Unveiling Mechanistic Insights and Photocatalytic Advancements in Intramolecular Photo-(3 + 2)-Cycloaddition: A Comparative Assessment of Two Paradigmatic Single-Electron-Transfer Models

Abstract

The synthesis of 1-aminonorbornane (1-aminoNB), a potential aniline bioisostere, through photochemistry or photoredox catalysis signifies a remarkable breakthrough with implications in organic chemistry, pharmaceutical chemistry, and sustainable chemistry. However, an understanding of the underlying mechanisms involved in these reactions remains limited and ambiguous. Herein, we employ high-precision CASPT2//CASSCF calculations to elucidate the intricate mechanisms regulating the intramolecular photo-(3 + 2)-cycloaddition reactions for the synthesis of 1-aminoNB in the presence or absence of the Ir-complex-based photocatalyst. Our investigations delve into radical cascades, stereoselectivity, particularly single-electron-transfer (SET) events, etc. Furthermore, we innovatively introduce and compare two SET models integrating Marcus electron-transfer theory and transition-state theory. These models combined with kinetic data contribute to recognizing the critical control factors in diverse photocatalysis, thereby guiding the design and manipulation of photoredox catalysis as well as the improvement and modification of photocatalysts.

Introduction

Recent research has highlighted the benefits of incorporating higher fractions of sp³ carbons (Fsp³) as surrogates for aromatic rings in drug discovery.¹ Such substitutions have shown significant advantages in terms of their pharmacokinetics and toxicology. Drug molecules with saturated motifs have demonstrated improved potency, solubility, and metabolic stability while exhibiting lower incidences of adverse metabolic processing events such as plasma protein binding and phospholipidosis.² This has led to an increased interest in the development of new saturated building blocks, especially caged and bridged polycyclic motifs, offering access to a more diverse chemical space and increased potential for pharmaceutical chemistry.^1c,3,4

Despite the ease of synthesis, aniline, a commonly used motif in library generation, is prone to deleterious metabolic processing, particularly CYP450 inhibition. Consequently, aniline is recognized as one of the most problematic structural alerts in drug discovery endeavors.⁵ An intriguing approach in drug discovery involves the use of general analogues of amine-substituted bridged-ring compounds that share similar sizes and shapes with aniline. These compounds can be visualized as potential aniline bioisosteres,^4a addressing certain limitations associated with aniline. As a paradigm, the application of 1-aminonorbornanes (1-aminoNBs) has been limited due to the synthetic challenges posed by S_N2 reactions at bridgeheads that result in Walden inversion.⁶ On the other hand, alternative approaches that involve multiple steps, including sequential Diels–Alder reactions and Curtius rearrangements, often encounter challenges such as rigorous reaction conditions and relatively low yields.⁷ Intramolecular free radical cyclization represents another strategy for synthesizing novel ring systems.⁸ Della et al. reported the cyclization of a modified 4-methylenecyclohexylmethyl radical into an intramolecular oxime ether, leading to the formation of bridgehead-substituted aminoNB derivatives.⁹ However, the conventional initiation conditions show unfavorable environmental behavior due to the utilization of toxic tin hydride reagents and tend to lead to competitive side reactions. The limited scope of suitable radical precursors also hinders the evolution of this method.

Over the past few decades, the field of organic synthesis has witnessed remarkable advancements through the development of photochemical methodologies, with particular emphasis on visible-light-mediated photoredox catalysis. Notably, researchers represented by MacMillan,¹⁰⁻¹⁷ Yoon,¹⁸⁻²⁰ Stephenson,²¹⁻²⁴ and some other groups²⁵⁻³² have contributed significantly to the establishment of these cutting-edge techniques. This innovative protocol offers a diverse range of methodological strategies for constructing carbon–carbon and carbon–heteroatom bonds or complex chemical building blocks.¹⁰⁻³² The Stephenson research group made a noteworthy contribution in 2019 by reporting two highly efficient photochemical intramolecular formal (3 + 2)-cycloaddition methods, which delivers the product of 1-aminoNBs under exceptionally mild conditions.²² The treatment of cyclopropylimines with violet light (390 nm) generates the corresponding Schiff base-protected 1-aminoNBs, i.e., the precursors of C1-NH2 1-aminoNB targets with good yields in the absence of photocatalyst (see Scheme 1A).^22b,33 However, relatively high-energy near-ultraviolet light may cause unproductive decomposition reactions, although this approach offers the advantage of not requiring a noble metal catalyst. In a comparative manner, starting materials N,N-dialkylaminocyclopropanes are sensitized by visible-light photocatalyst Ir[dF(CF₃)ppy]₂(dtbbpy)(PF₆) (3) to yield N,N-dialkylaminoNBs (see Scheme 1B).^22c There is minimal potential for undesirable side reactions arising from the photoexcitation of the substrate itself. The crucial aspect lies in the adaptability between the substrate and the photocatalyst, encompassing factors such as energy levels, redox potentials, and kinetic reaction rates.^10,18,21 In comparison to traditional intramolecular radical cyclization, these methods simplify synthetic procedures, broaden the scope of applicable substrates, and circumvent toxic initiators.^8,9,22 In general, these photochemical or photocatalytic transformations for building 1-aminoNB blocks enrich modern synthetic methodology while holding highly great potential in solving the dilemma of drug metabolism.

Scheme 1. Photochemical (A) and Photocatalytic (B) Intramolecular (3 + 2)-Cycloaddition Reactions of Aminocyclopropanes (AminoCPs) to Synthesize 1-AminoNBs.

