Does the Neophyl-Like Rearrangement Play a Decisive Role in

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Does the Neophyl-Like Rearrangement Play a Decisive Role in Intramolecular Cyclization of Iminyl Radicals? A Combined Quantum Chemistry and Numerical Simulation Investigation of the Cyclization Mechanism and Product Distributions of Bicyclic 2-Allyl-2-methyl-2,3dihydro-1H-inden-1-iminyl Radical and Several Iminyl Model Compounds Lang Yuan, Cai-Xin Jia, Hong-Jie Qu, Yu-juan Chi, and Hai-Tao Yu J. Org. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.joc.8b03134 • Publication Date (Web): 29 Jan 2019 Downloaded from http://pubs.acs.org on January 31, 2019

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The Journal of Organic Chemistry

Does the Neophyl-Like Rearrangement Play a Decisive Role in Intramolecular Cyclization of Iminyl Radicals? A Combined Quantum Chemistry and Numerical Simulation Investigation of the Cyclization Mechanism and Product Distributions of Bicyclic 2-Allyl-2-methyl-2,3-dihydro-1H-inden-1-iminyl Radical and Several Iminyl Model Compounds Lang Yuan, Cai-Xin Jia, Hong-Jie Qu, Yu-Juan Chi,* and Hai-Tao Yu*

Key Laboratory of Functional Inorganic Material Chemistry (Ministry of Education) and School of Chemistry and Materials Science, Heilongjiang University, Harbin 150080, P. R. China

ABSTRACT: In this study, we performed a theoretical investigation of the intramolecular cyclization of bicyclic 2-allyl-2-methyl-2,3-dihydro-1H-inden-1-iminyl radical 1 along with several iminyl model compounds. The results were used to comparatively evaluate the reaction mechanism suggested previously, in which the neophyl-like rearrangement was deemed to play a decisive role. The present computation and numerical simulation identify the experimentally observed endo product in the high-temperature cyclization of 1. The product results from a kinetically controlled endo cyclization-reduction pathway involving an initial reversible 5-exo ringclosure/ring-opening

process,

not

via

5-exo

cyclization/neophyl-like

rearrangement/endo-radical reduction pathway as proposed previously. Considering many available theoretical and experimental results, the neophyl-like rearrangement seems to play only a minor role in the intramolecular cyclization of N- and C-centered radicals. The structural effect of cyclized radical intermediates of bicyclic 1 leads to a lower thermodynamic reaction energy of exo cyclization than of endo cyclization, which

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together with the temperature effect should be responsible for the formation of the dominant endo product in the high-temperature region. Additionally, this investigation provided further insight into the cyclization of 1 and compounds structurally similar to 1; that is, control of endo- or exo-regioselective products is readily available by regulating the reaction temperature.

1. INTRODUCTION

Access to mono- and polycyclic compounds can be accomplished by intramolecular cyclization proceeding via the attack of reactive radicals onto an unsaturated bond.1−3 Many investigations have indicated that such ring-closure reactions are generally thermodynamically favorable and kinetically feasible because of the formation of a new σ bond and appropriate approach trajectory in cycloadditions.4,5 Nitrogen-containing heterocycles can be easily constructed by this strategy by utilizing compounds that can generate iminyl radicals as radical precursors.6,7 Available reports have indicated that the intramolecular cyclization of iminyl8 and carbon-centered radicals1,2 onto vinyl groups often provides exo cyclized products despite the possible formation of endo-products9 via a directly competitive endo cyclization and/or an indirect neophyl-like rearrangement pathway, as shown in Scheme 1. Generally, the regioselectivity of such intramolecular radical cyclization is controlled by the kinetic barriers to the competitive exo and endo cyclization reactions1,10, while the neophyl-like rearrangement and the subsequent radical reduction have only minor effects11. The stereoselectivity is often determined by the kinetic barriers to cyclization that proceeds in the same ring-closure mode but leads to different stereoisomers1c,5f,12 and/or the possible racemization of substrates and radical reactants 11d,11e,13; the racemization of stereoselectively cyclized radical intermediates and products is virtually impossible because the newly formed stereocenter is endocyclic, as shown in Scheme 1. However, Bowman and coworkers found that the intramolecular cyclization of bicyclic 2-allyl-2-methyl-2,3-dihydro-1H-inden-1-iminyl radical 1 results in the 6-endo product 2 rather than the expected exo-product 5 (Scheme 2).14 This reaction was proposed to proceed via a direct 5-exo cyclization to form radical


