Theoretical Study for Evaluating and Discovering Organic Hydride Compounds as Potential Novel Methylation Reagents

Methylation reaction is a fundamental chemical reaction that plays an important role in the modification of drug molecules, DNA, as well as proteins. This work focuses on seeking potential novel methylation reagents through a systematic investigation of the thermodynamics and reactivity of methyl-substituted organic hydride radical cations (XH•+s). In this work, 45 classical and important XH•+s were designed to investigate the relationship between their structure and reactivity, to find excellent or potential methylation reagents. The Gibbs free energy and activation free energy of XH•+ to release the methyl radical in MeCN at 298.15 and 355 K are calculated with the density functional theory (DFT) method to quantitatively measure the reactivity of XH•+ as a methylation reagent in this work. The relationships between structures and reactivities on XH•+s as methylation reagents are well examined. Since we have calculated the Gibbs free energy and activation free energy of trifluoromethyl-substituted organic hydride compound radical cations (X′H•+) releasing trifluoromethyl radicals in MeCN with the DFT method in our previous work, accordingly, the relationship of thermodynamics and reactivity between X′H•+ releasing trifluoromethyl radical and XH•+ releasing methyl radical is discussed in detail. Excitingly, 4 XH•+s (1H•+, 3H•+∼4H•+, and 44H•+) are found to be excellent methyl radical reagents, while 9 XH•+s (5H•+, 6H•+, 9H•+, 10H•+, 12H•+, 13H•+, 15H•+, 43H•+, and 45H•+) are found to be potential methyl radical reagents in chemical synthesis. The molecular library and reactivity database of novel methylation reagents could be established for synthetic chemists to query and use. Our work may offer a theoretical basis and reference experience for screening different substituted organic hydride compounds (YRHs) as alkylation reagents.


INTRODUCTION
The introduction of the methyl group to drug molecules is helpful to improve their binding affinity, biological availability, and metabolic stability (called "magic methyl effect"), which greatly changes the pharmacological properties of bioactive molecules. 1−5 Methylation plays an important role in the modification of drug molecules, DNA, as well as proteins. 1−5 According to different reaction mechanisms, the methylation agents are divided into three classes, i.e., electrophilic methylation reagents, nucleophilic methylation reagents, and free radical methylation reagents. 6 At present, great progress has been made in the methylation reaction. 7−27 Many chemists have made outstanding contributions in this field, and a large number of new methyl reagents 10−16 and new methylation reactions have been developed, 17−27 especially electrocatalytic, 16,17 visible-light-induced, 9 or transition-metal-catalyzed 18−22 methylation, in recent years. In 2021, Dixon and co-workers published an important review about C−H methylation in chemical synthesis, which covered the various methylation reagents and diverse strategies employed to realize the selective installation of the C−Me bond in extensive chemical structures. 7 However, there still are challenges in the methylation process, including (1) developing milder, economic, and green methylation methods, and (2) achieving higher chemical selectivity as well as stereoselectivity. It is urgent and inspiring to develop novel and excellent methylation reagents to be used in various drug synthetic reactions or other chemical reactions.
Recently, various substituted organic hydride compounds, especially 4-substituted-Hantzsch esters, have been widely investigated as alkylation reagents in chemical reactions. 28−30 Therefore, we initiated a project to evaluate and reveal the reactivities of substituted organic hydride compounds as alkylation reagents in chemical reactions two years back. It is well known that, for a chemical reaction, Gibbs free energy (ΔG o ) is the thermodynamic driving force, which reflects whether the reaction can happen or not, while activation free energy (ΔG ≠ ) is an important kinetic parameter that reflects the reaction rate. 31 For substituted organic hydride compounds (XRH), XRH could be activated as XRH •+ by single-electron oxidants, photocatalysts, or electrochemical conditions, 28−31 and the key step is the elementary step of XRH •+ releasing R • , 31 so the Gibbs free energy [ΔG°R D (XRH •+ )] and the activation free energy [ΔG RD ≠ (XRH •+ )] of the XRH •+ releasing the R-radical could be used to quantitatively measure the reactivity of XRH as the alkylation reagent (RD is an abbreviation for radical-donating in this work).