Despite the fruitful progress and the proposal of some plausible mechanisms, there remains a dearth of experimental evidence regarding the mechanisms involved in visible-light-mediated photoredox catalysis.³⁴ Highly active radical intermediates pose challenges for detection even with advanced techniques such as EPR (electron paramagnetic resonance) spectroscopy³⁵ or time-resolved spectroscopy. This results from the fact that these radicals are often not isolated but engaged in rapid propagation steps, leading to strong interactions with the initiator or catalyst, various substrates, and leaving groups.^36a,36b,36d Theoretical investigations can overcome this limitation by offering a means to better comprehend the mechanisms of radical-mediated photochemical reactions. However, an accurate description of electron correlation effects is essential for theoretical investigations to provide valuable insights. Over the past decades, our research group has developed a robust method known as the multiconfiguration perturbation theory together with the orbital localization strategy and the configuration selection strategy and has proven successful in exploring single-electron-transfer (SET)-driven photocatalytic reactions mediated by transition metal or actinide complexes, as well as other photochemical conversions.³⁶ These research endeavors lay the foundation for the development of theoretical models for photosensitized electron-transfer reactions and contribute to the establishment of an integral strategy for evaluating electron-transfer rates in excited states.

In this study, we build upon our previous work and employ the combined CASSCF (complete active space self-consistent field) and CASPT2 (complete active space second-order perturbation theory) computations associated with the polarizable continuum model (CASPT2//CASSCF/PCM) to investigate the intramolecular photo-(3 + 2)-cycloaddition involved in the synthesis of 1-aminoNBs elaborated earlier. On the one hand, the exemplification of photoredox catalysis reactions serves to refine and enhance the SET theoretical model that we have proposed; on the other hand, it provides new valuable theoretical guidance for photochemical drug design and synthesis and the construction of chemical building blocks.

Methods

The hybrid CASPT2//CASSCF/PCM method was used to calculate the minimum energy profiles (MEPs) for 1, 1′ and EC(3–4). The computational strategies of orbital localization and configurational selection were applied to the multiconfiguration perturbation calculations in this work, which ensured that the selected orbitals were closely related to the photophysical and photochemical processes based on numerous test calculations and careful examinations. All-electron basis sets were employed for nonmetal atoms, while an ab initio energy-consistent scalar-relativistic pseudopotential with the corresponding basis set, ECP60MWB (8s7p6d2f1g)/[6s5p3d2f1g], was applied for the Ir atom to account for its relativistic effects. Solvent effects were included in all optimizations and intrinsic reaction coordinate (IRC) computations using the polarizable continuum model for the acetonitrile matrix. The phosphorescence lifetimes were evaluated according to the Einstein spontaneous emission formula. The SET rate constants were calculated based on Marcus electron-transfer theory, while the rate constants via an energy barrier in an adiabatic potential energy surface were computed by the transition-state theory. The intersystem crossing (ISC) rates were estimated using the Condon approximation. For more computational details, see Sections S1–S4 in the Supporting Information.

Results and Discussion

Photochemical Intramolecular (3 + 2)-Cycloaddition Reaction of Cyclopropylimine via a Masked N-Centered Radical Strategy

Our computational analysis begins with the UV–vis absorption properties of benzofused cyclopropylimine 1 (see Section S2.1 in the Supporting Information). The calculated absorption spectrum reproduces the experimentally observed absorption bands and provides a detailed understanding of the electronic transitions involved. The Schiff base system exhibits two prominent absorption bands at 310 nm (oscillator strength f = 0.50) and 252 nm (f = 0.36), along with a much weaker absorption at 387 nm (f = 0.01). These findings align well with the experimental measurements of two intense absorptions centered around 300 and 250 nm, as well as one “invisible” absorption at approximately 385 nm, which becomes apparent upon a substantial increase in concentration, typically by approximately 2 orders of magnitude.^22b Based on population analyses, the two spectroscopic bright states are assigned as the π → π* transitions, denoted as S_PP1(¹ππ*) and S_PP2(¹ππ*), respectively, while the dark state is assigned as the n → π* transition, denoted as S_NP(¹nπ*). The discrepancy in oscillator strengths can be attributed to an orbital overlap, as the parallel π and π* orbitals maximize the overlap but the perpendicularity of the n and π* orbitals necessitates out-of-plane bending. Notably, the species with the singly occupied nitrogen lone pair in the S_NP(¹nπ*) state bears a resemblance to nitrogen-centered radicals,³⁷ thus referred to as masked N-centered radicals, which can serve as the electrophilic component capable of reacting with the nucleophile. Moreover, the n → π* transition of imine 1, settling in the UVA region (320–400 nm), displays an evident bathochromic shift relative to carbonyl compounds. For instance, the nπ* state of chalcone derivatives is usually found in the medium ultraviolet region (280–320 nm).³⁸ The relatively large resolution between the n → π* transition and other absorption maxima offers the potential for selective excitation of this specific transition for imine 1. This effect contributes to excluding other possible unexpected deactivation channels and improves functional group tolerance, distinguishing it from classic carbonyl photochemistry. For example, upon UVB/UVC irradiation, 2′-hydroxy-chalcone undergoes various transitions and multiple photochemical events like excited-state intramolecular proton transfer (ESIPT), which complicates regulation, as evidenced by our previous research.³⁸