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intermediate 3, followed by a neophyl-like rearrangement to generate endo radical intermediate 4 and a further radical reduction to form endo-product 2, as shown in Scheme 2. The direct endo cyclization-reduction mechanism appears to have been ruled out by the authors.14 Although neophyl-like rearrangement pathways have been suggested by many investigators, 15 available reports have identified their minor possibility as a favorable pathway in some reaction systems because of the high kinetic barrier relative to direct reduction of cyclized radical intermediates.11 If the neophyl-like rearrangement has enough kinetic advantage over the transformation between the competitive exo- and endo-cyclized radicals (Scheme 1), it will definitely have an important impact on the regio- and stereochemistry of the cyclization of systems such as 1. Thus, which role the neophyl-like rearrangement plays in the cyclization of 1 and structurally similar molecules becomes an interesting issue.

Scheme 1. Typical Intramolecular Radical Cyclization Pathways

Scientifically, two other possible mechanisms are expected. The first involves direct competition between 5-exo and 6-endo radical cyclization reactions; i.e., if the 6-endo cyclization-reduction pathway is kinetically favorable over the corresponding 5-exo pathway, the endo-product should be dominant.5c,9,16 The second possible mechanism is that if the reduction of the cyclized radical intermediate in the exo pathway is the rate-determining step and



kinetically less favorable than the endo cyclization and/or reduction, the kinetically favored exo cyclized radical would undergo a reverse ring-opening reaction to re-form the radical reactant, followed by a further endo cyclizationreduction pathway to form the endo-product. Although the speculation seems to be scientifically reasonable, so far, no available reports have supported such a mechanism.

Scheme 2. Proposed Mechanism for Intramolecular Cyclization of Bicyclic Radical 1 by Bowman and Coworkers

To understand the mechanism of the cyclization reactions similar to that shown in Scheme 2 and to determine which hypothesis mentioned above is true, we herein performed a combined quantum mechanics and numerical simulation computation for 1 and several iminyl model compounds. Further, we discussed the effect of geometric and electronic structures, thermodynamics, and kinetics on the preferred cyclization pathway and product. This study provides not only deeper insight into the nature of intramolecular cyclization of N-centered radicals but also an application of numerical simulation to analyze potential energy profiles involving complex reaction pathways.


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2. COMPUTATIONAL DETAILS

All computations presented in this study were performed with the Gaussian 09 software package.17 The geometries of stationary points were located using Becke’s half-and-half hybrid DFT-BHandHLYP functional18 in conjunction with the double-ζ Hay and Wadt effective core potential (ECP) basis set LanL2DZ19 for the Sn atom and the 6-311++G(d,p) basis set20 for other atoms. Such a computational level has been proven to be capable of providing reliable stationary point geometries and relative energies for the intramolecular ringclosure reactions of carbon- and nitrogen-centered radicals (see Supporting Information).4b,10d, 11c-11g Unrestricted computation without symmetry constraints was used in optimizations. The nature of the located stationary points, i.e., no imaginary frequency for minima and only one imaginary frequency for transition states, was confirmed by vibration frequency calculations using the Hessian matrix built numerically at the same level of theory as the geometry optimizations. Additionally, frequency calculations can provide thermodynamic corrections to the electronic total energies of the located stationary points, which are further used to obtain temperature-dependent enthalpies and Gibbs free energies. All of the transition states were analyzed by intrinsic reaction coordinate (IRC)21 calculations, which identified their connections to the forward and reverse minima. Solvent effects were considered in all computations using the self-consistent reaction field (SCRF) method22 with the polarizable continuum model (PCM).23 The solvent, either methylbenzene or tertbutylbenzene, was selected based on available experiments. 14,24 To

evaluate

the

structure-

and

temperature-dependent

regio-

and

stereoselectivity and reaction mechanism, we established a system of kinetic differential equations for all elementary reactions on a constructed reaction potential energy profile. The time-dependent concentration equations of reactants, intermediates, and products are directly built by the forward and reverse rate constants of each elementary reaction, which are readily available using traditional transition state theory (TST).25 Because it is difficult to obtain an analytical solution of such a multivariable system of differential equations, we employed a numerical simulation method to obtain the numerical solution. The



