Competitive Heavy-Atom Tunneling Reactions Controlled Through Electronic Effects

Graphical Abstract

Benzazirines with increasingly stronger electron-donating C4 substituents, generated in cryogenic matrices, exhibit different quantum mechanical tunneling (QMT) selectivities, shifting from ring-expansion to ketenimines, to ring-opening giving nitrenes. This demonstrates how subtle changes in electronic effects can be used to fine-tune QMT reactivity.

Abstract

Controlling QMT reactivity remains exceptionally challenging and largely unexplored, as it requires rationales distinctly different from those used for classical chemical reactivity. Herein, we investigated how QMT reactivity can be controlled using electronic substituent effects. Benzazirines, which have the exceptional feature to react via two competitive QMT pathways, were used as model compounds. Three novel derivatives with increasingly stronger electron-donating substituents at C4 [R = OH, N(CH₃)₂, and N(CH₂)₄] were generated in argon matrices at 3 K. Remarkably, different QMT selectivities were observed in all benzazirines. As the electron-donating strength of the substituent increases, the QMT ring-opening to nitrene starts to compete with the QMT ring-expansion to ketenimine, becoming the dominant process for the strongest electron-donating substituent [N(CH₂)₄]. A theoretical analysis of the substituent effects on the QMT reactivity of benzazirines was performed and compared with the experimental data for these and other C4 derivatives. Overall, the results compellingly demonstrate how subtle changes in electronic effects can be used to fine-tune QMT selectivity.

1 Introduction

Chemical reactivity has traditionally been understood by considering that reactants transition to products by overcoming a defined transition state (TS).^{1, 2} This conceptual framework has guided the development of reactivity principles,^3-5 and has enabled chemists to predict and manipulate chemical reactions. However, nuclei can permeate through a potential energy barrier that they would classically not have enough energy to overcome, by a phenomenon known as quantum mechanical tunneling (QMT). Consequently, chemical reactions driven by QMT can defy established reactivity principles, leading to the formulation of new reactivity paradigms.^{6, 7} Likewise, attaining control over QMT reactions often requires alternative approaches compared to those used for non-QMT reactions, because features such as barrier widths and particle mass although essentially irrelevant in classical reactivity are pivotal in QMT reactivity. For instance, enzymologists have successfully used mutagenesis to alter the global protein dynamics and modulate hydrogen transfer distances conducive to QMT reactivity.⁸ Some of us have demonstrated that specific conformational changes induced by external near-IR light on small organic molecules can activate hydrogen QMT.⁹ Others have discussed the control of QMT through the application of external electric fields,¹⁰ distinct solvation effects,¹¹ or isotopic labeling of key atoms.¹² Electronic substituent effects, although commonly used to modulate classical reactivity through changes in the reaction barrier height,^{13, 14} should have a distinct and more profound consequence on QMT reactivity through their effect on both barrier height and width.^{15, 16} A systematic investigation on the QMT anti to syn OD-rotamerization in para-substituted benzoic acids revealed that classical Hammett substituent constants σ do not correlate well with QMT rate constants and had to be replaced with QMT-specific σ^t-values.¹⁷ In pursuit of advances to attain control over QMT reactivity, we investigate here how electronic substituent effects direct the selective outcome of competitive heavy-atom QMT reactions occurring from a single reactant.

The probability of QMT decreases exponentially with the square root of the mass of the tunneling particle. Consequently, hydrogen QMT is the predominant phenomenon in QMT chemical reactivity.^{18, 19} Nonetheless, experimental observation of heavy-atom QMT, involving second-row elements, was documented already in the mid-1970s,²⁰ and has significantly advanced in the last two decades.^21-24 Particularly noteworthy are investigations involving 2H-benzazirines 3, which have provided valuable insights into heavy-atom QMT reactivity.^25-30 Derivatives of 3 can be generated by the photoisomerization of arylnitrenes 2, which are typically accessed through denitrogenation of the corresponding arylazides 1. However, detection of benzazirines 3 poses significant challenges due to their highly reactive nature and QMT instability (i. e., the notion that QMT can preclude a molecule to be isolable and detected, even though it should be according to a semiclassical interpretation).^{31, 32} For instance, in the photochemistry of parent phenylnitrene 2a isolated under cryogenic matrices (T=12 K), cyclic ketenimine 4a formed without the detection of intermediate benzazirine 3a (Scheme 1a).^{33, 34} The ring-expansion of 3a to 4a has a computed energy barrier of a few kcal mol⁻¹,³⁵ which should allow its capture at cryogenic temperatures. However, as shown in section 3 of the supporting information (SI), computations indicate that a very fast QMT from 3a to 4a should make 3a elusive. Computations also indicate that the inclusion of electron-donating substituents at position C4 can significantly increase the ring-expansion barrier height,³⁶ which should decrease the QMT probability and allow the capture of benzazirine derivatives 3. Indeed, the spectroscopic observation of heavy-atom QMT reactivity was first reported for the ring-expansion of 4-thiomethyl-2H-benzazirine 3b to the corresponding ketenimine 4b (Scheme 1b).²⁵ Surprisingly, some of us later revealed that in the case of 4-amino-2H-benzazirine 3c, the potential energy surface (PES) is sufficiently affected to allow for the QMT ring-opening to 2c, which can efficiently compete with the QMT ring-expansion to 4c, with a product distribution 2c : 4c of 15 : 85 (Scheme 1c).²⁸

