and 2.

diene/β-isothapsenol (Scheme 1) begins with irregular condensation of GPP, or species derived from it,6 with DMAPP (R = OPP = diphosphate) to form cyclobutylcarbinyl cation 3.7 A ring-expanding 1,2-alkyl shift, in analogy to reactions involved in the biosynthesis of other terpenes,7 would then form secondary cyclopentyl carbocation 4. Although secondary carbocations are often avoided in terpene-forming carbocation cascade reactions,3 it is possible that the relief of ring strain upon formation of 4 and steric shielding of the carbocation center by flanking quaternary carbons could allow this secondary cation to exist as a minimum. Attack of the nearby π-bond to form another secondary carbocation (5) would involve the net trade of a π-bond for a σ-bond, again potentially allowing 5 to be a minimum (although this is less likely on the basis of previously examined cases).3 A 1,2methyl/1,2-hydride/1,2-methyl shift sequence would lead to carbocation 8. Loss of a proton would lead to 2 (for R = OH), and net loss of a proton and elimination of H−R (perhaps via water loss from 2) would produce 1. The energetic viability of the 3→4→5→6→7→8 series of reactions was examined using mPW1PW91/6-31+G(d,p)// B3LYP/6-31+G(d,p) calculations.8−10 This computational recipe has been applied previously, with success, to many terpene-forming carbocation reactions.3 These calculations

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RESULTS AND DISCUSSION Isothapsadiene/β-Isothapsenol Formation Mechanism. The previously proposed1 mechanism for biosynthetic carbocation cyclization/rearrangement that leads to isothapsa© 2018 American Chemical Society

Received: March 29, 2018 Published: April 23, 2018 5724

DOI: 10.1021/acs.joc.8b00800 J. Org. Chem. 2018, 83, 5724−5730

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The Journal of Organic Chemistry Scheme 2. Computed 3→8 Reaction Pathwaya

Scheme 1. Putative Biosynthetic Carbocation Cyclization/ Rearrangement Mechanism for Formation of Isothapsadiene (1) and β-Isothapsenol (2)a

a

Relative energies (italics, kcal/mol, mPW1PW91/6-31+G(d,p)// B3LYP/6-31+G(d,p), relative to that of 3) for each minimum are shown next to each structure and, for transition state structures, next to the connecting arrows. Bonds elongated due to strong hyperconjugation and bonds involved in 3-center 2-electron bonding are highlighted in red (predicted lengths in Å).

Scheme 3. Interconverting Conformers of Isothapsadiene (1)

a

According to ref 1.

were carried out on a model system where R = H, rather than OH or OPP. We did not examine all conformers of each structure, but rather sought an energetically viable pathway, since the structure of an enzyme that leads to 8, and would constrain the conformation flexibility of its precursors, is not known. The results of these calculations suggest a pathway that differs considerably from that shown in Scheme 1 (see Scheme 2 for structures and energies and the Supporting Information for atomic coordinates for all structures). We were able to locate minima corresponding to structures 3, 4, and 5. Not surprisingly, the formally empty p orbital in 3 is strongly hyperconjugated to one of the adjacent C−C bonds in the cyclobutyl group, causing it to lengthen to 1.62 Å. The related C−C bond that is not as well-aligned with the carbocation p orbital is 1.57 Å long. Carbocation 4 also shows strong hyperconjugation, with the C−C bond connected to its homoprenyl tail elongated to 1.66 Å. Carbocation 5 is not a simple secondary carbocation, but instead sports a cyclic 3center 2-electron delocalized bonding array that is characteristic of “nonclassical” carbocations.11 An additional minimum (5′) was found that is 5 kcal/mol lower in energy than 5; this minimum is related to 5 by a 1,2-alkyl shift that converts a secondary (here, nonclassical) carbocation substructure to a

tertiary carbocation substructure (again, significantly hyperconjugated). The pathways relating these minima are not simple. The transition state structure that, based on its geometry, appears to convert 3 to 4 actually connects 3 to 5′ (via a ca. 5 kcal/mol barrier), according to intrinsic reaction coordinate (IRC) calculations.12 While structures resembling 4 are found along the reaction coordinate, these are not minima; i.e., 4 is only a minimum when it is not in a conformation that is productive for cyclization. Note that the results of these calculations indicate that 5′, rather than 5, is likely to be formed. However, given past results on other terpene-forming carbocation cascade reactions, we suspect that the pathway downhill from the transition state structure following 3 may bifurcate,13 allowing access to both 5′ and 5 (the relative amounts of each thereby being controlled by both inherent3e and enzyme-induced dynamic effects). This contention could be tested via dynamics trajectory calculations,13b but these are beyond the scope of the current work. We were able to find a transition state structure for the direct conversion of 5′ to 5 via a shift of the methine group that bridges in 5. This transition state structure is approximately 6 kcal/mol higher in energy than 5′, a low enough barrier such 5725


