Theoretical investigation on the nature of 4-substituted Hantzsch esters as alkylation agents

Abstract

Recently, a variety of 4-substituted Hantzsch esters (XRH) with different structures have been widely researched as alkylation reagents in chemical reactions, and the key step of the chemical process is the elementary step of XRH˙⁺ releasing R˙. The purpose of this work is to investigate the essential factors which determine whether or not an XRH is a great alkylation reagent using density functional theory (DFT). This study shows that the ability of an XRH acting as an alkylation reagent can be reasonably estimated by its ΔG^≠_RD(XRH˙⁺) value, which can be conveniently obtained through DFT computations. Moreover, the data also show that ΔG^≠_RD(XRH˙⁺) has no simple correlation with the structural features of XRH, including the electronegativity of the R substituent group and the magnitude of steric resistance; therefore, it is difficult to judge whether an XRH can provide R˙ solely by experience. Thus, these results are helpful for chemists to design 4-substituted Hantzsch esters (XRH) with novel structures and to guide the application of XRH as a free radical precursor in organic synthesis.

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1 Introduction

It is well known that the Hantzsch ester (HEH₂, Scheme 1) was first synthesized by Hantzsch, a German chemist, in 1881.¹ Due to the simple synthesis method and excellent reduction performance, HEH₂ has long been used as an organic hydrogen molecular reductant to hydrogenate various types of unsaturated compounds.^2–4 HEH₂ releases two hydrogen atoms or hydrogen ions to unsaturated substrates while itself aromatizes into pyridine compounds, meanwhile the unsaturated bonds (C=C, C=N, C=O, etc.) in the substrates are reduced. Organic synthetic chemists have done excellent research work in designing novel catalysts, expanding new reaction substrate and improving product chirality and yield using HEH₂ as reducer. Since 2013, chemists found that 4-substituted Hantzsch esters (XRH, Scheme 1) can break C–C bond and release alkyl radical (R˙) under the condition of photocatalysis.⁵ Then R˙ reacts with electron-activated substrate to produce alkyl substitution or alkyl addition products, and hundreds of literatures have reported the alkylation reaction between XRH with various substrates.^6–18

Scheme 1 Structures of HEH₂ and XRH investigated in this work.

There are two main mechanisms (Scheme 2) for the reactions of XRH as alkylating agents reacting with substrates. Under certain specific wavelength, the photocatalyst (PC) is activated into an excited state photocatalyst (PC*) with strong single electron oxidation ability. PC* oxidizes XRH to XRH˙⁺ and transforms itself into PC˙⁻, a strong single electron reducer. XRH˙⁺ is an unstable and active key intermediate, which will release R˙ to substrate. The first mechanism^7–12 is that PC˙⁻ reduces the reaction substrate (R₁–G) to R₁–G˙⁻, subsequently, R₁–G˙⁻ releases stable G⁻ group to generate R₁˙. Recombination of R˙ and R₁˙ radicals generates the desired product R₁–R. Since the concentrations of R˙ and R₁˙ are very low in solution, hydrogen-abstraction by the radicals may possibly occur as a side-reaction (Mechanism 1 in Scheme 2). Alkylation of haloalkanes is a typical reaction of this mechanism. The second mechanism^13–18 is that R˙ reacts with unsaturated substrate (such as R₂=R₂) to form active free radical intermediate RR₂–R₂˙ first, then RR₂–R₂˙ obtains electrons from PC˙⁻ and protons from XH⁺ to form alkylation product RR₂–R₂H (Mechanism 2 in Scheme 2). After carefully analyzing the reaction mechanism of XRH acting as alkylating reagents, it is clear that the key step is the elementary step of XRH˙⁺ releasing R˙ (Scheme 3), but not all XRH with various R substituent groups in 4-position can give the alkyl radicals, for example, 4-Ph-HEH cannot provide Ph˙ in alkylation reaction.

