DFT study on reaction mechanism of di-tert-butylphenol to di-tert-butylhydroxybenzoic acid

Experimental studies on the Kolbe–Schmitt reaction and its side reactions have made great progresses; however, the relative theoretical studies fall behind. In order to study the mechanism of the Kolbe–Schmitt reaction with 2,6-di-tert-butylphenol and 2,4-di-tert-butylphenol as reactants, we carried out theoretical calculation studies at the M06-2X/Def2-SVP/SMD level of theory using the Gaussian 09 D.01 software package. For the reactant 2,6-di-tert-butylphenol, there is a dynamic equilibrium between the main product and side product, which can rapidly transform into each other at 160 °C by crossing the Gibbs free energy barrier of 14.1 kcal/mol. Moreover, the relative Gibbs free energy of the main product and side product is close; both of them may be observed in the experimental system. However, for 2,4-di-tert-butylphenol, the main product is thermodynamically favorable due to its lower Gibbs free energy, while the side product is kinetically favorable due to the lower activation energy barrier; the main product and the side product compete with each other. We hope the study can shed light on the Kolbe–Schmitt reaction.


Introduction
Aspirin, the most widely used drug, can be synthesized by acetylation reaction of salicylic acid [1]. In 1859, Kolbe and his assistant Schmitt developed the synthesis method of salicylic acid by means of sodium phenoxide and CO 2 at 125 °C and 100 atm, named as the Kolbe-Schmitt reaction [1][2][3][4][5]. The possible mechanism is as follows: (1) Sodium phenoxide captured CO 2 , and then the carboxylation reaction occurred to form the C(sp 2 )-C(sp 3 ) bond between CO 2 and the C atom in the phenyl ring. (2) The proton transferred from the C(sp 3 ) atom to the phenoxide O atom, leading to sodium 4-hydroxybenzoate, which can be easily acidified to salicylic acid.
Theoretical studies on Kolbe-Schmitt reactions are relatively less reported. Zoran Markovic and co-workers systematically investigated the Kolbe-Schmitt reaction, including the effect of different MOPh (M = alkali, Li, K, Rb, Cs) salts on carboxylation reactions [22], the structure of the KOPh-CO 2 complex [23], and the possible mechanisms of the intramolecular proton transfer step [23]. Yan and coworkers studied the reaction mechanism, reaction energy barriers, and some key intermediates of the Kolbe-Schmitt reaction between 2,5-dichlorophenoxide and CO 2 [24].
Stanescu and Achenie investigated the solvent effects on Kolbe-Schmitt reaction kinetics; they found that solvents with a high dielectric constant will lead to reversible reaction and lower yields of products [25]. Sheng and Himo studied decarboxylase-catalyzed Kolbe-Schmitt reactions by DFT calculations [16].
The Kolbe-Schmitt reaction is usually accompanied by a side reaction; that is, alkali hydroxybenzoate (HOC 6 H 4 COOM, M = alkali) reacted with alkali phenoxide (MOPh), leading to phenol (HOPh) and dialkali salicylate (MOC 6 H 4 COOM), as depicted in Fig. 1. The side reaction will limit the yield to less than 50%, resulting to a great waste of substrates [26,27]; however, less attention was paid. Choosing sodium 2,5-dichlorophenoxide as a substrate, Yan and co-workers studied the side reaction both experimentally and theoretically, they proposed that (1) the side product is originated from the main product, (2) the side reaction is responsible for the low yield of the main product, and (3) the side reaction is exothermic, and the formation of the side product is more thermodynamic favorable than that of the main product.
However, sodium 2,5-dichlorophenoxide has an electrondeficient aromatic ring; are these conclusions still valid for electron-rich phenoxide? Besides originating from the main product, is there any other possible reaction pathway to form the side product? In order to solve these questions, we choose the two reactions depicted in Fig. 1 to carry out theoretical calculation studies. We hope our study can bring new insights to the side reaction of the Kolbe-Schmitt reaction.

Computational methods
The Kolbe-Schmitt reaction generally adopts conditions of 140-160 °C and 6-8 MPa, and dimethylbenzene is used as the solvent [24,26]; therefore, in the theoretical calculations, the permittivity (eps) and dynamic permittivity (epsinf) of the solvent model are set as 2.4 and 1.9, respectively. The geometries of all the structures were optimized within the Gaussian 09 D.01 program [28] using the M06-2X-D3 [29,30] method with the Def2-SVP basis set. The vibrational frequency was also calculated at the same level to ensure that the optimized structures are at the minimum or saddle point of the potential energy surface. The solvent effect was considered by employing the solvation model based on density (SMD) [31]. IRC calculations [32,33] are also performed at the same level to ensure that each transition state is connected to the corresponding reactant and product. The Shermo software [34] was used to calculate the Gibbs free energy of all optimized structures at 160 °C and 8 MPa. And the optimized structures were displayed in the CYLview [35] software.

Results and discussion
Reactions that generate P(A) and P(B) are defined as the main reactions, and those that generate side-P(A) and side-P(B) as side reactions. The following is the mechanisms of these reactions and the changes of Gibbs free energies.