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Figure 1. Experimental (normal text) and computed (bold italics; IEFPCM(acetone)-mPW1PW91/6-311+G(2d,p)//B3LYP/6-31+G(d,p)) chemical shifts (ppm vs TMS in acetone) and mean absolute deviations (MAD) for isothapsadiene (1) conformers A and B. Top (red): 13C shifts. Bottom (blue): 1H shifts.

peaks, while at 213 and 193 K (in acetone-d6) exchange slowed sufficiently to give discrete 1H and 13C NMR signals for each conformer (Supporting Information). Integration of isolated 1H signals of the conformers indicated a ratio of 77:23 at 193 K. When an equilibrium Boltzmann distribution was assumed, this ratio would correspond to an energy difference of ca. 0.46 kcal/ mol at 193 K. Two low energy conformers of isothapsadiene (1) were located using the B3LYP/6-31+G(d,p) DFT method (Scheme 3 and Figure 1).5,8,10 1H and 13C chemical shifts for these conformers were computed at the IEFPCM(acetone)mPW1PW91/6-311+G(2d,p)//B3LYP/6-31+G(d,p) (scaled) level.3,8−10,15−17 As shown in Figure 1, the computed and experimental shifts match each other closely, indicating that the computed structures of A and B are consistent with the experimental data. Conformer A is predicted to be 0.05−0.8 kcal/mol lower in energy than conformer B, depending on the level of theory employed (Figure 2).8−10,15−19 These results are thus in good agreement with the 0.46 kcal/mol energy difference calculated from NMR measurement of conformer ratios. The fact that these conformers, which are related by a chairflip of their cyclohexane rings, are close in energy makes sense given that both have four neighboring methyl groups arrayed in axial−equatorial−axial−equatorial positions. A pathway for chair-flipping was determined at the B3LYP/6-31+G(d,p)

that 5 can be formed by way of 5′ even if the aforementioned bifurcation does not provide a means of accessing 5 directly. Carbocations 6−8 are unremarkable, each benefiting from expected hyperconjugation. Formation of carbocation 6 is an exothermic process, as a tertiary carbocation is formed and some ring strain is released. We located a structure that appears to correspond to a transition state structure for direct interconversion of 5 and 6; this structure is only 6 kcal/mol higher in energy than 5. The imaginary vibrational mode associated with this transition state structure corresponds primarily to a conformational change that serves to remove bridging and align the formally empty p orbital at the carbocation center with the C−C bond to the methyl group that migrates to form 6. Carbocation 6 is easily converted to 7 by another low barrier (of approximately 6 kcal/mol). Carbocations 7 and 8 will likely be in equilibrium (because they are close in energy and interconverted by way of a small barrier, approximately 5 kcal/mol from 7) until deprotonation by an appropriately positioned enzyme active site residue occurs.14 Overall, the conversion of 3 to 8 is highly exothermic and involves only small barriers, as is often the case for cyclization/rearrangement processes that lead to terpene natural products.3 Isothapsadiene Conformers. As previously reported,1 several peaks were markedly broadened in the 298 K 13C NMR spectrum of 1 (in C6D6). Raising the temperature narrowed the 5726