Scheme 2 Two mechanisms of XRH being used as alkylation reagents in chemical reactions.

Scheme 3 Key elementary step of XRH being used as alkylation reagents in chemical reactions.

Then we begin to wonder: why some structures of XRH (R = Bn, tert-Bu, cyclohexyl, allyl, etc.) are excellent alkylation reagents, while some structures of XRH (R = Ph, thienyl, etc.) cannot be used as alkylation reagents, and what determines whether an XRH can be a good alkylation reagent? At present, the above question have not been well answered, and it is difficult to determine these important thermodynamic and kinetic data by experimental methods. Therefore, there is an urgent need for an accurate and reliable theoretical method to guide the experimental design in the field of organic synthesis. Further study on the thermodynamic and kinetic properties of the key intermediate XRH˙⁺ releasing R˙ can guide chemists to better design 4-substituted Hantzsch esters (XRH) as novel alkylation reagents and understand the alkylation mechanism in organic synthesis.

Owing to the rapid development of density functional theory (DFT)^19–23 in recent years and the large enhancement of computational capability, the thermodynamic driving forces and activation energies of chemical reactions could be accurately computed by employing suitable density functionals. Based on the important structure of 4-substituted Hantzsch esters (XRH) reported in previous literatures, 17 XRH have been well-designed in this work (Scheme 4). The thermodynamic driving forces [free energy change, ΔG^o_RD(XRH˙⁺)] and activation Gibbs free energies [ΔG^≠_RD(XRH˙⁺)] of different structures of XRH˙⁺ releasing R˙ were computed using DFT, and the essential factors determining whether or not an XRH is alkylation reagent have been revealed in detail in this work.

Scheme 4 Chemical structures of 17 XRH examined in this work.

2 Computational section

Molar free energy change of XRH˙⁺ releasing R˙ [ΔG^o_RD(XRH˙⁺)], molar enthalpy changes of XRH˙⁺ releasing R˙ [ΔH^o_RD(XRH˙⁺)], and activation free energy of XRH˙⁺ releasing R˙ [ΔG^≠_RD(XRH˙⁺)] were computed in this work.

All quantum chemical calculations in this work were performed using Gaussian 09,^19a and wave function analysis was performed using Multiwfn 3.7.^19b First, find out the transition state of XRH˙⁺ releasing R˙, and calculate the Gibbs free energy and enthalpy of reactant, transition state and product of each elemental step. Through analyzing the difference between reactant and product, free energy changes and enthalpy changes of XRH˙⁺ releasing R˙ were obtained. The activation free energy and activation enthalpy could be obtained by comparing the reactant and the transition state in similar method.

First, the reactants, transition states and products of elemental step were geometrically optimized to convergence using the functional B3LYP²⁰ and the basis set 6-31G(d,p).²¹ DFT-D3 empirical dispersion correction (BJ damping)²² was applied, and SMD solvent model²³ (acetonitrile as the solvent) was used during the computation. After geometrical optimization, the vibration analysis was carried out using the same parameters. The results of vibration analysis showed that there is no imaginary frequency for all reactants and products; meanwhile, only one imaginary frequency was found for each transition state, and the direction of imaginary frequency was the same as that of C–C bond stretch, indicating that the transition states were correct. Intrinsic reaction coordinate (IRC) was then calculated for each transition state, and electron spin density analysis of IRC-derived products showed that the cleavage products were alkyl radicals, not alkyl cations. Then, the thermodynamic correction was applied for each reactant, transition state and product at 298.15 K. The free energy was obtained by adding the single point energy to the Gibbs free energy correction value, and the enthalpy was obtained by adding the single point energy to the enthalpy correction value. Reaction rate constant (k₂) was obtained by Eyring equation [k₂ = (k_BT/h)exp(−ΔG^≠/RT)].