The relaxation paths for the intramolecular (3 + 2)-cycloaddition reaction of substrate 1 are illustrated in Figures 1 and S7. Upon violet light photoirradiation at 387 nm, 1 is instantaneously promoted in the Frank–Condon (FC) region of the S_NP(¹nπ*) state. Structurally, the initial decay in this state is characterized by the elongation of the N12=C13 double bond from 1.339 to 1.364 Å and a notable increase in the C1N12C13 bond angle from 125.33 to 149.11°, accompanied by geometric adjustments of chemical bonds within the nitro phenyl ring, which exactly reflects the characteristic of the singly occupied orbitals for the S₀ → S_NP(¹nπ*) transition. These structural changes readily relax the cyclopropylimine to the local minimum of the S_NP(¹nπ*) state (S_NP-Min) with an 8.3 kcal·mol^–1 energy decrease, leading to the generation of a masked N-centered radical intermediate. Because of the inherent strain in the cyclopropane ring, the C1–C3 bond is compelled to undergo a homolytic fragmentation (1.555 → 2.185 Å), resulting in radical migration from the N-center (N12) to the C-center (C3) and the production of the C-center radical intermediate, Int-C3 (see Figure S6). Int-C3 shows a growing diradical characteristic because of enhanced separation of the paired electrons. To our surprise, no energy barrier was found computationally in this process, but a downhill pathway (6.5–7.0 kcal·mol^–1) was observed following a flat trajectory. This implies that the entire sequence from the photoexcitation to the complete scission of C1–C3 bond proceeds extremely smoothly with a total of 14.0–16.0 kcal·mol^–1 energy release, so that can be regarded as a single-step process. Mulliken population analyses reveal that an abundant amount of negative charge initially on N12 becomes dispersed around the π-conjugated moiety after photoexcitation [i.e., S₀-R (−0.4665) → FC of S_NP (−0.3943)]. This redistribution of charge enables the singly occupied lone pair on N12 to combine with the nearly coplanar nucleophilic C–C σ bond of the adjacent cyclopropane (C13N12C1C3 dihedral angle: 30.36°) (see Figures S5B and S6). It turns out that throughout the decay from FC of S_NP to Int-C3, the N12–C1 bond undergoes concerted shortening (1.399 → 1.277 Å) besides the homolysis of the C1–C3 bond, suggesting the formation of a N12=C1 double bond. Population analyses show that the π bond of the N12=C1 double bond is approximately perpendicular to that of the N12=C13 bond. In other words, the two π bonds are oriented in an upright configuration with respect to each other. In accordance with potential energy scans, geometry optimizations, and CASPT2//CASSCF calculations, it was found that when the initial structures of 1 attempted to incorporate the C–C σ bond of the cyclopropane into the N12=C13 double bond to form a three-center–four-electron (3c–4e) π bond³⁹ instead of a N12=C1 double bond, the barrier for the homolysis of the C1–C3 bond would be promoted to about 22.0 kcal·mol^–1 that was exceedingly difficult to surmount (see Figure S5A). The initial conformations of 1 thus play a crucial role on the progress of this photoreaction (see Section S2.2 in the Supporting Information for more details). In general, the synergism of the charge redistribution from S₀ to S_NP(¹nπ*) and the strain present in the cyclopropane ring facilitates the breaking of the cyclopropyl C–C bond through a barrierless pathway. Note that a competitive nonradiative inactivation channel for S_NP(¹nπ*) is observed as a rapid internal conversion when the C1–C3 bond is elongated to 1.953–1.984 Å, denoted as CI(S_NP/S₀)-C1C3. S_NP(¹nπ*) energetically degenerates with S₀ in this conical intersection region, and through this channel, the system will return swiftly to the initial reactant, S₀-R, along a steep, downhill pathway of the ground state. Therefore, to ensure that most substrate is transformed into intermediate Int-C3, imine 1 needs to be repeatedly subjected to photoexcitation, which seriously reduces the quantum yield of this photoreaction. As a critical consequence, the masked N-centered radical intermediate is almost unlikely to be entrapped due to its rapid deactivation to either the reactant or the carbon radical intermediate, but Int-C3 exhibits a different behavior and can potentially be detected.

Figure 1.

MEPs for the photochemical intramolecular (3 + 2)-cycloaddition reaction of cyclopropylimine 1. The highlighted characteristic points of 1 are schematically shown together with the numbering scheme in red, the key bond distances (Å), and bond angles (degree). The hydrogen atoms are omitted for clarity. The kinetic data are also provided. These computational results were obtained at the CASPT2//IRC/CASSCF(14e/13o)/PCM level of theory in an acetonitrile solvent.

The exposed carbon radical centered on the C3 atom imposes a strong attraction on the intramolecular electron-deficient olefin, acting as a nucleophile. This interaction drives the movement of C3 toward the olefin moiety. The C3-centered n orbital is gradually converted into the σ orbital between C3 and C4. As the distance between C3 and C4 is reduced to about 2.257 Å (TS-C3C4), a conspicuous energy drop will occur in the energy levels of both the S₀ and S_NP(¹nπ*) states. Simultaneously, the energetic splitting gradually diminishes between these states. The complete C3–C4 bond formation (3.146 → 1.578 Å) results in the collapse of the π orbital of olefin associated with the breakage of the C4=C7 double bond (1.360 → 1.531 Å) by overcoming a medium barrier (TS-C3C4: 7.8 kcal·mol^–1). Meanwhile, a stable six-membered ring skeleton is constructed successfully, accompanied by the radical migration from the imine-centered C3 radical (Int-C3) to the olefin-centered C7 radical (Int-C7) (see Figure S6). This cyclization can be characterized as 6-exo-trig, whose first prefix means six atoms in the forming ring, the second indicates that the breaking bond is exocyclic to the forming ring, and the third signifies the sp² hybridization (trigonal) at the ring closure point.⁸ Similarly, when the carbon radical centered on the C7 atom is unmasked, an intense attraction between C7 and the intramolecular electron-poor N12=C1 double bond prompts the C7-centered n orbital to integrate into the C7–C1 σ orbital (3.899 → 1.604 Å) by surmounting a middle-sized barrier (TS-C7C1: 8.2 kcal·mol^–1). However, another internal conversion region is determined between S_NP(¹nπ*) and the ground state when the C7–C1 distance decreases to around 2.655 Å, denoted as CI(S_NP/S₀)-C7C1, which allows for an effective decay to the ground state. The existence of CI(S_NP/S₀)-C7C1 lowers the C7–C1 bonding energy barrier from 8.2 to 6.2 kcal·mol^–1 and ultimately accomplishes the generation of the end product (S₀-P) along a downhill path on the ground state. This process is characterized by various structural adjustments besides the generation of the C7–C1 bond (3.899 → 1.583 Å), including the breakage of the N12=C1 double bond (1.290 → 1.404 Å), the decreased C1N12C13 bond angle (148.79 → 124.03°), the restoration of the N12=C13 double bond (1.328 → 1.344 Å), as well as the formation of a double-five-membered bridged-ring moiety (5-exo-trig).

