Formation of α,β-Unsaturated Imines in Apolar Aprotic Solvent: Effect of Hidden Acid Catalysts Analyzed by Theoretical Calculations

A theoretical investigation of the 1,2-additon and 1,4-addition reactions of benzylamine to crotonaldehyde in toluene solution is reported in this study, including the effect of trace amounts of acetic acid (AcOH) and methanesulfonic acid (CH3SO2OH). We have determined the reaction free energy profile and performed a detailed microkinetic analysis. Our results point out that this reaction system needs catalysis to take place and it was found that CH3SO2OH is a powerful catalyst, outperforming AcOH in lowering the free energy barrier for the 1,2-addition reaction, which leads to the formation of α,β-unsaturated imine. On the other hand, the 1,4-addition reaction has the direct nucleophilic attack of benzylamine to the β-carbon of s-cis conformation of crotonaldehyde as the rate-determining step, corresponding to slow kinetics. Our results suggest that the experimentally observed formation of the imine can be explained by the presence of hidden acid catalysts present in the reaction medium.


Introduction
Brønsted acids are important catalysts in a wide number of organic reactions, 1,2 whose efficiency will depend on the choice of the most suitable acid 3 and on the characteristics that it aims to achieve at the end of synthesis.Brønsted acids can be classified in terms of their chirality and acidity. 1,2Chiral Brønsted acids can be weak acids 1 as thiourea derivatives 4 used in reactions such as Diels-Alder, 5 cyanosilylation, 6 and Aza-Henry. 7Their catalytic function is associated with the formation of hydrogen bonds stabilizing the substrate. 8They can also be stronger acids as chiral phosphoric acids derivatives 1 used in reactions such as Mannich 9 and cycloaddition/annulation, 10 whose activation occurs by ion pairing and/or hydrogen bonding depending on the electronic properties of substrate 11 and the pK a of the acid. 12hile chiral Brønsted acids are mainly used for their selectivity by generating a chiral environment, achiral Brønsted acids provide an increase in activity. 13They can be strong, such as p-toluenesulfonic acid, which is an effective additive in the synthesis of 4-aryl-NH-1,2,3-triazoles, 14 or its monohydrate version, which is an efficient catalyst in the synthesis of highly substituted pyridines. 15A classic example of a weak achiral Brønsted acid is acetic acid, which is used as an additive to promote the synthesis of 1,4,5-trisubstituted 1,2,3-triazoles 16 and as a catalyst in the synthesis of N-substituted 2-amino-3-cyanopyrroles. 17 In some situations, the presence of an acid in solution is not evident, as it may be present in undetectable amounts as an impurity in a reagent or solvent.In a 2013 report, Di Stefano and co-workers 18 observed that imine metathesis reactions took place in the absence of the free amine.The authors hypothesized that this behavior was due to the possible presence of an acid in trace amounts in the reaction medium, which would be catalyzing the reaction.This was confirmed by the addition of a proton sponge, which inhibited the reaction, and by the addition of trifluoromethanesulfonic acid (CF 3 SO 3 H), which accelerate the process. 18his is not a single case.In 2020, Valle and co-workers 19 conducted a reaction between epoxychalcone and semicarbazide hydrochloride in a methanol solution but failed to obtain carboxamide pyrazol-4-ol as a product.Using a theoretical methodology, it was verified that this result is justified by the presence of hydrochloric acid in the solution, which catalyzes the dehydration reaction of carboxamide pyrazol-4-ol.The experimental confirmation came in the same work when they obtained phenylpyrazole with a yield of 80% from the dehydration reaction of phenylpyrazol-4-ol catalyzed by hydrochloric acid. 19lso in 2020, a theoretical study 20 investigated the formation of imine from the reaction between methylamine and acetaldehyde in a toluene solution.Although a second molecule of methylamine, carbinolamine, and water were investigated as possible catalysts of the reaction, only when considering acetic acid as a catalyst was possible to obtain free energy barriers in agreement with experimental results. 20In this case, the presence of acetic acid is due to the reaction between one of the reagents, acetaldehyde, with oxygen in the air, 21 being an impurity that is difficult to eliminate completely. 22As an additional example, in a recent review paper by Meijer and co-workers, 23 the authors discuss as an impurity can play an important role in the reproducibility of experiments in supramolecular systems.One example was the catalytic effect of the presence of trace amounts of K 2 CO 3 in the catalysis of a Michael addition.