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Two low energy conformer families, each family consisting of four different −CH2OH conformations of the same bicycle conformer, were located at the B3LYP/6-31+G(d,p) level of theory (Scheme 4 and Figure 4).5,8,10 1H and 13C chemical shifts for these conformers were again computed at the IEFPCM(acetone)-mPW1PW91/6-311+G(2d,p)//B3LYP/631+G(d,p) (scaled) level.3,8−10,15−17 As shown in Figure 3, the computed and experimental shifts match each other closely, indicating that the computed structures of A and B are consistent with the experimental data. The lowest energy conformer of A is predicted to be 1.5−2.2 kcal/mol lower in energy than the lowest energy conformer of B, depending on the level of theory employed (Figure 4);8−10,15−17,19,20 this is in reasonable agreement with the 1.13 kcal/mol energy difference calculated from NMR measurement of conformer ratios. A pathway for chair-flipping for a representative conformer was determined at the B3LYP/6-31+G(d,p) level (Figure 4), and the conversion of A to B again involves passage through a half-chair transition state structure to form a boat-like intermediate that is converted to B by way of another halfchair transition state structure. The overall free energy barrier from A to B through the boat-like intermediate is predicted to be 8.4 kcal/mol with B3LYP/6-31+G(d,p). NMR line shape simulation calculations for 2, using the conformer ratios and 13C chemical shift differences measured at 203 K, indicated an exchange rate of ca. 1.5 × 103 s−1 at 300 K (see the Supporting Information). The implied forward rate constant for A→B, ca. 90 s−1, corresponds to a ΔG‡ of 14.9 kcal/mol, markedly higher than that predicted using B3LYP/631+G(d,p). Consequently, single point energy calculations with several different methods were performed on the first half-chair transition state structure, and its energy relative to A was found to vary with the level of theory used (8.4−13.4 kcal/mol, Figure 4). This variation appears to be due in large part to an overestimation, to varying degrees, of the importance of an interaction between the OH proton and the nearby π-bond in the half-chair transition state structure. Predicted OH···Cπ distances are shorter by 0.03 and 0.07 Å in the transition state structure than in A, indicating that this interaction strengthens as the transition state structure is reached, selectively stabilizing this structure and lowering the predicted barrier relative to that for the system shown in Figure 2, which lacks a hydroxyl group. However, the experimentally determined barrier is not lower for β-isothapsenol than for isothapsadiene, indicating that the OH−π interaction is washed out in solution as hydrogen bonding between the hydroxyl group and acetone molecules predominates. To put this hypothesis to the test, the CH2OH group was replaced by a CH3 group and the barrier recalculated. Predicted barriers for this OH-free system were 13.6, 14.2, and 14.5 kcal/mol with the IEFPCM(acetone)-mPW1PW91/6-311+G(2d,p), SMD(acetone)-M06-2X/6-311+G(2d,p), and SMD(acetone)ωB97X-D/6-311+G(2d,p) levels of theory, respectively, all in reasonable agreement with the experimental barrier for conformer interconversion for β-isothapsenol.21

Figure 2. Computed energies of stationary points involved in the interconversion of isothapsadiene (1) conformers: A ⇌ B. Relative free energies (kcal/mol) computed with B3LYP/6-31+G(d,p) are shown in normal text. Relative electronic energies computed with IEFPCM(acetone)-mPW1PW91/6-311+G(2d,p)//B3LYP/6-31+G(d,p), SMD(acetone)-M06-2X/6-311+G(2d,p)//B3LYP/6-31+G(d,p), and SMD(acetone)-ωB97X-D/6-311+G(2d,p)//B3LYP/631+G(d,p) are shown in italics, bold, and underlined text, respectively. The red portion of the molecule flips in the left-hand process, while the blue portion of the molecule flips in the right-hand process.

level. As shown in Figure 2, the conversion of A to B involves passage through a half-chair transition state structure to form a boat-like intermediate. This intermediate is converted to B by way of another half-chair transition state structure.20 The barrier for this process (from A) is computed to be approximately 14 kcal/mol, corresponding to a room temperature half-life in the fractional millisecond range, which is consistent with the observed 125 MHz 13C NMR peak broadening. Line shape simulation calculations for the 300 and 343 K 13C NMR spectra (Supporting Information) gave approximate exchange rates of 5 × 103 s−1 and 7 × 104 s−1, corresponding to activation free energies (ΔG‡) of ca. 13.4 and 13.6 kcal/mol, respectively. This agrees quite well with the value determined by DFT calculations. In subambient 500 MHz 1H NMR spectra, broadening of isolated downfield peaks of 1 was also seen. Line shape simulation calculations for the 253 K 1H NMR spectrum gave an exchange rate of ca. 180 s−1. For the 213 K data, where signals for both conformers appeared, the calculated exchange rate was about 3 s−1. Combining the exchange rate estimations from the 1H and 13C NMR data permitted calculation of approximate values of ΔH‡ and ΔS‡ of the conformational exchange from an Eyring plot (see the Supporting Information). β-Isothapsenol Conformers. Low-temperature NMR experiments on 2 in (CD3)2CO were run at 203 K. Measured 1 H and 13C chemical shifts are shown in Figure 3 in normal text. As in the case of 1, 30 sharp peaks appeared in the 13C spectrum, 15 for each conformer, and integration of several isolated 1H signals gave a ca. 94:6 ratio of major and minor conformers. This corresponds to a theoretical energy difference of ca. 1.13 kcal/mol.