According to TST (transition-state theory) calculations, the rates of the 6-exo-trig and 5-exo-trig radical cyclization steps can be estimated as 1.1 × 10⁷ and 1.7 × 10⁸ s^–1, respectively, indicating that the 6-exo-trig radical cyclization serves as the rate-determining step for the overall reaction. Notably, product 1-aminoNB (2) has analogous absorption properties with reactant 1 (see Section S2.1 in the Supporting Information), suggesting the possibility of the inverse reaction occurring simultaneously, with 2 as the reactant and 1 as the product. However, by backward analyses of the MEPs, we found that a sizable barrier for the breaking of the C3–C4 bond (>30.0 kcal·mol^–1) turned off the energy-accessible channel after the formation of Int-C7. As a result, the system returns to S₀-P (2) from S_NP(¹nπ*) to S₀ via CI(S_NP/S₀)-C7C1. The estimated rate of inverse reaction (10^–11 to 10^–10 s^–1) is 17–18 orders of magnitude lower than that of the forward reaction (∼10⁷ s^–1), thereby ensuring the forward equilibrium shift for this photoreaction. Unfortunately, the absorption of product 2 also inevitably reduces the quantum efficiency of this photoreaction. On the whole, this violet-light-mediated intramolecular (3 + 2)-cycloaddition strategy takes over the kinetically unfavorable mechanistic pathway under thermal control (barrier: ∼80 kcal·mol^–1) to afford 1-aminoNBs efficiently.

Potential Origin of Diastereoselectivity for C7-Alkyl Mono-Substituted Cyclopropylimine in the Intramolecular (3 + 2)-Cycloaddition Reaction

Stephenson et al. discovered an intriguing experimental phenomenon that the 1-aminoNB product was in favor of the anti-configuration for C7-alkyl monosubstituted cyclopropylimine regardless of whether the original olefin geometry was the E-isomer or the Z-isomer.^22b Two cis–trans isomers, 1′-E and 1′-Z, were inspected to explore the origin of this diastereoselectivity by CASPT2//CASSCF calculations (see Figures 2 and S8). Starting from the C7 radical intermediate of 1′-E, i.e., Int-C7-E, the system can overcome a medium energy barrier (4.2 kcal·mol^–1) and subsequently decay to the product 2′-anti along a downhill relaxation path through CI(S_NP/S₀)-C7C1-E, in combination with the formation of a C7–C1 bond (3.630 → 1.611 Å). However, the production of 2′-syn requires an additional rotation of the C4–C7 bond (C3C4C7H14 dihedral angle: 84.47 → −87.63°) to generate another C7 radical intermediate, denoted as Int-C7-Z. The rotation introduces a little high barrier (8.8 kcal·mol^–1) owing to the eclipsed conformation of transition state TS-EZ (C3C4C7H14 dihedral angle: ∼0°). TST calculations reveal that the rotation of the C4–C7 bond is less effective than the shortening of the C1–C7 bond (2.3 × 10⁶ s^–1 for the former, 3–4 orders of magnitude smaller than the latter 5.6 × 10⁹ s^–1), leading to the predominance of 2′-anti product (3.0:1 anti:syn dr measured in the experiment).

Figure 2.

Structural evolutions along the critical points of relaxation paths with their relative energies (kcal·mol^–1) for 1′ starting from Int-C7. Hydrogen atoms are omitted for clarity, except H14.

As for the 1′-Z system, the less stable intermediate, Int-C7-Z, will get involved immediately after the 6-exo-trig radical cyclization step. In this case, C7 can be smoothly bonded to C1 to form the 2′-syn product through CI(S_NP/S₀)-C7C1-Z by surmounting a barrier of 3.9 kcal·mol^–1. Alternatively, the C4–C7 bond can competitively rotate by surpassing a lower barrier of 2.9 kcal·mol^–1. The efficiency of bond rotation slightly exceeds that of instant transformation (5.8 × 10¹⁰ and 8.3 × 10⁹ s^–1, respectively), which triggers off the conformational change from Int-C7-Z to the more stable intermediate, Int-C7-E, that prefers the 2′-anti product. Additionally, the inverse reaction of the 2′-syn product on the S_NP(¹nπ*) state will continuously increase the concentration of Int-C7-Z, facilitating the equilibrium shift from Int-C7-Z to Int-C7-E. It is the mutual transformation of intermediates and the occurrence of inverse reaction for 2′-syn that allow the 1′-Z system to possess a similar tendency with 1′-E toward the 2′-anti product. In summary, diastereoselectivity for C7-alkyl-monosubstituted cyclopropylimine primarily originates from kinetic control.

Photophysical Properties for Isolated Photocatalyst 3

To elucidate the origin of the ultraviolet–visible-light absorption band of photosensitizer 1, its absorption spectrum was simulated at the CASPT2//CASSCF/PCM level of theory (see Section S3.1 in the Supporting Information). Qualitatively, the near-degenerate occupied d orbitals (t_2g) of the Ir(III) metal center have three electron pairs with an equal probability of being promoted to the unoccupied π* orbitals of the three similar ligands upon irradiation, i.e., S₀ → S_MLCT (d → π*), resulting in a total of nine similar metal-to-ligand charge-transfer (MLCT) excited states. They should have appeared in close proximity to each other at the spectrum. However, as shown in Figure S10, these nine MLCT states locate at different positions in the absorption spectrum, giving rise to a broad absorption band spanning over 200 nm, ranging from 240 to 480 nm. The strong couplings driving the linear combinations of nine MLCT states significantly extend the absorption band to the visible range and simultaneously improve the intensity of the maximum MLCT absorption (368 nm, oscillator strength f = 0.18, highlighted with a red line in Figure S10). The maximum absorption with acceptable intensity is principally responsible for the visible absorption band that can be utilized directly in photoredox catalysis. The calculated spectrum is in good agreement with the experimentally observed band ranging from 250 to 500 nm with the maximum absorption centered at 370–380 nm. Careful comparisons reveal that the computed vertical excitation energies of ILCTs (intraligand charge transitions), MLCTs, and LLCTs (ligand-to-ligand charge transfers) together with their oscillator strengths well reproduce the features of experimental spectrum for photocatalyst 3.⁴⁰ Notably, the absorption band predicted by TDDFT calculations exhibits a relatively narrow range compared to the experimental findings, while the CASPT2//CASSCF calculations give a better description⁴¹ because the latter method takes dynamic correlation effects and couplings into account preferably.⁴²