In recent years, our research group has been investigating the impact of the presence of carboxylic acids as contaminants in the imine formation reactions, and in the conjugate 1,4-addition reactions using acetic acid as a model catalyst. 20,24Regarding the formation of imines, acetic acid catalyzes the transfer of protons in the formation of carbinolamine and its dehydration, with the concentration having a direct impact on the reaction rate. 20n the Michael reactions, it also catalyzes the protontransfer step, although in this case, the proton-transfer step is not the rate-determining one.Nevertheless, catalysis is essential for the reaction to take place. 24n this work, we have investigated the acid-catalyzed competition between 1,2 versus 1,4 addition reactions involving a primary amine and a,b-unsaturated aldehyde.As a model system, we have used benzylamine and crotonaldehyde in a toluene solution, which experimentally leads only to the formation of imine (Scheme 1). 25 In order to verify the influence of the kind of acid contaminant on the reaction mechanism and kinetics, we chose two prototype acids: methanesulfonic acid and acetic acid.We performed the elucidation of the respective reaction mechanism and determined the free energy profiles, followed by a detailed microkinetic analysis.

Electronic structure calculations with continuum solvation model
The reaction between crotonaldehyde and benzylamine can form 1,4-addition products as well as 1,2-addition products, but experimentally only the latter is observed. 25ne of the ways to obtain accurately free energy for each structure at a reasonable computational cost is to use a composite method. 26In a composite method, less expansive although accurate functionals (hybrid Generalized Gradient Approximation (GGA) functionals) are used effectively for geometry optimization, and then single-point calculations are carried out to obtain reliable electronic energy with more reliable functionals (hybrid meta GGA functionals). 26n a 2016 benchmarking study of 59 functionals, 27 B3LYP and X3LYP hybrids performed between 70 and 80% compared to the double-hybrid xDH-PBE0, the better functional for structural parameters of small and medium-sized organic molecules, according to the authors' analysis. 27More recently, Karton and Spackman 28 investigated the performance of 52 functionals in obtaining structures for 122 species and their impact on the subsequent energy calculation with CCSD(T) involved in the W1-F12 theory.Among the six hybrids GGA with excellent performance, the X3LYP functional presented a root-mean square-deviation (RMSD) of 0.25 kJ mol -1 (0.06 kcal mol -1 ) and a mean-absolute deviation (MAD) of 0.18 kJ mol -1 (0.04 kcal mol -1 ), which makes it a recommended functional for geometry optimization in composite methods, with slightly better performance than B3LYP. 28Thus, geometry optimizations and harmony frequencies calculations were performed with X3LYP 29 functional and def2-SVP 30 (ma-def2-SVP 31 for N and O) basis set.As it is a reaction carried out in a toluene solution, we included the effect of the solvent in the geometry optimizations through the continuum solvation model SMD (solvation model based on density). 32he functional chosen for single point energy calculations was the M06-2X, which in a 2017 benchmarking study 33 of 200 functionals, had an uncertainly of 2.6 kcal mol -1 for barrier high.Thus, single-point calculations were performed with the M06-2X functional 34 with the def2-TZVPP basis set 30 (ma-def2-TZVPP for N and O). 31 The solvation free energy was obtained through single-point calculations at SMD/X3LYP/def2-SVP (ma-def2-SVP for N and O) level of theory.The solution phase free energy (G sol ) was determined by equation 1.
G sol = E el + G n + ∆G solv + 1.89 kcal mol -1 (1) Scheme 1. Reaction between benzylamine and crotonaldehyde in toluene solution with a molecular sieve as a drying agent.