In order to verify the applicability and accuracy of the calculation method in this work, first we calculated the molar enthalpy changes of four XRH˙⁺ releasing H˙ using the above method (termed “calculation values” in this work). The molar enthalpy changes of XRH˙⁺ releasing H˙ determined by the calorimetric titration method in previous literature were termed “experimental values”.²⁴ The calculated value and the experimental value are listed in Table 1, and the data shows that the deviation between calculated values and the experimental values is less than 2.0 kcal mol⁻¹. Therefore, considering the experimental measurement error, it is appropriate to use the above calculation method to study the energy changes of XRH˙⁺ releasing R˙, and the results obtained are accurate and reliable.

Table 1 Comparison between DFT calculation data and experimental data (kcal mol⁻¹)

Compounds	ΔH^oHD(XRH˙^+) (DFT)^a	ΔH^oHD(XRH˙^+) (exp)^a	ΔΔH^oHD^b
a The unit is kcal mol^−1.b ΔΔH^oHD = ΔH^oHD(XRH˙^+) (DFT) − ΔH^oHD(XRH˙^+) (exp), the unit is kcal mol^−1.
	30.27	31.40 (ref. 24a)	−1.13
	30.72	32.20 (ref. 24a)	−1.48
	26.85	27.80 (ref. 24b)	−0.95
	27.85	29.80 (ref. 24b)	−1.95

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3 Results and discussions

The calculation results, ΔH^o_RD(XRH˙⁺), ΔG^o_RD(XRH˙⁺) and ΔH^≠_RD(XRH˙⁺), ΔG^≠_RD(XRH˙⁺) are presented in Table 2.

Table 2 Thermodynamic data and activation free energy data of XRH˙⁺ releasing R˙

XRH	ΔH^oRD(XRH˙^+)^a	ΔG^oRD(XRH˙^+)^a	ΔH^≠RD(XRH˙^+)^a	ΔG^≠RD(XRH˙^+)^a
a The unit is kcal mol^−1.
1RH	0.48	−12.15	3.29	3.47
2RH	9.43	−3.13	3.24	3.44
3RH	17.76	4.75	13.92	12.95
4RH	13.16	−0.02	5.68	5.38
5RH	13.71	0.58	9.64	8.66
6RH	11.49	−2.42	4.76	4.59
7RH	17.15	5.60	15.32	13.62
8RH	7.73	−7.33	1.44	1.17
9RH	5.37	−7.73	3.22	3.11
10RH	12.79	−1.28	7.77	7.45
11RH	13.47	−0.11	2.05	3.37
12RH	17.16	1.88	6.65	6.39
13RH	15.64	2.27	0.85	0.83
14RH	38.83	26.85	32.81	31.80
15RH	27.12	15.17	22.49	22.28
16RH	27.29	1.60	21.93	21.48
17RH	32.77	21.72	26.95	26.60

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3.1 ΔG^o_RD(XRH˙⁺)

In order to discover the influence of structural factors on ΔG^o_RD(XRH˙⁺) values, the free energies changes of 17 XRH˙⁺ releasing R˙ are listed in Fig. 1 for comparison. From Fig. 1, it is evident that the free energy changes of breaking C–C bond for XRH˙⁺ releasing R˙ varies greatly with the substituents, which ranges from −12.15 to 26.85 kcal mol⁻¹. Among 4-substituted Hantzsch ester structures investigated in this work, the Gibbs free energy of XRH˙⁺ releasing R˙ increased from ΔG^o ≪ 0 (−12.15 kcal mol⁻¹) to ΔG^o ≫ 0 (26.85 kcal mol⁻¹). 1RH˙⁺ (4-allyl-substituted Hantzsch ester) has the lowest ΔG^o_RD(XRH˙⁺) value as −12.15 kcal mol⁻¹, and 14RH˙⁺ (4-dimethylaminophenyl substituted Hantzsch ester) has the highest value of ΔG^o_RD(XRH˙⁺) as 26.85 kcal mol⁻¹, and the former is 39 kcal mol⁻¹ lower than the latter. The thermodynamic data show that 1RH is the best alkylation reagents which spontaneously offers allyl radical in acetonitrile under the reaction condition of 298.15 K; in contrast, 14RH cannot give 4-dimethylaminophenyl group in chemical reactions. Such a large range of ΔG^o_RD(XRH˙⁺) values (−12.15–26.85 kcal mol⁻¹) indicates that the R group in the parent structure of XRH has a great influence on the value of ΔG^o_RD(XRH˙⁺), and the strength of C–C bond varies greatly in different structures of XRH˙⁺.

