Letter pubs.acs.org/OrgLett
Mechanistic Information from Nonstationary Points Anup Rana, M. Emin Cinar, Debabrata Samanta, and Michael Schmittel* Department of Chemistry and Biology, Organische Chemie 1, Universität Siegen, Adolf-Reichwein-Strasse 2, D−57068 Siegen, Germany S Supporting Information *
ABSTRACT: The thermal cyclization of enyne−carbodiimides substituted at both the alkyne and carbodiimide terminus showed two curved Hammett correlations (log k/k0 against σp) that were fully reproduced by DFT (density functional theory) computational results. The latter suggest a concerted mechanism, but the transition state (TS) analysis failed to reveal any mechanistic insight about the reason for a curved Hammett correlation. Instead a preTS inspection, i.e., examination of the electronic and steric details on route between reactant and TS, furnished a detailed picture of the mechanism.
T
he meticulous inspection of stationary points along the potential energy surface (PES) to identify mechanistic information has a long and triumphant history, in particular for physical organic chemistry after teaming up with computational investigations.1 A large amount of attention is typically given to the rate-determining step with its preceding minimum, the transition state (TS), and the corresponding product because agreement between computed and experimental kinetic data, e.g., see kinetic isotope effects,2 provides a solid base for any mechanistic hypothesis derived therefrom. Here, we show that at the concerted vs stepwise boundary3 the mechanistic information is not necessarily revealed from a review of the stationary points. Instead, the examination of nonstationary points between reactant(s) and rate-determining TS, a preTS inspection, provides the important clues. Over many years, the C2−C6 diradical cyclization of enyne− allenes has been investigated by numerous authors.4,5 For the cyclization of the related enyne−carbodiimides 1 (Scheme 1), we
Figure 1. Comparison of the onset temperatures in the thermal cyclization of 1a and 3.
furnishing a curved Hammett relationship that separated electron-donating and -withdrawing groups (Figure 2). At the
Scheme 1. Thermal Cyclization of Enyne−carbodiimides 1a− k with Polar Substituents at Either Terminus
Figure 2. Hammett plots of rate constants for 1a−k vs σp (Table S1). Experimental (top)8 and computed (bottom) data. Subscripts X and Y stand for series X (left) and Y (right).
proposed in 1998 a stepwise mechanism involving a diradical intermediate6 based on MR-CI + Q computations (DZP basis set) and experimental kinetic data, which showed an onset temperature difference of only 21 °C between 1a and 3 (Figure 1).6 A notable solvent dependence suggested some polar contributions in the TS of 1, a phenomenon well-known at the boundary of diradicals and zwitterions.7 To elucidate the polar effects, a detailed kinetic study was thus undertaken in 2008 by studying two groups of enyne−carbodiimides (Scheme 1), one substituted at the alkyne (series X) and the other at the carbodiimide terminus (series Y).8 The relative rates of each series nicely correlated with the substituent constants σp © XXXX American Chemical Society
time, the curvature was explained by a changeover from a coarctate mechanism9 involving a carbene intermediate (with X, Y = EWG) to a zwitterion (with X, Y = NMe2, OMe) mechanism, with the carbene intermediate indirectly supported by isolation of product 88 (Scheme 2) and the latter by the notable rate accelerations in polar solvents. Received: November 17, 2015
A
DOI: 10.1021/acs.orglett.5b03310 Org. Lett. XXXX, XXX, XXX−XXX
Letter
Organic Letters Scheme 2. Formation of Product 8 Indirectly Suggested Involvement of the Carbene Intermediate 6
Table 1. Computations at the BLYP/6-31+G* Level and Experimental Free Energy of Activation for 1 at 120 °C compd 1
computed free energy of activation ΔG⧧120 (kcal mol−1)
experimental free energy of activationa ΔG⧧120 (kcal mol−1)
a b c d e f g h i j k
28.2 28.5 28.5 28.3 26.8 24.8 28.4 28.8 28.3 26.8 24.1
27.9 29.5 28.6 28.5 27.0 21.5 28.4 27.9 27.9 25.7 20.8
To better resolve the putative mechanistic changeover in the thermolysis of 1 as reflected by the curved Hammett relationship, we decided to undertake a computational study. For that reason, we computed the PES for 1a by varying the C2−C6 and C7−C8 bond distances at BLYP/6-31G* level of theory (Figure 3).
a
Experimental free energies of activation were derived from experimental rate constants8
experimentally found onset temperature difference (97 vs 118 °C). This unexpectedly small ΔΔG⧧ may be ascribed to a ground-state destabilization of 3 by 4.3 kcal mol−1 (Figures S4 and S5) and a different C7−C8 distance in the TS (2.50 and 2.64 Å for 1a and 3). Equally, formation of 8 from 5 may be explained by a competitive pathway (SI) that does not involve the postulated carbene trapping as depicted in Scheme 2. But what is the reason for the curvature in the Hammett plots of 1 if there is no change in mechanism? Curved Hammett correlations10 have been previously observed in substitution, elimination, acyl-transfer, and oxidation reactions.11 The traditional explanation for such phenomena is attributed to (a) a change in mechanism, (b) a single mechanism with a different extent of bond formation and cleavage or a change of the charge character in the TS, and (c) a different balance of polar and resonance effects by different substituents in the TSs.12 Option (a) can be eliminated due to the full agreement of experimental and computational data and the computational evidence for a concerted mechanism for 1. To evaluate option (b), we calculated (i) the asynchronicity (Δd) at the TS (Figure 4),
Figure 3. Potential energy surface (BLYP/6-31G*; grid: 30 × 30; smoothed) for the thermal cyclization of 1a. The numerical values represent the respective bond distances in Å.