The first term on the right side is the electronic energy (E el ) obtained at M06-2X/def2-TZVPP (ma-def2-TZVPP for N and O) level of theory.The second term on the right side refers to the nuclear contributions to rotational, vibrational, and translational contributions to the free energy (G n ) obtained at SMD/X3LYP/def2-SVP (ma-def2-SVP for N and O) level of theory.The third term on the right side refers to the solvation free energy (∆G solv ) obtained at SMD/X3LYP/ def2-SVP (ma-def2-SVP for N and O) level of theory.The fourth term (1.89 kcal mol -1 ) is the correction of the standard state from 1 atm to 1 mol L -1 .[37] Kinetics analysis and microkinetic modeling of the reactions Initially, we performed a general kinetics analysis of the reaction between benzylamine and crotonaldehyde in a toluene solution, deducing the kinetic law from the ratedetermining step, with the rate constants being calculated using the conventional transition state theory: where k b is the Boltzmann constant, T is temperature, h is the Planck constant, R is the gas constant and ∆G ‡ is the activation Gibbs free energy.
We have also performed microkinetic modeling, which considers the rate constants of each step as well as the concentration of the species, thus providing a better description of the kinetic behavior.All the microkinetic modeling was done with the Kintecus program 38 and the details are in the Supplementary Information (SI) section.

Results and Discussion
As discussed in our previous work, 39 there are two main pathways in which the reaction between a primary amine and a a,b-unsaturated aldehyde or ketone can occur: 1,2-addition and 1,4-addition.In this work, we have explored the mechanistic pathways between crotonaldehyde and benzylamine aimed to explain why 1,2-addition products are obtained while 1,4-addition product is not.The direct bimolecular mechanism is very high in ∆G ‡ and participation of a second amine molecule in the transition state is also kinetically inviable.Thus, we have considered that some acids may be present as contaminants in one of the reagents or even in the solvent, which could have an important catalytic effect.Because aldehydes are easily oxidated by oxygen, carboxylic acid is a usual contaminant.In the case of toluene solvent, sulfur compounds, and the corresponding acids could also be present.Therefore, we have considered the role of two different acids as model catalysts of this reaction system: acetic acid and methanesulfonic acid.
Crotonaldehyde, an a,b-unsaturated aldehyde, is structurally composed of two main functional groups: a carbonyl and a double bond.These two functional groups are separated by a single bond, which, having the freedom to undergo rotation, can give rise to two conformational isomers: s-trans crotonaldehyde and s-cis crotonaldehyde (Scheme 2).In terms of energy, the s-trans conformation is more favorable than the s-cis conformation, but isomerization can occur with free energy in solution of 2.4 kcal mol -1 .

1,2-Addition reaction of benzylamine to crotonaldehyde via concerted mechanism and amine-catalysis
The first step of the 1,2-addition reaction of benzylamine (BnNH 2 ) to crotonaldehyde leads to the formation of carbinolamine MS1ac (Figure 1), with a free energy in solution of 6.2 kcal mol -1 , or carbinolamine MS1at (not presented), with a free energy in solution of 6.4 kcal mol -1 .Different possibilities of transition states that could lead to the formation of carbinolamine were investigated.The first possibility considered was a direct bimolecular mechanism, in which there is the transfer of a proton from the nitrogen atom to the oxygen atom simultaneously with the formation of the carbon-nitrogen bond through the nucleophilic attack of BnNH 2 to the carbonyl carbon.The transition state considering the s-cis conformation of crotonaldehyde (TS1ac) has a free energy barrier of 38.4 kcal mol -1 , while a transition state considering the s-trans conformation of crotonaldehyde (TS1at, not presented) has a free energy barrier of 39.8 kcal mol -1 .The kinetic unfeasibility of a concerted mechanism is clear, as already verified in other theoretical studies. 20,24he second possibility of a transition state was the transfer of protons from the nitrogen atom of BnNH 2 to the oxygen atom of crotonaldehyde, aided by a second molecule of BnNH 2 , synchronously with the formation of the carbon-nitrogen bond between the first ones.In this case, a transition state of the s-cis conformation of Scheme 2. Equilibrium between the conformational isomers of crotonaldehyde.crotonaldehyde (TS2ac, not presented) has a free energy barrier of 36.1 kcal mol -1 and considering the s-trans conformation of crotonaldehyde (TS2at), the value of free energy barrier becomes 36.1 kcal mol -1 .Both options were ineffective in lowering free energy barriers.