Fig. 1 Visual comparison of ΔG^o_RD(XRH˙⁺) among the 17 XRH in acetonitrile at 298.15 K.

Through comprehensive analysis and evaluation of ΔG^o_RD(XRH˙⁺), the results show that XRH˙⁺ is possible (but not necessarily) to be an excellent R˙ donors which are determined by the R substituents in 4-position. If R substituents in XRH˙⁺ are not aromatic substituents, XRH˙⁺ would be used as alkylation reagent; in contrast, if R substituents in XRH˙⁺ are aromatic substituents, XRH˙⁺ would not be used as R˙ donors.

3.2 ΔG^≠_RD(XRH˙⁺)

From columns 5 in Table 2, it is clear that the ΔG^≠_RD(XRH˙⁺) values of XRH˙⁺ releasing R˙ range from 0.83 to 31.80 kcal mol⁻¹. As shown in Fig. 2, ΔG^≠_RD(XRH˙⁺) value of 13RH˙⁺ releasing R˙ is the smallest (0.83 kcal mol⁻¹); hence, the rate constant of 13RH˙⁺ releasing R˙ (1.53 × 10¹² M⁻¹ s⁻¹) is greater than diffusion speed (10¹⁰ M⁻¹ s⁻¹); while ΔG^≠_RD(XRH˙⁺) value of 14RH˙⁺ releasing R˙ is the largest (31.80 kcal mol⁻¹), so the rate constant of 14RH˙⁺ releasing R˙ is lowest with 2.87 × 10⁻¹² M⁻¹ s⁻¹ at 298.15 K in acetonitrile, which indicates that the reaction of 14RH˙⁺ releasing R˙ is extremely slow, and therefore 14RH cannot be used as R˙ donor in chemical reaction. The predicted rate constants of XRH˙⁺ releasing R˙ in this work range from 2.87 × 10⁻¹² to 1.53 × 10¹² (M⁻¹ s⁻¹). Thus, it can be seen that there are many important chemical reactions in vivo or in vitro whose rates cannot be directly measured using experimental methods up to now. The reason is that some reactions are too fast, some are too slow and some have no detectable signals, etc. Because the accuracy of the calculation results is verified by experimental measured values, the rate constants of XRH˙⁺ releasing R˙ that cannot be measured experimentally can be estimated by the activation energy calculation method used in this work. Among the 17 XRH structures examined, ΔG^≠_RD(XRH˙⁺) values of 13 XRH (1RH–13RH) are less than 16 kcal mol⁻¹ (k₂ = 6.29 × 10² M⁻¹ s⁻¹ at 298.15 K), ΔG^≠_RD(XRH˙⁺) values of 4 XRH (14RH–17RH) span from 21.48 to 31.80 kcal mol⁻¹ (1.07 × 10⁻³ to 1.07 × 10⁻¹¹ M⁻¹ s⁻¹ at 298.15 K). The ΔG^≠_RD(XRH˙⁺) values indicate that 1RH–13RH could be selected as R˙ donor in chemical reactions, while 14RH–17RH cannot provide R˙ as alkylation reagents. Further taking their structures into consideration, we find that R substituents in 14RH–17RH are aromatic substituents and the ΔG^≠_RD(XRH˙⁺) of XRH˙⁺ releasing R˙ all larger than 21.4 kcal mol⁻¹ which means 4-aromatic-group substituted Hantzsch esters cannot be used as R˙ donors. If R substituents in XRH˙⁺ are not aromatic substituents, XRH˙⁺ (1RH–13RH) would be good R˙ donors in radical reactions.

