Theoretical Exploration of Energy Transfer and Single Electron Transfer Mechanisms to Understand the Generation of Triplet Nitrene and the C(sp3)–H Amidation with Photocatalysts

Mechanistic explorations and kinetic evaluations were performed based on electronic structure calculations at the CASPT2//CASSCF level of theory, the Fermi’s golden rule combined with the Dexter model, and the Marcus theory to unveil the key factors regulating the processes of photocatalytic C(sp3)–H amidation starting from the newly emerged nitrene precursor of hydroxamates. The highly reactive nitrene was found to be generated efficiently via a triplet–triplet energy transfer process and to be benefited from the advantages of hydroxamates with long-range charge-transfer (CT) excitation from the N-centered lone pair to the 3,5-bis(trifluoromethyl)benzoyl group. The properties of the metal-to-ligand charge-transfer (MLCT) state of photocatalysts, the functionalization of chemical moieties for substrates involved in the charge-transfer (CT) excitation, such as the electron-withdrawing trifluoromethyl group, and the energetic levels of singlet and triplet reaction pathways may regulate the reaction yield of C(sp3)–H amidation. Kinetic evaluations show that the triplet–triplet energy transfer is the main driving force of the reaction rather than the single electron transfer process. The effects of electronic coupling, molecular rigidity, and excitation energies on the energy transfer efficiency were further discussed. Finally, we investigated the inverted behavior of single-electron transfer, which is correlated unfavorably to the catalytic efficiency and amidation reaction. All theoretical explorations allow us to better understand the generation of nitrene with visible-light photocatalysts, to expand highly efficient substrate sources, and to broaden our scope of available photosensitizers for various cross-coupling reactions and the construction of N-heterocycles.

A s expected by Ciamician one century ago, 1 chemists have been devoted to finding ways to use sunlight as a renewable energy source to enable various photochemical transformations, broadening the range of chemical synthesis under the consideration of green and sustainable development. 2−11 However, most organic molecules tend to be photoactivated only by high-energy photons of the ultraviolet (UV) region. 12−14 To resolve this challenging issue, more attention was paid to the indirect excitation of organic molecules, which can be achieved through photocatalytic single-electron transfer (SET) or energy transfer (EnT). Seminal studies on visible light photocatalysis were conducted separately by the groups of MacMillan, 15 Yoon, 16 and Stephenson, 17 having created a promising platform for new bond-forming protocols and synthetic methodologies.
As a prominent example, nitrene can be applied as a critical reactive intermediate for the synthesis of valuable N-containing molecules, 18−31 which is mainly generated by the photolysis of various precursors. 28,32−34 However, the direct photolysis of nitrene precursors requires very harsh short-wavelength irradiation, which leads to poor functional group tolerance and competitive photodecomposition processes that diminish the reaction yield. 32−34 The strategy of indirect excitation with the help of visible-light photocatalysts, for example, polypyridyl complexes of ruthenium or iridium, was used to overcome this problem. In 2011, Liu and co-workers first reported that a nitrene radical anion can be generated by one-electron reduction of the aryl azide, in which [Ru(bpy) 3 ] 2+ was employed as the photocatalyst. 35 Inspired by the pioneering work, more examples of C−N bond formation such as C−H amidation reactions, amination reactions, and cycloaddition through nitrene intermediates were explored, accompanied by the photocatalysis of vinyl azides, benzoyl azides, and carbamoyl azides in the presence of Ru-based complexes. 36−39 Yoon and co-workers further extended this strategy to azidoformate, which acts as the nitrene source to produce diverse aziridines via alkene aziridination reactions. 40 Instead of Ru-based photocatalysts, Ir(III)-based complexes emerged to be the most effective in this reaction. [Ir(ppy) 2 (dtbbpy)] + and fac-Ir(ppy) 3 were also reported in N−O-containing nitrene precursors, 41,42 showing different activities or selectivities compared with Ru-based complexes. Combinations of nitrene precursors and visible-light photocatalysts have attracted increasing attention from chemists.