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script code used in numerical simulations was written based on the MATLAB (Version R2016b) platform; see Ref. 11e for details. To estimate the stereoelectronic effect of an elementary reaction, we employed Marcus theory26 to separate the thermodynamic contribution ( E therm ) and intrinsic reaction barrier ( E 0 ) from the activation reaction barrier ( E  ). The intrinsic barrier represents the stereoelectronic requirement of a thermoneutral process without thermodynamic bias and can be calculated by the equation

1 E    r E  (E  ) 2  E   r E 2 E 0  2

(1)

where  r E is the thermodynamic reaction energy.

3. RESULTS AND DISCUSSION

The calculated thermodynamic and kinetic data, product branching ratios, and constructed potential energy profiles for all of the presently investigated reactions are given in the Supporting Information. The geometries of the stationary points located in Cartesian coordinates are also provided in the Supporting Information. Unless otherwise specified, all energies discussed in the main text refer to the solvent-corrected energies computed at the BHandHLYP/6311++G(d,p)-LanL2DZ level of theory and at the boiling point of the solvent used, that is, 383.8 K and 442.2 K for methylbenzene and tert-butylbenzene, respectively. Furthermore, the electronic total energies used in the discussion include the zero-point vibrational energy (ZPVE) correction. 3.1 Pathways and product branching ratios of the intramolecular cyclization of 1. Figure 1 gives the BHandHLYP-optimized potential energy profile of the radical cyclization-reduction reaction shown in Scheme 2. Two rotamers exist for radical reactant 1, i.e., (R)-1a and (R)-1b, which readily interconvert by means of carbon-carbon single bond rotation via the low-lying transition state TS1. (R)-1a and (R)-1b can undergo diastereoselective 5-exo cyclization to form radical intermediates (R,S)- and (R,R)-3, followed by reduction by the hydrogen donor HSnBu3 to generate the diastereomeric exo-


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products (R,S)- and (R,R)-5, respectively. Alternatively, they can also undergo 6endo ring closure to form endo cyclized radical 4, which can abstract the H atom of HSnBu3 to give endo-product 2. Furthermore, the exo cyclized radical intermediates (R,S)- and (R,R)-3 can undergo neophyl-like rearrangement to endo radical intermediate 4 via fused-ring intermediates 6 and 7, respectively.

Figure 1. Computed cyclization-reduction potential energy profile of the bicyclic radical 1.

The 5-exo cyclization of (R)-1a and (R)-1b is kinetically more favorable than their 6-endo ring closure, as observed by the relative Gibbs free energies of 19.70 and 21.30 kcal/mol for the 5-exo cyclization transition states TS2 and TS3 vs 21.20 and 22.79 kcal/mol for the 6-endo cyclization transition states TS4 and TS5. Furthermore, the interconversion between the 5-exo and 6-endo cyclized radical intermediates via neophyl-like rearrangement is kinetically less favorable than their direct reduction by HSnBu3. It seems that the neophyl-like rearrangements cannot lead to a redistribution of the ratio of exo- to endoproducts 2 and 5, as observed in many intramolecular cyclization reactions of carbon- and nitrogen-centered radicals.11 Although the 5-exo cyclization via TS2 (19.70 kcal/mol) is kinetically the most favorable among all cyclization reactions, the reduction of the



corresponding 5-exo cyclized radical (R,R)-3 through TS12 (23.23 kcal/mol) is kinetically less favorable (at least 0.44 kcal/mol) than all elementary reactions on the 6-endo cyclization-reduction pathways (see Figure 1). This implies that the kinetically preferred exo cyclized radicals (R,S)- and (R,R)-3 would rather undergo reverse ring-opening to re-form reactant 1, followed by a further 6-endo cyclization-reduction to form endo-product 2, than direct reduction to exoproduct 5, as shown in the reaction mechanism in Scheme 3. Therefore, the product branching ratio should be controlled by the energy height of the reduction transition state relative to the cyclization transition state, not by neophyl-like rearrangements. This qualitative prediction is inconsistent with the mechanism proposed previously; that is, the regioselective products are redistributed by neophyl-like rearrangements.14

