Stereoelectronic and dynamical effects dictate nitrogen inversion during valence isomerism in benzene imine

Abstract

Benzene imine (1) ⇌ 1H-azepine (2) isomerization occurs through sequential valence and endo–exo isomerism. Quantum chemical and quasiclassical trajectory (QCT) simulations reveal the coupled reaction pathway – ring-expansion followed by N-inversion to the most stable isomer, exo-1H-azepine (Exo-2). Direct-dynamics produce a mixture of endo- and exo-1H-azepine stereoisomers and govern the endo-1H-azepine (Endo-2) ⇌ exo-1H-azepine (Exo-2) ratio. Exo-2 is computationally identified as the most stable product while Endo-2 is fleetingly stable with a survival time (S_T) ∼50 fs. N-Methyl substitution exclusively results in an exo-1-methyl-1H-azepine isomer. F-substitution at the N-site increases the barrier for N-inversion and alters the preference by stabilizing Endo-2. Interestingly, the exo-1-fluoro-1H-azepine (minor product) is formed through bifurcation via non-statistical dynamics. A highly concaved Arrhenius plot for 1a → 2a highlights the influence of heavy-atom tunneling on valence isomerism, particularly at low temperatures. Heavy-atom tunneling also results in a normal N–H(D) secondary KIE above 100 K even though the increase in hybridization from sp² to sp³ at nitrogen should cause an inverse KIE classically.

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Introduction

The equilibrium between bicyclo[4.1.0]hepta-2,4-diene and cyclo-hepta-1,3,5-triene has been a subject of active interest.¹ Ring-expansion is also known for oxygen (benzene-oxide ⇌ oxepin), nitrogen (benzene imine ⇌ 1H-azepine), sulfur (benzene sulfide ⇌ thiepine), and phosphorus (benzene phosphane ⇌ 1H-phosphepine).^2,3 All of them undergo disrotatory electrocyclic rearrangement to form the ring-opened product.⁴ However, stereoelectronic induction can influence the reaction mechanism and conformations of strained molecules (see Scheme 1a).^5,6

Scheme 1 (a) Ring expansion reactions in substituted bicyclo[4.1.0]hepta-2,4-dienes. (b) Schematic possible reaction pathways for benzene imine (1).

For example, 1H-azepine with 8π-electrons exists in a boat conformation as expected from its anti-aromatic Hückel electron count.⁷ Based on DFT calculations, Dardonville et al. estimated an anti-aromatic destabilization of 10.8 kcal mol⁻¹ for 1H-azepine by computing its protonation energies.⁸ Ragyanszki and co-workers studied the oxidation of the anti-aromatic N-methyl-1H-azepine to the non-aromatic N-oxide of azepine.⁹ 1H-Azepine, and its derivatives are also known to undergo rapid dimerization via (6 + 4)π exo-cycloaddition.¹⁰

Further, ring expansion of benzene imine into 1H-azepine (1 → 2) can in-principle also be accompanied by an inversion at the N-center (see Scheme 1b). Since the NMR spectra of 1H-azepine remain invariant in the range −90 °C to + 130 °C, Paquette et al. suggested that the inversion barrier should be less than 5.7 kcal mol⁻¹.¹¹ Additionally, they could not gather any signature for the existence of benzene imine in this temperature range. Therefore, Exo-2 is expected to be the thermodynamically most stable product. However, the mechanism is still unknown and a possible reaction pathway can be either stepwise (1 → 2 → 3) or coupled (1 → 2, 3) for the formation of 1H-azepine analogs.