Fig. 2 Visual comparison of ΔG^≠_RD(XRH˙⁺) among the 17 XRH in acetonitrile at 298.15 K.

3.3 Entropy change and activation entropy change

Since Gibbs free energies [ΔG^o_RD(XRH˙⁺)], enthalpy changes [ΔH^o_RD(XRH˙⁺)], activation energies [ΔG^≠_RD(XRH˙⁺)] and activation enthalpy changes [ΔH^≠_RD(XRH˙⁺)] were obtained now, we calculated the entropy changes (ΔS^o_RD) and activation entropy changes (ΔS^≠_RD) of XRH˙⁺ releasing R˙ which are listed in Table 3.

Table 3 Entropy changes and activation entropy changes of XRH˙⁺ releasing R˙

XRH	ΔS^oRD^a	ΔS^≠RD^b
a From the equation, ΔS = (ΔH − ΔG)/T, the unit is cal mol^−1 K^−1.b From the equation, ΔS^≠ = (ΔH^≠ − ΔG^≠)/T, the unit is cal mol^−1 K^−1.
1RH	42.39	−0.60
2RH	42.13	−0.66
3RH	43.65	3.26
4RH	44.22	0.99
5RH	44.07	3.28
6RH	46.69	0.58
7RH	38.75	5.69
8RH	50.53	0.91
9RH	43.98	0.36
10RH	47.24	1.09
11RH	45.57	−4.42
12RH	51.26	0.87
13RH	44.85	0.08
14RH	40.21	3.37
15RH	40.12	0.72
16RH	39.24	1.50
17RH	37.09	1.18

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From Table 3, it is found that the entropy changes of XRH˙⁺ releasing R˙, ΔS^o_RD, range from 38.75 to 51.26 cal mol⁻¹ K⁻¹, and the activation entropy changes of XRH˙⁺ releasing R˙, ΔS^≠_RD, range from −4.42 to 5.69 cal mol⁻¹ K⁻¹. ΔS^o_RD are positive values (cal mol⁻¹ K⁻¹), which indicates that the chemical process of XRH˙⁺ releasing R˙ is the large entropy increase process. While the span of activation entropy changes of XRH˙⁺ releasing R˙, ΔS^≠_RD, is less than ±5 cal mol⁻¹ K⁻¹, which indicates that the chemical structures of XRH˙⁺ do not change greatly in the transition state.

3.4 Main factors affecting free energy changes and activation free energy changes of XRH˙⁺ releasing R˙

3.4.1 Thermodynamic driving force and activation free energy. Because the XRH structure investigated in this work is 1,4-dihydropyridine compounds, only the R substituents in 4-position are different. In order to further explore the intrinsic relationship between the thermodynamic driving forces [ΔG^o_RD(XRH˙⁺)] and the activation energy [ΔG^≠_RD(XRH˙⁺)], relationships between them are shown in Fig. 3. It can be seen from Fig. 3 that there is a certain correlation between the thermodynamic driving force and activation free energy changes of XRH˙⁺ releasing R˙, that is, ΔG^≠_RD(XRH˙⁺) increases along with the increase of ΔG^o_RD(XRH˙⁺). But for all chemical reactions, there is no good linear correlation between ΔG^≠ and ΔG^o. This phenomenon shows that the thermodynamic driving force has an important influence on the activation energy, but it is not the only decisive factor.²⁵

Fig. 3 Relationship between the activation free energies of 17 XRH˙⁺ releasing R˙ and the corresponding free energy changes of XRH˙⁺ releasing R˙ in acetonitrile at 298.15 K.