In 2020, we investigated the essential factors that determine whether a 4-substituted organic hydride radical cation (XRH •+ ) is a great alkylation reagent and evaluated the reactivity of various XRH •+ s as alkylation agents (Scheme 1a). 31 In 2021, we further evaluated the antioxidant reactivities of XRH •+ s with different substituents (Scheme 1b), 32 and in 2022, we have calculated the Gibbs free energy [denoted as ΔG°R D (X′H •+ ) (for 298 K) and ΔG°′ RD (X′H •+ ) (for 355 K)] and the activation free energy [denoted as ΔG RD ≠ (X′H •+ ) (for 298 K) and ΔG ≠ ′ RD (X′H •+ ) (for 355 K)] of 47 trifluoromethyl-substituted organic hydride compound radical cations (X′H •+ ) releasing the trifluoromethyl radical in MeCN at 298. 15 and 355 K with the density functional theory (DFT) method (Scheme 1c). 33 Fifteen XH •+ s with a 1,4-dihydropyridine structure and three XH •+ s with a 3,4-dihydropyrimidin-2one structure are identified to be novel excellent and potential trifluoromethylation reagents, respectively, according to their reactivity data. 33 Inspired by Prof. Dixon's review and our previous work, we continued to focus on seeking potential novel methylation reagents through systematic investigation of the thermodynamics and reactivities of methyl-substituted organic hydride radical cations (XH •+ s) (Scheme 1d). Unlike trifluoromethylsubstituted 46H •+ and 47H •+ in our previous work, the transition states (TS) of methyl-substituted 46H •+ and 47H •+ could not be located. Therefore, in this work, 45 classical and important XH •+ s (Scheme 2) were selected to investigate the relationship between their structures and reactivities, including effects of heteroatoms, substituents, conjugation in structure, etc., to find potential novel methylation reagents. The Gibbs free energy and the activation free energy of XH •+ s to release the methyl radical in MeCN at 298.15−355 K are calculated with the DFT method in this work. The molecular library and the reactivity database of novel methylation reagents could be established for synthetic chemists for query and use.

RESULTS AND DISCUSSION
Quantum chemical calculations and wave-function analyses in this work were performed using Gaussian 16, 34 Figure  1a. It can be seen from Figure 1a  At the same time, the relationship between ΔG ≠ ′ RD (XH •+ ) and ΔG°′ RD (XH •+ ) is shown in Figure 1b. A certain linear correlation between ΔG ≠ ′ RD (XH •+ ) and ΔG°′ RD (XH •+ ) is also f o u n d w i t h t h e e q u a t i o n Δ G ≠ ′ R D ( X H • + ) = 0.895ΔG°′ RD (XH •+ ) + 16.434 (R 2 = 0.925, defined as eq 2), which can be used to predict the ΔG ≠ ′ RD (XH •+ ) value at 355 K when the ΔG°′ RD (XH •+ ) is available. If eq 1 is compared with eq 2, it can be found that the two activation free energy equations have almost exactly the same slope, while the intercept of eq 2 is larger than that of eq 1 by 1.85, which indicates that for two methyl radical transfer reactions with the same thermodynamic driving forces at 298.15 and 355 K, the ΔG ≠ ′ RD (XH •+ ) value at 355 K is 1.5 kcal/mol larger than the ΔG RD ≠ (XH •+ ) value at 298.15 K. Deeper reflecting on the activation free energy equations (eq 1), 0.899ΔG°R D (XH •+ ), is considered as the reaction driving force, but the intercept (very larger than 0) undoubtedly belongs to reaction resistance, so the activation free energy is the sum of both reaction driving force [0.899ΔG°R D (XH •+ )] and reaction resistance (intercept, because the intercept is a very large positive value to greatly reduce the thermodynamic driving force according to its definition in eq 1). The  Table 1, all 45 XH •+ s can be divided into three classes (see Figures 1 and 2) using ΔG°R D (XH •+ ) and ΔG RD ≠ (XH •+ ) values as the judgment criteria, which had been verified in our previous work. 33 Table 2. ΔG°′ RD (Table S1), which clearly show that they belong to excellent methyl radical reagents at 355 K in MeCN, which strongly supported the above deduction.  (Figure 1b). Taking the calculation accuracy into consideration, XH •+ s in class 2 can be used as potential methyl radical reagents by regulating various reaction solvents and raising the reaction temperature appropriately to achieve ΔG°′ RD (XH •+ ) values below 0.

