The Activating Effect of Strong Acid for Pd-Catalyzed Directed C–H Activation by Concerted Metalation-Deprotonation Mechanism

A computational study on the origin of the activating effect for Pd-catalyzed directed C–H activation by the concerted metalation-deprotonation (CMD) mechanism is conducted. DFT calculations indicate that strong acids can make Pd catalysts coordinate with directing groups (DGs) of the substrates more strongly and lower the C–H activation energy barrier. For the CMD mechanism, the electrophilicity of the Pd center and the basicity of the corresponding acid ligand for deprotonating the C–H bond are vital to the overall C–H activation energy barrier. Furthermore, this rule might disclose the role of some additives for C–H activation.


Results and Discussion
Since C-H activation is usually involved in the rate-determining step (RDS),  we hypothesized the relative free energy of transition states of C-H cleavage (ΔGTS ≠ ) can determine the reactivity. The CMD mechanism was chosen for C-H activation, which usually has the lowest barrier among the frequently proposed mechanisms [57,58]. The transition state for the SEAr mechanism could not be located (see Figure S1, Supplementary Materials). Five substrates with different DGs were chosen; these substrates have previ- The activating effect of a strong acid on Pd(II)-Catalyzed directed C-H activation has been known for a long time. Many kinds of C-H functionalization can be promoted by TFA or TfOH, such as carboxylation, [41] olefination, [42] arylation, [43,44] fluorination, [45] carbonylation, [46] trifluoromethylation, [47] amidation, [48] and oxygenation [49,50]. However, current understanding of the nature of strong acid-assisted C-H activation is still limited [51,52]. Fujiwara proposed that strong acid as a solvent facilitates the generation of highly cationic species([PdX] + ) through ligand exchange (Scheme 3), which are very electrophilic. Cyclopalladium intermediates can be formed through the electrophilic aromatic substitution (SEAr) of the C-H bond [53]. Other researchers have had a similar opinion to Fujiwara regarding the activating effect of strong acid [41][42][43][44][45][46][47][48][49][50].

Results and Discussion
Since C-H activation is usually involved in the rate-determining step (RDS),  we hypothesized the relative free energy of transition states of C-H cleavage (ΔGTS ≠ ) can determine the reactivity. The CMD mechanism was chosen for C-H activation, which usually has the lowest barrier among the frequently proposed mechanisms [57,58]. The transition state for the SEAr mechanism could not be located (see Figure S1, Supplementary Materials). Five substrates with different DGs were chosen; these substrates have previ- The activating effect of a strong acid on Pd(II)-Catalyzed directed C-H activation has been known for a long time. Many kinds of C-H functionalization can be promoted by TFA or TfOH, such as carboxylation, [41] olefination, [42] arylation, [43,44] fluorination, [45] carbonylation, [46] trifluoromethylation, [47] amidation, [48] and oxygenation [49,50]. However, current understanding of the nature of strong acid-assisted C-H activation is still limited [51,52]. Fujiwara proposed that strong acid as a solvent facilitates the generation of highly cationic species([PdX] + ) through ligand exchange (Scheme 3), which are very electrophilic. Cyclopalladium intermediates can be formed through the electrophilic aromatic substitution (SEAr) of the C-H bond [53]. Other researchers have had a similar opinion to Fujiwara regarding the activating effect of strong acid [41][42][43][44][45][46][47][48][49][50].

Results and Discussion
Since C-H activation is usually involved in the rate-determining step (RDS),  we hypothesized the relative free energy of transition states of C-H cleavage (ΔGTS ≠ ) can determine the reactivity. The CMD mechanism was chosen for C-H activation, which usually has the lowest barrier among the frequently proposed mechanisms [57,58]. The transition state for the SEAr mechanism could not be located (see Figure S1, Supplementary Materials). Five substrates with different DGs were chosen; these substrates have previously been studied by experiments [38][39][40]49]. Trimeric [Pd(OAc)2]3 was chosen as the reference point of DFT calculations [67][68][69]. X-ray crystallography has provided evidence Scheme 3. Ligand exchange process.