In the second step of this mechanism, there is the formation of s-trans a,b-unsaturated imine (MS2bt) through the dehydration of carbinolamine MS1ac, with free energy in solution of -2.1 kcal mol -1 .Another conformational isomer possible is the s-cis a,bunsaturated imine (MS2bc), but its free energy in solution is 0.9 kcal mol -1 .Therefore, it is thermodynamically less favorable.The first possibility of the transition state investigated for this step was the breaking of the bond between the carbon atom and the oxygen atom, and the deprotonation of the nitrogen atom, leading to the formation of the final products, imine, and water.Relatively high values were obtained for the barriers considering both isomers, with TS1bc presenting a value of 54.9 kcal mol -1 and TS1bt a value of 51.6 kcal mol -1 .We have also considered the transfer of a proton from the nitrogen atom to the oxygen atom aided by a second molecule of BnNH 2 .The transition state considering the s-cis conformation of crotonaldehyde (TS2bc) has a free energy barrier of 45.1 kcal mol -1 , and a transition state considering the s-trans conformation of crotonaldehyde (TS2bt) has a free energy barrier of 45.3 kcal mol -1 .Thus, these mechanisms do not explain the kinetics viability of the reaction and other mechanisms are taking place.

1,2-Addition reaction of benzylamine to crotonaldehyde catalyzed by acetic acid
The first acid chosen to investigate was acetic acid (AcOH) and the free energy profile is presented in Figure 2. Initially, a complex can be formed between BnNH 2 and AcOH (MS1Ac, not presented) with free energy in solution of 1.1 kcal mol -1 .In sequence, there is the nucleophilic attack of BnNH 2 to the carbonyl carbon of crotonaldehyde, and the transfer of a proton between the nitrogen atom of BnNH 2 to the oxygen atom of crotonaldehyde assisted by AcOH (TS3at).This step has a free energy barrier of 16.9 kcal mol -1 , leading to the formation of a complex between AcOH and newly formed carbinolamine (MS3at) with free energy in solution of 5.0 kcal mol -1 .This complex can dissociate, forming the carbinolamine MS1ac and AcOH with free energy in solution of 6.2 kcal mol -1 .
In the last step, there is the dehydration of carbinolamine MS1ac, leading to the formation of the s-trans a,b-unsaturated imine MS2bt, with free energy in solution of -2.1 kcal mol -1 .In this case, AcOH also catalyzes the transfer of a proton from the nitrogen atom to the hydroxide ion, forming a complex between MS1ac and AcOH, named MS3bt, with free energy in solution of 4.6 kcal mol -1 .The transition state catalyzed by AcOH (TS3bt) has a free energy barrier of 21.4 kcal mol -1 and its impact on the kinetic depends on the concentration of AcOH.It is worth observing the huge catalytic effect of AcOH, decreasing the ∆G ‡ by 30 kcal mol -1 .

1,2-Addition reaction of benzylamine to crotonaldehyde catalyzed by methanesulfonic acid
The second investigated acid catalyst was methanesulfonic acid (CH 3 SO 2 OH).Because it is a stronger acid than AcOH, we initially verified a possible formation of an ion pair between BnNH 2 and CH 3 SO 2 OH, which was found (Figure 3).In the structure, called MS1PI, it is possible to observe the retention of a proton from CH 3 SO 2 OH by the nitrogen atom from amine (BnNH 2 ), with free energy in solution of -4.8 kcal mol -1 .Because the toluene solvent has a very low dielectric constant, this ion pair does not dissociate.A recent study 40 has reported the formation of aggregates between organic basis and strong organic acids in low-polarity solvents.