Scheme 1

Summary of results reported under matrix-isolation conditions: (a) The photochemistry of phenylnitrene 2a yields only ketenimine 4a;³³ (b) the photochemistry of nitrene 2b yields 4-thiomethyl-2H-benzazirine 3b which then undergoes QMT ring-expansion to ketenimine 4b;²⁵ (c) 4-amino-2H-benzazirine 3c undergoes competitive QMT ring-opening to 2c vs QMT ring-expansion to 4c (2c : 4c=15 : 85).²⁸

The discovery of two competitive QMT pathways in benzazirines 3 establishes these species as ideal systems for investigating electronic substituent effects in the selectivity of QMT reactions. In this context, we considered the inclusion of increasingly stronger electron-donating substituents at position C4, selecting them based on the values of Hammett substituent constants (σ) (Scheme 2).³⁷ Thus, first the hydroxyl substituent [σ_p(OH)=−0.37] was chosen to bridge the electron-donating strengths of the previously studied thiomethyl [σ_p(SCH₃)=0.00] and amino [σ_p(NH₂)=−0.66] substituents. Then, the dimethylamine substituent [σ_p(N(CH₃)₂)=−0.83] was selected to provide an electron-donating strength superior to that of the amino substituent. Finally, the 1-pyrrolidine (N(CH₂)₄) substituent was chosen as potentially the strongest electron-donating substituent (even though its Hammett constant is unknown). Herein, we report the successful generation of the three novel C4-substituted benzazirine targets (3d, 3e, and 3f) in argon matrices at 3−18 K. We investigated their QMT reactivities and analyzed the effects of C4 substitution on the competitive QMT ring-opening vs. QMT ring-expansion reactions. Our findings emphasize the profound influence of substitution on QMT reactivity and selectivity, surpassing the conventional expectation solely based on reaction barrier height, which typically governs classical reactivity.

Scheme 2

2H-Benzazirines with progressively stronger electron-donating substituents at position C4. The generation and QMT reactivity of benzazirines 3d, 3e, and 3f are described for the first time in this study, whereas those of 3b and 3c were previously reported.^{25, 28}

2 Results and Discussion

2.1 Direct Observation of QMT Reactivity in 4-Substituted-2H-Benzazirines

2.1.1 4-Hydroxy-2H-Benzazirine

The 4-hydroxy-phenylazide 1d precursor was synthesized and monomers of the sample were isolated in an Ar matrix at 3.5 K (details are given in Sections 1.1 and 1.2 of the SI). The corresponding IR spectrum shows the most characteristic ν(OH) and ν(N₃)_as bands at 3645/3634 and 2119/2078 cm⁻¹ (Figure S2 and Table S1). The hydroxyl group of 1d can adopt syn- and anti-conformation relative to the azide group. However, it is known that fast QMT OH-rotamerization occurs from the high-energy to the low-energy conformation of phenols and derivatives in argon matrices. A detailed discussion of this topic is addressed elsewhere.²⁹ Therefore, only the most stable anti-1d is expected to be isolated. The high similarity between IR spectra of syn-1d and anti-1d makes their discrimination difficult, but a better agreement between the experimental IR spectrum and the computed IR spectrum of anti-1d is observed in some IR regions (Figure S3). The subsequent photolysis of anti-1d was induced at 260 nm, and it generated triplet 4-hydroxy-phenylnitrene ³2d (minor amount) and anti-5-hydroxy-1-aza-1,2,4,6-cycloheptatetraene anti-4d (major amount) (Figure S4). To produce or convert a desirable photoproduct, we used an irradiation strategy based on UV-Vis spectroscopic data and photochemistry experiments reported for the amino derivative.²⁸ Accordingly, we found that irradiation at 350 nm completely converted ketenimine anti-4d to triplet nitrene ³2d (Figure S5). Characteristic IR bands of ³2d were identified at 1573, 1278, 1170, and 816 cm⁻¹ in agreement with the B3LYP/6-311+G(2d,p) computed vibrational modes of ³2d at 1576 [ν(CC)], 1267 [ν(CO)], 1155 [δ(OH)], and 813 [γ(CH)] cm⁻¹. Distinctive IR bands of anti-4d were observed at 1891, 1591, 1305, 1147, and 796 cm⁻¹ in agreement with the computed vibrational modes of anti-4d at 1903 [ν(C=C=N)_as], 1593 [ν(C=C)_as], 1309 [ν(C=C=N)_s], 1148 [ν(CO) − δ(OH)], and 799 [γ(CH)] cm⁻¹. A more detailed assignment of the IR spectra of ³2d and anti-4d is provided in Tables S2 and S3. The Ar matrix enriched with ³2d was then irradiated at 435 nm, which allowed the generation of target 4-hydroxy-2H-benzazirine syn-3d efficiently (Figure S6). Characteristic IR bands of syn-3d were observed at 1716, 1594, 1235, 1172/1149, and 808 cm⁻¹ in good correspondence with the computed vibrational transitions of syn-3d at 1749 [ν(C=N)], 1593 [ν(C=C)_as], 1228 [ν(CO)+δ(OH)], 1155 [ν(CO) − δ(OH)], and 811 [γ(CH)] cm⁻¹. Comprehensive assignments of the IR spectra of syn-3d are presented in Table S4.