Against our expectations, we could not locate any intermediate along the reactive reaction coordinate; rather, we identified the singlet diradical 1a_INT as a dead end with no direct exit route to the product. By comparison with experimental data, the 6-31+G* basis set gave better results than 6-31G*. Hence, we reoptimized all stationary points on the PES at BLYP/6-31+G* level and searched for the presence of any reactive diradical intermediate. Again, we could not find any productive intermediate on the PES, suggesting a concerted mechanism for the thermal cyclization of 1a. The calculated free energy barriers for the cyclization of enyne−carbodiimides 1b−k, all operating via a concerted mechanism, are in very good agreement with the experimental kinetic data (Table 1). Hammett correlations with the calculated rate constants revealed exactly the same curvature like the experimental kinetic results (Figure 2). As an interim conclusion one has to state that the C2−C6 cyclization of enyne− carbodiimides seems to follow a concerted pathway with no intermediate, quite in contrast to earlier claims.8 The premise of a concerted mechanism, however, requires that equally all other pieces of evidence for a stepwise mechanism collected over the years, such as the low barrier for ipsocyclization of 3 and the formation of 8 from 5, have to be reconsidered. Notably, the parent 1a and the sterically encumbered enyne−carbodiimide 3 exhibit a computed free energy barrier difference ΔΔG⧧ of only 2.2 kcal mol−1 for the concerted pathway, which is in rather good agreement with the
Figure 4. Correlations (subscripts X and Y stand for the series X and Y) of asynchronicity Δd at TS, dipole moment μ at TS, and ground-state stabilization energy (GSE) of 1 all vs σp. B
DOI: 10.1021/acs.orglett.5b03310 Org. Lett. XXXX, XXX, XXX−XXX
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Organic Letters (ii) TS σ-contraction,13 (iii) Mulliken and natural bond orbital (NBO) charges, and (iv) the dipole moment at the TS (Figure 4), but none of them would correlate with σp in an analogous manner as the rate constants for both series X and Y (Figure 2). To check the balance of polar and resonance effects, i.e., option (c), Yukawa−Tsuno diagrams of log(k/k0) vs σp + r+(σp+ − σp) and σp + r−(σp− − σp) were plotted by varying r = 0−1, which, however, did not lead to any linear correlation (Table S2). All known reasons for curvature in Hammett correlations were thus met with failure. Furthermore, no correlations were detected with aromaticity in the TS as measured by the nucleus-independent chemical shift (NICS) or the harmonic oscillator model of aromaticity (HOMA) index (Table S6). Houk’s14 distortion/interaction model (see the SI) also failed to rationalize our findings. Finally, the impact of ground-state stabilization10f on the starting material was considered by checking isodesmic reactions, such as 1a + PhNMe2 → 1f + PhH (Figure 4). After failing to find a reason for the curvature by inspection of both the TS and reactant, we decided to compare qualitatively the energy profiles of enyne−carbodiimide (concerted) and enyne−allene (stepwise) cyclizations. From a large battery of studies,4,5 it has become evident over the years that enyne− allenes follow the stepwise pathway in their thermal cyclization. The idealized reaction coordinate (Figure 5) shows a rate-
Figure 6. (Left) Scanning of C2−C6 bond distance by 0.025 Å from 1a. (Right) Comparison of scan results of 1a, 1b, and 1f.
real TS. The electronic energy gap between the real TS and that at the 57th point is only 0.02 kcal mol−1. All these facts reflect how close one can approach the real TS of 1 by scanning one bond distance only. For mechanistic insight, all molecular orbitals were analyzed beginning from the reactant at five-step intervals. The 45th point is the first point where some electron density, found in the HOMO−1 (Figure S1), arises between C7 and C8. At that point, the C2−C6 bond formation is well progressed (1.94 Å), while the C7−C8 bond distance is still at 3.37 Å. Thereafter, the same analysis was performed for all other enyne−carbodiimides 1b−k. A representative comparison of 1a, 1b, and 1f (Figure 6, right) shows that at the 45th point the electronic energy of all three compounds is already well pronounced, so that an inspection at this point may shed some light on the cause for the curvature in the Hammett plots. An in depth NBO analysis at the 45th point showed four major stabilizing orbital interactions, i.e., π1 → π2*, π1 → π3*, π2 → π1*, and π3 → π1*, to be relevant in the cyclization of enyne− carbodiimides 1a−k (Figure 7). Their individual contribution to
Figure 5. Two idealized reaction coordinates. The solid blue curve represents the thermal cyclization of enyne−allenes and the red one that for enyne−carbodiimides.
