Dynamical Effects along the Bifurcation Pathway Control

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Dynamical Effects Along Bifurcation Pathway Control Semibullvalene Formation in Deazetization Reactions Nilangshu Mandal, and Ayan Datta J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b09533 • Publication Date (Web): 09 Jan 2018 Downloaded from http://pubs.acs.org on January 10, 2018

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The Journal of Physical Chemistry

Dynamical Effects Along Bifurcation Pathway Control Semibullvalene Formation in Deazetization Reactions Nilangshu Mandal, Ayan Datta*

Department of Spectroscopy, Indian Association for the Cultivation of Science, 2A and 2B Raja S.C. Mallick Road, Kolkata – 700032, India. Email: [email protected]

ABSTRACT:

Post-transition-state dynamics during the deazetization of 3 resulting in two degenerate semibullvalenes (4 and 5) have been investigated with density functional theory (DFT) and quasi-classical trajectory (QCT) calculations. Removal of N2 from 3 occurs through a synchronous and concerted pathway through an ambimodal transition-state (TS1). In addition to TS2, the exclusively anticipated product from minimum energy pathway (MEP) calculations, trajectories initiated from TS1 produce 4, TS2 and 5 in 1:1:1 ratio. Isotopic substitutions (12C(13C/14C)-H(D) at 1-2 positions) result in purely Newtonian kinetic isotope effects (4:5 ~1.4 for 13C1-13C2), an unequivocal evidence for dynamics controlled product formation.

Tetrazine (1) is known to act as an electron deficient diene for inverse electron demand Diels-Alder reactions with electron-rich dienophiles and has been extensively utilized in total synthesis for molecules like streptonigrin.12-15 Souer et al. have demonstrated an efficient method for the production of semibullvalenes (4 and 5) by the extrusion of N2 from tetrazine (1) and bis-cyclopropene (2).16 Such efficient and fast cycloaddition reactions are widely used in bio-orthogonal chemistry.17-19 Tetrazine cycloaddition reactions have been successfully utilized in live cell imaging with various dienophiles.21-22 Cyclopropene derivatives are one of the best dienephiles as they are highly strained as well less hydrophobic in nature. Recently, using molecular dynamic study, Houk and co-workers established the nature of Diels-Alder reactions of tetrazines with alkenes alongwith N2 extrusions from adducts.23 Singleton and co-workers reported cycloadditions of cyclopentadiene with diphenylketene and dichloroketene and found nonstatistical recrossing to be essential to describe the correct isotope effects.24 Using dynamic effect, Thomas et al. elucidated the mechanism through which product selectivity is controlled in the Diels-Alder cycloadditions of 3methoxycarbonylcyclopentadienone with 1,3-dienes.25 Recently, Houk and co-workers explored the origin of periselectivity in the ambimodal [6+4] cycloadditions of tropone to demethylfulvene using dynamical calculations.26 Tantillo and co-workers showed that carbocation-π interactions can manipulate dynamic behaviors of post-transition-state bifurcation reactions.27 Stopped flow kinetic studies of tetrazine cycloaddition toward sequential transition states have been reported by Sadasivam et al.28 Similarly, Yamataka and co-workers have established dynamic path bifurcation in the Beckmann reaction.29 Recently, Lόpez and co-workers have theoretically studied dynamical effects in [3,3] sigmatropic rearrangement along bifurcation pathways.30 Houk31 and Tantillo32 have reviewed several examples of post-TS bifurcations in organic reactions.

INTRODUCTION One of the most popular models to understand kinetic preferences of chemical reactions has been the transition-state theory (TST) or its improved variant considering statistical recrossing (the variational transition-state theory, VTST).1-2 However, several evidences have emerged recently wherein post-transition state non-statistical dynamics and recrossing become essential to qualitatively describe the outcome of organic reactions.3-8 For such cases, a static picture based on potential energy surface (PES) can give only the thermodynamic picture accurately while, product selectivity, regioselectivity are controlled by dynamics of nuclear motions and momenta of the atoms along non-internal reaction coordinate (non-IRC) pathways for bifurcation reactions.9-10 Reaction between tetrazine (1) and bis-cyclopropene (2) producing two degenerate semibullvalenes is one such example (Scheme 1).11