Syn-4-hydroxy-2H-benzazirine syn-3d spontaneously undergoes ring-expansion reaction to ketenimine anti-4d in the dark (Figure 1 and Scheme 3). The computed IR spectra of the most energetic OH conformers anti-3d and syn-4d do not show a good match with the experimental results, which is in agreement with the expectation that these species cannot be isolated in argon matrices (Figure S7).²⁹ The putative formation of triplet nitrene ³2d was excluded based on the absence of its signals in the corresponding difference IR spectrum. The kinetics of the spontaneous reaction of syn-3d to anti-4d was measured in an Ar matrix at 3.5 and 18 K by collecting IR spectra over time using a longpass filter blocking light above 2200 cm⁻¹ (details given in the section 1.5 of the SI). Approximate rate constants of k_3d(3.5K)=3.4×10⁻⁵ s⁻¹ (τ_1/2=5.6 h) and k_3d(18K)=3.9×10⁻⁵ s⁻¹ (τ_1/2=4.9 h) were obtained by fitting the experimental data with first-order exponential decay equations (stretched exponential fittings, to account for dispersive kinetics, give similar results: see Figure S8). The essentially unchanged reaction rates upon an up to five-fold increase of the temperature provides strong evidence for the occurrence of QMT in the ring-expansion of syn-3d to anti-4d. The contribution of IR-induced reactivity resulting from the short-time exposure to filtered IR light (νc̃>2200 cm⁻¹) during spectral acquisition was found to be negligible (details are given in the section 1.5 of the SI).

Figure 1

(a) Experimental difference IR spectrum showing changes after keeping syn-4-hydroxy-2H-benzazirine syn-3d in an Ar matrix at 3.5 K in the dark for 8 h. The downward IR bands are due to the consumption of syn-3d and the upward IR bands due to the formation of anti-5-hydroxy-1-aza-1,2,4,6-cycloheptatetraene anti-4d. (b) Computed B3LYP/6-311+G(2d,p) IR spectra of syn-3d (negative bands, orange circles) and anti-4d (positive bands, orange squares).

Scheme 3

Summary of the observed reactivity involving syn-4-hydroxy-2H-benzazirine 3d generated in an Ar matrix at 3.5 K.

2.1.2 4-Dimethylamino-2H-Benzazirine

Monomers of the 4-dimethylamino-phenylazide 1e precursor were isolated in an Ar matrix at 3.5 K (details given in sections 1.1 and 1.2 of the SI). The corresponding IR spectrum and vibrational assignments are provided in Figure S10 and Table S5. The subsequent photolysis of 1e induced at 255 nm gives triplet 4-dimethylamino-phenylnitrene ³2e as the exclusive product (Figure S11). Characteristic IR bands of ³2e were observed at 1588, 1369, 1325, 944, and 803 cm⁻¹ in a good match with the B3LYP/6-311+G(2d,p) computed vibrations of ³2e at 1588 [ν(CC)], 1356 [ν(CN_dme)], 1313 [ν(CN_nit)], 933 [ν(N(CH₃)₂)_s], and 800 [γ(CH)_ring] cm⁻¹. A comprehensive assignment of the IR spectrum of ³2e is given in Table S6. The matrix enriched with triplet nitrene ³2e was then irradiated at 450 nm yielding a mixture of 4-dimethylamino-2H-benzazirine 3e and 5-dimethylamino-1-aza-1,2,4,6-cycloheptatetraene 4e (Figure S12). Although the dimethylamine group adopts distinct orientations in ³2e, 3e, and 4e, each exhibits only a single conformer, as described in detail in section 4 of the SI.

Benzazirine 3e spontaneously rearranges in the dark to give both triplet nitrene ³2e and ketenimine 4e (Figure 2 and Scheme 4). Distinctive IR bands of 3e appear at 1728, 1494, 1317, 934, and 794/785 cm⁻¹ in agreement with the computed vibrational modes of 3e at 1754 [ν(C=N)], 1495 [ν(C=C)_s], 1313 [ν(CN_dme)], 922 [ν(N(CH₃)₂)_s], and 811 [γ(CH)_ring] cm⁻¹. A detailed assignment of the IR spectrum of 3e is provided in Table S7. After the complete transformation of 3e, irradiation at 350 nm induces the clean conversion of 4e to ³2e (Figure S13). Characteristic IR bands of ketenimine 4e appear at 1886, 1580, 1333, 1125, and 678 cm⁻¹ in good correspondence with the computed IR spectral bands of 4e at 1901 [ν(C=C=N)_as], 1579 [ν(C=C)_as], 1327 [ν(CN_dme)], 1121 [ν(C=C=N)_s], and 681 [γ(CH)_ring] cm⁻¹. A more extensive assignment of the IR spectrum of 4e is given in Table S8. Based on the IR spectral information regarding the photoreaction of 4e to ³2e, the spontaneous rearrangement of 3e in the dark could be estimated to produce a ³2e : 4e ratio of 30 : 70 (details are given in the section 1.4 of the SI).

Figure 2

(a) Experimental difference IR spectrum showing changes after keeping 4-dimethylamino-2H-benzazirine 3e in an Ar matrix at 3.5 K in the dark for 24 h. The downward bands are due to the consumption of 3e and the upward bands due to the formation of triplet 4-dimethylamino-phenylnitrene ³2e and 5-dimethylamino-1-aza-1,2,4,6-cycloheptatetraene 4e. (b) Computed B3LYP/6-311+G(2d,p) IR spectrum of 3e (black line, blue circles), ³2e (gray line, blue triangles), and 4e (black line, blue squares). The intensities of the computed IR bands 3e, ³2e, and 4e were multiplied by −1.0, 0.3, and 0.7, respectively.