determining C2−C6 bond formation (first step) that is followed by the closure of the C7−C8 bond (second step). A projection of typical reaction coordinates for enyne−allene (blue curve) and for enyne−carbodiimide cyclizations (red curve) on top of each other suggests that in the concerted TS of the latter the C2−C6 binding has merged with the C7−C8 bond formation. As a result, the contributions of the initial C2−C6 binding are obscured in the TS. This insight suggested to search in the preTS region of the concerted carbodiimide reaction as there we expected to see the changeover, like that of enyne−allenes, from the C2−C6 to the follow-up C7−C8 bond formation. To find this nonstationary point (represented roughly by the vertical line in Figure 5, i.e., the starting point for the virtual second step, i.e., C7−C8 bond formation) on the PES, we decided to critically consider all steps in the cyclization of 1a from the starting material to the TS. By decreasing the C2−C6 bond distance stepwise by 0.025 Å from the reactant to the TS, leaving the C7−C8 free to optimization, we obtained the graph depicted in Figure 6 (left). Upon decreasing the C2−C6 bond distance, both carbodiimide CN bonds elongate although they are perpendicular to each other. Once the C2−C6 bond distance approaches the one of the TS the structure collapses (after the 57th point) to the product region because of an unimpeded approach of C7 and C8. At point 57, i.e., prior to the collapse, the C2−C6 bond distance is 1.64 Å, which is almost the same as in the
Figure 7. Colored structures: Two orbital interactions contributing to the stability of 1a at the 45th point. Black and white structures: The four relevant orbital interactions at the 45th point of 1a.
the interaction energy as a function of σp is shown in Figure 8, right. The addition of all four interaction energies furnishes the total stabilizing interaction energy, which correlates with σp (Figure 8, left) for both series in exactly the same manner as do the experimental and computational kinetic data (Figure 2). Thus, the information provided by the orbital interactions is the one that is relevant for the kinetics from a mechanistic point of view. An analysis of the individual contributions for series X, i.e., compounds 1a−f (Figure 8, top right), indicates that for donor substitution the π1 → π3* interaction dominates, while for neutral and EWG substituents the π3 → π1* and π1 → π2* interactions almost cancel. For series Y, i.e., 1a,g−k (Figure 8, bottom right), the situation is somewhat more complicated; the interaction analysis shows that donor-substituted cases are dominated by several interactions (π1 → π2*, π1 → π3*, π3 → π1*) that add up almost pari passu. On the side of neutral and EWG substituents for 1a,g−k, the sum of all four interaction cancels mostly. This complexity prevents us from drawing a C
DOI: 10.1021/acs.orglett.5b03310 Org. Lett. XXXX, XXX, XXX−XXX
Organic Letters
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Letter
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We are indebted to the DFG for financial support (Schm 647/ 18-1) and to the Universität Siegen for providing the Linux Cluster HorUS for computations.
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Figure 8. (Left) Correlation of the total orbital interaction energies (IEs) of 1 against σp. (Right) The individual (dashed lines) and the total IEs (solid red and blue line) are plotted against σp (reference R = H is set to zero). Subscripts X and Y stand for the series X (top) and Y (bottom).
simple electron push−pull mechanisms for the true ratedetermining process in the thermal cyclization of 1a−k. Why are those interactions not visible at the real TSs? For comparison, a reaction profile for the thermal cyclization of enyne−allene 1a′ was computed at the same DFT level. Interestingly, all of the interactions depicted for enyne− carbodiimide 1a at the 45th point are present in the C2−C6 TS of enyne−allene 1a′ as well, but they vanish as the system moves on to the diradical intermediate and C7−C8 TS. Thus, in the course of further structural and electronic changes the original interactions become invisible. By the same token, the relevant interactions in the enyne−carbodiimide cyclization, as illustrated in Figure 7, already become invisible in the TS due to the second bond formation. Is there a hidden transition state (hTS)15 at or near the 45th point? Actually, the analysis by IRC gradient norm fails to detect a hTS, thus lending even more importance to a preTS inspection! The current finding suggests that many concerted reactions with highly asynchronous bond formations, in which the first bondforming process has the predominant influence on the rate, may benefit from a preTS analysis. Our study reveals that a concerted, but highly asychronous, mechanism is operative for the thermal cyclization of enyne− carbodiimides 1a−k. Due to the asynchronicity, a TS inspection does not reveal the orgin of the rate changes and of the curved Hammett correlation. Rather, preTS inspection at the nonstationary point just prior to formation of the second bond reveals the various underlying interactions that guide the rate and as a result the curved Hammett correlation. In summary, the traditional heuristics using mechanistic information from the analysis of stationary points fails in our system. A strategy is presented that uses the analysis of nonstationary points (preTS inspection).
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REFERENCES
ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.orglett.5b03310. Full list of calculations, optimized geometries, and number of imaginary frequencies (PDF) D
DOI: 10.1021/acs.orglett.5b03310 Org. Lett. XXXX, XXX, XXX−XXX