Scheme 4.
The SEAr and CMD mechanism for Pd−catalyzed directed C−H activation.

Results and Discussion
Since C-H activation is usually involved in the rate-determining step (RDS),  we hypothesized the relative free energy of transition states of C-H cleavage (ΔGTS ≠ ) can determine the reactivity. The CMD mechanism was chosen for C-H activation, which usually has the lowest barrier among the frequently proposed mechanisms [57,58]. The transition state for the SEAr mechanism could not be located (see Figure S1, Supplementary Materials). Five substrates with different DGs were chosen; these substrates have previously been studied by experiments [38][39][40]49]. Trimeric [Pd(OAc)2]3 was chosen as the reference point of DFT calculations [67][68][69]. X-ray crystallography has provided evidence Scheme 4. The S E Ar and CMD mechanism for Pd-catalyzed directed C-H activation.

Results and Discussion
Since C-H activation is usually involved in the rate-determining step (RDS),  we hypothesized the relative free energy of transition states of C-H cleavage (∆G TS = ) can determine the reactivity. The CMD mechanism was chosen for C-H activation, which usually has the lowest barrier among the frequently proposed mechanisms [57,58]. The transition state for the S E Ar mechanism could not be located (see Figure S1, Supplementary Materials). Five substrates with different DGs were chosen; these substrates have previously been studied by experiments [38][39][40]49]. Trimeric [Pd(OAc) 2 ] 3 was chosen as the reference point of DFT calculations [67][68][69]. X-ray crystallography has provided evidence that when a strong acid such as TFA or TfOH is used, the OAc − in the palladium acetate can be exchanged with TFA − or OTf − to form Pd(TFA) 2 or Pd(OTf) 2 [48,[70][71][72]. As shown in Figure 1, for all of the five substrates, the ∆G TS = using three different Pd catalysts is in the same order: The order of reactivity is consistent with the experimental results, [38][39][40]73,74] indicating our DFT calculation is reliable.
Next, energy decomposition strategy was used to explore the origin of the activating effect for directed C-H activation by strong acid [63,[75][76][77][78]. As shown in Scheme 5, ΔGTS ≠ can be decomposed into two parts: ΔG1 and ΔG2 ≠ . ΔG1 is the reaction energy caused by the coordination between the DG and the Pd catalyst. ΔG2 ≠ represents the energy needed to proceed with the C-H activation from int1. This strategy can reflect how the three different Pd catalysts influence ΔG1 and ΔG2 ≠ , respectively.  Figure 2b). The order of ΔG2 ≠ is different from that of ΔG1, and the C-H activation energy barrier of Pd(TFA)2 is the lowest. It was generally believed that a more electrophilic Pd catalyst would result in a lower barrier for the C-H activation step in the past [41][42][43][44][45][46][47][48][49][50]. However, our results do not support this belief: the electrophilicity of Pd(OTf)2 is strongest, but its Next, energy decomposition strategy was used to explore the origin of the activating effect for directed C-H activation by strong acid [63,[75][76][77][78]. As shown in Scheme 5, ∆G TS = can be decomposed into two parts: ∆G 1 and ∆G 2 = . ∆G 1 is the reaction energy caused by the coordination between the DG and the Pd catalyst. ∆G 2 = represents the energy needed to proceed with the C-H activation from int1. This strategy can reflect how the three different Pd catalysts influence ∆G 1 and ∆G 2 = , respectively.
Next, energy decomposition strategy was used to explore the origin of the activating effect for directed C-H activation by strong acid [63,[75][76][77][78]. As shown in Scheme 5, ΔGTS ≠ can be decomposed into two parts: ΔG1 and ΔG2 ≠ . ΔG1 is the reaction energy caused by the coordination between the DG and the Pd catalyst. ΔG2 ≠ represents the energy needed to proceed with the C-H activation from int1. This strategy can reflect how the three different Pd catalysts influence ΔG1 and ΔG2 ≠ , respectively.  