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CONCLUSIONS The results of DFT calculations on possible biosynthetic routes to the isothapsane sesquiterpenoids suggest that an unexpected tertiary carbocation with a [3.3.0]bicyclooctane core is likely formed during the cyclization/rearrangement reaction cascade. Thereafter, facile conversion to a nonclassical [4.3.0]bicyclononyl carbocation provides the carbon skeleton for all 5727


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Figure 3. Experimental (normal text) and computed (bold italics; IEFPCM(acetone)-mPW1PW91/6-311+G(2d,p)//B3LYP/6-31+G(d,p)) chemical shifts (ppm vs TMS in acetone) and mean absolute deviations (MAD) for β-isothapsenol (2) conformers A and B. (For each, there are four conformers of similar energies resulting from rotation about the CH−CH2OH and CH2−OH bonds, which have been included in a weighted average using IEFPCM(acetone)-mPW1PW91/6-311+G(2d,p)//B3LYP/6-31+G(d,p) relative energies. See the Supporting Information for details. The lowest energy CH2OH rotamers for A and B are shown.) Top (red): 13C shifts. Bottom (blue): 1H shifts.

Scheme 4. Interconverting Conformers of β-Isothapsenol (2)a

a

For each of A and B, there are four conformers of similar energy resulting from rotation about the CH−CH2OH and CH2−OH bonds. (See the Supporting Information for details.) Figure 4. Computed energies of stationary points involved in the A ⇌ B interconversion of β-isothapsenol (2). Relative free energies (kcal/ mol) computed with B3LYP/6-31+G(d,p) are shown in normal text. Relative electronic energies computed with IEFPCM(acetone)mPW1PW91/6-311+G(2d,p)//B3LYP/6-31+G(d,p), SMD(acetone)-M06-2X/6-311+G(2d,p)//B3LYP/6-31+G(d,p), and SMD(acetone)-ωB97X-D/6-311+G(2d,p)//B3LYP/6-31+G(d,p) are shown in italics, bold, and underlined text, respectively. The red portion of the molecule flips in the left-hand process, while the blue portion of the molecule flips in the right-hand process.

of the irregular bicyclic sesquiterpenoids of L. grayi, including isothapsadiene (1) and β-isothapsenol (2). In addition, the DFT-computed 1H and 13C chemical shifts for 1 and 2 are consistent with experimentally reported shifts. Together, the theoretical and experimental results indicate that, for both 1 and 2, there are two low energy conformations of the bicyclic framework that are close in energy and connected by high enough barriers that both can be observed in low-temperature NMR experiments. 5728