Despite the fruitful experimental accomplishment in this research field, there are still many unsolved issues that are essential to be settled to understand the mechanism of photocatalysis reactions. First, it is very difficult to capture or characterize the highly reactive nitrene in experiments, if not impossible. However, this intermediate plays a critical role in the key steps of the organic reactions discussed above. An accurate theoretical model is also lacking to study the generation of nitrene, especially from precursors with N−O bonds, such as hydroxamates and oxadiazolines. 43 Multiconfigurational calculations on excited-state electronic structures are required for carbenes and nitrenes to adequately describe their physical and chemical properties, 44,45 which make them more nontrivial and computationally expensive. Second, although the photophysics and photochemistry of Ruand Ir-based catalysts, such as the metal-to-ligand charge transfer (MLCT) absorption in the visible-light region, have been studied in depth, 46,47 the driving force of the photocatalytic mechanism relevant to the formation of nitrene is still unclear. On the one hand, numerous useful molecular transformations in the search for novel agents and drugs have been achieved through the single electron transfer (SET) process, 48−63 which is potentially accessible in this case. On the other hand, energy transfer photocatalysis has emerged as a highly valuable strategy for substrate activation and new chemical bond formation in organic synthesis, 64−66 which may be useful to enhance the photon-energy-utilization efficiency in the present system. Neither the SET nor the EnT process can be directly detected by experiments currently, leaving a lot of room for theoretical computations. Finally, all experimental evidence indicate that the yield of photocatalytic reactions is determined by multiple factors for the ideal donor−acceptor combinations of SET-or EnT-mediated processes. Attention to thermodynamic factors, for example, the energy matching between donor and acceptor, is insufficient to understand the principle for regulating photocatalytic efficiencies. Kinetic factors have to be taken into consideration, which rely on the high-level treatment of excited-state electronic structures of the donor and acceptor.
Recently, Chang and co-workers developed a newly emerged photosensitization strategy (Scheme 1), 67 in which hydroxamates were identified as nitrene precursors to access synthetically valuable products. Interestingly, a triplet nitrene intermediate can be generated under mild conditions and immediately applied in situ to the intramolecular C(sp 3 )−H amidation reactions, thus producing 2-oxazolidinones in the presence of Ru(bpy) 3 (PF 6 ) 2 as a photosensitizer. This novel strategy represents a revelatory example of inert C−H bond activation with an extremely large bond dissociation energy (>100 kcal mol −1 ) using visible-light irradiation of ruthenium complexes with relatively low emission energy (40−50 kcal mol −1 ). To compensate a large amount of energy shortage, functional cooperation may be required to flexibly arrange N− O bond cleavage, C−H bond dissociation, and C−N bond generation. Many functional moieties associated with photoinitiated electron transition, donor−acceptor interactions related to electron transfer or exchange, and radical-mediated remote migration of functional groups should be considered. Most importantly, theoretical estimations of the SET and EnT rates based on high-level electronic structure calculations are necessary to determine the kinetic basis for regulating the photocatalytic efficiencies and the combination strategies between available photocatalysts and nitrene precursors.
In this study, the multiconfiguration perturbation theory at the second-order perturbation (CASPT2) level with a complete active space self-consistent field (CASSCF) wave function was employed to map minimum energy profiles (MEPs) in the ground and excited electronic states. The Scheme 1. Intramolecular C(sp 3 )−H Amidation with Hydroxamate (1) as the Nitrene Precursor through the Catalyzed Energy Transfer from an Electronically Excited Photosensitizer (2 a ) generation of a nitrene intermediate from the newly emerged precursor of hydroxamates through [Ru(bpy) 3 ] 2+ -sensitized photolysis as well as the subsequent intramolecular C(sp 3 )−H amidation reaction were explored based on electronic structure calculations. Then, the efficiencies of possible energy transfer and single-electron transfer between the photocatalyst and the nitrene precursor were analyzed and discussed in detail. These provide the thermodynamic and kinetic bases for establishing the first theoretical model associated with the exploration of the reaction mechanism and regulation strategy of photogenerated nitrene through photosensitization.