Motivated by such growing interest in reactions of tetrazenes, we have computationally studied the reaction between tertrazine (1) and bis-cyclopropene (2) resulting in 3 which subsequently forms degenerate semibullvalenes (4 and 5) through a bispericyclic transition state. Herein, we represent static density functional theory (DFT) calculations for the 3 → semibullvalenes (4 and 5). We have incorporated various functional groups on biscyclopropene (R = H, F, Cl, Br, OH, CN, NH2, Me and Et) to investigate the effects on their activation barriers, relative energies as well as in their valley ride inflection points (VRIs). We also perform detailed quasi-classical trajectory simulations from the

Scheme 1: Synthetic pathway for semibullvalene formation through deazetization of 3. 1

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ambimodal transition state structure to examine the dynamical behavior. Newtonian kinetic isotope effects (KIEs) were computed to describe the origin of kinetic selectivity through isotope labeling.

COMPUTATIONAL METHODS All the structures are optimized at B3LYP/6-31G(d) and M062X/6-31G(d) levels of theory. For estimation of the barrier heights a higher basis set, TZVP was also utilized. All the static electronic structure calculations were performed with Gaussian 09.33 For a comprehensive understanding concerning “on-the-fly” behavior of the bifurcation pathways, the trajectories were propagated from the ambimodal transition state structure (TS1) (shown in Figure 1(a) and Figure 2(b)) at B3LYP/6-31G(d) level of theory. Normal mode sampling was performed by addition of the zero-point energy for each real normal mode of the TS followed by Boltzmann sampling to get a set of coordinates for trajectory propagation at 300K. The usage of TS distribution is necessary to get an unbiased product distribution. A velocity-Verlet algorithm was used to integrate the classical equations of motion using the Singleton’s Progdyn24 program with time step of 1 fs. The rate constants were computed using TheRate34 program. Rice– Ramsperger–Kassel–Marcus (RRKM) calculations were carried out using the Beyer–Swinehart direct count algorithm35-36. Product 4 and 5 were used as the starting points for lifetime calculations.

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Substitutions

TS1

VRI

TS2

4

5

I (R = H) II (R = F) III (R = Cl) IV (R = Br) V (R = CN) VI (R = OH) VII (R = NH2) VIII (R = Me) IX (R = Et)

12.5 11.9 11.8 11.7 11.9 11.7 11.5 12.2 12.3

6.8 5.9 6.1 6.0 2.0 6.0 6.0 6.8 6.8

-41.6 -48.3 -47.4 -47.7 -40.6 -46.4 -44.2 -42.1 -42.0

-46.4 -48.8 -48.9 -48.8 -47.3 -47.4 -47.9 -46.8 -47.4

-46.4 -52.1 -50.4 -50.7 -44.7 -49.5 -47.4 -45.6 -45.4

Table 1: Zero-point energy (ZPE) corrected relative free energies at B3LYP/6-31G(d) level of theory at 298.15K for I-IX with respect to 3. Energies are in kcal/mol. The intrinsic reaction coordinates (IRC) connect 3 with TS2 via TS1 in I (R = H). For all other reactants (II-IX), IRC connects 3 with the most stable of the semibullvalene (4 or 5) through TS1 without a detour into TS2 (shown in Figure S23–S28 and Table S3 in Supp. Info. file). Clearly, electronic perturbation by functional groups that break the high symmetry in TS1 can tune the reaction pathway. For I, a C2v symmetry is maintained all along the IRC from 3 to TS2, whereas for the substituted analogues, only a Cs symmetry is preserved along 3 to 4/5. The structures at TS1 and VRI-point and TS1 and 5 for I and III (R = Cl) are respectively shown in Figure 1 (a) – 1(d). For I, the VRIpoint is responsible for the bifurcation into 4 and 5 alongwith the formation of TS2. Specifically, for either C-N bond length of 2.13 Å, νimaginary(1)= 367.5i cm-1 results in the formation of TS2 while νimaginary(2)=149.6i cm-1 results in the formation of the two degenerate semibullvalene products namely, 4 and 5 at B3LYP/631G(d) level in I (Figure S22, Supp. Info. file).