In Scheme 2, we have used different substitutions at the N-site to examine the stereoelectronic effects on the valence isomerization of Endo-1. Obtaining a detailed reaction mechanism and understanding the effect of the stereoelectronic influence on the potential energy surface for the Endo-1 → Endo-2/Exo-2 isomerizations require further time-resolved mechanistic investigation using quasi-classical MD simulations.^12–14 Additionally, the dynamics at sub-cryogenic temperatures would be dictated by quantum mechanical tunneling (QMT) instead of over-the-barrier crossing at ambient temperatures.^15–27 In this context recently, Sander and co-workers have reported unequivocal signatures of heavy-atom tunneling for the benzene oxide – oxepin equilibrium at 3 K.²⁸ The present article investigates post-transition state bifurcation reaction pathways for benzene imine ⇌ 1H-azepine. MD simulations were performed from the rate-limiting transition states to decipher the non-statistical effects on the stereoselectivity (Endo-2 : Exo-2) during the valence isomerism.²⁹ Heavy-atom tunneling is shown to be the major pathway for ring expansion, particularly at low temperatures.

Scheme 2 Valence isomerism in benzene imine (1) derivatives to their 1H-azepine (2) analogs.

Computational details

Geometry optimization was performed at the M06-2X/6-31+G(d,p) level of theory with the Gaussian 16 (ver A.03) suite of programs (see the ESI, Page S2† for calibration and benchmarking).^30,31 Reaction energies and activation barriers were investigated for Endo-1 → Exo-1, Endo-2, Exo-2, and their analogs (R = –F, and –CH₃). The reactant, product, and transition-state were confirmed by intrinsic reaction coordinate (IRC) and harmonic frequency calculations.³² In addition, for computation of the reaction rates at low temperatures, the transition states (TS) were located using canonical variational transition-state theory (CVT) along the reaction path s where free-energy maximizes at the same level as used for geometry minimization.³³ Tunneling corrections were incorporated within the rate coefficient calculations using the small-curvature tunneling (SCT) approximation.³⁴ These were implemented within Gaussrate 17-B by interfacing with Gaussian 16 and Polyrate 17-C.^35,36 Quantized reactant state tunneling (QRST) calculations were performed to determine the reaction rates accurately at sub-cryogenic temperatures.³⁷

Further, the ambient temperature behavior of Endo-1 for R = –H, –F, and –CH₃ was studied using quasiclassical direct-dynamics simulations in the gas phase at 298.15 K. Reaction trajectories were simulated from rate-limiting sampled TS(1 → 2) structures using the Singleton's Progdyn code interfaced with Gaussian 16 (see the ESI for TS-sampling details, Fig. S4†).^38–41 The reaction trajectories were simulated to the forward and backward directions until either one of the products or the reactants is formed. The classical equations of motion were integrated with a velocity-Verlet algorithm.⁴² The energies and derivatives were calculated on the fly with the M06-2X/6-31+G(d,p) level. The time step for integration is 1 fs. Thresholds for bond formations, trajectory terminations, and in-house code for trajectory characterization are shown on Page S8 and S50.†

Results and discussion

Benzene imine (Endo-1) can isomerize to exo-1H-azepine (Exo-2) either by ring expansion followed by N-inversion or vice versa. Both the plausible pathways are presented in Fig. 1.

Fig. 1 Two plausible mechanistic pathways for the formation of exo-1H-azepine, Exo-2 from benzene imine, Endo-1.

Each involves two steps and crossing two barriers, namely 1 → 2 → 3 or 1 → 4 → 3 with ΔG^‡_1→2 followed by ΔG^‡_2→3 or ΔG^‡_1→4 followed by ΔG^‡_4→3 respectively. The kinetic preference of either depends on the relative magnitudes of these barriers. Table 1 lists them for the various substituents on the nitrogen head. The exo-1H-azepine Exo-2 is the most stable isomer irrespective of the substituent. Therefore, the benzene imine ⇌ 1H-azepine equilibrium will shift towards the 1H-azepine side. This result is in agreement with previous experiments.¹¹

Table 1 Relative free energies and free energies of activation at 298.15 K (in kcal mol⁻¹) for 1 → 2 → 3 and 1 → 4 → 3 at the M06-2X/6-31+G(d,p) level of theory