Scheme 4

Summary of the observed reactivity involving 4-dimethylamino-2H-benzazirine 3e generated in an Ar matrix at 3.5 K.

The kinetics of the spontaneous transformation of 3e was measured in Ar matrices at 3.5 and 18 K by collecting several IR spectra over time using a longpass filter blocking light above 2200 cm⁻¹ (otherwise the sample was kept in the dark). Approximate rate constants of k_3e(3.5K)=3.7×10⁻⁵ s⁻¹ (τ_1/2=5.2 h) and k_3e(18K)=3.9×10⁻⁵ s⁻¹ (τ_1/2=5.0 h) were obtained by fitting the experimental data with first-order exponential decay equations (stretched exponential fittings, to account for dispersive kinetics, give similar results: see Figure S14). The observation of similar reaction rates at temperatures of 3.5 and 18 K strongly indicates the occurrence of QMT. Moreover, the ³2e : 4e product ratio from the spontaneous transformation of 3e was estimated to be identical at 3.5 and 18 K (30 : 70 vs 33 : 67, respectively). These data clearly support the occurrence of two independent and competitive QMT reactions, namely the QMT ring-opening of 3e to ³2e and the QMT ring-expansion of 3e to 4e. Considering a first-order reaction of a single reactant to give two different products, approximate rate constants of k_2e(3.5K)=1.1×10⁻⁵ s⁻¹ (τ_1/2=17.3 h) and k_4e(3.5K)=2.6×10⁻⁵ s⁻¹ (τ_1/2=7.4 h) were obtained for the QMT formation of ³2e and 4e, respectively. The contribution of IR-induced reactivity resulting from the short-time exposure to filtered IR light (νc̃>2200 cm⁻¹) during spectral acquisition was found to be negligible (details are given in the section 1.5 of the SI).

2.1.3 4-Pyrrolidine-2H-Benzazirine

The 4-pyrrolidine-phenylazide 1f precursor was prepared and monomers were deposited in an Ar matrix at 3.5 K (Figure S16 and Table S9; details are given in sections 1.1 and 1.2 of the SI). The photolysis of 1f at 255 nm produces triplet 4-pyrrolidine-phenylnitrene ³2f as the sole product (Figure S17). Distinctive IR bands of ³2f were observed at ~1589, ~1464, 1384, 1322, and 802 cm⁻¹ in good correspondence with the B3LYP/6-311+G(2d,p) computed vibrational modes of ³2f at 1590 [ν(CC)], 1463 [ν(CN_pyr)+ν(CC)], 1379 [ν(CN_pyr) − ν(CC)], 1314 [ν(CN_nit)], and 799 [γ(CH)_ring] cm⁻¹. A more complete assignment of the IR spectrum of ³2f is presented in Table S10. The generation of 4-pyrrolidine-2H-benzazirine 3f was challenging and only a small amount could be isolated after short-time irradiation (a few minutes) of ³2f at 450 nm (Figure S18). The 5-pyrrolidine-1-aza-1,2,4,6-cycloheptatetraene 4f formed as the major product. Although distinct pyrrolidine ring-puckering can give rise to two pairs of conformers for these species (3f / 3f′ and 4f / 4f′, which are essentially indistinguishable by IR spectroscopy due to their similar spectra), only the most stable conformer 3f is expected to be observed in argon matrices, as will be discussed in section 2.2. As the transformation of 3f is expected to yield conformer 4f, the presence of 4f in the matrix experiments is assumed. The presence of conformer 4f′ cannot be ruled out, but for simplicity, it will not be discussed as it exhibits an essentially indistinguishable IR spectrum compared to 4f. Clean re-conversion of ketenimine 4f to triplet nitrene ³2f was achieved by irradiation at 350 nm (Figure S19). Characteristic IR bands of 4f appear at ~1873, 1584, 1337, 1113, and 779 cm⁻¹ in good match with the computed vibration of 4f at 1884 [ν(C=N=C)_as], 1583 [ν(C=C)_as], 1334 [ν(CN_pyr)], 1116 [ν(C=C=N)_s+δ(CH)], and 787 [γ(CH)_ring] cm⁻¹. Comprehensive assignments of the IR spectrum of 4f are given in Table S11.