Reactions of potassium 2,6-di-tert-butylphenoxide (A) as the reactant
The reaction mechanism of potassium 2,6-di-tert-butylphenoxide (A) and CO 2 is shown in Fig. 2. At first, A binds with CO 2 through an O-K coordination bond to form the complex A-CO 2 with the Gibbs free energy increase of 1.7 kcal/mol. Then, CO 2 is electrophilically added to C4 of the benzene ring through the transition state TS1-A to obtain the electrophilic addition product IM1-A. From A-CO 2 to TS1-A, the Gibbs free energy barrier needed to be overcome is only 11.3 kcal/mol. Then, the reaction may go through two different pathways: one is the rotation of the carboxyl in CO 2 , which makes two O atoms in CO 2 coordinate with the K atom, and the reaction goes through the transition state TS2-A with the free energy increase of 6.6 kcal/mol to form the intermediate IM2-A; the other one is the occurrence of intramolecular proton transfer reaction through TS2-A'. Since the transition state TS2-A' has a four-membered ring structure, which has larger ring tension, its free energy is much higher than that of TS2-A. Therefore, the subsequent reaction of TS2-A' will not be investigated. After the formation of IM2-A, the O-K coordination bond breaks and the intermediate IM3-A is formed through TS3-A, which needs to cross the Gibbs free energy barrier of 1.5 kcal/mol from IM2-A. In IM3-A, the K atom is connected with the CO 2 moiety and the original phenol completely changes to a benzoquinone structure. Next, IM3-A combines with a molecule of A to obtain the intermediate IM4-A with the energy increase of 0.3 kcal/mol. In IM4-A, the O atom of the benzoquinone structure in IM3-A forms a new coordination bond with the K atom of A, and the O atom in A forms a weak hydrogen bond with the H atom on C4 in IM3-A. Afterwards, the intermediate IM5-A can be obtained through intermolecular H + -K + exchange reaction in TS4-A. IM5-A can remove a molecule of A-phenol (2,6-di-tert-butylphenol) to obtain side-P(A) directly, or undergo an O-H hydrogen bond formation through IM6-A and a intramolecular H + -K + exchange reaction again through TS5-A to generate IM7-A. Finally, the decomposition of IM7-A gives the main product P(A) and a molecule of A. It can be seen from the potential energy diagram that there is a dynamic equilibrium between the side product side-P(A) and the main product P(A), which can rapidly transform into each other at 160 °C by crossing the Gibbs free energy barrier of 14.1 kcal/ mol. Moreover, the relative Gibbs free energy of side-P(A) and P(A) is close; both of them may be observed in the experimental system. For the Kolbe-Schmitt reaction of A (potassium 2,6-di-tert-butylphenoxide), the calculated Gibbs free energies and imaginary frequencies are shown in Table 1; the optimized structure are shown in Fig. S1.   Fig. 2 The mechanism of the Kolbe-Schmitt reaction in which A (potassium 2,6-di-tert-butylphenoxide) participates. The Gibbs free energies of [A + CO2] were set to 0.0 kcal/mol as a reference

Reactions of potassium 2,4-di-tert-butylphenoxide (B) as the reactant
The reaction mechanism of potassium 2,4-di-tert-butylphenoxide (B) and CO 2 as reactants is shown in Fig. 3. B binds with CO 2 through an O-K coordination bond to form the complex B-CO 2 with the Gibbs free energy increase of 2.6 kcal/mol firstly. Afterwards, CO 2 is electrophilically added to C6 of the benzene ring through the transition state TS1-B to obtain the electrophilic addition product IM1-B. From B-CO 2 to TS1-B, the Gibbs free energy barrier needed to be overcome is only 11.2 kcal/mol. The hydrogen atom at the C6 position in IM1-B transfers to the  From B as the reactant to the side product side-P(B), the Gibbs free energy drops by 12.5 kcal/mol. Although the Gibbs free energy decrease of the main product P(B) is more than that of side-P(B), which indicates that it is favorable in thermodynamics, the activation energy required of side-P(B) is lower, which is dynamically advantageous, so the main product P(B) and the side product side-P(B) compete with each other. Starting from IM2-B', the reaction may also form the main product P(B) through TS3-B'', but this process can not actually occur due to the high free energy of TS3-B''. For the Kolbe-Schmitt reaction of B (potassium 2,4-di-tert-butylphenoxide), the calculated Gibbs free energies and imaginary frequencies are shown in Table 2; the optimized structures are shown in Fig. S2.

Conclusions
In summary, we have theoretically studied the Kolbe-Schmitt reactions and corresponding side reactions of potassium 2,6-di-tert-butylphenoxide (A) and potassium 2,4-di-tert-butylphenoxide (B). For the reactions starting from A, the main product P(A) and side product side-P(A) can convert to each other due to the dynamic equilibrium between them. However, for the reactions starting from B, the main product P(B) is thermodynamically favorable due to its lower relatively Gibbs free energy, while the side product side-P(B) is kinetically favorable due to the lower activation energy barrier of reaction pathway. We hope the study can shed light on the Kolbe-Schmitt reaction.
Author contribution Neng-Zhi Jin, Qi-Bin Zhang: data analysis, writingreview and editing. Rong Liu: data analysis and discussion. Pan-Pan Zhou: calculations and data collection. Availability of data and material All data about Cartesian coordinates is available, which is in supporting information.

Conflict of interest
The authors declare no competing interests.