	1a (R = H)	1b (R = F)	1c (R = CH3)
1 (Endo-1)	0.0	0.0	0.0
ΔG^‡1→2	4.4	5.7	5.2
2 (Endo-2)	0.3	−0.1	0.6
ΔG^‡2→3	1.4	6.7	0.5
3 (Exo-2)	−2.7	−2.0	−3.8
ΔG^‡1→4	18.0	—	17.1
4 (Exo-1)	3.7	−0.5	1.4
ΔG^‡4→3	5.5	6.4	4.3

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In terms of the preference for either 1 → 2 → 3 or 1 → 4 → 3 (see Fig. 1), ring expansion followed by the inversion pathway (a process-I) is more favorable than inversion followed by expansion (process-II). For example, in 1a, ΔG^‡_1→2 = 4.4 kcal mol⁻¹ and ΔG^‡_2→3 = 1.4 kcal mol⁻¹ while ΔG^‡_1→4 = 18.0 kcal mol⁻¹ and ΔG^‡_4→3 = 5.5 kcal mol⁻¹.

The high inversion barrier for Endo-1 → Exo-1 (ΔG^‡_1→4 (inversion) = 18.0 and 17.1 kcal mol⁻¹ for 1a and 1c respectively) arises due to the ring-strain in the three-membered aza-ring, which aggravates in the transition-state due to the planarity of the N-site. In contrast, the stereoelectronic modulation using R = –F leads to the cleavage of the bridging bond (rate-limiting step) of the 1b and disfavors the planarity of N–F with the cyclopropane ring in TS(1 → 4) for the 1 → 4 → 3 reaction pathway and therefore, its TS could not be located (process-II).⁴³

Following the kinetically favorable 1 → 2 → 3 pathway (coupled valence isomerism along the C–C bond and endo–exo isomerism via N-inversion) 1a, 1b, and 1c show remarkable variation in their relative ΔG^‡_1→2 (expansion) and ΔG^‡_2→3 (inversion). For 1a the free-energy of activation for ring expansion is three times more than that for inversion, while for 1b, both the barriers are comparable. For 1c, the activation barrier for N-inversion is the smallest, ΔG^‡_2c→3c = 0.5 kcal mol⁻¹. Ironically, 1b and 1c are isoelectronic, yet their significant differences in the N-inversion barriers make them ideal candidates to compare the product distributions between endo- and exo-1H-azepine conformational isomers viz.2b/3b and 2c/3c and contrast with the parent benzene imine ⇌ 1H-azepine, 2a/3a. See ESI Fig. S1–S3† for schematic potential energy surfaces for 1a, 1b, and 1c.

Valence isomerism in endo-benzene imine is an example of a dynamically rich system where rapid C–C bond dissociation assists N–H inversion. The rate-limiting C1–C6 bond activation facilitates both the ring expansion and N-inversion (see Fig. 2). The quasiclassical direct-MD simulations reveal a chameleonic transition state TS(1a → 2a) and the non-statistical effects on the product count (Endo-2 : Exo-2).^44–48

Fig. 2 Representative reaction pathways for the valence isomerization assisted nitrogen inversion of 1a.

Fig. 2 depicts a typical trajectory and the time-resolved formation of azepine isomers (2a and 3a). A total of 142 reaction trajectories were propagated from rate-limiting TS(1a → 2a) (see ESI Fig. S4† for details). The reaction trajectories passing through the TS(1a → 2a) zone can be characterized as “normal” trajectories if they follow the IRC-pathway (1 → 2 → 3) or “flyby” trajectories when they skip the minimum energy pathway (bypassing the 2a-zone) and directly traverse to TS(2a → 3a), finally forming 3a.

Out of the 142 reaction trajectories, 108 (76%) “normal” reaction trajectories led to exo-1H-azepine (3a) while 20 (14%) “flyby” reaction trajectories afford the TS(2a → 3a) and finally fall to the exo-1H-azepine (3a) zone. Only 6 (4%) trajectories are found in the simulation that produces endo-1H-azepine (2a) up to 1 ps. The remaining 8 (6%) re-cross to either the reactant (1a) or product (3a) zones. This indicates a post-transition state bifurcation reaction where dynamical effects govern the stereoselectivity. The selectivity (2a : 3a) for the 1a → 2a, 3a ring-opening reaction is ∼1 : 21.