RESULTS AND DISSCUSSION Table 1 represents the relative energy change in terms of ∆G (at 298 K) for the conversion of 3 to semibullvalenes (4 and 5) with loss of N2 for I-IX. It is clear that the activation energy for the first-step (3 → TS2 or 3 → 4 or 3 → 5) is significantly higher than that for the degenerate cope-rearrangement (4 ↔ 5 via TS2). ‡ For example, in I (R = H), ∆G1 (3 → TS2 /3 → 4/ 3 → 5) =12.5 kcal/mol (10.2 kcal/mol at B3LYP/aug-cc-pVTZ level) while ‡ ∆G2 (4 → 5) = 4.8 kcal/mol (3.8 kcal/mol at B3LYP/aug-ccpVTZ level). Calculations at a higher basis set clearly do not alter the basic picture of the potential energy surface (PES), see Supp. Info. for further details. The computed reaction energies and barriers are in excellent agreement by previous reports on I by Birney and co-workers.11 Substitution by functional groups reduces the barrier for the rate-determining step with the ‡ maximum lowering, ∆∆G1 =1.0 kcal/mol occurring for R = NH2. Due to substitution, the degeneracy of 4 and 5 is lost and the relative stability of 4 and 5 can be understood based of the electron withdrawing/donating nature of the substituents. For IIIV and VI, preference for 5 over 4 arises as a consequence of the electron-withdrawing nature of the groups that increases the scharacter of the adjacent bonds (See Supp. Info. File for NBO analyses). This results in an increment in internal angle between the bonds (within the cyclopropyl ring) that makes 4 unstable. For VII-IX presence of electron-donating groups results in reduced scharacter of the adjacent bonds and lower internal angle within the ring. This stabilizes 4. In case of V, inspite of the electron withdrawing nature of –CN, its conjugation with the cyclopropane ring makes product 4 relatively more stable.

Figure 1: (a) and (b) are optimized TS1 structures for I (R = H) and III (R = Cl). (c) Valley ridge inflection (VRI) point for I (R = H). (d) Optimized chloro substituted semibullvalene (5). These structures are optimized at B3LYP/6-31G(d) level of theory. Interestingly, for II-IX, the IRC did not encounter the VRI-point close to the TS1 region and is located further right from TS1 (along the mass-weighted reaction coordinate, s). Hence, the steepest descent path from the saddle point structure (TS1) along IRC produces the thermodynamically more stable product 2


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The Journal of Physical Chemistry quantum chemical calculations (using B3LYP/6-31G(d) level of theory) (c) Plot for the scatter in the C1-C2 and C4-C5 bondlengths across the 60 sampled TS1 structures.

amongst 4 or 5. A generalized potential energy surface schematically represents the bifurcation pathway for deazetization of I (Scheme 2).

Normal mode sampling was conducted on the dynamical bottleneck structure at 300 K to obtain an ensemble of TS1 structures (See computational section for details). An overlay of 25 sampled structures for TS1 is shown in Figure 2(a). To verify the suitability of the sampling method, we have plotted the C1-C2 and C4-C5 bonds (See Figure 2(b) for atom numbering in the TS1 structure) of 60 sampled TS1 structures, which is represented in Figure 2(c). The transition zone is depicted schematically within an ellipsoid in which both bond lengths are 1.63 Å ± 0.01 Å. This region conserves > 98% of the transition state geometry. Total 303 trajectories were propagated from TS1 in both forward and backward directions of which 269 were productive. Reactant (3) and products (4, 5 and TS2) were defined by the choice of specific cut-offs: C1–C24.0 Å for 5 and C1–C2>2.1 Å, C4–C5>2.1 Å, C3–N16>4.0 Å and C6–N17>4.0 Å for TS2. Amongst the 269 productive trajectories, 91 trajectories reached 4, 88 trajectories reached 5 and rest (90) of them arrived at TS2. Out of the 34 unproductive trajectories, some of them recrossed back into the reactant or product side. Therefore, there is an approximately 1:1:1 ratio for the formations of 4, 5 and TS2 from the dynamical bottleneck structure (TS1), which might be due to equal dynamic racing of different modes while trajectory propagation.37 The plots of the trajectories (Figure 3) reveal that they move along TS1 → VRI and subsequently bifurcate to produce either 4 or 5 or TS2. From the IRC calculations one observes that though the minimum energy pathway connects the two saddle points (TS1 and TS2) yet it becomes unstable at the VRI point. Therefore, beyond VRI, the trajectories have a freedom to diverge towards the alternative product valleys (4 and 5). Snapshots for the formation of 4, 5 and TS2 from typical trajectories are shown in Figure S3. Interestingly, formations of these structures are concerted and proceed only through the critical structures (TS1, VRI point) without forming any intermediate. Figure 3(a) shows the trajectories that lead to TS2. Formation of “probable synthetic transition state” has been indicated in previous reports.11, 38-39 Figure 3(b) clearly depicts the production of the degenerate semibullvalenes (4 and 5) via a bifurcating pathway through VRI. Concomitant cleavage of both the C–N bonds (C3–N16 and C6– N17) occurs within ~15 fs during backward and forward trajectory propagations in a synchronous manner. Similarly, production of TS2 also follows a synchronous pathway wherein both C1–C2 and C4–C5 bonds break simultaneously. When both the C–N bonds are ~4.0 Å, formation of TS2, 4 and 5 were confirmed during trajectory simulations using the cut-off criteria listed above. Previous experimental studies by Carpenter et al. for the thermal deazetization of 2,3-Diazabicyclo[2.2.1]hept-2-ene also revealed a synchronous cleavage of two C-N bonds.40 Interestingly, the computed average time for the trajectories to arrive at TS2, 4 and 5 (Table 2) from 3 are similar. To explore the chemical importance of the VRI point, few trajectories were also simulated for V (R = CN), where two products (4 and 5) are inequivalent (activation energy 6.6 kcal/mol and 4.1 kcal/mol with respect to 4 and 5 respectively). Dynamic pictures clearly show the preference of 4 over 5. This dynamical preference can easily justifiable from their thermodynamic stability order (ΔΔG (4-5) = -2.6 kcal/mol). Nonetheless, by stereo-electronic switching one can manipulate the chameleonic behavior of the