Scheme 3. Presently Proposed Cyclization Mechanism of Bicyclic Radical 1

To evaluate the above-proposed reaction mechanism (Scheme 3) and quantitatively determine the product branching ratio, we performed a numerical simulation for this reaction at 383.8 K. Figure 2 gives the numerically simulated


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time-dependent concentration distribution of reactants, intermediates, and products. When the simulation is just beginning, (R)-1a and (R)-1b immediately reach thermodynamic equilibrium concentrations, independent of the initial (R)1a-to-(R)-1b ratio, as shown in Figure 2(a). Apparently, this is because they have a low-lying interconversion transition state (TS1) and lie in a deep potential well (Figure 1). As the reaction proceeds, the concentrations of (R)-1a and (R)-1b quickly decrease to approximately zero within only 0.15 s (Figure 2(a)), accompanied by the formation and disappearance of 5-exo cyclized radical intermediates (R,R)- and (R,S)-3 (Figure 2(b)). The 5-exo cyclized products (R,R)- and (R,S)-5 quickly reach constant concentrations and maintain these concentrations in the following simulation (Figures 2(a) and 2(c)). Note that the concentration of (R,R)-3 reaches a maximum (18%) at approximately 0.0025 s (see inset of Figure 2(b)) and decreases to zero at approximately 0.15 s (Figure 2(b)). However, the concentration of the corresponding product (R,R)-5 is only 10% (Figure 2(a)), which evidently indicates that (R,R)-3 undergoes a reverse ring-opening reaction to form (R)-1b. This agrees well with the analysis of the mechanism described above. Furthermore, it takes only 0.3 s for the endo-radical 4 to reach a maximum concentration (80.2%), followed by a slow decrease with the formation of the corresponding endo-product 2. Finally, 2 reaches a constant concentration of 84% accompanied by exhaustion of the 6-endo cyclized radical intermediate 4 at a simulation time of 10 s (Figure 2(c)).

Figure 2. Numerically simulated time-dependent concentration distribution of reactants, intermediates, and products for the intramolecular radical cyclization of 1.

The numerically simulated results clearly show that the higher-lying reduction transition states (TS11 and TS12) of exo cyclized radicals (R,R)- and



(R,S)-3 than of both endo-cyclization transition states (TS6 and TS7) and the subsequent reduction transition state (TS10) should be responsible for the formation of the preferred endo-product 2. Such a reaction mechanism (Scheme 2) is very rare. In the majority of intramolecular radical cyclization reactions,2,6,11 the distribution of regioselective cyclization products is often controlled by cyclization, not the reduction or oxidation of the cyclized radical intermediates. It should be noted that the reaction temperature often results in different regioselective products.11d,11e,27 We performed Gibbs free energy corrections for the key transition states on the reaction potential energy profile shown in Figure 1. The results plotted in Figure 3 indicate that the relative Gibbs free energies of the cyclization and reduction transition states decrease with decreasing temperature. Note that the rate-determining transition states for the kinetically favorable exo and endo pathways are TS12, which separates exo-radical (R,R)-3 and its reduction product (R,R)-5, and TS4 for the 6-endo cyclization of (R)-1b, respectively, at 383.8 K. As the temperature decreases below 383.8 K, TS12 becomes closer to TS4 and finally becomes lower (≤ 322 K) than TS4. Such a temperature effect predicts that the exo cyclization-reduction pathway (R)-1b  TS2  (R,R)-3  TS12  (R,R)-5 will become kinetically more favorable than the endo pathway (R)-1b  TS4  4  TS10  2 when the temperature is below approximately 322 K. Therefore, the exo-product (R,R)-5 can be considered the kinetically controlled preferred product at a relatively low temperature. The prediction above is well supported by further numerical simulation. As a representative example, Figure 4(a) plots the numerically simulated timedependent concentration distribution of radical reactants, intermediates, and products at 298 K. The results indicate that at a simulation time of approximately 20 s, the exo-products (R,R)- and (R,S)-5 reach constant concentrations, and endo cyclized radical intermediate 4 approaches its maximum concentration. As the simulation proceeds, the concentration of 4 decreases, and that of endo-product 2 increases. When the simulation time is longer than approximately 300 s, endoproduct 2 reaches a steady concentration with complete exhaustion of 4. The final product branching ratio of (R,R)-5:2:(R,S)-5 is 72.2:19.9:7.9. Therefore, the preferred product is exo-product (R,R)-5 at 298 K.