3.4.2 The stability of R˙ and ΔG^≠_RD(XRH˙⁺). It can be seen from the above discussion that many XRH with different structures can be used as R˙ donor. ΔG^≠_RD(XRH˙⁺) values range from 0.83 to 13.62 kcal mol⁻¹, and the difference between the fastest and slowest rate constant is 10¹⁰. Through the previous discussion, we have known that the thermodynamic driving force is an important factor affecting the activation energy of the reaction. Then, does it exist an internal relationship between the stability of R˙ and the reaction activity of XRH˙⁺ releasing R˙ ΔG^≠_RD(XRH˙⁺)? Considering the chemical process of XRH˙⁺ releasing R˙ with different structure, XRH˙⁺ → XH⁺ + R˙, it is found that the values of molar free energy of XRH˙⁺ releasing R˙ [ΔG^o_RD(XRH˙⁺)] do reflect the relative stabilities of R˙. The smaller ΔG^o_RD(XRH˙⁺) is, the more stability R˙ is. On the basis of ΔG^o_RD(XRH˙⁺) values computed in this work, the R˙ stability order in 1RH to 17RH molecules investigated in this work is 1R > 9R > 8R > 2R > 6R > 10R > 11R > 4R > 5R > 16R > 12R > 13R > 3R > 7R > 15R > 17R > 4R (Fig. 4). But according to the ΔG^≠_RD(XRH˙⁺) values, the order of reactivity is 13R > 8R > 9R > 11R > 2R > 6R > 4R > 12R > 10R > 5R > 3R > 7R > 16R > 15R > 17R > 14R (Fig. 4). It is clear that there are significant differences between the order of stability of R˙ and the order of ΔG^≠_RD(XRH˙⁺), and the stability of R˙ is not the decisive factor of ΔG^≠_RD(XRH˙⁺). The results also show that the influence of structural factors on ΔG^≠_RD(XRH˙⁺) is multifaceted and complicated.

Fig. 4 The order of R˙ stability and activation free energies of 17 XRH˙⁺ releasing R˙.

3.4.3 Substituent effect. For 14RH, 16RH and 15RH, the R substituents at the 4-positions are p-dimethylaminophenyl, phenyl and p-nitrophenyl respectively, all of which are benzene ring structures with different p-substituents. Dimethylamino group (σ_p = −0.83) and nitro group (σ_p = −0.78) are relatively strong electron-donating and electron-withdrawing groups respectively. We designed these two groups in order to change the ability of XRH˙⁺ releasing R˙ to provide aromatic free radicals by tremendously changing the electronegativity of substituents. The relevant data are compared in Fig. 5. According to Fig. 5, the following conclusions can be made: (1) when the 4-position is a strong electron-donating group (dimethylamino group), free energy changes and activation energy changes of XRH˙⁺ releasing R˙ increased significantly (about 5–10 kcal mol⁻¹). (2) When the 4-position is a strong electron-withdrawing group (nitro group), free energy changes and activation energy changes of XRH˙⁺ releasing R˙ changed slightly (<1.5 kcal mol⁻¹). The above calculation results show that the change of electronegativity of benzene ring does not make XHR the donor of aromatic benzene free radicals. No matter it is electron-donating group or electron-withdrawing group, the abilities of XHR˙⁺ releasing R˙ are decreased, meanwhile the effect of electron-donating group on ability of XHR˙⁺ releasing R˙ is greater than that of electron-withdrawing group.²⁶

Fig. 5 Effects of substituent groups on the activation free energy and free energy changes of XRH˙⁺ releasing R˙ (energy unit: kcal mol⁻¹).

3.4.4 Influence of steric hindrance and stability of R˙. For 4-substituted Hantzsch esters 7RH, 5RH, 6RH and 8RH, R substituent groups are methyl, ethyl, isopropyl and tert-butyl (Fig. 6), respectively. The steric resistance of the substituents increases gradually with increasing of the stability of R˙. From Fig. 6, it is found that ΔG^o_RD(XRH˙⁺) of XRH˙⁺ releasing R˙ decrease from 5.60 to −7.33 kcal mol⁻¹, ΔG^≠_RD(XRH˙⁺) of XRH˙⁺ releasing R˙ decrease from 13.62 to 1.17 kcal mol⁻¹, as gradually increasing of steric hindrance and stability of R˙ from 7RH˙⁺ to 8RH˙⁺ (Fig. 6).