Figure 2b). The order of ΔG2 ≠ is different from that of ΔG1, and the C-H activation energy barrier of Pd(TFA)2 is the lowest. It was generally believed that a more electrophilic Pd catalyst would result in a lower barrier for the C-H activation step in the past [41][42][43][44][45][46][47][48][49][50]. However, our results do not support this belief: the electrophilicity of Pd(OTf)2 is strongest, but its For all of the five substrates, the order of ∆G 1 using the three different Pd catalysts can be summarized as ∆G 1 [Pd(OTf) 2 ] < ∆G 1 [Pd(TFA) 2 ] < ∆G 1 [Pd(OAc) 2 ] (see Figure 2a), which is in the reverse order of electrophilicity of the Pd catalysts: Pd(OTf) 2 > Pd(TFA) 2 > Pd(OAc) 2 [48]. For ∆G 1 , the conclusion can be drawn that the more electrophilic Pd catalyst results in better coordination with DGs. For ∆G 2 = , all of the five substrates have the consistent order: Figure 2b). The order of ∆G 2 = is different from that of ∆G 1 , and the C-H activation energy barrier of Pd(TFA) 2 is the lowest. It was generally believed that a more electrophilic Pd catalyst would result in a lower barrier for the C-H activation step in the past [41][42][43][44][45][46][47][48][49][50]. However, our results do not support this belief: the electrophilicity of Pd(OTf) 2 is strongest, but its C-H activation energy barrier is not the lowest. Therefore, the reason why the C-H activation energy barrier of Pd(TFA) 2 is the lowest needs further study. C-H activation energy barrier is not the lowest. Therefore, the reason why the C-H activation energy barrier of Pd(TFA)2 is the lowest needs further study. Inspection of the TS by the CMD mechanism demonstrated that ΔG2 ≠ is related to the metal center's electrophilicity and the basicity of the acid ligand (Scheme 6a). To investigate the influence of electrophilicity and basicity on ΔG2 ≠ separately, an intermolecular model was built to decompose the effect of the two factors (Scheme 6b).  Figure 3, sub5 was chosen as an example for the intermolecular model study. In each row, the Pd catalyst in the three TSs is the same, but with three different external acid ligands, i.e., OAc − , TFA − and OTf − . From each row, we can see how the basicity of acid ligands influences ΔG2 ≠ . In each column, the external acid ligand in the three TSs is the same, but with three different Pd catalysts, i.e., Pd(OAc)2, Pd(TFA)2, Pd(OTf)2. Inspection of the TS by the CMD mechanism demonstrated that ∆G 2 = is related to the metal center's electrophilicity and the basicity of the acid ligand (Scheme 6a). To investigate the influence of electrophilicity and basicity on ∆G 2 = separately, an intermolecular model was built to decompose the effect of the two factors (Scheme 6b). C-H activation energy barrier is not the lowest. Therefore, the reason why the C-H activation energy barrier of Pd(TFA)2 is the lowest needs further study. Inspection of the TS by the CMD mechanism demonstrated that ΔG2 ≠ is related to the metal center's electrophilicity and the basicity of the acid ligand (Scheme 6a). To investigate the influence of electrophilicity and basicity on ΔG2 ≠ separately, an intermolecular model was built to decompose the effect of the two factors (Scheme 6b).  Figure 3, sub5 was chosen as an example for the intermolecular model study. In each row, the Pd catalyst in the three TSs is the same, but with three different external acid ligands, i.e., OAc − , TFA − and OTf − . From each row, we can see how the basicity of acid ligands influences ΔG2 ≠ . In each column, the external acid ligand in the three TSs is the same, but with three different Pd catalysts, i.e., Pd(OAc)2, Pd(TFA)2, Pd(OTf)2.  Figure 3, sub5 was chosen as an example for the intermolecular model study. In each row, the Pd catalyst in the three TSs is the same, but with three different external acid ligands, i.e., OAc − , TFA − and OTf − . From each row, we can see how the basicity of acid ligands influences ∆G 2 = . In each column, the external acid ligand in the three TSs is the same, but with three different Pd catalysts, i.e., Pd(OAc) 2 , Pd(TFA) 2 , Pd(OTf) 2 . From each column, we can see how electrophilicity of the Pd catalysts influences ∆G 2 = . The three diagonal transition states, which have the same external acid ligand and the ligand of Pd catalysts, are most similar to our intramolecular mechanism. For each row, the C-H activation energy barrier of the intermolecular model decreases with increasing basicity of the external acid ligand. The Pd(X) 2 _OAc transition states have the lowest energy barrier. The energy differences between the OAc − and TFA − ligands are about 4.6 and 6.3 kcal/mol, and the similar gaps between the TFA − and OTf − ligands are about 5.6 and 6.8 kcal/mol. For each column, the C-H activation energy barrier of the intermolecular model decreases with the increasing electrophilicity of the Pd catalyst, and the Pd(OTf) 2 _X transition states have the lowest energy barrier. The energy difference between the Pd(OAc) 2 and Pd(TFA) 2 catalysts is about 13.9~15.8 kcal/mol, much larger than the gap of 2.1~3.1 kcal/mol between the Pd(TFA) 2 and Pd(OTf) 2 catalysts. Therefore, the Pd(OTf) 2 _OAc transition state with the strongest basicity of the OAc − ligand and the strongest electrophilicity of the Pd(OTf) 2 catalyst has the lowest energy barrier among the nine intermolecular models.

