Stabilization of Two Radicals with One Metal: A Stepwise Coupling Model for Copper-Catalyzed Radical–Radical Cross-Coupling

Transition metal-catalyzed radical–radical cross-coupling reactions provide innovative methods for C–C and C–heteroatom bond construction. A theoretical study was performed to reveal the mechanism and selectivity of the copper-catalyzed C–N radical–radical cross-coupling reaction. The concerted coupling pathway, in which a C–N bond is formed through the direct nucleophilic addition of a carbon radical to the nitrogen atom of the Cu(II)–N species, is demonstrated to be kinetically unfavorable. The stepwise coupling pathway, which involves the combination of a carbon radical with a Cu(II)–N species before C–N bond formation, is shown to be probable. Both the Mulliken atomic spin density distribution and frontier molecular orbital analysis on the Cu(II)–N intermediate show that the Cu site is more reactive than that of N; thus, the carbon radical preferentially react with the metal center. The chemoselectivity of the cross-coupling is also explained by the differences in electron compatibility of the carbon radical, the nitrogen radical and the Cu(II)–N intermediate. The higher activation free energy for N–N radical–radical homo-coupling is attributed to the mismatch of Cu(II)–N species with the nitrogen radical because the electrophilicity for both is strong.

a spin-crossover process with energy barrier when the spin state of the reactants is a triplet and the coupling product is a singlet (Fig. 2). In this case, the energy barrier could be represented by the minimum energy crossing point (MECP) [36][37][38] , the energy of which plays a significant role in determining the reaction mechanism and selectivity [38][39][40][41][42] . Surprisingly, these issues have seldom been discussed in transition metal-catalyzed radical-radical cross-coupling reactions. More effort should be devoted to reveal the detailed reaction pathway and the origin of the cross-combination selectivity.
Here, we describe our theoretical understanding of transition metal-catalyzed radical-radical cross-coupling reactions [43][44][45] . As shown in Fig. 3, for a catalytic system that contains two different radical species (R· and R'·), a low oxidation state transition metal would preferentially coordinate with one radical (for example, the radical R·) and combination with the other radical would be less favored. The generated organometallic intermediate M n+1 − R could be regarded as a metal-containing radical species. Subsequent reaction between this radical and R'· has two competitive paths. In the concerted coupling pathway, radical R'· would directly attack the R moiety of M n+1 -R, and the formation of an R-R' bond and homolytic cleavage of a M-R bond occurs synchronously through the MECP. While in the stepwise coupling pathway, radical R'· would initially combine with the metal center and form a high oxidation state organometallic complex through the MECP; that is the transition metal simultaneously stabilizes two radical species. The product R-R' is finally obtained by a two electron transfer process. Although the concerted radical-radical coupling mode is usually proposed in previous work 20,46 , our computational results reveal that the stepwise coupling mechanism is more favored for transition metal-catalyzed radical-radical cross-coupling. Here, the copper-catalyzed oxidative C(sp3)-H/N-H coupling of sulfoximine with cyclohexane ( Fig. 4) is studied using density functional theory (DFT) calculations as an example to prove this new viewpoint 21 . Both the mechanism and selectivity of this reaction will be discussed in this work.

Computational Methods
All the DFT calculations were carried out with the GAUSSIAN 09 series of programs 47 . DFT method B3-LYP 48,49 with a standard 6-31G(d) basis set (SDD 50 basis set for Cu) was used for geometry optimizations. Harmonic vibrational frequency calculations were performed for all of the stationary points to confirm if the points were local minima or a transition structure and to derive the thermochemical corrections for the enthalpies and free energies. In this study, the stability of wavefunction has been tested for singlet, doublet, and triplet state intermediates. All the test results confirmed that the wavefunction is stable under the perturbations considered. The solvent effects were considered by single point calculations on the gas-phase stationary points with an SMD continuum solvation model 51 . The M06 functional 52 with the 6-311+ G(d, p) basis set (def2-TZVP basis set for Cu) 42 was employed to calculate the solvation single point energies in a cyclohexane solvent to provide more accurate energy information [53][54][55][56] . The Gibbs free energy of each stationary point calculated by M06 is provided for discussion of the energy. The Mulliken atomic spin density of certain atoms was also calculated using the same method. The optimized structures were displayed using CYLview 57 .