Under visible light irradiation, photocatalyst 3 is initially populated in the FC region of the MLCT singlet state S_MLCT(¹dπ*) with the maximum absorption (368 nm, f = 0.18) and rapidly decays to its minimum S_MLCT(¹dπ*)-Min that energetically degenerates with the MLCT triplet state T_MLCT(³dπ*) at the singlet–triplet crossing STC(S_MLCT/T_MLCT) (see Figure S11). Due to strong relativistic effects of Ir metal, the spin–orbit coupling constant (SOC) in the STC region is calculated to be about 50.0 cm^–1, which allows a fast intersystem crossing (k_ISC = 19.0 × 10¹² s^–1) and relaxes the low-lying emissive T_MLCT(³dπ*) state to its minimum T_MLCT(³dπ*)-Min, producing a 472 nm phosphorescence emission. The picosecond-scale intersystem crossing inhibits the fluorescence emission usually at the nanosecond scale and shortens the phosphorescence lifetime to the microsecond level (13.7 μs).⁴³ Our calculations are in consistent with the experimental results that the phosphorescence emission of 3 is measured at λ_em = 470 nm in acetonitrile solution characterized by a long lifetime (2.3 μs),⁴⁰ which provides a wide time window for the competitive coexistence of a photocatalysis reaction channel. The calculated lifetime is about 1 order of magnitude longer than the actual value since nonradiative events cannot be neglected in practice (the photoluminescence quantum yield of 3 is around 68%). Moreover, the energy gap between T_MLCT(³dπ*)-Min and the ground-state minimum S₀-Min, i.e., the adiabatic excitation energy of 3, amounts to about 70.0 kcal·mol^–1 (see Figure S11 and Table S4). However, there are minimal disparities in structural parameters between T_MLCT(³dπ*)-Min and S₀-Min, as quantitatively evidenced by a mere 0.05 Å root-mean-square deviation (RMSD) value for their structures (see Figures S12 and S13). This negligible structural variation between the excited state and the ground state facilitates such an effective ground-state recovery of the photocatalyst in the repeated absorption–emission or photocatalytic cycles that optical energy can be fully exploit.

Reductive SET-Driven Carbon Radical Formation via the Strain-Driven Homolysis of the Cyclopropane Ring

Unlike the case of the isolated photocatalyst, in the presence of tertiary amine substrate, the intermolecular dipole–dipole interaction between photocatalyst 3 and amine 4 is instantaneously triggered by the photoenhanced dipole moment of the MLCT excitation from the Ir(III) center to the di-tert-butyl bipyridine ligand (dtbbpy). The interaction induces an opposite dipole moment, mainly distributed in the (C1–C2–C3)^δ+–N8^δ− structural region of amine 4, which expands the electron donation ability of N8 (see Table S6). Along the decay from FC of S_MLCT to T_MLCT-Min for the 3–4 encounter complex, denoted as EC(3–4), the C1–C3 bond is initially activated (1.523 → 1.527 Å) accompanied by a degree of planarization of amine 4 (C9N8C1C10 dihedral angle: 134.28 → 143.88°) owing to the photoenhanced dipole–dipole interaction and the charge redistributes from S₀-Min to T_MLCT-Min (see Figures 3, 4, and S16). Then, a moderate barrier of 5.0 kcal·mol^–1 is overcome to drive the further C1–C3 bond elongation (1.527 → 1.532 Å) and the slightly N8–C1 bond shortening (1.461 → 1.459 Å) in combination with the further remarkable planarization of amine 4 (C9N8C1C10 dihedral angle: 143.88 → 158.66°). This preadjusted step promotes the lone pair electrons of N8 to the lowest-lying ligand π* orbital of T_MLCT-Min for the Ir catalyst^36b and brings the catalytic system to the conical intersection region between the T_MLCT precursor state and the EC(3–4) intermolecular charge-transfer triplet state T_CT(³nπ*), denoted as CI(T_MLCT/T_CT). Since photocatalyst 3 acts as an electron acceptor, this process is named reductive SET hereafter. CI(T_MLCT/T_CT) provides an energetically accessible channel to trigger the reductive SET and the radical initiation, thereby generating the zwitterionic complex of 3^•––4^•+ with a diradical configuration. Because of the intermolecular Coulomb interaction, cation 4^•+ approaches anion 3^•– (Ir–N8 distance: 7.686 → 7.561 Å), during which the C1–C3 bond is eventually activated (1.532 → 1.533 Å) with a concomitant planarization (C9N8C1C10 dihedral angle: 158.66 → 160.30°) induced by the N-centered radical cation for 4^•+. These structural reorganizations relax the catalytic system to a local minimum momentarily, producing a relatively stable amine radical cation intermediate, denoted as Int-N8 (see Figures 3, 4, and S16).⁴⁴ Mulliken population analyses indicate that a generous amount of negative charge is transferred from N8 to photocatalyst 3 after the reductive SET [i.e., N8: T_MLCT-Min (−0.5527) → Int-N8 (−0.0296) and Ir-dtbbpy: T_MLCT-Min (0.3553) → Int-N8 (−0.2693)], which allows the singly occupied lone pair of N8 to be capable of reacting with the nucleophilic C–C σ bond of the adjacent cyclopropane (see Table S6 for more details). Furthermore, Int-N8 shows an obvious increase in dipole moment compared with that in the T_MLCT-Min region (50.0 → 70.7 D). These pieces of evidence additionally confirm the occurrence of reductive SET.