Fig. 6 Effects of size and stability of substituent groups on the activation free energy and free energy changes of XRH˙⁺ releasing R˙ (energy unit: kcal mol⁻¹).

3.5 Judgment criteria of whether an XRH is a great alkylation reagent

Considering activation free energy of XRH˙⁺ releasing R˙ [ΔG^≠_RD(XRH˙⁺)], the judgment criteria of XRH being a good R˙ donor can be concluded reasonably (Table 4). Generally, in practice, an activation free energy (ΔG^≠) of 21 kcal mol⁻¹ is usually used as a criteria in determining whether a reaction could easily occur at room temperature, according to the Transition State Theory (TST);²⁷ an activation free energy of 21 kcal mol⁻¹ corresponds to a half-life of ∼4.5 min and a 97% completion time of 22.3 min at room temperature, which indicate that the reaction can be completed within an acceptable time. Accordingly, the following predictions can be made: (1) if the value of ΔG^≠_RD(XRH˙⁺) is larger than 21.0 kcal mol⁻¹ (k₂ < 2.42 × 10⁻³ M⁻¹ s⁻¹), XRH could not be used as alkylation reagent, like 14RH–17RH. (2) If the value of ΔG^≠_RD(XRH˙⁺) is larger than 17.5 kcal mol⁻¹ (k₂ ≤ 1 M⁻¹ s⁻¹), but smaller than 21.0 kcal mol⁻¹ (k₂ ≥ 2.42 × 10⁻³ M⁻¹ s⁻¹) XRH is a weak alkylation reagent. (3) If the value of ΔG^≠_RD(XRH˙⁺) is larger than 12.0 kcal mol⁻¹ (k₂ ≤ 9.71 × 10³ M⁻¹ s⁻¹), but smaller than 17.5 kcal mol⁻¹ (k₂ ≥ 1 M⁻¹ s⁻¹) XRH is a medium alkylation reagent, like 3RH and 7RH. (4) If the value of ΔG^≠_RD(XRH˙⁺) is smaller than 12.0 kcal mol⁻¹ (k₂ > 9.71 × 10³ M⁻¹ s⁻¹), XRH is an excellent alkylation reagent, like 8RH–13RH. Since ΔG^≠_RD(XRH˙⁺) has no simple correlation with the XRH′ structure, the electronegativity and steric resistance, it is difficult to judge whether XRH can provide R˙ in chemical reactions solely by experience. The calculation method and results provided in this work are helpful to guide the application of XRH as a free radical donor in organic synthesis.

Table 4 Diagnoses of reactivity of XRH using as radical agent according to ΔG^≠_RD(XRH˙⁺)

XRH	ΔG^oRD(XRH˙^+)^a	ΔG^≠RD(XRH˙^+)^a	k2^b	Diagnose
a The energy unit is kcal mol^−1.b The unit is M^−1 s^−1.
1RH	−12.15	3.47	1.76 × 10^10	Excellent R˙ donor
2RH	−3.13	3.44	1.85 × 10^10	Excellent R˙ donor
3RH	4.75	12.95	1.95 × 10^3	Medium R˙ donor
4RH	−0.02	5.38	6.99 × 10^8	Excellent R˙ donor
5RH	0.58	8.66	2.74 × 10^6	Excellent R˙ donor
6RH	−2.42	4.59	2.66 × 10^9	Excellent R˙ donor
7RH	5.60	13.62	6.29 × 10^2	Medium R˙ donor
8RH	−7.33	1.17	8.59 × 10^11	Excellent R˙ donor
9RH	−7.73	3.11	3.24 × 10^10	Excellent R˙ donor
10RH	−1.28	7.45	2.12 × 10^7	Excellent R˙ donor
11RH	−0.11	3.37	2.09 × 10^10	Excellent R˙ donor
12RH	1.88	6.39	1.27 × 10^8	Excellent R˙ donor
13RH	2.27	0.83	1.53 × 10^12	Excellent R˙ donor
14RH	26.85	31.80	2.87 × 10^−11	Not R˙ donor
15RH	15.17	22.28	2.78 × 10^−4	Not R˙ donor
16RH	15.60	21.48	1.07 × 10^−3	Not R˙ donor
17RH	21.72	26.60	1.88 × 10^−7	Not R˙ donor