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Figure 3. Temperature-dependent relative Gibbs free energies of the cyclization and reduction transition states on the radical cyclization-reduction potential energy profile of 1.

Figure 4. Numerically simulated time-dependent concentration distribution of radical reactants, intermediates, and products at 298 K (a) and temperaturedependent product branching ratio (b) for the intramolecular radical cyclization of 1.



The fact that the temperature effect can result in different dominant cyclization products can be clearly observed from Figure 4(b) and Supporting Table S44. When the temperature is higher than 350 K, the concentration of the dominant endo-product 2 is over 70%. When the temperature drops to 310 K and further to 268 K, the concentration of the preferred exo-product (R,R)-5 ranges from 62.2% to 86.2%, and that of the minor product (R,S)-5 ranges from 8.6% to 5.4%; the corresponding diastereomeric excess (de) is 0.76 – 0.88, indicating high stereoselectivity. Therefore, for the intramolecular cyclization of 1, one can obtain highly regio- and stereoselective products by regulating the reaction temperature. 3.2 Effect of structure on regio- and stereoselectivity. The discussion above indicates that the regio- and stereoselectivity of the cyclization of exocyclic N-centered radical 1 is controlled by the relative transition state height of either radical cyclization or radical reduction; the latter is more susceptible to temperature, which makes the cyclization reaction favor endo and exo products at high and low temperatures, respectively. However, available experimental and theoretical investigations revealed that the intramolecular cyclization of acyclic N- and C-centered radicals onto vinyl moieties almost always prefer exo products.1,2,8 Thus, the regioselective products of the intramolecular cyclization of cyclic radicals such as 1 seem somewhat confusing. To further reveal the possible effect of structure on regio- and stereoselectivity, we explored several model compounds, i.e., cyclic radicals 8–11 and two experimentally available open-chain radicals 12 and 13,24 whose structures, along with those of the optimized cyclization products, are shown in Scheme 4. Supporting Figure S7 shows the computed temperature-dependent relative Gibbs free energies of cyclization and reduction transition states on the reaction potential energy profiles (see Figures S1-S4) of 8–11. The results indicate that 5exo cyclization of each system is kinetically more favorable than 6-endo cyclization, while reduction of the endo cyclized radical is advantageous over that of the exo cyclized radical. In the high-temperature region near the solvent boiling point, the reduction transition states of exo cyclized radicals lie higher than other transition states for reactants 8–11; thus, the endo product is predominant. With decreasing temperature, the reduction transition states of the


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exo cyclized radical become closer to and finally become lower than the exocyclization transition states for 8, 9, and 11. Thus, the exo-products increase gradually and finally become the dominant product instead of the endo-products. For radical reactant 10, the rate-determining transition states on the exo and endo cyclization-reduction pathways in the low-temperature region are TS43 and TS44, which become closer in relative Gibbs free energy with decreasing temperature (Supporting Figure S7 and Table S23). Thus, the concentrations of the exo- and endo-products become closer with decreasing temperature. Again, the neophyl-like rearrangement was found to be of minor importance in the cyclization of 8–11.

Scheme 4. Cyclization Products of Iminyl Radical 8–13



The computed product branching ratios (Figure 5) strongly support the estimations given above. At the solvent boiling point, each system exclusively gives the endo-product (> 95%). When the temperature is higher than 320 K, the cyclic radicals (R)-8 and (R)-9 provide the preferred endo-products (R)-14 and (R)-16, respectively, with concentrations higher than 80% (Figures 6(a) and 6(b)); the concentrations decrease to 59.1 and 58.7%, respectively, at 298.15 K. However, cyclization of (R)-10 provides the dominant endo-product (R)-18 with a concentration of 86.4% at 298.15 K (Figure 5(c)), while (S)-11 gives the endoproduct (S)-20 with a concentration of higher than 90% when T > 260 K (Figure 5(d)). Therefore, the room temperature radical cyclization of (R)-10 and (S)-11 can give highly regioselective endo-products but not exo-products.