Benzazirine 3f spontaneously rearranges in the dark to give both triplet nitrene ³2f and ketenimine 4f (Figure 3 and Scheme 5). Distinctive IR bands of 3f were observed at 1718, 1579, 1482, 1341/1335, ~943, and 773 cm⁻¹ in agreement with the computed vibrational transitions of 3f at 1745 [ν(C=N)], 1582 [ν(C=C)_as], 1477 [ν(C=C)_s], 1331/1323 [ν(CN_pyr) +/− δ(CH)], 930 [ν(N(CH₂)₂)_s], and 784 [γ(CH)_ring] cm⁻¹. A more detailed assignment of the IR spectrum of 3f is presented in Table S12. The kinetics of the spontaneous rearrangement of 3f was measured in Ar matrices at 3.5 and 18 K, and approximate rate constants of k_3f(3.5K)=3.4×10⁻⁴ s⁻¹ (τ_1/2=34 min) and k_3f(18K)=4.4×10⁻⁴ s⁻¹ (τ_1/2=26 min) were obtained (stretched exponential fittings, to account for dispersive kinetics, give similar results: Figure S20). A ³2f : 4f product ratio of 71 : 29 and 75 : 25 was measured at 3.5 and 18 K, respectively. The observation of similar reaction rates after increasing the temperature by a factor of five, associated with the formation of an equivalent product ratio, clearly indicates the occurrence of competitive QMT ring-opening of 3f to ³2f and QMT ring-expansion of 3f to 4f. Approximate rate constants of k_2f(3.5K)=2.4×10⁻⁴ s⁻¹ (τ_1/2=48 min) and k_4f(3.5K)=9.9×10⁻⁵ s⁻¹ (τ_1/2=117 min) were estimated for the QMT formation of ³2f and 4f, respectively (details are given in the section 1.5 of the SI). The contribution of IR-induced reactivity resulting from the short-time exposure to filtered IR light (νc̃>2200 cm⁻¹) during spectral acquisition was found to be negligible (details are given in the section 1.5 of the SI).

Figure 3

(a) Experimental difference IR spectrum showing changes after keeping 4-pyrrolidine-2H-benzazirine 3f in an Ar matrix at 3.5 K in the dark for 1 h. The downward bands are due to the consumption of 3f and the upward bands due to the formation of triplet 4-pyrrolidine-phenylnitrene ³2f and 5-pyrrolidine-1-aza-1,2,4,6-cycloheptatetraene 4f. (b) Computed B3LYP/6-311+G(2d,p) IR spectrum of 3f (black line, dark blue circles), ³2f (gray line, dark blue triangles), and 4f (black line, dark blue squares). The intensities of the computed IR bands 3f, ³2f, and 4f were multiplied by −1.0, 0.7, and 0.3, respectively.

Scheme 5

Summary of the observed reactivity involving 4-pyrrolidine-2H-benzazirine 3f generated in an Ar matrix at 3.5 K.

2.2 Computations of QMT Reactivity in 4-Substituted-2H-Benzazirines

To deepen our knowledge about the substituent effects on the possible competitive QMT reactions of benzazirines 3, we computed the corresponding potential energy surfaces (PES) and QMT rates. The NEVPT2(8,8)/6-311+G(2d,p)//CASSCF(8,8)/6-311+G(2d,p) level of theory was employed to compute the ring-opening reaction of 3d–f to ¹2d–f. This level was chosen because a multireference method with dynamic correlation is needed to correctly describe open-shell singlet nitrenes ¹2d–f and the corresponding reaction path from 3d–f. Note that the subsequent ISC from singlet ¹2d–f to triplet ground-state ³2d–f occurs much faster (ns time-scale)³⁸ and does not affect the reaction rate, which is entirely determined by the former reaction on the singlet surface. The CCSD(T)/cc-pVTZ//B3LYP/6-311+G(2d,p) level of theory was employed to compute the ring-expansion reaction of 3d–f to 4d–f. This level provides accurate energies for the single-reference wavefunction species involved in this reaction. Vibrationally adiabatic surfaces were computed using intrinsic reaction coordinates (IRC) with vibrational energy corrections containing all modes orthogonal to the reaction path. The QMT rates were then calculated by numerically integrating the corresponding permeation barrier using the Wentzel-Kramers-Brillouin (WKB) equations as implemented in TUNNEX.³⁹ The overall approach is equivalent to the one previously used to compute the competitive QMT reactions of 3c,²⁸ which demonstrates reasonably good agreement with experimental results (details are given in sections 2.2 and 2.3 of SI).

For syn-4-hydroxy-2H-benzazirine syn-3d, computations estimate a barrier height for the ring-opening to ¹2d of 3.8 kcal mol⁻¹ and for the ring-expansion to syn-4d of 7.7 kcal mol⁻¹ (Figure S22). In contrast to the reaction barrier height, the barrier width is substantially larger for syn-3d→¹2d than for syn-3d→syn-4d, 7.58 vs. 4.11 amu^1/2 bohr, respectively (Figure 4).⁴⁰ Although irrelevant from the classical point of view of chemical reactivity, the barrier width is a crucial factor to determine QMT reactivity and the emergence of tunneling control.⁷ Interestingly, this scenario is clearly manifested in the reactivity of syn-3d, with computations estimating QMT rate constants of 2.8×10⁻¹¹ s⁻¹ for the ring-opening syn-3d→¹2d (τ_1/2~790 a) and of 2.0×10⁻⁴ s⁻¹ for the ring-expansion syn-3d→syn-4d (τ_1/2~1 h). The subsequent QMT OH-rotamerization syn-4d→anti-4d is a much faster process (computed data: k=5.0×10⁴ s⁻¹ and τ_1/2=140 μs, Figure S23), which precludes the isolation of syn-4d in argon matrices. These theoretical results show good agreement with the experimental observation of tunneling control and exclusive QMT ring-expansion of syn-3d with the observation of anti-4d (τ_1/2 ~5 h).