Scheme 2: Bifurcation in the generalized potential energy surface for deazetization of I-IX producing degenerate semibullvalenes (4 and 5) and TS2. From the above IRC calculations in I-IX, it is evident that the balance between the three pathways (3 → TS1 → TS2 and 3 → TS1 → 4 or 3 → TS1 → 5) is actually very subtle and therefore, requires more detailed dynamical study. Additionally, since, neither of the species involved in this reaction are overtly polar (µ = 0–5 Debye), so polarity of the solvent(s) is unlikely to effect the overall mechanistic pathway (details are shown in Table S5–S6 of Supporting Information file). Hence, we believe that gas phase quasi-classical trajectory (QCT) analyses should indeed represent reasonable product distribution under ambient experimental conditions.

Figure 2: (a) Overlay of 25 sampled TS1 structures in I (R = H) (b) Optimized structure of TS1 for I (R = H) available from 3



and 14C isotopic substitution at various positions in 3 to tune the product selectivity in bifurcation (Figure 4 (A) – 4(D)). The IRCs are examined starting from the C2v saddle-point, TS1. For the dideuterated case (A), the IRC terminates at TS2 but for both B and C, the IRCs exclusively produce 4. The IRC expectedly prefers to propagate along the lighter atoms (C4 and C5) and hence, move more in this pathway to form the major product, 4. Even though this qualitative approach predicts the major product correctly yet unfortunately, it fails to indicate if the preference is modest or exclusive. To get a quantitative estimate for the kinetic selectivity, we have carried out quasi-classical trajectory calculations for all the four isotopomers. We have propagated 315, 359, 373 and 233 trajectories from TS1 of A, B, C and D respectively at 300 K (See Table 3). Products (4 and 5) were determined using the above mentioned cut-offs.

bifurcating point (See Supp. Info. for detailed dynamical outcomes).

Figure 3: Variations of C4-C5 vs C1-C2 bond lengths (in Å) of I (R = H), where (a) 30 representative trajectories for the formation of TS2. (b) 58 representative trajectories that result in formation of 4 and 5. The yellow and white asterisks represent TS1 and VRI respectively.

Species TS2 4 5

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Figure 4: Four isotopomers for 3 (R = H) on which direct dynamics calculations are performed.