Figure 5. Numerically simulated temperature-dependent product branching ratios for the intramolecular radical cyclizations of 8 (a), 9 (b), 10 (c), and 11 (d).

The cyclization product distributions of open-chain N-centered radicals 12 and 13 are completely different from those of cyclic 8–11. Figures 6c and 6d shows the temperature-dependent relative Gibbs free energy heights of key transition states on the corresponding potential energy profiles (Figures 6a and


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6b). It can be noted from Figure 6 that the exo-cyclization transition states are at least 3.6 kcal/mol lower than the endo-cyclization transition states. Furthermore, the reduction transition states of the exo cyclized radical intermediates are lower than those of the endo cyclized radical intermediates in the investigated temperature range. This result shows that intramolecular cyclization of 12 and 13 always prefers exo products. The neophyl-like rearrangement does not lead to a redistribution of regioselective products relative to the distribution of the cyclized radical intermediates. This agree well with available experimental observation.24 Such a favorable pathway and regioselective product are very similar to those of the corresponding carbon-centered radicals,1,2 which can be well predicted by the Baldwin rules.28 Furthermore, racemization of 12 and 13 occurs very readily because of very low racemic barriers; by further considering the racemization of the cyclization radical intermediates (Figures 6(a) and 6(b)), we can conclude that the cyclization products of 12 and 13 should be racemic. The numerical simulations conclusively prove this prediction; that is, almost no endo-products can be observed throughout the investigated temperature range, and the exo-products of 12 and 13 are rac-23b/rac-23a with a concentration ratio of 4.87 (273.1 5 K)–2.68 (383.8 K) and rac-25a/rac-25b with a concentration ratio of 2.61 (273.1 5 K) – 1.63 (442 K), respectively. 3.3 Mechanism of regioselectivity. As mentioned above, for the open-chain N-centered radicals 12 and 13, the lower reduction transition state height of exo cyclized radicals than of endo cyclized radicals, which behaves oppositely to the cyclic N-centered radicals 1, 8, 9, 10, and 11, providing preferred endo products at high temperatures, leads to dominant formation of exo-products. The less favorable cyclization-reduction pathway is that possessing the highest kinetic barrier and may be either the cyclization or the reduction step. For cyclic 1, 8, 9, and 11, the pathways with the highest-lying transition states are 6-endo cyclization reactions in the low-temperature region and reduction of exo cyclized radical intermediates in the high-temperature region, thus providing exo- and endo-products in the low- and high-temperature regions, respectively. However, the cyclization-reduction reactions of the open-chain N-centered radicals 12 and 13 always prefer exo-products because the pathway possessing the highest-lying transition state is either endo cyclization or reduction of endo cyclized radicals throughout the investigated temperature range.



Figure 6. Temperature-dependent relative Gibbs free energies ((c) and (d))of the cyclization and reduction transition states on the cyclization-reduction potential energy profiles ((a) and (b)) of the iminyl model compounds 12 and 13.

Next, we explore the possible factors that affect the regioselectivity of cyclization reactions, that is, why 1, 8, 9, and 11 prefer endo- and exo-products at high and low temperatures, respectively, but 12 and 13 favor exo-products throughout the investigated temperature range. In the following discussion, we use 1 and 12 as representative cyclic and open-chain radical reactants, respectively. As is widely known, the height of a transition state depends not only on the stereoelectronic effect in forming the activation transition state but also on the thermodynamic reaction energy and temperature effect. To distinguish these effects on regioselectivity, we employed Marcus theory26 to determine the stereoelectronic and thermodynamic contributions to the reaction barriers. The stereoelectronic effect, i.e., the intrinsic reaction barrier, can be feasibly obtained