Class 3: Not Methylation Reagents or Easily Synthesized Methyl-Substituted Organic Hydride
Compounds. XH •+ s with 5 kcal/mol <ΔG°R D (XH •+ ) and 18 kcal/mol <ΔG RD ≠ (XH •+ ) have the lowest reactivities, which cannot be used as methyl radical reagents in organic synthesis ( Figure 1). 33 If we want to make an attempt to increase the temperature making ΔG°R D (XH •+ ) < 0, the temperature should be extremely larger than 150°C [150°C (7H) ∼ 700°C (32H), Table 1], which is greatly beyond the boiling point of common solvents. Instead, since XH •+ s in class 3 have high ΔG°R D (XH •+ ) and ΔG RD ≠ (XH •+ ) values (indicating high thermodynamic and kinetic stabilities, respectively), XH •+ s in class 3 can be easily synthesized using excellent or potential methylation reagent XH •+ s in class 1, class 2, or other methylation reagents. Our work provides important basic calculation data and a guidance method to synthetize methylsubstituted organic hydride compounds as well.
The classification of methylation reagents including three classes, the corresponding judgment criteria, as well as the contained XH •+ s investigated in this work are clearly displayed in Table 3 for chemists to quickly select and use in organic synthesis or drug modification.
Through further comparison on the computed results at 355 K (   Table S2. As shown in Table S2, it is not difficult to find that ΔG RD ≠ (XH •+ ) (−0.42 kcal/mol ≤ ΔΔG ≠ ≤ 0.06 kcal/mol), ΔH RD ≠ (XH •+ ) (0.02 kcal/mol ≤ ΔΔH ≠ ≤ 0.15 kcal/mol), and Δ(TΔS ≠ ) (−0.03 kcal/mol ≤ Δ(TΔS ≠ ) ≤ 0.60 kcal/mol) almost do not change when the temperature increases from 298.15 to 355 K, which also imply that the structure changes between the initial state (IS) and the transition state (TS) at 298. 15    For the effects of the methyl group in different positions on XH •+ releasing methyl radicals, it is also found that the methyl groups at the 1-N-position of the 1,2-dihydro organic hydrides (Scheme 4d) do not have much effect as in the 1-N-position of 1,4-dihydropyridines (Scheme 4b). Maybe it is the position of the methyl substitution resulting in the interesting phenomenon. It is well known that the energy difference between the initial state (IS) and the final state (FS) determines the thermodynamic driving forces ΔG o , while the energy difference between the initial state (IS) and the transition state (TS) determines the activation free energy ΔG ≠ . Similar to 1,4dihydropyridines, the methyl substitution in the 1-N-position of the 1,2-dihydro organic hydrides should have made XH •+ worse methyl radical donors; however, the methyl substitution made XH have a higher energy in the initial state (G IS ) than that of the final state after releasing the methyl radical because of the large steric hindrance, so the thermodynamic driving force (ΔG o = G FS − G IS ) does not decrease too much compared with unmethylated 1,2-dihydro organic hydride. In addition, the large steric hindrance greatly promotes the release of the methyl radical in the transition state, so the activation free energy does not increase too much compared with unmethylated 1,2-dihydro organic hydride. Perhaps that is why the methyl groups at 1-N of the 1,2-dihydro organic hydrides do not have much effect as in the 1,4-dihydropyridines.