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EXPERIMENTAL SECTION

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ASSOCIATED CONTENT

of Monoterpenes, Sesquiterpenes, and Diterpenes. Top. Curr. Chem. 2000, 209, 53−95. (3) For reviews on quantum chemical calculations on terpeneforming carbocation cascades, see: (a) Tantillo, D. J. Biosynthesis via Carbocations: Theoretical Studies on Terpene Formation. Nat. Prod. Rep. 2011, 28, 1035−1053. (b) Tantillo, D. J. The Carbocation Continuum in Terpene Biosynthesis - Where are the Secondary Cations? Chem. Soc. Rev. 2010, 39, 2847−2854. (c) Tantillo, D. J. Recent Excursions to the Borderlands between the Realms of Concerted and Stepwise: Carbocation Cascades in Natural Products Biosynthesis. J. Phys. Org. Chem. 2008, 21, 561−570. (d) Hare, S. R.; Tantillo, D. J. Dynamic Behavior of Rearranging Carbocations − Implications for Terpene Biosynthesis. Beilstein J. Org. Chem. 2017, 13, 1669. (e) Tantillo, D. J. Importance of Inherent Substrate Reactivity in Enzyme Promoted Carbocation Cyclization/Rearrangements. Angew. Chem., Int. Ed. 2017, 56, 10040−10045. (4) For reviews on quantum chemical calculations of NMR chemical shifts, see: (a) Lodewyk, M. W.; Siebert, M. R.; Tantillo, D. J. Computational Prediction of 1H and 13C Chemical Shifts: A Useful Tool for Natural Product, Mechanistic and Synthetic Organic Chemistry. Chem. Rev. 2012, 112, 1839−1862. and references therein. (b) Willoughby, P. H.; Jansma, M. J.; Hoye, T. R. A Guide to Smallmolecule Structure Assignment through Computation of (1H and 13C) NMR Chemical Shifts. Nat. Protoc. 2014, 9, 643−660. (c) Alkorta, I.; Elguero, J. Computational NMR Spectroscopy. In Computational Spectroscopy: Methods, Experiments and Applications; Grunenberg, J., Ed.; Wiley-VCH: Weinheim, Germany, 2010; p 37. (d) Tantillo, D. J. Walking in the Woods with Quantum Chemistry - Applications of Quantum Chemical Calculations in Natural Product Research. Nat. Prod. Rep. 2013, 30, 1079−1086. (e) Grimblat, N.; Sarotti, A. M. Computational Chemistry to the Rescue: Modern Toolboxes for the Assignment of Complex Molecules by GIAO NMR Calculations. Chem. - Eur. J. 2016, 22, 12246−12261. (f) Di Micco, S.; Chini, M. G.; Riccio, R.; Bifulco, G. Quantum Mechanical Calculation of NMR Parameters in the Stereostructural Determination of Natural Products. Eur. J. Org. Chem. 2010, 2010, 1411−1434. (5) For representative studies in which terpene structures were assigned, or assigned structures confirmed, using quantum chemical computations of NMR chemical shifts, see: (a) Vaughan, M. M.; Webster, F. X.; Kiemle, D.; Hong, Y. J.; Tantillo, D. J.; Wang, Q.; Coates, R. M.; Wray, A. T.; Askew, W.; O’Donnell, C.; Tokuhisa, J. G.; Boland, W.; Tholl, D. Formation of the Unusual Semivolatile Diterpene Rhizathalene by the Arabidopsis Class I Terpene Synthase TPS08 in the Root Stele is Involved in Defense Against Belowground Herbivory. Plant Cell 2013, 25, 1108−1125. (b) Mafu, S.; Karunanithi, P. S.; Palazzo, T. A.; Harrod, B. L.; Rodriguez, S. M.; Mollhoff, I. N.; O’Brien, T. E.; Tong, S.; Fiehn, O.; Tantillo, D. J.; Bohlmann, J.; Zerbe, P. Biosynthesis of the Microtubule-Destabilizing Diterpene Pseudolaric Acid B from Golden Larch Involves an Unusual Diterpene Synthase. Proc. Natl. Acad. Sci. U. S. A. 2017, 114, 974−979. (6) Poulter, C. D. Biosynthesis of Non-head-to-tail Terpenes. Formation of 1′-1 and 1′-3 Linkages. Acc. Chem. Res. 1990, 23, 70−77. (7) Hong, Y. J.; Tantillo, D. J. How Cyclobutanes are Assembled in Nature − Insights from Quantum Chemistry. Chem. Soc. Rev. 2014, 43, 5042−5050. (8) For the B3LYP density functional, see: (a) Becke, A. D. Densityfunctional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648−5652. (b) Becke, A. D. A New Mixing of Hartree−Fock and Local Density-functional Theories. J. Chem. Phys. 1993, 98, 1372−1377. (c) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-energy Formula into a Functional of the Electron Density. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 37, 785−789. (d) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields. J. Phys. Chem. 1994, 98, 11623−11627. (9) For the mPW1PW91 density functional, see: (a) Matsuda, S. P. T.; Wilson, W. K.; Xiong, Q. Mechanistic Insights into Triterpene Synthesis from Quantum Mechanical Calculations. Detection of