Figure 3.

(A) MEPs for the intramolecular (3 + 2)-cycloaddition reaction of cyclopropylamine 4 to produce 1-aminoNB 5 mediated by photocatalyst 3. The barriers of CI(T_MLCT/T_CT), TS-C1C3, TS-C3C4, and STC(T_CT/S₀)-C7C1 are defined to compare with the corresponding intermediates T_MLCT-Min, Int-N8, Int-C3, and Int-C7, respectively. The hydrogen atoms and PF₆^– have been omitted for clarity. The kinetic rates are also provided. These computational results were obtained at the CASPT2//IRC/CASSCF(14e/11o)/PCM level of theory in acetonitrile solvent. (B) Electron shifts among the orbitals involved in the photocatalysis and evolution of singly occupied molecular orbitals (SOMOs) of reductive triplet state.

Figure 4.

Summary of the photocatalytic cycle for the intramolecular (3 + 2)-cycloaddition reaction of cyclopropylamine 4 mediated by the photocatalyst 3. The geometries at the highlighted characteristic points are given along the reaction path in Figure 3A with their key bond distances (Å), dihedral angles (degree), and some other structural features. Photocatalyst 3^•– is omitted for TS-C1C3, Int-C3, TS-C3C4, and Int-C7 (see Figure S17 for their complete geometries). All hydrogen atoms and PF₆^– are omitted for clarity.

Driven by the reductive SET, the C1–C3 bond is gradually elongated (1.533 → 2.000 Å), which has to overcome a medium barrier of TS-C1C3 (5.5 kcal·mol^–1), significantly undermined by the strain of cyclopropane ring⁴⁵ and preparatory activation. In this process, the N8–C1 bond undergoes concerted shortening (1.459 → 1.300 Å) in combination with the rotation of the N8–C1 bond (C3C1N8C9 dihedral angle: −24.74 → 21.30°), indicating the partial formation of a N8=C1 double bond. Int-N8 thus falls into a shallow potential, which increases the detection probability of this intermediate. Once TS-C1C3 is surpassed, the system proceeds along a downhill path with the complete breaking of the C1–C3 bond (2.000 → 2.394 Å). Meanwhile, the N8=C1 bond is further shortened to 1.291 Å, fully rendered as a double bond, which can also be validated by the coplanarity of C2–C1–C6 and C9–N8–C10 moieties and the evolution of active orbitals. When the strain-driven homolysis of the cyclopropane ring completes, C3 is entirely exposed to get rid of the mutual interactions from the neighboring groups, leading to the generation of a more stable carbon radical Int-C3 with a slight energy decline (3.0 kcal·mol^–1) relative to Int-N8 (see Figures 3, 4, and S16). The reductive SET-driven concerted process enables radical migration along the intramolecular π and σ bond networks. As shown in Figure 3B, unpaired electron shifts can be undoubtedly achieved from the visible-light-generated nitrogen-centered radical cation to the carbon-centered radical intermediate. Mulliken population analyses reveal that the excess positive charge on N8 is partly dispersed on the C1–C2–C3 moiety after the electron shift [i.e., N8: Int-N8 (−0.0296) → Int-C3 (−0.3054) and C1–C2–C3: Int-N8 (−0.2369) → Int-C3 (0.0169)]. Based on these electronic structure calculations, it can be concluded that the radical migration progresses to accomplish the carbon radical formation through the strain-driven homolysis of the cyclopropane ring triggered by the excited-state SET. The high-level quantum-chemical calculations provide comprehensive information on geometric and electronic structure changes during the generation of intermediates, contributing to a better understanding of radical manners, so as to improve and design relevant reactions.

Kinetic Assessment of Multiple Events around Reductive SETs and Analyses and Comparisons of SET Models

To further explore the driving force behind the generation of Int-C3 from a kinetic perspective, we calculated the rates of various events around the reductive SET. On the basis of the CASPT2//CASSCF/PCM calculated physical parameters shown in Scheme 2A, the reductive SET rate is calculated to be about 1.2 × 10⁷ s^–1 in the polar matrix of acetonitrile according to Marcus electron-transfer theory. A key conclusion is that the reductive SET takes place competitively over the phosphorescence emission of photocatalyst 3 from T_MLCT-Min (k_p = 7.3 × 10⁴ s^–1) (see Figure 3A). It is a prerequisite of any photosensitized event that the sensitization rate surpasses the emission rate. Based on the energy level of Int-N8 and TS-C1C3, the rate of C1–C3 bond homolysis can be estimated as 6.6 × 10⁸ s^–1. Of note, the realistic reaction rate is not confined to this lower bound value since the energy barrier of the transition state is always overestimated compared with the free energy barrier. Therefore, the strain-driven C1–C3 bond homolysis definitely proceeds more efficiently than the reductive SET process definitely. Although relatively accurate free energy calculations are unachievable at the CASPT2//CASSCF level, it can still be concluded that the reductive SET is the rate-determining step for the entire process. These kinetic calculations reveal that enhancing the reductive SET rate will facilitate the generation of the carbon radical Int-C3 effectively. Considering the Marcus theory, which emphasizes the potential energy change between two minima in determining electron-transfer rates, improving the stability of critical intermediate Int-N8 suitably can profoundly accelerate the reductive SET. The above kinetic analyses may contribute to our better understanding of the functions of Lewis acidic salt additives for reaction optimization. For instance, ZnCl₂ can raise the yield of 1-aminoNB 5 from 63 to 84% and even enable partial productivity of 5 when utilizing the less oxidizing photocatalyst Ru(bpy)₃Cl₂ from 0 to 34%.^22c It is because that Lewis acidic salts can lower the energy of Int-N8 through modulation of amine oxidation potential (e.g., LiBF₄ can reduce the oxidation peak potential of aminoCP 4 from 1.02 to 0.98 V vs SCE in MeCN) to allow a faster nonadiabatic transition from T_MLCT(³nπ*) to T_CT(³nπ*), thereby increasing the yields. To sum up, the manipulation of N-centered radical cation Int-N8 can realize the regulation of this photoredox catalysis in both thermodynamics and kinetics.