Average time (fs) 116±14 112±14 116±11

Table 2: Average time-scales for producing either a product or TS2 starting from 3 (R = H). One simple test to experimentally determine the importance of post-transition state dynamics is to measure the kinetic isotope effects. 3 → TS1 being the rate-determining step would result in a kinetic isotope effect arising from ZPE and quantum mechanical tunneling (See Supp. Info. for computed rate constants, Table S7). Nevertheless, since the product selectivity occurs subsequent to TS1, kinetic isotope effects would be benign towards bifurcation7. Newtonian KIEs on the other hand, are indeed sensitive towards the motion of atoms along bifurcating potential surfaces.37, 41-42 With isotopic substitutions that make the products non-equivalent, the Newton’s second law would favor a product which arises through direct displacement along the steepest-descent path in mass-weighted coordinates (IRC). Herein, we used deuterium, 13C

Cases

A

B

C

D

No of trajectories

315

359

373

233

Trajectories affording 4 Trajectories affording 5 Isotopomer ratio (4:5) 95% confidence

141

179

196

134

137

146

143

84

1:1

1.2:1

1.4:1

1.6:1

1.3–0.8

1.4–1.1

1.5–1.2

1.8–1.4

Table 3: Results for the quasi-classical trajectories starting from TS1 of A, B, C and D respectively at B3LYP/6-31G(d) level. In case of A, product ratio between 4 and 5 still remains ~ 1:1 as that for the parent, non-isotopically labeled, I. This is expected as H/D replacement occurs only at the distal position. 4


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The Journal of Physical Chemistry AUTHOR INFORMATION

Interestingly, isotopic effects are anticipated to be large for substitutions only at the C1-C2 and C4-C5 positions. For a single 12 13 C/ C isotopic replacement (B), 4:5 is 1.2:1 which enhances to 1.4:1 in C for two 12C/13C isotopic replacements (along C1-C2). As a proof of principle, two 12C/14C isotopic replacements in the C1-C2 bond makes 4:5 as high as 1.6.43 This clearly indicates that pure Newtonian effects govern the KIEs for these deazetization reactions (for further details see the supporting information file). RRKM lifetimes of each case are also analyzed (Table 4) from which we observe that, an increment in mass can retard the extent of rearrangement between 4 and 5. Since, the products are stable till ~ 300 fs, one can experimentally observe the non-statistical population ratios (4:5) using a femtosecond time resolved transient 2D-IR (t-2D-IR) technique to probe the initial product ratios. We believe that, high sensitivity of t-2D-IR spectroscopy can provide a useful basis for characterizing these dynamical effects generated from their nuclear motions44-48 (for further details see the supporting information file).

Corresponding Author Corresponding 24734971.

Author:

[email protected].

Phone:

+91-33-

Notes The authors declare no competing financial interests. ACKNOWLEDGMENT NM thanks CSIR for JRF. AD thanks DST and BRNS for partial funding. We thank Professor Daniel A. Singleton for useful discussions regarding the use and applications of the Progdyn program. Dedicated to Professor Roald Hoffmann on his 80th birthday.

REFERENCES 1.

Molecules

Lifetime of 4 (fs)

Lifetime of 5 (fs)

2.

Parent (R =H)

314

314

3.

A (R = H)

327

327

B (R = H)

316

316

C (R = H)

321

321

D (R = H)

328

326

4.

5. 6.

Table 4: Computed RRKM lifetimes (in fs) of 4 and 5 for different isotopomers (A, B, C, D respectively) at 300K using B3LYP/631G(d) level of theory.

CONCLUSIONS

7.

In summary, we have shown that semibullvalene formation from 3 is concerted, synchronous, featuring a bispericyclic transition state (TS1) and is dictated by dynamical effects. Experimental evidence for post-transition-state dynamic control can be readily obtained by the observation of Newtonian kinetic isotope effects in the ratio of 4 and 5. We hope that our computational prediction would be subject to experimental test soon.

8.

9. 10.

ASSOCIATED CONTENT Supporting Information Method for quasi-classical trajectory (QCT) calculations, input parameters for Progdyn, normal mode sampling, snapshots from trajectories, variation of bond lengths obtained from QCTs, lifetimes, detailed analyses of dynamic selectivity study, uncertainties in the trajectory ratios, Simulations of V (R = CN), DFT calculations, VRI-point analysis, IRC for R = Cl from TS1, IRCs for substituted case, relative energies and stability analyses of different cases, implicit solvation study, computed rate constants, RRKM lifetimes, optimized cartesian coordinates and harmonic frequencies.

11. 12.

13.

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Dynamical Effects along the Bifurcation Pathway Control

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