■ METHODS
In this study, we adopt the CASSCF method combined with the relativistic energy-consistent ab initio pseudopotentials and corresponding basis sets to perform ab initio electronic structure calculations of substrates and photosensitizers. The combined "nonblack-box" strategies of orbital localization and configuration selection have been developed and described by our group. 68−72 Numerous test calculations were carried out to find a more systematic and logical approach aiming to describe electron transitions involved in a series of reaction processes such as triplet−triplet intermolecular energy transfer, nitrene formation via N−O bond cleavage, and C(sp 3 )−H activation driven by 1,5-hydrogen atom transfer (HAT). A total of 12e/10o and 12e/9o active spaces were employed to account for the excited-state relaxation of the deprotonated hydroxamate substrate (1 − ) with K 2 CO 3 as the base [1 − − K 2 CO 3 (H + )] and photocatalyst (2 a ), respectively. More details about the selection of all active spaces are provided in the Supporting Information (SI), Section S1 (shown in Figures S1−S12). An energy-consistent scalar-relativistic WBadjusted 28-electron core pseudopotential and the ECP28MWB (8s7p6d2f1g)/[6s5p3d2f1g] basis set 73 were applied to the Ru center, while the all-electron 6−31G* basis set was employed for the remaining atoms of photocatalysts and isolated hydroxamate substrate. Note that different basis sets were used for the calculation of redox potentials (SI, Section S4) and electron transfer rates (SI, Section S5.3).
The density functional theory (DFT) with the B3LYP functional was used to carry out preliminary geometrical optimizations and frequency analyses for all stationary points of minima and transition states. The single-root CASSCF method was used to optimize the minima in the ground and triplet excited states of the isolated photocatalysts, substrates, and their complexes, while the minima in the singlet excited state were optimized using the two-root CASSCF method. Conical intersections (CIs) were optimized using stateaveraged RASSCF with a five-root equal-weight procedure. Singlet− triplet crossings (STCs) were obtained by the optimization in the higher energy state while keeping the energies in the singlet and triplet states equivalent. 74,75 The minimum energy paths (MEPs) were mapped by the intrinsic reaction coordinate (IRC) computations to connect these critical points in the excited and ground states stage by stage. At each stage, the optimization starts from a nonstationary structure and ends up in a minimum, and then the steepest descent paths at different stages are linked together. The mass-weighted coordinates are used in IRC with the unit of (amu) 1/2 ·Bohr. The refined single-point energy calculations of all of these structures were recalculated at the CASPT2 level of theory based on the zero-order five-root state-averaged RASSCF wave functions. Spin−orbit couplings (SOCs) between the singlet and triplet states were computed using the five-root state-averaged CASSCF state interaction (CASSI) computations with effective spin−orbit terms for metal atoms. 76,77 All DFT and CASSCF calculations were implemented using the Gaussian program package, 78 while the CASPT2 and CASSI computations were carried out using the Molcas 8.0 program package. 79 EnT rates were calculated based on the approach within the general formalism of nonradiative transition models, which was first developed by Lin et al., 80−83 and has been successfully applied to the mechanism exploration of photocatalytic systems by our group. 72 Starting from the Born−Oppenheimer approximation and the Fermi's golden rule, the EnT rate constant is given as follows where Φ and Θ denote electronic and nuclear wavefunctions, respectively; i and f are the initial and final adiabatic electronic states, respectively; Ĥ′ is the transition operator that represents the nonadiabatic effect and perturbs the system from state i to state f; u and v represent the nuclear vibrational states corresponding to electronic states i and f, respectively; E iu and E f v are energies of vibronic states; and P iu is the Boltzmann factor. The nuclear part in eq 1 is considered to be the Franck−Condon (FC) term and can be obtained on the basis of the multidimensional harmonic oscillator model as follows ω j is the vibrational frequency of the jth normal mode; ω i→f is the adiabatic energy difference between electronic states i and f; and χ denotes the nuclear wavefunction of harmonic oscillators. According where φ D* and φ D are singly occupied molecular orbitals of the donor (denoted as D); φ A* and φ A are singly occupied molecular orbitals of the acceptor (denoted as A); and 1 and 2 denote the two exchanged electrons in the processes of triplet−triplet energy transfer. The right side of eq 4 can be further expanded as follows where (ij|kl) is a two-electron integral; (i, j) and (k, l) are the basis sets associated with electrons 1 and 2, respectively; and c is the coefficient of the singly occupied orbitals. Estimation of the rates of energy transfer and other critical processes are further discussed in the SI, Section S5.

Photophysical Properties of the Substrate and the Photosensitizer Suggest an Indirect Excitation of Deprotonated Hydroxamates
The formation of the deprotonated hydroxamate substrate with K 2 CO 3 as the base [1 − − K 2 CO 3 (H + )] was simulated and confirmed to be an exothermic process (see SI, Section S3.1).