As shown in
However, for the three diagonal transition states with the same external acid ligand and ligand of Pd catalysts, electrophilicity and basicity show an opposite trend. For example, although the electrophilicity of the metal center in Pd(OTf) 2 is the strongest, the basicity of the acid ligand (OTf − ) is the weakest. The Pd(TFA) 2 _TFA transition state has the lowest energy barrier considering the influence of the external acid ligand's basicity and the Pd catalyst's electrophilicity, consistent with the lowest C-H activation energy barrier of Pd(TFA) 2 in the intramolecular CMD process. According to the above discussion, it can be concluded that for the CMD mechanism, the electrophilicity of Pd catalysts and the basicity of acid ligands are critical to C-H activation.
Molecules 2021, 26, x 5 of 9 From each column, we can see how electrophilicity of the Pd catalysts influences ΔG2 ≠ . The three diagonal transition states, which have the same external acid ligand and the ligand of Pd catalysts, are most similar to our intramolecular mechanism. For each row, the C-H activation energy barrier of the intermolecular model decreases with increasing basicity of the external acid ligand. The Pd(X)2_OAc transition states have the lowest energy barrier. The energy differences between the OAc − and TFA − ligands are about 4.6 and 6.3 kcal/mol, and the similar gaps between the TFA − and OTf − ligands are about 5.6 and 6.8 kcal/mol. For each column, the C-H activation energy barrier of the intermolecular model decreases with the increasing electrophilicity of the Pd catalyst, and the Pd(OTf)2_X transition states have the lowest energy barrier. The energy difference between the Pd(OAc)2 and Pd(TFA)2 catalysts is about 13.9~15.8 kcal/mol, much larger than the gap of 2.1~3.1 kcal/mol between the Pd(TFA)2 and Pd(OTf)2 catalysts. Therefore, the Pd(OTf)2_OAc transition state with the strongest basicity of the OAc − ligand and the strongest electrophilicity of the Pd(OTf)2 catalyst has the lowest energy barrier among the nine intermolecular models.
However, for the three diagonal transition states with the same external acid ligand and ligand of Pd catalysts, electrophilicity and basicity show an opposite trend. For example, although the electrophilicity of the metal center in Pd(OTf)2 is the strongest, the basicity of the acid ligand (OTf − ) is the weakest. The Pd(TFA)2_TFA transition state has the lowest energy barrier considering the influence of the external acid ligand's basicity and the Pd catalyst's electrophilicity, consistent with the lowest C-H activation energy barrier of Pd(TFA)2 in the intramolecular CMD process. According to the above discussion, it can be concluded that for the CMD mechanism, the electrophilicity of Pd catalysts and the basicity of acid ligands are critical to C-H activation.  Inspired by the lowest activation energy of Pd(OTf) 2 _OAc, we hypothesized that C-H activation via an intermolecular CMD mechanism with a strong electrophilic Pd catalyst and strong external base may be favored, and some experiments support our hypothesis. In Yu's work, the combination of Pd(OTf) 2 and N-Methyl-2-pyrrolidone (NMP, a stronger base than TfO − ) is crucial for C-H fluorination [45]. Our calculations indicate that the NMP-assistant intermolecular C-H activation process is about 9 kcal/mol lower in energy than the intramolecular C-H deprotonation by TfO − (see Figure 4a). Buchwald and coworkers found that the combination of Pd(OAc) 2 /TFA and DMSO can improve the yield of C-H arylation [44]. They proposed that palladium black formation could be slowed by the addition of DMSO (10 mol%). Our calculations indicate that DMSO, a stronger base than TFA − , can also promote intermolecular deprotonation (see Figure 4b). As shown in Figure 4 and Figure S3 (Supplementary Materials), our calculations demonstrated that the intermolecular mechanism is more favorable than the intramolecular mechanism for the above two studies. Our findings might disclose the role of some additives for C-H functionalization.
Inspired by the lowest activation energy of Pd(OTf)2_OAc, we hypothesized that C-H activation via an intermolecular CMD mechanism with a strong electrophilic Pd catalyst and strong external base may be favored, and some experiments support our hypothesis. In Yu's work, the combination of Pd(OTf)2 and N-Methyl-2-pyrrolidone (NMP, a stronger base than TfO − ) is crucial for C-H fluorination [45]. Our calculations indicate that the NMP-assistant intermolecular C-H activation process is about 9 kcal/mol lower in energy than the intramolecular C-H deprotonation by TfO − (see Figure 4a). Buchwald and coworkers found that the combination of Pd(OAc)2/TFA and DMSO can improve the yield of C-H arylation. [44] They proposed that palladium black formation could be slowed by the addition of DMSO (10 mol%). Our calculations indicate that DMSO, a stronger base than TFA − , can also promote intermolecular deprotonation (see Figure 4b). As shown in Figure 4 and Figure S3 (Supplementary Materials), our calculations demonstrated that the intermolecular mechanism is more favorable than the intramolecular mechanism for the above two studies. Our findings might disclose the role of some additives for C-H functionalization.

