Rapid and Accurate Estimation of Activation Free Energy in Hydrogen Atom Transfer-Based C–H Activation Reactions: From Empirical Model to Artificial Neural Networks

A well-performing machine learning (ML) model is obtained by using proper descriptors and artificial neural network (ANN) algorithms, which can quickly and accurately predict activation free energy in hydrogen atom transfer (HAT)-based sp3 C–H activation. Density functional theory calculations (UωB97X-D) are used to establish the reaction system data sets of methoxyl (CH3O·), trifluoroethoxyl (CF3CH2O·), tert-butoxyl (tBuO·), and cumyloxyl (CumO·) radicals. The simplified Roberts’ equation proposed in our recent study works here [R2 = 0.84, mean absolute error (MAE) = 0.85 kcal/mol]. Its performance is comparable with univariate Mulliken-type electronegativity (χ) with the ANN model. The ANN model with bond dissociation free energy, χ, α-unsaturation, and Nolan buried volume (%Vburied) successively improves R2 and MAE to 0.93 and 0.54 kcal/mol, respectively. It reproduces the test sets of trichloroethoxyl (CCl3CH2O·) with R2 = 0.87 and MAE = 0.89 kcal/mol and accurately predicts the relative experimental barrier of the HAT reactions with CumO· and the site selectivity of CH3O·.


■ INTRODUCTION
With the increasing demand of sustainable development, use of the sp 3 C−H bond function in chemical synthesis has received great attention because it can provide a practical solution to upgrade abundant hydrocarbon raw materials into valuable products. 1−11 The hydrogen atom transfer (HAT)-based method provides an effective strategy for hydrocarbon activation and has been widely used. 2,12−20 However, the prediction of reactivity is still a challenge. The reactivity is closely related to the C−H bond strength and the choice of Hextracting radicals. 21−32 Understanding the reaction mechanisms and predicting the reactivity should assist a more reasonable and effective design of C−H activation reactions. 33 −38 The activation free energy is a key parameter for the mechanism, reaction rate, and selectivity of chemical reactions. The prediction of the activation free energy helps to achieve a comprehensive understanding of chemical reactions and to construct chemical reaction diagrams, thus accelerating catalyst design. However, the activation free energy estimation is timeconsuming, both experimentally and computationally, leading to a bottleneck effect on the rapid catalyst design and characterization.
In experimental work, the reaction rate constant is determined by running multiple experiments at different temperatures, and then the activation free energy can be obtained by application of the Eyring equation. In computational science, quantum chemistry methods can evaluate the activation free energy by identifying the transition states along a given reaction path. It is inevitable to spend a lot of computational cost to deal with complex chemical processes involving many reactions. 39,40 In this situation, it is very valuable to achieve rapid and accurate prediction of activation free energies in C−H activation reactions.
As an empirical model, the Bell−Evans−Polanyi (BEP) correlation is widely used to quickly estimate the activation energy. 41 It correlates the activation energy with reaction energy through ΔE ‡ = γΔE r × n + ξ. Tedder found the existence of a BEP correlation between the rate constant and the C−H bond strength for H-abstraction reactions from alkanes by various radicals (CH 3 ·, CF 3 ·, Br·, etc.). 42 44 However, as the organic system becomes more and more complex, people cannot observe the simple linear relationship between the activation energy and the bond energy. 45−48 In addition to bond energy or reaction energy, Roberts pointed out that polar effects, steric effects, and unsaturation should be considered when discussing various HAT reactions in the liquid and gas phases. In addition, his study has emphasized and quantified the polar effects. 49 Tedder proposed that the polar effects in the HAT of CH 3 · and CF 3 · will cause a deviation from the BEP correlation. 42 Our previous study used DFT calculations to explore the selectivity of dimethyldioxirane (DMDO) in the C−H oxidation of various compounds, and it revealed a different BEP correlation between the C−H bonds in saturated and unsaturated compounds. 46 This bimodal BEP correlation was also found in HAT from sp 3 C−H bonds to the cumyloxyl radical by Bietti et al. All these precedents urged us to think about the influence of nonlinear characteristics and factors other than thermodynamics in HAT.