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by separating the thermodynamic contribution from the activation energy barrier, see Eq. 1. For cyclization steps, we will use the energetically favorable 5-exo and 6endo cyclization pathways, (R)-1b  TS2  (R,R)-3 and (R)-1b  TS4  4 for cyclic reactant 1 and 12b  TS73  42b and 12b  TS71  43 for openchain reactant 12, to discuss the stereoelectronic effect. As shown in Figure 7 and Supporting Table S48, the intrinsic reaction barrier to the 5-exo cyclization of (R)-1b into (R,R)-3 via TS2 is 16.89 kcal/mol, which is apparently lower (4.40 kcal/mol) than the barrier (21.29 kcal/mol) to the 6-endo cyclization to form 4 through TS4. This is very similar to the cyclization of 12b; i.e., the intrinsic reaction barrier (15.93 kcal/mol) to the 5-exo cyclization into 42b via TS73 lies 5.16 kcal/mol below that (21.09 kcal/mol) of the 6-endo cyclization into 43 via TS71. Therefore, cyclization of (R)-1b and 12b in exo mode has less steric hindrance than the competitive endo cyclization. It seems that for (R)-1b and 12b, the trajectory for approach along the Bürghi-Dunitz attack angle5c is readily accommodated via exo attack relative to endo attack. For 12, it can be noted from Figure 7 and Supporting Table S48 that the 6endo cyclization of 12b  43 is less favorable in terms of reaction energy than the 5-exo cyclization of 12b  42b (-5.85 vs -7.41 kcal/mol). Thus, the thermodynamic contribution to kinetics not only decreases the energy barriers (18.27 vs 12.44 kcal/mol) and Gibbs energy barriers (ΔG≠, 20.42 vs 14.11 kcal/mol) but also further increases the difference (5.83 kcal/mol) between the energy barrier and the aforementioned intrinsic reaction barriers (21.09 vs 15.93 kcal/mol with the difference of 5.16 kcal/mol). For 1, the thermodynamic contribution to kinetics does not make the 6-endo cyclization of (R)-1b  4 advantageous over the 5-exo cyclization of (R)-1b  (R,R)-3 in terms of the energy barrier (17.88 vs 16.75 kcal/mol) and Gibbs energy barrier (20.22 vs 18.72 kcal/mol), although the reaction energy of the 6-endo cyclization of (R)-1b into 4 is more favorable than the 5-exo cyclization to form (R,R)-3 (-7.11 vs -0.28 kcal/mol); that is, 4 is thermodynamically more stable than (R,R)-3 by 6.83 kcal/mol, as listed in Supporting Table S48. Thus, for the cyclic and open-chain radical reactants 1 and 12, 5-exo cyclization is more kinetically favorable than 6endo cyclization in terms of the steric hindrance of radical attack.



Figure 7. Calculated intrinsic reaction barriers ( E 0 ), activation barriers ( E  ), Gibbs barriers (ΔG≠), and relative Gibbs free energies (ΔΔG) of transition states on the radical cyclization-reduction pathways of (R)-1b and 12b. All energies are in kcal/mol.

For 1, the intrinsic reaction barriers to the energetically preferred exo reduction pathway (R,R)-3  TS12  5 and the endo reduction pathway 4  TS10 2 are 15.24 and 15.80 kcal/mol, respectively. For the open-chain radical reactant 12, the intrinsic reaction barriers to the favorable exo reduction pathway 42b  TS75 23b and the endo reduction pathway 43  TS76  22 are 16.50 and 17.86 kcal/mol, respectively (see Figure 7 and Supporting Table S48). The lower intrinsic reaction barrier to the former pathway than to the latter demonstrates a lower steric compression in exo reduction processes for systems 1 and 12, which apparently results from a lower stereoelectronic requirement for the hydrogen abstraction of HSnBu3 by exocyclic radicals than that by endocyclic