Further, Fig. 3(a) represents two “normal” reaction trajectory propagations and time-resolved variation of the critical structural parameters (d, θ, and ϕ) during valence isomerization (benzene imine → 1H-azepine). The green-colored trajectory defines the reaction path that affords endo-1H-azepine (2a) which is found stable up to 1 ps during MD simulation. In contrast, the blue trajectory follows the ultrafast decay along the steepest descent path and eventually falls towards the exo-1H-azepine (3a) product zone.

Fig. 3 (a) “Normal” trajectories represent the pathways for the formation of 2a and 3a, (b) “flyby” trajectories traverse to TS(2a → 3a) and eventually fall to the 3a product side, the (c) average time (Δt) required for the 1a → TS(1a → 2a) path and the (d) average survival time (S_T) for the endo-1H-azepine (2a) product.

These flyby reaction trajectories were found highly concerted and follow shorter dynamical routes to reach the 3a-product zone in the potential energy surface. In Fig. 3(b) a typical “flyby” trajectory (violet line) shows its transit from TS(1a → 2a) to TS(2a → 3a) and falls into the 3a-product basin without forming Endo-2 (2a). On the other hand, the orange line first approaches the TS(2a → 3a) zone, takes a short trip at the 2a-zone, and finally populates the exo-1H-azepine, Exo-2 (3a) basin.⁴⁹

Further, the lower thermodynamic stability of endo-1H-azepine (ΔG (2a and 3a) = 3.0 kcal mol⁻¹) and small activation barrier (ΔG^‡ = 1.4 kcal mol⁻¹) for the N–H inversion populates the 3a product basin. From Fig. 3(c), we can estimate that the average time (Δt) required to reach the rate-limiting transition state TS(1a → 2a) is 30.2 ± 8.0 fs. We have also calculated the survival time (S_T) using the cut-offs: 2a appears when d(C1–C6) > 2.19 Å, θ(C1–N7–C6) > 98° and ϕ(H13–C6–N7–H14) > 135° whereas 2a disappears when d(C1–C6) > 2.38 Å, θ(C1–N7–C6) > 98° and ϕ(H13–C6–N7–H14) > 104°. The survival time (S_T) vs. probability plot indicates that the average survival time (S_T) of 2a is 49.7 ± 19.5 fs (see Fig. 3(d)). Therefore, the signature of the endo-1H-azepine (2a) formation can be traced using spectroscopic techniques.^50,51

Additionally, the electronic and dynamical effect control on stereoselectivity was investigated by introducing R = –F and –CH₃ at the inversion center. In Fig. 4(a), the relative free energy surface dictates an “interrupted” shift.⁵² The valence isomerism mediated inversion is decoupled at endo-1F-azepine (2b). In general, we can apply such a potential energy surface manipulation strategy either by stabilizing Endo-2 or destabilizing the N-inversion barrier for these coupled reactions. Interestingly, the stronger electron-withdrawing substitutions not only increase the Endo-2 → Exo-2 inversion barrier but also disfavors the transition state of direct Endo-1 → Exo-1 isomerization. In the case of –F substitution, the 1b → 2b → 3b → 4b pathway connects 1b ⇌ 4b. In contrast, TS(1c → 4c) connects 1c ⇌ 4c (Endo-1 → Exo-1) with a significantly higher activation energy barrier (E_a = 17.1 kcal mol⁻¹). However, such isolobal –CH₃ stereoelectronic induction accelerates the formation of exo-1CH₃-azepine (3c) (see, Fig. 4(b)). In this case, 2c → 3c isomerization has such a small barrier which makes it a highly coupled pathway (1c → 3c), a “dynamical” shift.⁴⁸

Fig. 4 (a and b) Evolution of the potential energy surfaces, where “interrupted” shift and “dynamical” shift denote the modification strategies to isolate the endo-1F-azepine (2b) and exo-1CH₃-azepine (3c), respectively.