Additionally, the MECP location program 58-60 developed by Harvey and co-workers was used in this study to gain the structures of MECPs at the B3-LYP/6-31G(d) (SDD basis set for Cu) level of theory. The single point energies of the MECPs, which were calculated at M06/6-311+ G(d,p) (def2-TZVP basis set for Cu) in cyclohexane, have also been determined. The global electrophilicity ω° and global nucleophilicity N°, which are employed to measure the electron compatibility of free radicals, were gained at the UB3-LYP/6-31G(d) (SDD for Cu) level using [61][62][63] :    where μ° is the global chemical potential of radicals, which could be obtained by μ° ≈ (E α,°H OMO + E β,°L UMO )/2, and η° is the global chemical hardness of radicals, which could be obtained using OMO and E β,°L UMO are corresponding orbital energies of the HOMO in α molecular orbitals and the LUMO in β molecular orbitals. In Eq. 2, DCM represents a dicyanomethyl radical [61][62][63] .

Results and Discussion
In the selected copper-catalyzed C-N coupling reaction, di-tert-butyl peroxide (DTBP), which could decompose to tert-butoxyl radicals, was used as the radical initiator 21 . Reactants sulfoximine 1 and cyclohexane 2 could react with the tert-butoxyl radical, leading to the generation of a nitrogen radical and a carbon radical, respectively. The C-N bond is considered to be constructed through radical-radical cross-coupling. In our theoretical calculation, the formation of a carbon radical and a nitrogen radical was first studied. As the homolysis of DTBP (4) is endergonic by 18.6 kcal/mol, the relative free energy of each tert-butoxyl radical (5) was determined to be 9.3 kcal/mol (Fig. 5a). Subsequent radical substitution between radical 5 and cyclohexane 2 resulted in the generation of carbon radical 7 via transition state 6-ts (Fig. 5b); the activation free energy for the whole process was 22.7 kcal/mol. The free energy of carbon radical 7 was found to be 0.8 kcal/mol relative to DTBP. An analogous process between radical 5 and reactant 1 could generate nitrogen radical 9 through 8-ts with an activation free energy of 22.1 kcal/mol (Fig. 5c), which is only 0.6 kcal/mol lower than that of the formation of carbon radical 7. The formation of radical 9 was determined to be endergonic by 9.5 kcal/mol. Therefore, both the carbon radical and the nitrogen radical are able to be generated in this reaction and carbon radical 7 is more stable than nitrogen radical 9.
In the experiment, the addition of Cu(acac) 2 facilitated the transformation 21 . To determine its role in this reaction, the interaction between the existing radicals and Cu(acac) 2 was studied. A radical could either oxidize the metal by forming a covalent bond or purely coordinate with the metal; both of these two cases have been These WBI values imply that new covalent bonds are formed when these singlet intermediates are generated. Moreover, the sum of individual WBI of copper in 10a-sing, 10b-sing, and 10c-sing is found to be 2.39, 2.15, and 2.43, respectively. Thus, these three complexes all involve a Cu(III) center. From the energy point of view, the combination of a tert-butoxyl radical with Cu(acac) 2 , which forms a singlet Cu(III) complex 10a-sing, was endergonic by 15.5 kcal/mol. Meanwhile, the generation of a triplet Cu(II) complex 10a-trip through radical coordination was endergonic by 3.8 kcal/mol, which is 11.7 kcal/mol lower than the formation of 10a-sing. For the interplay between carbon radical 7 and Cu(acac) 2 , the formation of Cu(III) complex 10b-sing or Cu(II) complex 10b-trip were endergonic by 5.2 or 2.6 kcal/mol, respectively. Moreover, the tendency of free energy for the interaction between nitrogen radical 9 and Cu(acac) 2 remained the same. These data indicate that Cu(acac) 2 would rather coordinate with these radical species than form a Cu(III) complex under these conditions. The generation of tert-butoxide anion and a Cu(III) complex from 10a-sing is also determined to be endothermic by 77.9 kcal/mol (See SI for details). Consequently, the mechanism proposed in the experiment that involves the formation of tert-butoxide anion and a Cu(III) complex could be safely ruled out. Most importantly, the energy information obtained for radical coordination has shown that the catalyst Cu(acac) 2 does not have the capability of stabilizing radicals 5, 7, or 9.