The photophysical properties of [1 − − K 2 CO 3 (H + )] were calculated and are listed in Table 1. Interestingly, the two lowest-lying singlet excited states exhibit a significant chargetransfer (CT) characteristic and are denoted as S CT1 ( 1 nπ*) and S CT2 ( 1 nπ*) with transition energies of 72.4 and 76.8 kcal mol −1 , respectively. The N5-centered orbital in the vertical direction with the N5−O6 bond (n N5⊥ ) and the π* orbital of 3,5-bis(trifluoromethyl)benzoyl ring were characterized as singly occupied molecular orbitals. The long-range charge transfer across the carbonyl bridge can be further confirmed by an increase in the dipole moment and migration of 0.5−0.6 e − from the nitrogen center to the benzoyl moiety. The two electron-withdrawing groups of trifluoromethyl facilitate the dispersion of excess negative charge and notably lower the transition energies. The vertical excitation energies of 1 ππ* excitation centered in the aromatic ring (S PP1 , S PP2 ) are larger than 100 kcal mol −1 . On the one hand, the CT characteristic of the lowest-lying excited states may play an essential role in the generation of nitrene as the 3,5-bis(trifluoromethyl)benzoyl ring functions as the leaving group. On the other hand, although the energetic level of S CT1 (395 nm) is close to the visible-light region, the absorption intensity for the S 0 → S CT1 transition is too small (f = 6.7 × 10 −4 ), ruling out the direct excitation of the substrate under experimental conditions. In the absence of a photocatalyst, a similar path involving T CT1 ( 3 nπ*) with a transition energy of 49.5 kcal mol −1 also has a low photon-energy-utilization efficiency because of the spinforbidden transition from the ground state ( f: less than 1.0 × 10 −7 ; SOC constant: 2.2 cm −1 ). We further examined the photosensitization strategy through indirect activation and started with accurate theoretical predictions of the photophysical properties of photosensitizers. As polypyridyl complexes of ruthenium are widely used as optimal photocatalysts, we focused on the absorption spectra of [Ru(bpy) 3 ] 2+ (2 a ) and [Ru(dmb) 3 ] 2+ (2 b ) in this study. As shown in Figure 1 and Table S1, CASPT2//CASSCF calculations can well reproduce the MLCT absorption band of 2 a , which ranges from 360 to 466 nm and agrees with the experimentally measured band with broad width. 84,85 The introduction of a methyl group on the bipyridine ligand for 2 b results in an extended band width between 353 and 495 nm ( Figure S14 and Table S3) and a slight red shift of the maximum MLCT absorption λ max (2 a : 414 nm → 2 b : 466 nm). The predicted λ max is closely correlated to experimentally measured values for 2 a and 2 b (452−457 nm) 46,47 as well as the irradiation wavelength (456 nm) used for the photosensitized nitrene generation in Chang's study. 67 Similar to our previous computations, 68,69,72 MLCT absorption bands of Rubased complexes studied here also originate from the strong coupling among all possible electron transitions from metal to various ligands, which provides a potential way to tune the intensity of the maximum MLCT absorption of photocatalysts.

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It is worth noting that previous experiments have revealed that this photosensitized C−H amidation reaction takes place in high yields both in the gas phase (70%) and in a weakly polar environment (1,1,2,2-tetrachloroethane: 75%; dichloromethane: 70%), while it is less effective in polar media (acetonitrile: 9%; N,N-dimethylformamide: <5%). 67 On account of these observations, all computations in the present study were implemented without the consideration of solvents, except for redox potential calculations as discussed in the SI, Section S4. Additional vertical excitation energy calculation on 2 a with weakly polar dichloromethane and our previous results using polar acetonitrile 72 also confirm the effect of the solvent on the absorption spectra of 2 a and the amidation reaction of hydroxamates (see Table S2 and Figure S14).