Figure 4

The intrinsic reaction coordinate (IRC) profiles for syn-3d→¹2d and syn-3d→syn-4d reactions computed at the NEVPT2(8,8)/6-311+G(2d,p)//CASSCF(8,8)/6-311+G(2d,p) and CCSD(T)/cc-pVTZ//B3LYP/6-311+G(2d,p) levels of theory, respectively. The IRC energies are relative to the absolute energy of syn-3d and include ZPVE corrections of 3N-7 vibrations. The gray horizontal line represents half of the collision frequency. The QMT half-lives τ_1/2 from the vibrational ground state of syn-3d were computed using the WKB approach (section 2.3 of the SI).

For 4-dimethylamino-2H-benzazirine 3e, the computations turn out to be troublesome and did not provide sufficiently accurate PESs to enable reliable calculations of QMT reaction rates. The PESs associated with reactions 3e→¹2e and 3e→4e must account for the rotation of the dimethylamine group because it adopts different orientations in ¹2e, 3e, and 4e (a detailed discussion is given in section 4 of the SI). The computations at CASSCF/6-311+G(2d,p) and NEVPT2(8,8)/6-311+G(2d,p)//CASSCF(8,8)/6-311+G(2d,p) levels estimate similar barrier heights of ~3.1 kcal mol⁻¹ for the ring-opening 3e→¹2e. However, the CASSCF method fails to describe the correct geometry of ¹2e and finds a global minimum in which the dimethylamine group adopts a significative out-of-plane geometry. NEVPT2 single-point corrections show that such a geometry is energetically higher by 1.7 kcal mol⁻¹ than a nearly-planar one. Because of the incompatibility of the methods, implementing NEVPT2 single point corrections on top of the IRC computed at the CASSCF level would not improve the accuracy of the PES (Figure S25). In fact, the computed QMT rate using the CASSCF PES (k=4.0×10⁻⁶ s⁻¹; τ_1/2=48 h) is in better agreement with experimental measurements (k_2e(3.5K)=1.1×10⁻⁵ s⁻¹; τ_1/2=17.3 h) than the computed QMT rate using the NEVPT2//CASSCF PES (k=3.6×10⁻¹⁰ s⁻¹; τ_1/2=60 a). For 3e→4e, two distinct transition states (TSs) were found connecting the minima. The PES associated to the lower-lying TS′ (7.5 kcal mol⁻¹ at the CCSD(T)/cc-pVTZ//B3LYP/6-311+G(2d,p) level) requires a ~60° rotation of the dimethylamine group prior to reaching the TS, which precludes the occurrence of QMT (Figure S26a). In case of the PES associated to the higher-lying TS′′ (8.7 kcal mol⁻¹ at the CCSD(T)/cc-pVTZ//B3LYP/6-311+G(2d,p) level), the ~60° rotation of the dimethylamine group occurs after the TS. In the PES computed at B3LYP/6-311+G(2d,p), such rotation does not affect the permeation barrier because it occurs after the QMT process (outside the PES turning points) (Figure S26b). The corresponding computed QMT rate is k=8.4×10⁻⁶ s⁻¹ (τ_1/2=23 h), which is in (fortuitous) agreement with the experimental measurements (k_4e(3.5K)=2.6×10⁻⁵ s⁻¹; τ_1/2=7.4 h). However, implementing CCSD(T) single point corrections on top of the IRC computed at the B3LYP level leads to a PES that now includes some rotation of the dimethylamine group in the QMT process (within the PES turning points) (Figure S26c). This modification significantly increases the permeation barrier and consequently leads to an extremely low QMT rate (k=2.6×10⁻¹⁹ s⁻¹; τ_1/2=8.5×10¹⁰ a). Overall, even though these computations fail to yield sufficiently accurate rate constants, they provide important insights by revealing that the shape of the PESs can enormously affect the QMT probabilities.¹⁵

For 4-pyrrolidine-2H-benzazirine 3f, computations estimate a barrier height for the ring-opening to ¹2f of 1.4 kcal mol⁻¹ and for the ring-expansion to 4f of 8.0 kcal mol⁻¹ (Figure S27). A second conformer 3f′, differing from 3f by distinct ring-puckering of the pyrrolidine ring, was also found. The IR spectral signatures of the 3f and 3f′ are virtually indistinguishable. However, according to the computations, conformer 3f′ is thermodynamically and kinetically less stable than 3f (Figure S27), and it should not be isolable due to very fast QMT (3f′→¹2f barrier height is 0.8 kcal mol⁻¹ and the corresponding QMT rate is k=3.0×10⁷ s⁻¹; τ_1/2~2.3×10⁻⁸ s).⁴¹ Therefore, it is reasonable to assume that only the most stable 3f and its corresponding QMT transformations were observed in the matrix-isolation experiments. For this scenario, computations estimate the QMT ring-opening 3f→¹2f with k=1.3×10³ s⁻¹ (τ_1/2=0.5 ms) to be considerably faster than the QMT ring-expansion 3f→4f with k=1.6×10⁻⁵ s⁻¹ (τ_1/2=12 h) (Figure 5). Although significantly overestimating the rate of the former reaction, computations show qualitative agreement with the experimental observation of QMT being faster for the ring-opening 3f→¹2f (k_2f(3.5K)=2.4×10⁻⁴ s⁻¹; τ_1/2=48 min) than for the ring-expansion 3f→4f (k_4f(3.5K)=9.9×10⁻⁵ s⁻¹; τ_1/2=2 h), and the contrasting QMT reactivity in comparison to 3d.