Conclusions
In summary, the activating effect of strong acid for Pd(II)-catalyzed directed C-H functionalization was investigated with DFT calculations. Our results were consistent with previous experimental results and disclosed that the origin of the activating effect by strong acid comes from two parts: ΔG1 (coordination energy between the DG and the Pd catalyst) and ΔG2 ≠ (C-H activation energy). For the CMD mechanism, the electrophilicity of the Pd center and the basicity of the related acid ligand for deprotonation of the C-H bond is vital to the overall C-H activation energy barrier. This rule can be used to explain the role of some additives for C-H activation. It is hoped that our study could be used to improve the reactivity of some C-H functionalization reactions. Figure S1: The scan of C-H bond of cationic species ([PdOAc] + ), Figure  S2: The relative free energy of different intermediates of sub2, Figure S3: The relative free energy barrier of the intermolecular model.

Conclusions
In summary, the activating effect of strong acid for Pd(II)-catalyzed directed C-H functionalization was investigated with DFT calculations. Our results were consistent with previous experimental results and disclosed that the origin of the activating effect by strong acid comes from two parts: ∆G 1 (coordination energy between the DG and the Pd catalyst) and ∆G 2 = (C-H activation energy). For the CMD mechanism, the electrophilicity of the Pd center and the basicity of the related acid ligand for deprotonation of the C-H bond is vital to the overall C-H activation energy barrier. This rule can be used to explain the role of some additives for C-H activation. It is hoped that our study could be used to improve the reactivity of some C-H functionalization reactions.
Supplementary Materials: Figure S1: The scan of C-H bond of cationic species ([PdOAc] + ), Figure S2: The relative free energy of different intermediates of sub2, Figure S3: The relative free energy barrier of the intermolecular model.

Conflicts of Interest:
The authors declare no conflict of interest.
Sample Availability: Samples of the compounds are not available from the authors.