Triplet Nitrene Stems from the Charge-Transfer Excitation of Deprotonated Hydroxamates and Facilitates C(sp 3 )−H Activation
Considering the indirect excitation of substrates, the MEP for the photogeneration of triplet nitrene was mapped through the direct population in the T CT1 ( 3 nπ*) state of [1 − − K 2 CO 3 (H + )] (see Figure 2). Compared with the singlet CT state, the vertical excitation energies for S 0 → T CT1 ( 3 nπ*) transition show a significant red shift (see Table S10). The minimum of the triplet CT state, denoted as T CT1 ( 3 nπ*)-Min, is energetically 5.0 kcal mol −1 lower than the Franck−Condon (FC) point. The structural adjustments from FC to T CT1 ( 3 nπ*)-Min include a shortened N5−O6 bond (1.49 → 1.40 Å) and an elongated O6−C7 bond (1.29 → 1.45 Å), accompanied by the migration of 0.5 e − from N5 to the leaving group of 3,5-bis(trifluoromethyl)benzoyl (see Table S14). Subsequently, the electron-withdrawing group of trifluoromethyl induces negative charge redistribution on the leaving group and causes the elongation of the N5−O6 bond along a flat path until 1.64 Å. Meanwhile, the singly occupied π* orbital of the leaving group at T CT1 ( 3 nπ*)-Min evolves into a repulsive σ* orbital, making the N5−O6 bond fission highly effective. Finally, an intermediate (IM1) is generated along a downhill path.
In the process of IM1 generation, the homogeneous decomposition of the N5−O6 σ bond leaves an unpaired electron around N5 along the direction parallel (denoted as . Therefore, two unpaired electrons simultaneously distribute at the same atom of N5 with parallel spin, which are labeled n N5// and n N5⊥ in Figure 2, respectively, demonstrating the formation of N-centered triplet diradical species at an N5−O6 distance of 1.85 Å. It is also accompanied by the structural adjustments of C7−O6 and C7−O8 bonds in the leaving group via two electrons pairing between one from the initial charge-transfer transition (i.e., CT1) and another from the N5−O6 σ bond fission. The Mulliken population analysis reveals that the excess negative charge mainly distributes in the O6−C7−O8 part, suggesting the formation of a carboxylate anion as the leaving group. The remaining part of the N5-centered species exhibits a neutral characteristic. More details of charge redistribution among different parts can be seen in the SI, Section S3.5. As an important consequence, IM1 produces six valence electrons, which is less than the normal seven-electron configuration of a nitrogen atom. This leads to the formation of triplet nitrene (IM1) with an electron-deficient characteristic. The electron-deficient N5 in IM1 tends to attract the H9 atom, triggering the subsequent hydrogen atom transfer (HAT) with the cleavage of the C1−H9 bond and the formation of the N5−H9 bond. The corresponding transition state labeled TS HAT (T 1 ) was determined in the path of the triplet state with an energy barrier of 14.4 kcal mol −1 . The C1− N5 diradical intermediate (denoted as IM2) is generated after overcoming this barrier. The TS HAT (T 1 ) is 4.2 kcal mol −1 lower than the FC point of the T CT1 ( 3 nπ*) state, which allows the MEP for the formation of IM2 to arrange between the energy levels of 49.5 kcal mol −1 (577 nm) and 30.8 kcal mol −1 (928 nm) in comparison with the commonly known bond dissociation energy beyond 100 kcal mol −1 of the C(sp 3 )−H bond. This can be further assisted by the excess energy from a possible EnT process. Benefiting from the photogeneration of triplet nitrene and the structural advantages of hydroxamate substrate, the challenging task of the remote sp 3 hybrid C−H activation becomes easier and proceeds under mild conditions, allowing the occurrence of the visible-light-driven, Rucomplex-sensitized photocatalytic amidation.

Singlet Path has a Dual Characteristic for the C−H Amidation Reaction
The counterpart reaction path in the singlet state is also shown in Figure 2. It can be identified as a side channel against the formation of triplet nitrene. First, a singlet−triplet crossing (STC) was determined at an N5−O6 distance of 1.73 Å and labeled STC(T CT1 /CSS) according to the closed-shell singlet (CSS) configuration, in which the intersystem crossing (ISC) from T CT1 ( 3 nπ*) to CSS takes place with relatively high efficiency in the timescale of picoseconds (see Table S17). The CSS energy profile underlies the triplet path when the N5−O6 bond length is shorter than 1.73 Å. Both the ISC rate and the energetic level suggest a possible bypass channel to decrease the quantum yield of triplet nitrene. Second, with an increase in the N5−O6 distance, the characteristic of the singlet state changes to an open-shell configuration and is therefore referred to as the open-shell singlet (OSS). The energy level of OSS exceeds the triplet profile. Finally, a sizeable barrier larger than 40 kcal mol −1 is encountered along the singlet reaction path and denoted as TS HAT (OSS). This barrier is too large to cross with excess energies accumulated in previous steps. In other words, the singlet path is accessible via STC(T CT1 /CSS) but nonproductive for the amidation reaction.