Multiple linear regression (MLR) is one strategy to consider the effect of several variables on activation energy. Roberts and Steel proposed an improved form of the Evans−Polanyi equation (Roberts' equation) involving reaction thermodynamics, radical electronegativity differences, and conjugate delocalization of the unpaired electron and structural factors, which work well for a variety of HAT reactions with different H-extracting radicals. 49 Our recent work simplified Roberts' equation with reaction energy, radical electronegativity differences, and unsaturation and led to good results for the HAT reactions of 26 sp 3 C−H bonds by alkoxyl radicals, with R 2 = 0.89 and mean absolute error (MAE) and root mean square error (RMSE) values of 0.9 and 1.1 kcal/mol, respectively (compared with the DFT calculations). 50 On the other hand, the significant advancement of machine learning (ML) technology provides a new strategy for solving various chemical problems. The artificial neural network (ANN), as one of the most popular ML methods, is a datadriven adaptive method. Due to its parallel structure and the ability to simulate arbitrary functions, it can be regarded as a kind of multiple nonlinear regression that can handle complex nonlinear problems. 51 By establishing the potential correlations from the data, the ANN can solve problems that involve unknown relationships. Nowadays, the ANN is actively used in various chemical fields, such as quantum chemistry, virtual screening of molecular materials, and synthetic pathways of chemical substances. 52,53 While our study was ongoing, Hong et al. have provided an ML approach for reactivity prediction in photoredox-mediated HAT catalysis. 54 In the present study, we aim to (1) apply the ANN model to the HAT-based sp 3 C−H activation to achieve the goal of rapid and accurate prediction of the activation free energy, (2) assess the performance of the simplified Roberts' equation proposed in our recent study, 50 and (3) compare the performance between MLR and ANN with the same physical variables. The substrate C−H bonds have been expanded ( Figure 1). We added a series of hydrogen donor substrates to build the model on the basis of our previous work 46 [including allylic, benzylic, formylic, and α-heteroatom (O, N, S) group]. The activated C−H bond is highlighted in red. In addition to methoxyl (CH 3 O·), trifluoroethoxyl (CF 3 CH 2 O·), and tertbutoxy (tBuO·), cumyloxyl (CumO·) was also used as the Hextracting radical. Alkoxyl radicals are easily available and can be highly efficient for the abstraction of H atoms. They are powerful tools for the catalytic activation of hydrocarbons under mild reaction conditions. Zuo et al. achieved the C−H functionalization of short-chain alkanes (methane, ethane, etc.) utilizing cerium salts and alcohols under mild reaction conditions with CH 3 O·, CCl 3 CH 2 O·, and CF 3 CH 2 O· being used as the H-extracting radicals. 55 Bietti carried out systematic kinetic studies of HAT reactions by CumO·. 48 These experimental data are helpful to verify the theoretical model. ■ METHOD Database. We established data sets for the alkane sp 3 C−H activation by various alkoxyl radicals: CH 3 O·, CF 3 CH 2 O·, tBuO·, and CumO· (Tables S1−S4). The data sets were used to build the model. The C−Hs listed in Figure 1 were studied. The substrates and H-extracting radicals were selected to  consider polar effects, steric effects, and α-unsaturation effects. Figure 2 shows an example of the HAT step by the alkoxyl radical. 55 All calculations were carried out with Gaussian 16. 56 The geometries of minima and transition states were optimized using UωB97X-D 57 with the 6-31G (d) 58 basis set in the gas phase. Vibrational frequency analyses confirmed the nature of the structures as either local energy minima or first-order saddle points (transition states). Single point energies with a more extensive basis set were obtained with UωB97X-D/6-311++G (d,p) 59 on the optimized geometries. The solvent effect of CH 3 CN on the reaction was estimated by using the SMD model. 60 Figure 3 shows an example of the data sets. The "sub" and "rad" qualifiers represent the descriptors of the substrate and H-extracting radical, respectively. The bond dissociation free energies (BDFEs) of the substrate C−H and alkoxyl radical O−H were both taken into consideration. The polar effect was    quantified by the Mulliken-type electronegativity. The Mulliken-type electronegativity of the X· radical (χ x ) is defined in eq 1, where IE and EA are the X· vertical ionization energy and vertical electron affinity, respectively.
Δχ AB (Δχ AB = χ A − χ B , A−H + B· → A· + BH) reflects the electronegativity difference between the substrate and Hextracting radical. The unsaturation effect refers to whether an unsaturated group adjacent to the investigated C−H is present. The "0" and "1" qualifiers are used for "saturated" C−H and "unsaturated" C−H bonds, respectively. The Nolan buried volume (%V buried ) 61 is used to consider the steric effect (see Section S8 for the detailed calculation). ANN Model. Figure 4 is an overview of the ANN model. Activation barriers and descriptors were all obtained by DFT methods. The ANN model was trained on the basis of appropriate descriptors.