Both theoretical and experimental studies have suggested that a Cu(I) species might be the active catalyst in copper-catalyzed coupling reactions [64][65][66][67] . Lei and co-workers observed a Cu(I) β -diketonate species by Operando IR and X-ray absorption spectroscopy, which is proven to be the active catalyst for the copper-catalyzed carbon-carbon coupling reaction 68 . Inspired by these studies, we propose that an active β -diketone Cu(I) complex, which could be formed from Cu(acac) 2 , might be the real catalytic species formed in this C-N coupling reaction. As shown in Fig. 7, the nucleophilic addition of tert-butoxyl radical 5 towards the middle carbon (C2) of the diketonate through transition state 11-ts would result in a reduction of Cu(acac) 2 . The generated Cu(I) complex 13-sing was determined to be singlet because the free energy of the corresponding triplet compound is 29.1 kcal/mol higher than that of 13-sing (See Figure S3 for details). As the spin state of the reactants before the reduction is a triplet, a minimum energy crossing point 12-MECP is located between 11-ts and 13-sing. The relative energy of 12-MECP is found to be 10.8 kcal/mol. Optimized structures, shown in Fig. 7, suggest that the length of the O2-C2 bond in 12-MECP is 1.42 Å, which is 0.39 Å shorter than that in 11-ts (1.81 Å). Moreover, the distance of Cu-O2 in 12-MECP is 0.23 Å longer than that in 11-ts. These data confirm that 12-MECP occurs later relative to transition state 11-ts.
Subsequent coordination of nitrogen radical 9 toward Cu(I) complex 13-sing would generate a Cu(II) intermediate 15′. The dissociation of complex 14 then forms Cu(II) β -diketonate intermediate 15, the relative free energy of which is found to be − 34.3 kcal/mol. Meanwhile, the WBI value of newly formed Cu-N in 15 is shown to be 0.64 (Fig. 7), suggesting this bond is a covalent bond. Moreover, the sum of WBI values of Cu is 1.48, which further confirms that the oxidation state of copper in complex 15 is + 2. Likewise, carbon radical 7 and oxygen radical 5 may combine with the copper center, generating cyclohexyl Cu(II) 16 and tert-butoxyl Cu(II) 17 through associated intermediate 16′ and 17′, respectively. Although the formations of different Cu(II) complexes are all exergonic, the relative free energy of 16 is 10.8 kcal/mol higher than that of 17 while the relative free energy of 17 is 4.4 kcal/mol higher than that of 15, which indicates that the binding capability of nitrogen radical 9 with Cu(I) is the strongest. In addition, the coordination of the tert-butoxyl radical to Cu(II) intermediate 15 was also taken into account. The formation of a triplet Cu(II) complex 18-trip (the relative free energy of singlet structure was found to be 2.6 kcal/mol higher, see Figure S4 for details) was endergonic by 5.7 kcal/mol, which is energetically unfavorable. Obviously, subsequent transformation would not occur through complex 18-trip. Therefore, the Cu(I) species 13-sing would preferentially stabilize the nitrogen radical in this reaction, and the Cu(II)-N β -diketonate intermediate 15 is most likely to be the startup species for the following transformation.
For the radical-radical combination of Cu(II) intermediate 15 with carbon radical 7, two possible pathways were calculated and are summarized in Fig. 8. In the stepwise coupling pathway (Fig. 8a), carbon radical 7 could initially coordinate to Cu(II) intermediate 15, forming a triplet Cu(II) complex 19-trip with a free energy increase of 1.6 kcal/mol. The corresponding singlet state, which is more stable by 12.9 kcal/mol, could also be obtained as Cu(III) complex 19-sing through a minimum energy crossing point 20-MECP. The relative energy of 20-MECP is determined to be − 28.2 kcal/mol, which is merely 6.6 kcal/mol higher than Cu(II) intermediate 15.  The formation of Cu(III) intermediate 19-sing is thereby thermodynamically favorable and kinetically feasible. Structural analysis shows that the newly forming C-Cu bond in 19-trip reaches a length of 3.03 Å, while this bond length decreased to 2.19 and 2.02 Å in 20-MECP and 19-sing, which implies that the interaction between carbon radical and the metal center becomes stronger along the reaction coordinate. Besides, the WBI bond order of Cu-C in 19-trip is determined to be 0.04, which means almost no covalent interaction exist between Cu and C. In complex 19-sing, the sum of WBI values of Cu is 2.06, confirming that the oxidation state of copper is + 3. Moreover, the WBI bond order of Cu-C in 19-sing is found to be 0.59, which suggests this Cu-C is a strong covalent bond. The structural analysis and bond order results thereby account for the high stability of singlet state 19-sing. The C-N bond is then constructed through a two-electron transfer/reductive elimination transition state 21-ts, and Cu(III) is reduced to Cu(I) simultaneously. The activation free energy of this step is determined to be only 7.0 kcal/mol, and the formation of Cu(I) complex 22 is exergonic by 35.7 kcal/mol.