All 1D and 2D NMR spectra were acquired on a Bruker Avance 500 spectrometer using a 5 mm BBO probe and TOPSPIN 1.3 pl 8 software, as previously described.1 The experimental temperatures were taken to be the nominal probe temperature. Dynamic NMR spectral line shape analysis was done using the gNMR software program.22 Exchange rates were determined by visually comparing simulated and experimental spectra, varying the simulation exchange rate to optimize matching of line widths of significantly broadened peaks. In the case of the 1H spectrum of 1, to minimize computation time, only six well-resolved downfield signals were simulated. Calculation of kinetic parameters followed ref 23. ΔG‡ values were computed from the forward rate constants, the latter being the product of the simulation exchange rate and the proportion of the minor conformer. For 1, an Eyring plot was constructed using experimental data at four temperatures: 343 and 300 K (13C NMR spectra) and 243 and 213 K (1H NMR spectra). Linear regression analysis of the data gave these approximate values: ΔH‡ = 10.7 kcal/mol; ΔS‡ = −8.6 cal/ mol (Supporting Information).

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.joc.8b00800. Coordinates and energies for computed structures, variable-temperature NMR spectra and NMR line shape simulations for 1 and 2, and Eyring plot for isothapsadiene 1 (PDF) Computed NMR data for isothapsadiene (XLSX) Computed NMR data for β-isothapsanol (XLSX)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Dean J. Tantillo: 0000-0002-2992-8844 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to the US National Science Foundation (CHE1565933, CHE-1361807, and CHE-030089 for computer time via the XSEDE program) for support and Carla Saunders (UC Davis) for assistance with several calculations.

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REFERENCES

(1) Cool, L. G.; Vermillion, K. E.; Takeoka, G. R.; Wong, R. Y. Irregular Sesquiterpenoids from Ligusticum grayi Roots. Phytochemistry 2010, 71, 1545−1557. (2) For reviews on biosynthetic terpene formation mechanisms, see: (a) Christianson, D. W. Structural Biology and Chemistry of the Terpenoid Cyclases. Chem. Rev. 2006, 106, 3412−3442. (b) Christianson, D. W. Unearthing the Roots of the Terpenome. Curr. Opin. Chem. Biol. 2008, 12, 141−150. (c) Croteau, R. Biosynthesis and Catabolism of Monoterpenoids. Chem. Rev. 1987, 87, 929−954. (d) Cane, D. E., Cyclization Mechanisms, In Sesquiterpene biosynthesis. Elsevier, London, 1999, Vol. 2, 155−200. (e) Cane, D. E. Isoprenoid Biosynthesis. Stereochemistry of the Cyclization of Allylic Pyrophosphates. Acc. Chem. Res. 1985, 18, 220−226. (f) Cane, D. E. Enzymic Formation of Sesquiterpenes. Chem. Rev. 1990, 90, 1089−1103. (g) Davis, E. M.; Croteau, R. Cyclization Enzymes in the Biosynthesis 5729


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(19) For ωB97X-D, see: Chai, J.-D.; Head-Gordon, M. Long-range Corrected Hybrid Density Functionals with Damped Atom−atom Dispersion Corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615− 6620. (20) An alternative pathway for the A ⇌ B interconversion is possible in which the blue portion of the molecule in Figure 2 flips first, followed by the red portion. This pathway was not examined in full, but the results of preliminary calculations indicate that it has an overall barrier that is higher than that for the pathway shown. Slightly different conformers of the boat form shown in Figure 2 are theoretically possible, but their energies, and the energies for any transition state structures for their interconversion, are expected to be close to that of the boat-like structure shown. (21) As shown in Figure 4, the results of IEFPCM calculations for the β-isothapsenol barrier are much closer to experiment than those obtained using the SMD solvation model. While this may seem to indicate that OH−π interactions are treated reasonably well by the IEFPCM method (assuming that the difference is not due to the change in functionals used), we suspect that the better agreement between the IEFPCM calculations and experiment is a coincidence, given that both methods do not treat explicit solute−solvent hydrogen bonds directly. For details on differences between IEFPCM and SMD (which, as implemented in Gaussian, makes use of an IEFPCM protocol), see ref 15. (22) Budzelaar, P. H. M. gNMR v. 5.0.6.0. (23) Barquera-Lozada, J. E.; Quiroz-Garcia, B.; Quijano, L.; Cuevas, G. Conformational Properties of the Germacradienolide 6-Epidesacetyllaurenobiolide by Theory and NMR Analyses. J. Org. Chem. 2010, 75, 2139−2146.