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radicals. Because the reduction of the exo cyclized radical releases more energy than the endo reduction, the thermodynamic contribution thus further increases the kinetic advantage of the exo reduction pathway, as the energy barriers to the reduction of (R,R)-3 and 4 are 7.53 and 10.04 kcal/mol, respectively, and those to the reduction of 42b and 43 are 7.56 and 10.43 kcal/mol, respectively (Figure 7 and Supporting Table S48). Even if the temperature effect is taken into account, the Gibbs energy barriers of the exo and endo reduction reactions exhibit the same ordering: 21.32 vs 23.64 kcal/mol for (R,R)-3 and 4 and 20.51 vs 24.74 kcal/mol for 42b and 43. Such a result indicates an almost identical kinetic mode in reduction steps for the cyclization reactions of 1 and 12. After considering the energy height relative to the lowest-lying reactant isomer, the relative Gibbs free energies of the reduction transition states of endoradical 43 and exo-radical 42b maintain the same ordering (21.76 vs 15.30 kcal/mol) as their Gibbs energy barriers (24.74 vs 20.51 kcal/mol), which results from the lower exothermicity of endo cyclization than of exo cyclization. However, the relative Gibbs free energy (21.20 kcal/mol) of transition state TS10, which separates endo-radical 4 and endo-product 2, is lower than that (23.23 kcal/mol) of TS12, connecting exo-radical (R,R)-3 and exo-product (R,R)-5, which behaves apparently opposite to the aforementioned Gibbs energy barriers, i.e., 23.64 vs 21.32 kcal/mol, and indicates a favorable endo product over the exo product. This results from the higher exothermicity of endo cyclization than of exo cyclization, as the endo cyclized radical 2 lies 17.55 kcal/mol lower in relative Gibbs free energy than the exo-radical (R,R)-3 (Figure 1). Thus, for (R)1b, the lower thermodynamic reaction energy of exo cyclization than of endo cyclization, together with the temperature effect, results in the preferred endo cyclization pathway and product in the high-temperature region.

4. CONCLUSIONS

In this study, we performed a theoretical investigation of the cyclization mechanism and product distribution of bicyclic 2-allyl-2-methyl-2,3-dihydro1H-inden-1-iminyl radical 1 and several cyclic (8–11) and acyclic (12 and 13) model compounds at the BHandHLYP/6-311++G(d,p)-LanL2DZ level of theory. The conclusions are as follows.



(1) The neophyl-like rearrangement thus plays only a minor role in the radical cyclization of 1 and other model compounds. The intramolecular cyclization of the bicyclic iminyl radical 1, which gives the dominant endo-product 2, preferably proceeds through the endo cyclization-reduction pathway with an initial reversible 5-exo ring-closure/ring-opening process at high temperatures, not through the 5-exo ring-closure/neophyl-like rearrangement/endo-radical reduction mechanism suggested previously. (2) Changing the reaction temperature can result in different regio- and stereoselective products for the bicyclic iminyl radical 1. When T > 350 K, the concentration of the endo-product 2 is higher than 70%. When the temperature drops to 310–298.15 K, the concentrations of the exo-product (R,R)-5 and endoproduct 2 are 62.2–72.1% and 29.2–19.9%, respectively, with a concentration of minor product (R,S)-5 of 8.6–7.9%. Furthermore, the cyclic iminyl radicals 10 and 11 can give highly regio- and stereoselective endo cyclization products at room temperature. (3) Although the computational results of the intrinsic reaction barrier indicate that 5-exo cyclization of 1 has a lower stereoelectronic requirement than the completive endo cyclization, the relatively low thermodynamic stability of exo-cyclized radical intermediates resulting from structural and temperature effects leads to a higher-lying exo reduction transition state than endo cyclization and reduction; thus, the endo cyclization-reduction pathway providing the endoproduct 2 becomes kinetically favorable.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: Computed energies, product branching ratios, intrinsic reaction barriers, reaction potential energy profiles, temperature-dependent Gibbs energies and enthalpies (PDF) List of Cartesian coordinates of all calculated species (PDF)

AUTHOR INFORMATION Corresponding Authors


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*E-mail: [email protected]. *E-mail: [email protected]. ORCID Yu-Juan Chi: 0000-0002-4514-6092 Hai-Tao Yu: 0000-0003-3764-9201 Notes The authors declare no competing financial interest.

AUTHOR CONTRIBUTIONS L.Y., C.X.J., H.J.Q., and H.T.Y. performed the DFT, TST, and intrinsic reaction barrier computations. L.Y. and Y.J.C established system of kinetic differential equations and performed numerical simulations. L.Y. Y.J.C, and H.T.Y. performed the mechanism analysis. All authors contributed to the data interpretation and manuscript writing.

ACKNOWLEDGMENTS This work was supported by grant from the National Natural Science Foundation of China (No. 21173072).

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Investigation

of

Regioselectivity

and

Stereoselectivity

in

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