In the concerted coupling pathway (Fig. 8b), the C-N bond was formed via the nucleophilic addition of carbon radical 7 toward the nitrogen atom in Cu(II) intermediate 15. A minimum energy crossing point between the triplet and singlet potential energy surfaces was located as 23-MECP, the relative energy of which was found to be − 25.8 kcal/mol. Comparing these two pathways reveal that the concerted coupling mechanism is kinetically unfavorable, and the carbon radical would prefer to combine with the metal center before C-N bond formation. Further theoretical analysis has been carried out to elucidate the preference of the carbon radical for Cu(II). As shown in Fig. 9a, the Mulliken atomic spin density of copper atom in intermediate 15 is 0.47 while the corresponding value of the nitrogen atom is only 0.29, which indicates that the spin is mainly located at the metal center. Moreover, the singly occupied molecular orbital (SOMO) of 15 is determined to be the antibonding orbital of Cu-N π bond (Fig. 9b), and the corresponding bonding orbital is observed as SOMO-2. Thus, Cu(II) intermediate 15 should be an electron-donating radical species. On another hand, the proportion of SOMO on the Cu atom is calculated to be 0.98, which is much higher than that on N atom. Both the Mulliken atomic spin density distribution and frontier molecular orbital (FMO) analysis have proven that the combination ability of Cu with another radical is stronger than that of N. Consequently, the carbon radical would preferentially react with the metal center rather than nitrogen.
When the Cu(I) complex 22 was formed in this reaction, the C-N coupling product 3 would be finally obtained by ligand exchange using reactant 1 (Fig. 10). Generated Cu(I) species 24 with the coordination of reactant 1 would then react with tert-butoxyl radical 5, thereby regenerating the active Cu(II) species 15 by hydrogen transfer through a four-membered ring transition state 25-ts. The activation free energy was determined to be 22.7 kcal/mol, which is very close to the metal-free radical substitution transition state 8-ts (22.1 kcal/mol).
With the reliable mechanism in hand, we wanted to understand why the N-N homo-coupling did not take place in this reaction and sought to determine what would happen if the carbon radical 7 in the cross-coupling pathway was replaced with nitrogen radical 9. Computational results for these issues are shown in Fig. 11. Along the stepwise homo-coupling pathway (Fig. 11a), a triplet Cu(II) complex 26-trip would be formed with a free energy increase of 5.9 kcal/mol after the coordination of another nitrogen radical 9 to 15. The free energy barrier for this step is found to be 4.3 kcal/mol higher than that of the carbon radical coordination shown in Fig. 8a, which implies the coordination capability of a nitrogen radical to Cu(II) is weaker than that of a carbon radical. Subsequently, through a minimum energy crossing point 27-MECP, the triplet Cu(II) species 26-trip could be

Reactivity indices 7 (C·) 9 (N·) 15 (Cu II -N)
Global electrophilicity ω°0.99 3.54 3.12 Global nucleophilicity N°3.06 1.14 1.79 Table 1. Calculated global electrophilicity ω° and global nucleophilicity N°, in eV, for carbon radical 7, nitrogen radical 9, and Cu(II) intermediate 15. transformed to a singlet Cu(III) complex 26-sing, the formation of which is exergonic by 3.6 kcal/mol relative to 15. This process is less favored compared with the generation of 19-sing (Fig. 8a), which is exergonic by 11.3 kcal/mol. It is also noteworthy that the N-N bond formation via transition state 28-ts bears an activation free energy of 12.3 kcal/mol, and this value is 5.3 kcal/mol higher than that of the C-N bond formation transition state 21-ts. Additionally, the energy barrier of the minimum energy crossing point 30-MECP in the concerted coupling pathway reaches up to 17.6 kcal/mol (Fig. 11b), which is 3.2 kcal/mol higher than the activation energy through 28-ts (14.4 kcal/mol). These data confirms that the homo-coupling of nitrogen radicals could not take place in this reaction and also verify the preceding conclusion that the radical-radical coupling reactions would not proceed along the concerted coupling pathway. We have demonstrated that the N-N radical-radical homo-coupling is less favored compared with the C-N radical-radical cross-coupling because the bonding capacity of Cu(II) to a nitrogen radical is weaker than that to a carbon radical. An interesting phenomenon then arises from above study, which is that the low oxidation state Cu(I) species tends to combine with a nitrogen radical rather than a carbon radical; however, the generated high oxidation state Cu(II) species prefers to combine with the carbon radical instead of the nitrogen radical. Hence, copper could selectively stabilize two diverse radical species at different oxidation states. The principle behind this finding plays a vital role in determining the selectivity of radical-radical coupling reactions. Two reactivity indices that were introduced by Domingo and co-workers for free radicals, the global electrophilicity ω° and global nucleophilicity N°6 2 , have been used to clarify the origin of the selectivity in this work (Table 1) [69][70][71] , and a graphic illustration for the cross-coupling selectivity is also provided based on these data (Fig. 12).