Systematic Errors in B3LYP Cyclization Energies. Org. Biomol. Chem. 2006, 4, 530−543. (b) Adamo, C.; Barone, V. Exchange Functionals with Improved Long-range Behavior and Adiabatic Connection Methods without Adjustable Parameters: The mPW and mPW1PW Models. J. Chem. Phys. 1998, 108, 664−675. (10) (a) All DFT calculations were carried out with the following program: Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; et al. Gaussian 09, Revision B.01; Gaussian, Inc.: Wallingford, CT, 2010. (b) Molecular structures were visualized using the following program: Müller, N.; Falk, A.; Gsaller, G. Ball & Stick V.4.0a12, molecular graphics application for MacOS computers; Johannes Kepler University: Linz, Austria, 2004. (11) (a) Grob, C. A. Inductivity and Bridging in Carbocations. Acc. Chem. Res. 1983, 16, 426−431. (b) Brown, H. C. The Energy of the Transition States and the Intermediate Cation in the Ionization of 2Norbornyl Derivatives. Where is the Nonclassical Stabilization Energy? Acc. Chem. Res. 1983, 16, 432−440. (c) Olah, G. A.; Prakash, G. K. S.; Saunders, M. Conclusion of the Classical-nonclassical Ion Controversy based on the Structural Study of the 2-Norbornyl Cation. Acc. Chem. Res. 1983, 16, 440−448. (d) Walling, C. An Innocent Bystander Looks at the 2-Norbornyl Cation. Acc. Chem. Res. 1983, 16, 448−454. (e) Brown, H. C. The Nonclassical Ion Problem; Springer: New York, 1977. (12) (a) Gonzalez, C.; Schlegel, H. B. Reaction Path Following in Mass-weighted Internal Coordinates. J. Phys. Chem. 1990, 94, 5523− 5527. (b) Fukui, K. The Path of Chemical Reactions - the IRC Approach. Acc. Chem. Res. 1981, 14, 363−368. (c) Maeda, S.; Harabuchi, Y.; Ono, Y.; Taketsugu, T.; Morokuma, K. Intrinsic Reaction Coordinate: Calculation, Bifurcation, and Automated Search. Int. J. Quantum Chem. 2015, 115, 258−269. (13) (a) Ess, D. H.; Wheeler, S. E.; Iafe, R. G.; Xu, L.; Ç elebi-Ö lçüm, N.; Houk, K. N. Bifurcations on Potential Energy Surfaces of Organic Reactions. Angew. Chem., Int. Ed. 2008, 47, 7592−7601. (b) Hare, S. R.; Tantillo, D. J. Post-Transition State Bifurcations Gain Momentum − Current State of the Field. Pure Appl. Chem. 2017, 89, 679−698. (14) (a) Pemberton, R. P.; Ho, K. C.; Tantillo, D. J. Modulation of Inherent Dynamical Tendencies of the Bisabolyl Cation via Preorganization in epi-Isozizaene Synthase. Chem. Sci. 2015, 6, 2347−2353. (b) Hong, Y. J.; Tantillo, D. J. The Taxadiene-Forming Carbocation Cascade. J. Am. Chem. Soc. 2011, 133, 18249−18256. (15) For the IEFPCM method (the default method in Gaussian 09), see: (a) Tomasi, J.; Mennucci, B.; Cancès, E. The IEF Version of the PCM Solvation Method: An Overview of a New Method Addressed to Study Molecular Solutes at the QM ab initio Level. J. Mol. Struct.: THEOCHEM 1999, 464, 211−226. For the SMD solvation method, see: (b) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions. J. Phys. Chem. B 2009, 113, 6378−6396. (16) For the linear scaling approach, see: (a) Jain, R.; Bally, T.; Rablen, P. R. Calculating Accurate Proton Chemical Shifts of Organic Molecules with Density Functional Methods and Modest Basis Sets. J. Org. Chem. 2009, 74, 4017−4023. (b) Pierens, G. K. 1H and 13C NMR Scaling Factors for the Calculation of Chemical Shifts in Commonly Used Solvents using Density Functional Theory. J. Comput. Chem. 2014, 35, 1388−1394. (c) Scaling factors were obtained from http:// cheshirenmr.info. (17) The computed NMR data in benzene, which was used for the NMR experiments in ref 1, is included in the Supporting Information. (18) For M06-2X, see: Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-class Functionals and 12 Other Functionals. Theor. Chem. Acc. 2008, 120, 215−241. 5730


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