The back-propagation ANN model 62,63 was applied to predict the activation free energy. Through K-fold crossvalidation (k = 3), 64 the topology of the ANN model was finally determined with three hidden neurons and three hidden layers (see Table 1). The activation function was a tanh function ( = + h x tan ( ) 1 2 1 x 2 ) that allows the network to map any nonlinear process. The second-order optimization method was an implementation of the Levenberg−Marquardt (LM) algorithm. 65
Empirical Model. In HAT, the BEP correlation can be expressed as shown in eq 2, where ΔG ‡ is the activation free energy, ΔG r×n is the reaction free energy, BDFE sub and BDFE rad are the BDFE of the substrate C−H and alkoxyl radical O−H, respectively, and γ and ξ are obtained from linear regression analysis.
r n sub rad (2) Figure 5 shows the linear relationship of ΔG ‡ vs ΔG r×n for the reaction data sets of 60 sp 3 C−Hs (Figure 1) with four alkoxyl radicals (CH 3 O·, CF 3 CH 2 O·, tBuO·, and CumO·). The traditional BEP correlation obviously does not work here. Although the correlation is rough, the "saturated" and "unsaturated" C−Hs tend to be divided into two categories ( Figure 5) as found in our previous study. 46 The effects of the unsaturation and of the radical nature are responsible for the inadequacy of the BEP correlation. Figure 6a−d shows the scatter diagram of ΔG ‡ vs ΔG r×n for each alkoxyl radical. In comparison with CH 3 O·, the higher electronegativity CF 3 CH 2 O· radical is more reactive and yields a worse linear correlation. The steric effect also influences the BEP correlation, as is evident from a comparison of the differences between the ΔG ‡ vs ΔG r×n scatter plots for CH 3 O·, tBuO·, and CumO·. Due to the influence of different Hextracting radicals, the BEP correlation for the whole series is poor, as shown in Figure 5. Figure 7 shows the scatter diagram of ΔG ‡ vs Δχ 2 (Δχ = χ _sub − χ _rad ). This correlation is better than that of ΔG ‡ vs ΔG r×n , and the unsaturation effect is less marked, to the point that the "saturated" and "unsaturated" C−Hs can be classified into one category.
The results of Figure 7 imply that Δχ 2 plays a more important role than ΔG r×n in predicting the activation free energies with univariate linear regression. The importance of Δχ 2 is further proved by the random forest (RF) algorithm. 68 RF can provide a measure of the feature importance based on the mean decrease in impurity (MDI), and the impurity is calculated by the split criterion of the decision trees (entropy). 68 Figure 8 shows the feature importance of the unsaturation effect, Δχ 2 , and ΔG r×n analyzed by the RF algorithm. As shown in Figure 8, Δχ 2 plays the most important role, followed by ΔG r×n and the least important is the effect of unsaturation. It is worth mentioning, however, that the feature importance analysis based on MDI is biased to high cardinality features (typically numerical features, e.g., Δχ 2 ) and probably underestimates low cardinality features (binary features, e.g., the unsaturation effect). 69 Therefore, the impact of descriptors needs to be further analyzed. Though Δχ 2 shows a good correlation with ΔG ‡ , this is insufficient to accurately predict the activation free energy, especially using a simple linear relationship.
Then, the simplified Roberts' relationship developed in our recent work 50 was applied (eq 3).
This expression contains the reaction energy (ΔG r×n , ΔG r×n = BDFE _sub − BDFE _rad ), the unsaturation term (d), and the Mulliken-type electronegativity difference (Δχ, Δχ = χ _sub − χ _rad ) between the substrate and H-extracting radical. From an MLR analysis of our data sets, the coefficients for this simplified Roberts' relationship are shown in eq 4.
ANN Model. The ANN model was trained on the reaction data sets of 60 sp 3 C−Hs (Figure 1) with four alkoxyl radicals (CH 3 O·, CF 3 CH 2 O·, tBuO·, and CumO·) by using different descriptors. Figure 10a,b shows the activation free energies obtained by the ANN model (with only the BDFE and χ as descriptors, respectively) versus the DFT method. The BDFE can hardly be used to predict the activation free energy, as shown by R 2 = 0.62, MAE = 1.28, and RMSE = 1.62. The χ still works better than BDFE when used as the unique descriptor in the ANN model. This is reflected by R 2 = 0.85, MAE = 0.79, and RMSE = 1.03. It is worth noting that the performance of the single χ descriptor with the ANN model is comparable to the MLR of eq 4. Subsequently, we tried to add the descriptors. The combination of BDFE_sub, BDFE_rad, χ_sub, χ_rad, and α-unsaturation successively makes the R 2 improve to 0.92, accompanied by MAE = 0.60 and RMSE = 0.75, as shown in Figure 10c. After adding the %V buried , the ANN model performs best (R 2 = 0.93, MAE = 0.54, and RMSE = 0.68), see Figure 10d.