As shown in Table 1, the global electrophilicity ω° of carbon radical 7 is 0.99 eV while the ω° of nitrogen radical 9 is 3.54 eV, which suggests that the nitrogen radical 9 is a strong electrophile and carbon radical 7 is only a moderate electrophile. However, the global nucleophilicity N° of carbon radical 7 is calculated to be 3.06 eV, indicating that this radical is a strong nucleophile. Thus, the electron rich Cu(I) complex would preferentially combine with the electron deficient nitrogen radical 9 (Fig. 12). For the generated Cu(II)-N intermediate 15, which is a metal-contained radical species, the global electrophilicity ω° is determined to be 3.12 eV. As a strong electrophile, the combination of 15 with the electron deficient nitrogen radical is obviously unfavorable (Fig. 12). The higher energy barrier for N-N bond formation could also be attributed to the strong electrophilicity of nitrogen radical 9. In contrast, the combination of electrophile 15 with a nucleophilic carbon radical is energetically favorable. Subsequent C-N bond formation is also a facile process because the nucleophilicity of carbon radical was matched with the electrophilicity of the nitrogen radical. As a consequence, the chemoselectivity of cross-coupling in this study originates from the suitable matching of the electrophilicity of Cu(II)-N intermediate 15 with the strong nucleophilicity of carbon radical 7, as well as the matching of the nucleophilic carbon radical with the electrophilic nitrogen radical.

Conclusion
A stepwise coupling mechanism, where a metal center is able to successively stabilize two radical species, has been proposed and proven to be probable for copper-catalyzed C-N radical-radical cross-coupling reaction. The catalytic cycle starts with the coordination of the nitrogen radical to a Cu(I) complex, which is formed by the reduction of Cu(acac) 2 through a MECP, generating an active Cu(II)-N β -diketonate intermediate. This Cu(II)-N species preferentially combines with a carbon radical and forms a Cu(III) complex through another MECP. A subsequent two-electron transfer/reductive elimination process constructs the C-N bond. The concerted coupling pathway, in which the formation of a C-N bond and cleavage of a Cu(II)-N bond occurs simultaneously by the nucleophilic addition of a carbon radical to the nitrogen in a Cu(II)-N species, has been demonstrated to be unfavorable. Because both the Mulliken atomic spin density distribution and FMO analysis on this active Cu(II)-N species have shown that the Cu site is more reactive than the N site, the carbon radical tends to react with the metal center rather than nitrogen moiety.
Moreover, the calculations of global electrophilicity ω° and nucleophilicity N° for the carbon radical, the nitrogen radical, and the Cu(II)-N β -diketonate intermediate suggest that the carbon radical is a strong nucleophile while the nitrogen radical and the Cu(II)-N β -diketonate intermediate are strong electrophiles. The matching of the electrophilicity of the Cu(II)-N intermediate with the strong nucleophilicity of the carbon radical makes it easier for the combination of Cu(II) with the carbon radical and the subsequent C-N bond formation. Meanwhile, the conflict of the Cu(II)-N intermediate with the electrophilic nitrogen radical results in a higher energy barrier for N-N radical-radical homo-coupling, which uncovers the principle behind the cross-coupling selectivity. We believe this study provides a practical theoretical guide for the design of transition metal-catalyzed radical-radical cross-coupling. On the basis of electrophilicity and nucleophilicity of free radicals, diverse radical-radical cross-coupling could be achieved by the combination of a suitable transition metal with radical species.