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4 Conclusions

In this work, 4 characteristic physical parameters, ΔH^o_RD(XRH˙⁺), ΔG^o_RD(XRH˙⁺), ΔH^≠_RD(XRH˙⁺), ΔG^≠_RD(XRH˙⁺) of 17 important XRH releasing R˙ were calculated using DFT method. After careful discussion of the relevant thermodynamic and kinetic data, the following conclusions can be made: (1) through comprehensive analysis and evaluation of ΔG^o and ΔG^≠, it is found that XRH˙⁺ is possible (but not necessarily) to be an excellent R˙ donors which are determined by the R substituents in 4-position. (2) If R substituents in XRH are not aromatic groups, XRH˙⁺ can release R˙ as key intermediates, therefore XRH could be used as alkylation reagents. In contrast, if R substituents in XRH are aromatic substituents, the key intermediates XRH˙⁺ could not release aromatic radical in chemical reactions, so XRH with aromatic substituents could not be used as alkylation reagents. (3) The thermodynamic driving force (Gibbs free energy) has an important influence on the activation energy, but it is not the only decisive factor. (4) There are significant differences between the order of R˙ stability and the order of ΔG^≠_RD(XRH˙⁺), and the stability of R˙ is not the decisive factor of ΔG^≠_RD(XRH˙⁺). In addition, the influence of structural factors on ΔG^≠_RD(XRH˙⁺) is multifaceted and complicated. (5) Change of electronegativity of benzene ring does not make XHR be an aromatic free radical donor. (6) According to ΔG^≠_RD(XRH˙⁺) values, the kinetic ability of XRH˙⁺ releasing R˙ can be predicted reasonably. ① If the value of ΔG^≠_RD(XRH˙⁺) is larger than 21.0 kcal mol⁻¹, XRH could not be used as an alkylation reagent. ② If the value of ΔG^≠_RD(XRH˙⁺) is larger than 17.5 kcal mol⁻¹, but smaller than 21.0 kcal mol⁻¹, XRH is a weak alkylation reagent. ③ If the value of ΔG^≠_RD(XRH˙⁺) is larger than 12.0 kcal mol⁻¹, but smaller than 21.0 kcal mol⁻¹, XRH is a medium alkylation reagent. ④ If the value of ΔG^≠_RD(XRH˙⁺) is smaller than 12.0 kcal mol⁻¹, XRH is an excellent alkylation reagent.

It is known that the reaction conditions of XRH using as alkylation reagents are quite complex, and this paper focuses on the intrinsic properties of key intermediate XRH˙⁺ releasing R˙. Since ΔG^≠_RD(XRH˙⁺) has no simple correlation with the XRH's structure, the electronegativity and steric resistance, it is difficult to judge whether XRH can be used as an alkylation reagent in chemical reactions solely by experience. The calculation method and results provided in this work are helpful to guide the application of XRH as a free radical donor in organic synthesis.

Conflicts of interest

The authors declare no competing financial interests.

Acknowledgements

This study was supported by NSFC cultivation project of Jining Medical University (JYP2018KJ18 and JYP2019KJ25) and College Students' Innovative Training Plan Program of Jining Medical University (cx2020106).

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