Figure 5

The intrinsic reaction coordinate (IRC) profiles for 3f→¹2f and 3f→4f reactions computed at the NEVPT2(8,8)/6-311+G(2d,p)//CASSCF(8,8)/6-311+G(2d,p) and CCSD(T)/cc-pVTZ//B3LYP/6-311+G(2d,p) levels of theory, respectively. The IRC energies are relative to the absolute energy of 3f and include ZPVE corrections of 3N-7 vibrations. The gray horizontal line represents half of the collision frequency. The QMT half-lives τ_1/2 from the vibrational ground state of 3f were computed using the WKB approach (section 2.3 of the SI).

2.3 Assessing the Substituent Effect on the QMT Reactivity of 2H-Benzazirines

To better understand how the two possible competitive QMT reactions of benzazirines 3 are differently affected by the nature of the C4 substituent, a detailed comparative analysis was conducted on the computational and experimental results obtained for the C4-substituted derivatives (Scheme 2).

Considering the unsubstituted derivative (R = H) as reference (Figure 6), the computations indicate that the 3→¹2 ring-opening energy barrier decreases as the electron-donating strength of the C4 substituent increases [from 5.4 kcal mol⁻¹ for R = H down to 1.4 kcal mol⁻¹ for R = N(CH₂)₄]. Concomitantly, the corresponding reaction enthalpies significatively decreases as the electron-donating strength of the C4 substituent increases [from −0.9 kcal mol⁻¹ for R = H down to −5.7 kcal mol⁻¹ for R = N(CH₂)₄]. On the other hand, computations show that the 3→4 ring-expansion energy barrier increases for all C4 electron-donating substituents, but without correlating to their respective strength [from 5.1 kcal mol⁻¹ for R = H up to 7.3−8.0 kcal mol⁻¹ for R = NH₂, OH, and N(CH₂)₄]. The corresponding reaction enthalpies at most only slightly increase for the C4 electron-donating substituents and, again, without any correlation with their respective donor strength [varying between −4.5 kcal mol⁻¹ for R = H and NH₂ to −3.2 kcal mol⁻¹ for R = OH]. The pronounced effect and correlation trend found between the electron-donating strength of the C4 substituents and the energy barriers or reaction enthalpies for the 3→¹2 ring-opening can be partially rationalized by the stabilization of the open-shell nitrenes ¹2, which are electron-deficient species characterized by a quinoid-type structure with one unpaired electron localized mainly at the C4 carbon of the ring (Figure 6).

Figure 6

Energy profiles (ΔH_0K in kcal mol⁻¹) for 3→¹2 ring-opening and 3→4 ring-expansion reactions with R = H (3a), OH (3d), NH₂ (3c) and N(CH₂)₄ (3f) computed at the NEVPT2(8,8)/6-311+G(2d,p)//CASSCF(8,8)/6-311+G(2d,p) and CCSD(T)/cc-pVTZ//B3LYP/6-311+G(2d,p) levels of theory, respectively. Energy values are relative to the energy of the corresponding benzazirines 3, and for 3d and 3f, they refer specifically to the most stable conformation. For the R =N(CH₃)₂ derivative (3e), the substituent rotamerization occurs concomitantly with the ring-opening or ring-expansion reaction, which makes it difficult to compute the corresponding PES accurately (see, e.g., section 4 of the SI).

A particularly distinguishing feature of QMT reactivity is its high dependence on the barrier width of the reaction, which differs from classical reactivity that depends only on the barrier height.^{15, 42} Indeed, computations show that for the unsubstituted 3a, although the ring-opening 3a→¹2a and ring-expansion 3a→4a reactions have approximately the same barrier heights (~5 kcal mol⁻¹), the QMT ring-opening rate is 19 orders of magnitude slower than the QMT ring-expansion rate (Table 1). The key difference is the respective barrier widths, 8.63 vs. 3.22 amu^1/2 bohr (Figure S1).⁴⁰ Therefore, to achieve QMT reactivity control through substituent electronic effects, it is pivotal to capture their influence on the barrier width (more so than their influence on the barrier height), which might be roughly rationalized based on their changes in the enthalpy of the reactions.

Table 1. Experimental QMT rates (k_exp in s⁻¹) and half-lives (τ_1/2 in h) measured in Ar matrices at 3.5 K and computed QMT rates (k_comp in s⁻¹) for C4-substituted 2H-benzazirines 2.^[a]

C4 substituent	QMT ring-opening	kexp	τ1/2	kcomp	QMT ring-expansion	kexp	τ1/2	kcomp
H	3a→^12a	n.o.	n.o.	1.5×10^−18	3a→4a	n.o.	n.o.	7.5×10^1
SCH3	3b→^12b	n.o.	n.o.	n.c.	3b→4b	1.5×10^−5	12.8	n.c.
OH^b	3d→^12d	n.o.	n.o.	2.8×10^−11	3d→4d	3.3×10^−5	5.8	2.0×10^−4
NH2	3c→^13c	8.3×10^−6	23.3	1.9×10^−3	4c→3c	4.7×10^−5	4.1	3.3×10^−4
N(CH3)2	3e→^12e	1.1×10^−5	17.2	n.c.	3e→4e	2.6×10^−5	7.4	n.c.
N(CH2)4^b	3f→^12f	2.4×10^−4	0.8	1.3×10^3	3e→4f	1.0×10^−4	1.9	1.6×10^−5

• ^[a] The QMT rates measured for 3b and 3c were published elsewhere.^{25, 28} The computed QMT rates of unsubstituted 2H-benzazirine 3a (section 3 of the SI) is given for comparative purposes. Abbreviation n.o. stands for not observed whereas n.c. for not computed. For the dimethylamino derivative 3e, the rotamerization of this group occurs concomitantly with the ring-opening or ring-expansion reaction, which makes it difficult to compute the corresponding PES accurately and limit our ability to provide meaningful QMT rates. ^[b] Data refers to the most stable conformation.