As one can see, the methyl substitution in different positions has different methyl effects, and the effect is quite complicated and coupled with the factor of the chemical structure, such as methyl substitution in 2 and 6 positions makes XHs better methylation reagents, methyl substitution in the N-position makes XHs worse methylation reagents, and normally methyl substitution in the N-position of 1,2-dihydro-structures makes XHs better methylation reagents. These conclusions are derived from the ΔG RD o (XH •+ ) and ΔG RD ≠ (XH •+ ) data; however, unfortunately, we could not find a qualitative and quantitative analysis on the interesting results. Without doubt, the methyl group plays key roles in the configuration and energy of the initial state (IS), the transition state (TS), and the final state (FS), resulting in thermodynamic and kinetic differences compared with unmethylated organic hydrides. It is true that heteroatom substitution has significant impacts on the reactivities. Compared with the N-atom in organic hydrides, despite the O-atom and the S-atom being electronrich atoms, their electron-donating abilities are far less than those of the N-atom, which lead to higher activation energies and lower thermodynamics driving forces. We consider that maybe it is the huge difference in the electron-donating abilities among N, O, and S atoms that cause the significant heteroatom effects on the reactivities.

Heteroatom Substitution Has Significant Impacts on Reactivities. 2.2.2.1. Heteroatom Substitution in Five-
. The electron-withdrawing group in the 3-position could greatly improve reactivities of XH •+ to release the methyl radical from thermodynamics and kinetics, but the substituent constants or electron-withdrawing properties of substituents have no linear relationship with the changes in reactivities.
The effects of different substituents at different positions on reactivities of XH •+ to release the methyl radical are examined in Scheme 6b−e. It is clear that there are no obvious and simple substituent effects. This phenomenon shows that substituents do have important and complicated influences on the reactivity of XH •+ to release the methyl radical, but it will be difficult to predict the reactivity of XH •+ s as In all, the relationship between structures and reactivities on XH •+ releasing the methyl radical exhibits roughly the same regular pattern. 33 Perhaps, the above conclusions are also applicable for other substituted organic hydride compound radical cations releasing radical in chemical reactions.  33 This provides us the precious chance to investigate the relationship of thermodynamics and reactivity between trifluoromethyl-substituted organic hydride compound radical cations (X′H •+ ) releasing trifluoromethyl radical and methyl-substituted organic hydride compound radical cations (XH •+ ) releasing methyl radical.

Relationship of Reactivity between X′H
We tried to discover and evaluate the difference in reactivity on XH •+ and X′H •+ releasing the methyl or trifluoromethyl radical with the same structure except for the substituent from thermodynamic (ΔG RD o ) and kinetic (ΔG RD ≠ ) views. Then, we further computed the differences between ΔG RD Table S3); it is obvious that sometimes ΔΔG o2 are the negative values, while sometimes ΔΔG o2 are the positive values. The reason seems probably to be that ΔG RD o (XH •+ ) and ΔG RD o (X′H •+ ) differ to different extents in different skeletal structures. In addition, we also computed the differences between ΔG RD ≠ (XH •+ ) and in Table S3), which exhibited the same feature as the above Gibbs free energy that sometimes ΔΔG ≠2 are the negative values, while sometimes ΔΔG ≠2 are the positive values. In fact, there is indeed a correlation between ΔΔG ≠2 and ΔΔG o2 ( Figure S1a), ΔΔG ≠2 = 0.770ΔΔG o2 −1.830 (R 2 = 0.75) (defined as eq 3), meaning that the ΔΔG ≠2 values increase with the increase in ΔΔG o2 values. Considering eq 3, it is found that if the ΔΔG o2 is 2.38 kcal/mol, the computed ΔΔG ≠2 is greater than 0 kcal/mol. That is, if ΔΔG o2 is smaller than 2.38 kcal/mol, the computed ΔΔG ≠2 value is less than 0 kcal/mol. This means that the difference in thermodynamic driving forces (ΔΔG o2 ) between XH •+ releasing the methyl radical and X′H •+ releasing the trifluoromethyl radical is less than 2.38 