In order to further evaluate the predictive ability of the model, we used the reaction data of CCl 3 CH 2 O· as the test set (Table S5). The R 2 and MAE values obtained from the ANN model without %V buried are 0.80 and 1.10 kcal/mol, showing that the ANN model trained on the data set composed of CH 3 O·, CF 3 CH 2 O·, tBuO·, and CumO· can map the influence of the polarity changes of CCl 3 CH 2 O· (Figure 11a). By adding the %V buried term, the R 2 and MAE values improve to 0.87 and 0.79 kcal/mol, respectively, showing the importance of the steric effect (Figure 11b).
Furthermore, we predicted the experimental results by using the trained model. According to Bietti's research on the HAT reaction of CumO·, we collected another 45 sp 3 C−Hs from his study and used the ANN model trained on the DFT computational data to make predictions. To eliminate the final prediction bias caused by the errors of the DFT calculation and the experiment, the relative activation free energy was used here. Rate constants and relative activation free energies are provided in the Supporting Information (Table S6). Figure 12 compares the activation free energies predicted by the ANN model with the relative activation free energies of Bietti's experiments. The prediction results show that the ANN model containing %V buried can better map the influence of the CumO· steric effects and make more accurate predictions (R 2 = 0.70, MAE = 0.65, and RMSE = 0.80).
We also tried to predict the results of the CH 3 O· selectivity from Zuo's reports (Table S7). 70 The BDFE, χ, αunsaturation, and %V buried descriptors were used. Figure 13 includes the relative ratio of site selectivity and the activation free energies obtained by the ANN prediction and by the DFT calculation. The numbers marked in red indicate that the prediction error is over 2 kcal/mol, and the blue backgrounds indicate the main activation site predicted by the ANN model. Among the six substrates not included in the training set, 2,3dimethylbutane has been widely used as a standard substrate for evaluating selectivity in C−H bond functionalization. The α-tertiary carbon can be formed with good selectivity (ratio 97:3) when CH 3 O· was used as a HAT reagent. Comparing with the DFT-calculated and ANN-predicted activation free energies, the reaction site is the same. The tertiary C−H bond of adamantane can be functionalized and predicted as well. N-Hexane has three different types of C−H bonds in terms of steric hindrance and bond strength. In this case, CH 3 O· has high selectivity for the weaker methylene C−H bonds, and the  . DFT-computed vs predicted barriers using eq 4 for the reaction data sets of 60 sp 3 C−Hs (Figure 1) with four alkoxyl radicals (CH 3 O·, CF 3 CH2O·, tBuO·, and CumO·).

ACS Omega
http://pubs.acs.org/journal/acsodf Article predicted activation free energy at this site is also the lowest. In 2,4-dimethylpentane, CH 3 O· is used to obtain methine functionalization. Although the activation free energy predicted by the ANN model is lower, the selectivity is consistent with the experiment.

■ CONCLUSIONS
We have strived to achieve a rapid and accurate estimation of activation free energies in HAT-based C−H activation reactions with both an empirical method and the ANN model. First, we established a data set of 300 HAT reactions on the basis of DFT calculations. By simply analyzing the data set, we found that unsaturation effects are responsible for the poor performance of the BEP relationship, while the correlation between ΔG ‡ and Δχ 2 is better than that between ΔG ‡ and ΔG r×n . The simplified Roberts' equation proposed in our recent study also works here. Then, we used an ML method to establish a reactivity and selectivity prediction model based on appropriate descriptors. As a unique descriptor used in the ANN model, χ works better than the BDFE. Its performance is comparable with that of the simplified Roberts' equation. The introduction of %V buried can improve the generalization ability between different H-extracting radical and make more accurate predictions, which shows the  importance of steric effects. The authors declare no competing financial interest. The code for the ANN model, the csv file of data sets, and the cartesian coordinates of DFT-computed structures are freely available on GitHub. 71 The instructions on how to use the model are also provided.

■ ACKNOWLEDGMENTS
We are grateful to the Shanghai Sailing Program (No. 20YF1416000) for financial support of this research.