Accompanied by the formation of IM2, the energy level of the singlet state reaches close to the triplet reaction path, after which the singlet path plays a positive role in the generation of the final products. The details can be seen in Figure 2. First, the two singly occupied orbitals located at N5 and C1 in IM2 are perpendicular to each other in the plane of the azacycle. The rotation of the N5−H9 bond is thus required for the approaching of C1-and N5-centered diradical (see the evolvement of the H9−N5−O6 angle in SI, Figure S18). Then, a small barrier of 4.5 kcal mol −1 is overcome to access another STC between the triplet and the open-shell singlet (OSS) at a C1−N5 distance of 2.9 Å, referred to as STC(T 1 / OSS). The ISC transition occurs in the timescale of nanoseconds (see Table S17). Once the substrate populates in the open-shell singlet, the C1−N5 coupling takes place very easily along a sharp downhill path with a decrease in the C1− N5 distance, leading to the construction of the azacycle. When the C1−N5 distance is shortened to 2.5 Å, the open-shell singlet species transforms into the CSS configuration to generate the C−N bond. The final product 2-oxazolidinone (4) is 57.0 kcal mol −1 more stable than the reactant (S 0 -Min).
In brief, the singlet path is unfavorable for the early stage of the entire reaction while it becomes essential to the construction of the final products. This indicates that a refined adjustment of the singlet−triplet energy gap at critical points is possible to enhance the quantum yield of photocatalysis C−H amidation reactions

Kinetic Assessment of the Triplet−Triplet Energy Transfer Process is the Key to Understanding the Mechanism of the C−H Amidation Reaction Driven by Photosensitizers
The energy transfer from the excited photocatalyst 2 a to the deprotonated substrate 1 − may prompt the substrate to its triplet CT state directly through electron exchange. Although the adiabatic excitation energies listed in Table 2 suggest an  Figure 3. The photocatalyst 2 a is promoted by blue light irradiation (414 nm) at first, populating in the FC of S MLCT , and then speedily relaxing to its minimum. As observed in our previous studies, 68−72 the STCs between singlet and triplet MLCT states ( 1 dπ*/ 3 dπ*) are ubiquitous when the visible-lightinitiated photosensitizers just evolve out of the FC region. The strong relativistic effect of transition metal ions leads to the ultrafast ISC in the timescale of subpicoseconds (see Table  S17), thereby improving the quantum yield of the T MLCT state. The lifetime of T MLCT was experimentally measured to be up to 279 ns, 84,85 providing a wide time window for the competitive EnT process. The root-mean-square deviation (RMSD) between the optimized geometries of S 0 -Min and T MLCT -Min was as small as 0.06 Å, which demonstrates the strong ability of recovery (S 0 → T MLCT → S 0 ) for the subsequent photocatalytic process. As an energy acceptor, the substrate 1 − is promoted to its T CT1 ( 3 nπ*) state (see the right panel in Figure 3), followed by the formation of triplet nitrene and the C−H amidation as discussed above. The triplet−triplet energy transfer takes place within the supramolecular structure with short-range interactions and can be described based on an electron-exchange mechanism (i.e., the Dexter model). Here, we estimated the EnT rates using electron structure calculations in the ground and excited states as well as the Fermi's golden rule combined with the Dexter model. The results with the corresponding parameters are summarized in Tables 2 and S18. As expected, the EnT rate for the 2 a −1 − complex was calculated to be 2.4 × 10 10 s −1 , which exceeds that of the phosphorescence emission of the photosensitizer 2 a measured experimentally by 3 orders of magnitude. Kinetic