kcal/mol, and the activation energy of XH •+ to release the methyl radical is smaller than that of X′H •+ releasing the trifluoromethyl radical, i.e., XH •+ is a better radical donor than X′H •+ in kinetics. Besides, there is also no relationship of the sign (negative or positive values) between ΔΔG o2 and ΔΔG ≠2 . The above phenomenon confused us for a long time to unveil its mystery and reveal the essential reason. Eventually, we found the ΔG   (Figure 2b) also reveals the linear correlation with the equation ΔG RD ≠ (XH •+ ) = 0.863ΔG RD ≠ (X′H •+ ) + 3.324 (R 2 = 0.843, defined as eq 5), meaning that the ΔG RD ≠ (XH •+ ) values could be safely predicted by eq 5 if the ΔG RD ≠ (X′H •+ ) values are available. In addition, it also could be inferred that if the ΔG RD ≠ (X′H •+ ) values are smaller than 24.26 kcal/mol, the corresponding ΔG RD ≠ (XH •+ ) value is smaller than the ΔG RD ≠ (X′H •+ ) values, so the ΔΔG ≠2 present negative values and the corresponding XH •+ s are assigned to worse methyl radical precursors with a lower reactivity than the corresponding X′H •+ s as trifluoromethyl radical reagents. However, if the ΔG RD ≠ (X′H •+ ) values are more positive than 24.26 kcal/mol, the corresponding ΔG RD ≠ (XH •+ ) value is larger than the ΔG RD ≠ (X′H •+ ) values, so the ΔΔG ≠2 present positive values and the corresponding XH •+ s are better methyl radical reagents than X′H •+ s with a higher reactivity than the corresponding X′H •+ s as trifluoromethyl-radical reagents.
Moreover, when eq 5 was compared with eq 4, we were surprised to find that the two equations have almost the same slopes (0.863 vs 0.830) and intercepts (3.324 vs 3.773), indicating that the influence of thermodynamics from X′H •+ releasing the trifluoromethyl radical on that of XH •+ to release the methyl radical is similar to the influence of kinetics from X′H •+ to release the trifluoromethyl radical on that of XH •+ to release the methyl radical.
Based on the above analysis, the thermodynamic data and kinetic data have inherent and tight connections between X′H •+ releasing the trifluoromethyl radical and XH •+ releasing the methyl radical. Therefore, the relationship between Gibbs free energies [ΔG o ′ RD (XH •+ )] of XH •+ to release the methyl radical in MeCN at 355 K and Gibbs free energies , and the activation free energy of XH •+ to release the methyl radical at 355 K [ΔG ≠ ′ RD (XH •+ )] could be reasonably computed by employing the corresponding linear equations. The deep relationships reveal the important correlations between methyl and trifluoromethyl-substituted organic hydride compound radical cations (XH •+ and X′H •+ ), which is expected to guide chemists in better understanding the thermodynamics and reactivity of XH •+ and X′H •+ in alkylation reactions and is worthy of further exploration.

CONCLUSIONS
In summary, the ΔG RD o (XH •+ ) and ΔG RD ≠ (XH •+ ) of 45 classical methyl-substituted organic hydride compound radical cations (XH •+ ) releasing the methyl radical are computed with the DFT method. Four XH •+ s (1H •+ , 3H •+ ∼4H •+ , and 44H •+ ) are found to be excellent methyl radical reagents, while nine XH •+ s (5H •+ , 6H •+ , 9H •+ , 10H •+ , 12H •+ , 13H •+ , 15H •+ , 43H •+ , and 45H •+ ) are found to be potential methyl radical reagents in organic synthesis. This work uses the ΔG RD o (XH •+ ) and ΔG RD ≠ (XH •+ ) to quantitatively measure the reactivity of XH •+ as a methylation reagent and to establish the molecular library and reactivity database of new methylation reagents for synthetic chemists to query and use. From our work, it can be inferred that various 4-substituted-3,4-dihydropyrimidinones can be used as alkyl radical reagents in reactions just like various 4-substituted Hantzsch esters, which offer practical instructions for synthesis chemists to try and realize. Interesting correlations are found between thermodynamic and kinetic data of XH •+ (X′H •+ ) releasing the methyl radical and the trifluoromethyl radical, which would be helpful in understanding related alkylation mechanisms and quick estimation of related ΔG o and ΔG ≠ values. ■ ASSOCIATED CONTENT
Computation methods, Tables S1−S4, Figure S1, coordinate of reactants, coordinate of transition states, coordinate of products, and electron spin density of transition states of each XH •+ (PDF) ■