In Fig. 4(a) and (b), snapshots of typical trajectories are shown. The reaction trajectories are simulated from these rate-limiting transition states, TS(1b → 2b) and TS(1c → 2c) respectively. In the case of –F substitution, a typical trajectory affords 2b (Endo-2) within 109 fs and is stable in the simulation. However, the representative reaction trajectory forms 3c (Exo-2) within 275 fs.

The 3D plots depict the typical trajectories simulated from rate-limiting TSs, TS(1b → 2b) and TS(1c → 2c) respectively (see Fig. 5). In Fig. 5(a), two typical reaction trajectories are depicted. The red “normal” reaction trajectory elucidates the formation of 2bvia the steepest descent path (IRC-pathway), whereas the green flyby route shows the dynamical pathway (non-statistical) that can afford exo-product 3b formation for the valence isomerism in 1b. On the other hand, the orange and blue lines show fast conversion into the N-methyl substituted exo-1H-azepine (3c) (see Fig. 5(b)).

Fig. 5 3D-reaction plots for the valence isomerism reactions of (a) 1b → 2b, 3b and (b) 1c → 3c.

Further, we performed 156 reaction trajectorie simulations from the TS(1b → 2b) at the M06-2X/6-31+G(d,p) level of theory (see ESI Fig. S4 and S5† for details). In this case, out of 132 (85%) product forming reaction trajectories, 87 (56%) afford endo-1F-azepine, 2b. Interestingly, 45 (29%) reaction trajectories follow the dynamical (non-statistical pathways) routes to reach the exo-product (3b) zone. Therefore, the R = –F stereoelectronic modulation manipulates the stereoselectivity of the valence isomerism in 1b. The stereoselectivity (2b : 3b) of the reaction is 2 : 1.

In addition, a total of 145 reaction trajectories are propagated from the TS(1c → 2c) at the same level of theory (see ESI Fig. S4 and S5† for details). Out of 141 (97%) productive trajectories, 104 (72%) follow the IRC path. Interestingly, out of 37 (25%) “corner cutting” reaction trajectories, 36 directly traverse through the N–CH₃ inversion TS(2c → 3c) and further dynamically fall out to the 3c-zone, whereas only 1 “flyby” reaction trajectory leads to 2c-product viaTS(2c → 3c). We found that exo-1-methyl-1H-azepine 3c was the exclusive product (Endo-2 : Exo-2= 1 : 140).

On the other hand, out of 104 “normal” reaction trajectories, 32 were dynamically stepwise. The 32 stepwise trajectories “surf” the TS(2c → 3c) dividing the surface before leaving the TS zone. The average surfing time at the TS(2c → 3c) zone is 20.2 ± 7.4 fs (see the ESI, Fig. S5†). This is due to the conformational penalty which the methyl group needs to incur along the path 1c → TS(2c → 3c) while passing through the TS(2c → 3c) dividing the potential landscape. Quasielastic neutron scattering experiments are well-suited to recognize methyl-rotations in dynamically rich systems.⁵³

Further, quantum mechanical tunneling (QMT) effects are investigated and they significantly dictate the benzene imine ⇌ 1H-azepine dynamics. Considering that ΔG^‡_1→2 (expansion) is the rate-limiting step along the preferred 1 → 2 → 3 pathway, ring isomerization of endo-benzene imine (Endo-1) to endo-1H-azepine (Endo-2) essentially would involve motion of the two bridged carbons (C1 and C6 in Scheme 2). A qualitative estimation of the width of the barrier (w) is obtained by the difference in d(C1–C6) between the benzene imine and azepine. For 1a → 2a, w is only 0.75 Å which along with a small ΔG^‡_1a→2a = 4.4 kcal mol⁻¹ makes a strong case for heavy-atom tunneling.^54,55