Scheme 2. Sequential SET and TS Model for the Reduction Reaction of Intramolecular (3 + 2)-Cycloaddition (A) and Syncretic SET and TS Model for the Reduction Reaction of Amide-Directed Distal sp³ C–H Functionalization (B) Summarized Together with Their Key Kinetic Parameters in Polar Acetonitrile.

The reorganization energy of reductive SET λ(R) and back SET λ(B), the potential energy change of reductive SET ΔE(R) and back SET ΔE(B) as well as the activation energy ΔE^⧧ are given in kcal·mol^–1.

Our research group has reported a mechanistic insight for the amide-directed distal sp³ C–H functionalization.^36a In that work, we demonstrated that the formation of the carbon radical was energetically unfavorable and inefficient via a stepwise path involving PCET (proton-coupled electron transfer) of amide and subsequent 1,5-HAT (hydrogen atom transfer). Then, we proposed an alternative asynchronous concerted mechanism as well as an expanded SET model that combines Marcus electron-transfer theory and transition-state theory. As shown in Scheme 2B, there is not any local minimum between TS1 and CI(T_MLCT/T_21CT), which means that the catalytic system directly reaches the transition state for HAT after the reductive SET. Based on the energy barrier between TS1 and T_MLCT-Min, the rate of the asynchronous concerted HAT process can be estimated as 1.5 × 10² s^–1 in a polar solvent of acetonitrile. The stable carbon radical intermediate (IM1) emerging after TS1 is not only the product of HAT but also the outcome of the reductive SET. Therefore, the nonadiabatic transition rate from T_MLCT to T_21CT can be estimated as 6.9 × 10⁹ s^–1. Kinetic calculations evidence that the efficiency of nonadiabatic transition in this case can be accelerated by 2–3 orders of magnitude compared to the oxidation of aminoCP 4. This is mainly attributed to the formation of the stable carbon radical IM1. For the present case, the potential energy from T_MLCT-Min to IM1 decreases by 5.0–6.0 kcal·mol^–1 (see Scheme 2B), but for the reductive SET of intramolecular (3 + 2)-cycloaddition, the energy increases by around 7.0 kcal·mol^–1 (see Scheme 2A). In the expanded SET model, it is explicit that HAT is the rate-determining step; in other words, TS1 dominates the efficiency for the formation of IM1. Seen in this light, the phosphate utilized in the photocatalysis can be interpreted as a “cocatalyst” to effectively bring the barrier of TS1 down through a concerted bond breaking–formation mechanism, which changes the alkylation of remote C–H bonds from unproductive into high yielding (∼80%). This inference may be further supported by Knowles’ quenching experiments, where the phosphate improves the quenching efficiency of amide.⁴⁶

As for the two SET models, sequential model and syncretic model, there are still several similarities and differences that deserve emphasis. First, the discrepancy of rate-determining steps in the two models primarily arises from the inherent characteristics of photocatalytic reactions themselves. For the intramolecular (3 + 2)-cycloaddition reaction, it is relatively facile to fragment the slightly weak C–C bond of the cyclopropane ring, so SET becomes dominant. However, when it comes to breaking the inert C–H bond (bond energy >100.0 kcal·mol^–1),^36b HAT takes center stage unquestionably. Second, if a local minimum was found between CI(T_MLCT/T_CT) and TS1 (see the blue dotted line in Scheme 2B), the double-well potential model would degenerate into a classic sequential SET and TS model, in analogy to what is shown in Scheme 2A. Therefore, different electron-transfer models do not have definite boundaries and can be transformed into each other under particular circumstances. Finally, for both models, the energy level of the ground state continuously ascends along the reaction path in the early stage and eventually surpasses the energy curve of T_CT until a maximum (∼100.0 kcal·mol^–1 for both the models). The extreme rise of the S₀ potential energy curve acts as a functional hindrance to block the formation of carbon radical via a nonradiative transition from T_CT to the closed-shell state S₀, i.e., back SET. Fortunately, the efficiency of back SET is just 10² to 10⁴ s^–1 for both the models because of the small nonadiabatic coupling (<1.0 cm^–1) at the corresponding singlet–triplet crossing region. It is insufficient to completely intercept the photocatalytic reaction but only slightly lowers the quantum yield. In view of high-accuracy CASPT2//CASSCF/PCM calculations, the rate-determining steps can be predicted without any experimental data support for the excited-state electron-transfer processes, which is hence conducive to accomplishing the regulation of photoredox catalysis. Overall, these insights provide a deeper understanding of the electron-transfer mechanisms and offer guidance for fine-tuning photoredox catalytic reactions.