Experimentally, it was found that the two possible competitive QMT reactions are affected differently by the nature of the C4 electron-donating substituents (Table 1):

1. The rate of the QMT ring-opening 3→¹2 exhibits greater variability, with half-lives ranging from 48 min to undetectable within the timescale of days. Moreover, the QMT reaction 3→¹2 becomes faster as the electron-donating strength of the C4 substituent increases, i. e., k_2b and k_2d<k_2c<k_2e<k_2f. These observations align reasonably well with the computed QMT rates and can also be rationalized by the PES analysis, which demonstrates a correlation trend between the increase of the electron-donating strength of the C4 substituent and the decrease in the enthalpy of reaction (in conjunction with the decrease in the barrier height).

2. The rate of the QMT ring-expansion 3→4 exhibits smaller variability, with half-lives ranging from 1.9 to 12.8 h. Electron-donating substituents at C4 are important to decrease the rate of the QMT ring-expansion compared to the expected rate of the unsubstituted benzazirine, making the reactions amenable to experimental observation. However, a trend was not found between the set of electron-donating substituents and their QMT reaction rates for the 3→4 reaction (Table 1). These observations are fairly well reproduced by the computed QMT rates and are also compatible with the PES analysis, which suggests that the electron-donating C4 substituents induce at most a small increase in the enthalpy of the reaction (in conjugation with an increase in the barrier height), but without correlating with their respective strengths.

Remarkably, such a distinct substituent effect on the two QMT reactions enables us to attain control over the selectivity of the benzazirine QMT reactivity. We demonstrate here how to make the QMT ring-opening 3→¹2 competitive with the QMT ring-expansion 3→4 as the electron-donating strength of the C4 substituent increases, up to a point where it becomes the dominant process for the strongest electron-donating substituent 2f (Figure 7).

Figure 7

Product distribution of arylnitrene ³2 : ketenimine 4 (in %) formed by competitive QMT ring-opening vs ring-expansion reactions of benzazirine derivatives 3 in Ar matrices at 3 K in the dark. The product distribution of the QMT reactions of 3b and 3c were published elsewhere.^{25, 28}

3 Conclusions

We have investigated how QMT selectivity can be controlled by electronic substituent effects. Benzazirines 3 were used as model compounds due to their exceptional ability to react by two competitive QMT pathways. Three novel benzazirine targets with increasingly stronger electron-donating substituents at C4 [R = OH, N(CH₃)₂, and N(CH₂)₄] were successfully generated in argon matrices at 3−18 K, using the corresponding arylazides as starting materials. Remarkably, QMT reactivity with different selectivity was observed for all three benzazirines. As the substituent electron-donating strength increases, the QMT ring-opening to nitrene 2 starts to compete with the QMT ring-expansion to ketenimine 4, eventually dominating the process for the substituent with the highest electron-donating strength [N(CH₂)₄]. Computed QMT rates using the WKB model show qualitative agreement with the observed selectivities. The QMT ring-opening reaction 3→2 was found to be intrinsically more susceptible to electronic substituent effects than the QMT ring-expansion reaction 3→4. An interesting correlation was shown between the increase in substituent electron-donating strength, the increase in the QMT ring-opening rate 3→2, and the decrease in the corresponding enthalpy of reaction or barrier width (in conjunction with the decrease in the barrier height). Overall, this work reveals how subtle changes in electronic effects can be used to tune QMT selectivity. As harnessing QMT reactivity emerges as a promising approach to molecular design,^{43, 44} developing strategies to control QMT is essential. Our investigations provide fundamental insights into this fascinating field, which we hope will drive further advancements.

Acknowledgments

This work was supported by Project PTDC/QUI-QFI/1880/2020, funded by National Funds via the Portuguese Foundation for Science and Technology (FCT). The Coimbra Chemistry Centre – Institute of Molecular Sciences (CQC-IMS) is supported by FCT through projects UIDB/00313/2020 and UIDP/00313/2020 co-funded by COMPETE and the IMS special complementary funds provided by FCT. C.M.N. acknowledges FCT for an Auxiliary Researcher grant. J.P.L.R. acknowledges FCT for a PhD grant (https://doi.org/10.54499/2020.04467.BD). The authors acknowledge FCT Advanced Computing Project 2023.10449.CPCA.A2 and the Laboratory for Advanced Computing at University of Coimbra (UC-LCA) for providing computing resources that have contributed to the research results reported within this paper and Coimbra Laser Lab (CLL) for experimental facilities. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Advanced Grant No. 101054751 “COLDOC” to P.R.S.). Views and opinions expressed are those of the authors only and do not necessarily reflect those of the European Union or the European Research Council.

Conflict of Interests

The authors declare no competing interests.

Open Research

Data Availability Statement

The data that support the findings of this study are available in the supplementary material of this article.