evaluations were also performed on a series of donor−acceptor complexes with different substrates or photosensitizers. First, the removal of the electron-withdrawing group of trifluoromethyl from the leaving group leads to the unsubstituted hydroxamate derivative anion (1 a− ), and the EnT rate was estimated to be 3.8 × 10 8 s −1 . The slower EnT is mainly ascribed to a decrease in the electron-exchange coupling (|H 12 | 2 , 1.5 × 10 −9 → 1.8 × 10 −10 Hartree 2 ), but it is still operative in comparison with the phosphorescence lifetime. Second, in the presence of phenol (1 b− ) or methoxy (1 c− ), by substituting the leaving group of 1 − , the excitation energy of the triplet substrate increases by more than 30 kcal mol −1 , resulting in a significant decrease in the FC term and EnT rate. Third, the values of RMSD are a little higher than those in our previous study (0.1−0.2 Å), 72 which may raise the question about the harmonic oscillator assumption in the EnT rate calculations. In other words, the EnT process may take place far away from the minima of the triplet donor and/or ground-state acceptor. Although it cannot be ruled out rigorously at an affordable computational cost, the predominant role of energy transfer remains the same for this reaction despite the efficiency of appended EnT mechanisms. Finally, we replaced Ru-based photocatalysts with Ir complexes (3 a , 3 b , and 3 c ) and estimated the rates of energy transfer from the photosensitizers to substrate 1 − . EnT rates of the same order of magnitude (10 8 to 10 10 s −1 ) were obtained between Ru(2 a )and Ir(3)-based photosensitizers, which indicate a favorable energy transfer efficiency for Ir complexes to catalytically activate hydroxamate substrates. Interestingly, a highly efficient Ir-catalyzed EnT protocol was recently reported for the N−Ocontaining nitrene precursor toward sulfoximines and benzimidazoles starting from oxadiazolines, 41 suggesting the catalytic compatibility between the Ir-based photosensitizer and the newly emerged precursor. All computational evidence demonstrate that Ir-catalyzed nitrene transformation deserves to be further investigated through optimization strategies of the substrate compatibility and photosensitization conditions.
It is worth noting that the key factors of EnT efficiency disclosed in this study are more complicated than those reported in our previous study. 72 The theoretical investigation of intermolecular [2 + 2] photo-cycloaddition reactions, using tris(bipyridyl) ruthenium(II) as a photosensitizer, reveals that the change in the rigidity of the energy acceptor has a major contribution to different EnT rates, which is called "structure control". Although a similar tendency can be also seen in the present case (e.g., it can be seen from the RMSD a (0.46 → 0.58 Å) that the structure of substrate 1 a− is more flexible than that of 1 − ), their EnT rates are strongly influenced by electron-

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pubs.acs.org/jacsau Article exchange couplings, which is called "ecoupling control". The differences among the three Ir complexes (3 a , 3 b , and 3 c ) can also be attributed to combined structure control and ecoupling control (see Table S18). As discussed above, a decrease in the EnT efficiency from 1 − to 1 c− is determined by different excitation energies, which is called "energy control". Accurate calculations of these factors are extremely expensive. Fortunately, some machine-learning models have been developed in recent years to approximately predict values of electronic coupling and excitation energy. 86,87 This opens a new door to high-throughput screening of a large number of transition metal complexes and exhibits great potential in discovering novel photocatalysts with high energy transfer efficiency.