6-Exo-Trig Cyclization via Radical Addition and 5-Exo-Trig Cyclization Concerted with Oxidation Reaction of the Ir(II) Catalyst

The exposed C3 radical exerts an intense attraction on the intramolecular electron-deficient olefin, leading to an obvious boat conformation formation for 4^•+ of Int-C3 with a shortened C3–C4 distance (3.519 → 2.254 Å) (see Figure 4). These structural reorganizations propel the catalytic system toward a transition-state region by overcoming a moderate energy barrier (TS-C3C4: 5.3 kcal·mol^–1) (see Figures 3A and S16). Subsequently, a measurable energy drop is observed in both the energy level of S₀ and the reductive ³nπ* state with the gradually narrowing energetic splitting between them. This relaxation pathway is structurally characterized by the complete formation of C3–C4 bond (2.254 → 1.654 Å) and the breakage of C4=C7 double bond (1.379 → 1.539 Å). Population analyses reveal that the C3-centered n orbital is gradually converted into the σ orbital between C3 and C4 associated with the collapse of the π orbital of olefin during the C3–C4 bonding process. Moreover, a stable six-membered ring skeleton is constructed in the boat conformation (6-exo-trig), accompanied by the radical migration from the amine-centered C3 radical (Int-C3) to the olefin-centered C7 radical (Int-C7) (see Figure 3B). Although the six-membered ring in the boat conformation is not as stable as that in the chair conformation, Int-C7 still tends to adopt the boat conformation since it profits 5-exo-trig cyclization in the subsequent step. Further, TST calculations suggest that this process proceeds at a rate of 7.5 × 10⁸ s^–1, 6–7 orders of magnitude higher than the rate of backward radical inhibition event.

Starting from Int-C7, another radical addition happens due to the strong mutual attraction between the C7 radical and the intramolecular electron-poor N8=C1 that formed in the C1–C3 homolysis step. Its barrier is condensed to a tiny value of 1.8 kcal·mol^–1 because of the preformed boat conformation (see Figures 3A and S16). The energy gap between the energy level of S₀ and T_CT is also further narrowed until the second singlet–triplet crossing of STC(T_CT/S₀)-C7C1, associated with the gradually decreased C7–C1 distance (2.793 → 2.530 Å) and the elongation of the N8=C1 bond (1.294 → 1.315 Å) (see Figure 4). These structural adjustments essentially function as the preparatory steps for the recovery of photocatalyst 3 as well as the production of 1-aminoNB 5. STC(T_CT/S₀)-C7C1 serves as an energetically allowed relay to pair electrons around the N8 center via the nonadiabatic transition from the open-shell T_CT state to the closed-shell ground state (see Figure 3B). Since the Ir photoredox catalyst 3 acts as an electron donor during this radical termination, the electron transfer is identified as oxidative SET. Upon reaching the ground state, the catalytic system rapidly relaxes to the local minimum S₀-P for the final product 1-aminoNB 5 along a downhill path with a heat release of 62.5–64.5 kcal·mol^–1. This relaxation pathway involves the formation of a C7–C1 bond (2.530 → 1.616 Å) associated with the double-five-membered bridged ring (highlighted with blue and yellow polygons in Figure 4). Careful Mulliken population analyses reveal that the excess negative charge of the reduced Ir photocatalyst is transferred back to N8 and other parts of final product 5 after the oxidative SET [i.e., Ir-dtbbpy: Int-C7 (−0.0732) → S₀-P (0.6939) and N8: Int-C7 (−0.3617) → S₀-P (−0.6944)], indicating the regeneration of photocatalyst 3 (see Table S6). As shown in Scheme S1, the oxidative SET is more effective than the previous reductive SET (estimated as 1.1 × 10¹⁰ s^–1) owing to an amount of heat release (>60.0 kcal·mol^–1). For this whole photoredox catalysis, the reductive SET is still the rate-determining step.

Conclusions

In this study, we conducted comprehensive mechanistic research into the intramolecular photo-(3 + 2)-cycloaddition reactions of imine and amine substrates using high-precision CASPT2//CASSCF/PCM calculations. Our findings reveal that the imine substrates can directly harness visible light for initiation, thanks to their unique n → π* transition, whereas the amine substrates require the sensitization by the photocatalyst due to the absence of conjugated moieties. The native strain of the cyclopropane ring plays a crucial role in lowering the C–C homolysis barrier. The barrier virtually vanishes for the imine system, but the amine system still exhibits a moderate barrier. This discrepancy can be attributed to the smaller structural adjustment of imine substrates during the homolysis process, leading to a more favorable reaction pathway for them. Thus, the masked N-centered radical presents a higher reactivity than the N-centered radical cation. The irreversible 6-exo-trig and 5-exo-trig cyclizations serve as the radical propagation procedures, with the 5-exo-trig cyclization coinciding with the radical termination. The reaction of the imine system does not involve changes in the spin multiplicity, highlighting the barriers on the adiabatic states in regulating the reaction. However, the fast internal conversion between different states with identical spin multiplicity severely diminishes the quantum efficiency of this photoreaction, potentially imposing limitations on its further application. Regarding the photoredox catalytic system, the reaction predominantly takes place on the triplet states owing to strong relativistic effects of the Ir atom, thereby primarily tuned by the transitions between different states, especially SETs. The limited quantum yield of the photocatalyst itself and the occurrence of back SET are the main factors impeding the quantum efficiency. This difficulty may be addressed by a new high-efficiency catalyst design based on high-precision theoretical calculations.

Meanwhile, our analysis and comparison of two representative SET models provide a thorough understanding of their characteristics as well as their similarities and differences. By recognizing the distinct features of various photoredox catalyzes, we can employ the corresponding models associated with the high-precision quantum-chemical calculations to effectively achieve the fine-tuning of reactions. These models are also further enrichment and improvement of Marcus electron-transfer theory and the transition-state theory, which facilitate our enhanced comprehension of electron-transfer phenomena. Our research group will always be devoted to developing more SET models.⁴⁷ In general, these theoretical advancements hold promising prospects for the mechanism-guided molecular design of photocatalysts and the photochemical synthetic method design of new building blocks, especially saturated blocks suitable for pharmaceutical chemistry.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacsau.3c00542.

• Computational details on CASPT2//CASSCF, calculations of vertical excitation and adiabatic excitation for substrates and photocatalysts, phosphorescence lifetime calculations, redox potential calculations, rate constant calculations, charge translocation calculations, population analyses, conformational analyses, other possible reaction paths, single-point energies, Cartesian coordinates, and additional references (PDF)

The authors declare no competing financial interest.