Since ring expansion is endergonic along 1a → 2a, the reaction rates are obtained by performing SCT dynamical calculations along the reverse (exergonic) direction followed by scaling them by microscopic reversibility.⁵⁶ At 300 K, k^CVT+SCT (1a → 2a) = 1.84 × 10⁸ s⁻¹ while k^CVT (1a → 2a) = 1.75 × 10⁸ s⁻¹, acceleration by only 5% due to tunneling. However, at the liquid N₂ temperature, k^CVT+SCT (1a → 2a) and k^CVT (1a → 2a) are 1.51 × 10⁻¹ s⁻¹ and 3.64 × 10⁻² s⁻¹, respectively, a gain of 75% by tunneling. The Arrhenius plot of the reaction rate shows strong curvature at low temperatures in Fig. 6(a). At 40 K, k^CVT+SCT (1a → 2a) = 3.12 × 10⁻⁵ s⁻¹ which is nine-orders more than the pure classical over-the-barrier transit. Such large enhancements in reaction rates at sub-cryogenic temperatures make ring-opening a highly QMT driven process.

Fig. 6 (a) Arrhenius plot of the CVT and CVT + SCT rates (in s⁻¹) for 1a → 2a. (b) Displacement vectors for the normal mode of TS(1a → 2a). The directional motion of the N7–H bond is encircled.

Ring expansion along the C1–C6 bond also remotely affects the N–H bond at the bridgehead. The C1–N7–C6 bond angle increases from θ(C1–N7–C6) = 63.9° in 1a to θ(C1–N7–C6) = 82.4° in TS(1a → 2a). Natural Bond Orbital (NBO)⁵⁷ calculations at the M06-2X/6-31+G(d,p) level (see the ESI, Table ST5†) show that the hybridization at the N-center changes from sp² to sp³. This should classically result in an inverse secondary KIE.⁵⁸ Indeed, secondary H/D isotope effects at CVT are inverse at all temperatures. For example, k^CVT (1a → 2a)/k^CVT (1d → 2d) = 0.96, 0.89 and 0.32 at T = 300 K, 100 K and 10 K respectively. However, the normal mode for ring-expansion also shows motion along the N–H(D) bond in the translation vector for the TS, see Fig. 6(b). Therefore, because the H-atom is lighter than D, tunneling assists 1a → 2a preferentially over 1d → 2d. This makes the secondary KIE positive at high temperatures and reduces the extent of inverse secondary KIE with k^CVT+SCT (1a → 2a)/k^CVT+SCT (1d → 2d) = 1.08, 1.03, and 0.42 at T = 300 K, 100 K, and 10 K respectively.

Conclusion

Post-transition-state dynamics and quantum mechanical tunneling play an important role in the benzene imine ⇌ 1H-azepine equilibrium. This isomerism belongs to a peculiar class of pericyclic reactions where ring expansion dictates stereoselectivity. The C–C bond cleavage and N-inversion dynamics guide the rich diversity of endo-/exo-product outcomes. The dynamics can be selectively controlled by the electronic nature of the substituents on the N-end. While a strong electron-withdrawing group like –F decouples the ring-expansion and inversion pathways, for the –H/–CH₃ groups they are strongly entangled to result in the final ring-expanded form with N-inversion. At sub-cryogenic temperatures when the reaction is driven by quantum mechanical tunneling, heavy-atom tunneling governs the reaction due to the small width of the barrier for ring expansion. Such coupled valence isomerism and N-inversion are also anticipated for other norcaradienes wherein the stereoelectronic effects of the substituents are critical.

Data availability

The datasets supporting this article have been uploaded as part of the ESI.†

Author contributions

NM performed the research, Ankita ran QMT calculations; CH did dynamics setup; AD planned the project.

Conflicts of interest

The authors declare no competing financial interests.

Acknowledgements

NM thanks CSIR for SRF. AD and CH thank DST Inspire and IACS for the research fellowship. AD thanks TRC-DST and SERB grant no. DIA/2018/000013 and CRG/2020/000301 for partial funding.

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Footnote

† Electronic supplementary information (ESI) available: Schematic potential energy surfaces, QCT inputs, details of MD simulations, QMT inputs, CVT and CVT + SCT rates for valence isomerism, NBO analyses, Cartesian coordinates, energies, and harmonic frequencies and Awk Code. See DOI: 10.1039/d1sc04855d

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