Single Electron Transfer Mechanism Is Ruled Out Based on Thermodynamic and Kinetic Factors
The SET process, during which an electron is transferred from the photosensitizer to the substrate or vice versa, is also possible to trigger the subsequent C−H amidation reaction. We first considered its driving force controlled by thermodynamic factors. The computational details and results are listed in the SI, Section S4. On the one hand, the leaving group of 3,5-bis(trifluoromethyl)benzoyl may act as the electron acceptor for the reduction reaction of the substrate. However, the reduction potentials of hydroxamate substrate 1 and deprotonated substrate 1 − were predicted to be −1.59 and −2.54 V vs a saturated calomel electrode (SCE), respectively, which cannot be compensated by the oxidation potential of photocatalyst 2 a in its excited state (−0.81 V vs SCE 46,47 ). It can be concluded that the single electron reduction of the hydroxamate substrate seems extremely unlikely through the SET reaction initiated by the visible-light irradiation of Ru complexes. On the other hand, the oxidation potential of deprotonated substrate 1 − was estimated to be 0.44 V and lower than the reduction potential of 2 a in its excited state (0.77 V vs SCE 46,47 ). This means that the electron ejection of deprotonated substrate 1 − is energetically favorable, which agrees with the case of the hydroxamate substrate in the presence of the KO t Bu base using cyclic voltammogram measurements. 67 We further considered the kinetic factors based on the Marcus theory for the energetically accessible reductive quenching cycle of photocatalyst 2 a with deprotonated substrate 1 − . The computational details are shown in the SI, Section S5.3, and the results are displayed in Figure 4. The initial state of SET can be described as the complex of 1 − in the ground state and 2 a in the excited state, denoted as T MLCT according to the excitation characteristic of the photocatalyst. The final state is relevant to the SET from the N5-centered n orbital of 1 − to the ligand-centered π* orbital of 2 a , labeled T 21CT ( 3 nπ*). To our surprise, the rate calculation result exhibits an unusual picture of inverted behavior, which was proposed by Marcus and co-workers. 88 As shown in Figure 4, the energetic levels for all stationary points in the T 21CT ( 3 nπ*) state are lower than their corresponding counterparts in the precursor MLCT state (T MLCT ) of photocatalyst 2 a , and the corresponding −ΔG (approximately equal to a −ΔE of 2.28 eV) is greater than the reorganization energy (λ: 2.01 eV), leading to a much slower SET rate of 3.4 × 10 7 s −1 compared with the EnT rate (2.4 × 10 10 s −1 ). A significant decrease in dipole moment from the T MLCT -Min to the corresponding point in the T 21CT state (38.3 → 5.5 D) indicates the dispersion of excess negative charge of substrate 1 − during SET, which is further enhanced by the electron-withdrawing trifluoromethyl group. The large reorganization energy agrees with the shortened N5−O6 bond in the minimum of the T 21CT state compared with T MLCT -Min (1.44 → 1.35 Å).
In brief, possible SET processes accompanied by the reduction of the hydroxamate substrate are suppressed by thermodynamic factors, and the efficiency of oxidative SET for the deprotonated substrate is relatively low according to the kinetic assessment. The above analyses unequivocally demonstrated that the phototransformation of C−H amidation is predominately operative along the EnT path and thus excluded the contributions from the visible-light-driven SET between the nitrene precursor of hydroxamates and Ru-based complexes. The adjustment of the EnT efficiency should be paid more attention to in the present system. However, it is worth noticing that the unusual inverted behavior of energy profiles has never been observed in our previous studies in visible-light-driven SET reactions mediated by transition or actinide complexes. 68,69 Not only the energy gap between initial and final states but also the relationship between ΔG and λ should be examined carefully when tuning the efficiency of the SET process in future studies.

■ CONCLUSIONS
In this study, hydroxamates were theoretically rationalized to act as promising nitrene precursors rather than traditional azides for the triplet photosensitized C(sp 3 )−H amidation. Using accurate electronic structure calculations at the CASPT2//CASSCF level of theory, the advantage of hydroxamates was found to stem from the compatible longrange charge-transfer excitation with the MLCT state of the Ru-based photocatalyst. The electron-withdrawing leaving group significantly lowers the energy level of the CT excitation, which not only leads to the N−O bond fission under mild conditions but also facilitates the use of the ejected electron to construct the leaving group of the carboxylate anion and to generate the triplet nitrene. The electron-deficient nitrene is able to abstract the H atom of the remote C(sp 3 )−H through an energetically favorable transition state. Kinetic assessments of EnT and SET between photocatalysts and substrates were also implemented to disclose the controlling factors of photocatalytic efficiencies. The efficiency of the triplet−triplet EnT process was estimated to be much higher than that of SET, which can be controlled by more complicated factors than those in our previous study, including the rigidity of molecular structures, electronic coupling, and relevant excitation energies of the donor and acceptor. The SET mechanism can be excluded based on thermodynamic or kinetic factors. Interestingly, even if the single electron transfer from the substrate to the photocatalyst is allowed thermodynamically, our rate calculation based on the Marcus theory further revealed the inverted behavior in the present system, which may be the key factor suppressing this process in kinetics. To sum up, the present electronic structure calculations and kinetic evaluations provide valuable insights into the generation of highly reactive nitrene and the C(sp 3