In sequence, the CH 3 SO 3 -ion retakes the proton from the protonated BnNH 2 , which makes a nucleophilic attack to the carbonyl carbon of crotonaldehyde, with CH 3 SO 2 OH catalyzing the transfer of a proton from the nitrogen atom to the oxygen atom (TS4at).This transition state TS4at (s-trans conformational isomer) has a free energy of only 9.3 kcal mol -1 while its isomer (TS4ac) has a free energy of 9.6 kcal mol -1 , both in relation to s-trans crotonaldehyde, amine, and methanesulfonic acid.However, when looking at Figure 3, we can observe that the lowest energy point is MS1PI, resulting that ∆G ‡ =14.1 and 14.4 kcal mol -1 for TS4at and TS4ac, respectively.The product of this step is an ion pair between protonated carbinolamine and CH 3 SO 3 -, named MS4ac, with free energy in solution of -4.8 kcal mol -1 .The product of this step is substantially more stable than the free species, with MS1ac having free energy in solution of 6.2 kcal mol -1 in relation to MS4ac, a difference of 11.0 kcal mol -1 .In other words, MS4ac is the true intermediate.
In the next step, there is the dehydration of the carbinolamine in the MS4ac complex catalyzed by CH 3 SO 2 OH, also formed by retaking the proton from protonated carbinolamine.The CH 3 SO 2 OH species transfers a proton to the leaving hydroxide ion.Unlike of acetic acid, the proton remains on the nitrogen atom, forming an ion pair between the iminium ion and CH 3 SO 3 -(MS4bt).The corresponding transition state (TS4bt) has a free energy of 9.5 kcal mol -1 in relation to s-trans crotonaldehyde and 14.3 kcal mol -1 in relation to MS4ac.The ion pair formed after passing through TS4bt, denominated MS4bt, has a free energy in solution of -3.2 kcal mol -1 .The corresponding free species, a,b-unsaturated imine (MS2bt), and H 2 O, have free energy in solution of -2.1 kcal mol -1 .Overall, we can notice that sulfonic acid is a very powerful catalyst for this reaction, even overcoming acetic acid.Thus, this first analysis suggests that trace amounts of sulfonic and related acids could be very effective catalysts for this kind of reaction.

1,4-Addition reaction of benzylamine to crotonaldehyde
The 1,4-addition reaction occurs through the formation of a bond between the nitrogen atom from BnNH 2 and the b-carbon atom of crotonaldehyde and is followed by the protonation of the a-carbon of crotonaldehyde (Figure 4).In the first step, the transition state related to the s-trans conformation of crotonaldehyde has a free energy barrier of 28.8 kcal mol -1 .In the case of the s-cis conformation of crotonaldehyde, a lower barrier was obtained, with ∆G ‡ = 26.0kcal mol -1 (TS1cc).The introduction of the acetic acid molecule, catalyzing this step, does not lead to any gain in terms of stability.It makes the nucleophilic attack even more unfeasible, with TS3cc having a free energy barrier of 31.9 kcal mol -1 .The product of this step via TS1cc is the enol MS1cc, with free energy in solution of 5.1 kcal mol -1 .
Despite not being an effective catalyst in the first step, acetic acid can form a complex with the enol (MS1cc) forming MS2cc with free energy in solution of 8.8 kcal mol -1 .By forming a hydrogen bond with the hydroxyl group of the enol, acetic acid provides the stabilization for the charge that will be formed on the oxygen atom as a proton is transferred from it to the nitrogen atom.The transition state obtained (TS2cc) has a free energy barrier of 9.9 kcal mol -1 , leading to the formation of a zwitterion complexed with acetic acid (MS3cc), which has a free energy in solution of 11.4 kcal mol -1 .
In the final step of this reaction, acetic acid catalyzes the transfer of a proton from the nitrogen atom to the a-carbon of the zwitterion, as it reconstitutes itself.The transition state (TS4cc) has a free energy of 18.3 kcal mol -1 and leads to the formation of a 1,4-addition product complexed with acetic acid (MS5cc) with a free energy in solution of 1.8 kcal mol -1 .The decomplexation between these two species leads to the free 1,4-addition product (MS2ct) with free energy in solution of 1.4 kcal mol -1 .
We also consider the feasibility of CH 3 SO 2 OH to catalyze the 1,4-addition reaction (Figure 5).As mentioned earlier, initially there is the formation of an ion pair between BnNH 2 and CH 3 SO 2 OH (MS1PI) with free energy in solution of -4.8 kcal mol -1 , which leads to a lower concentration of free species available for the first step of the 1,4-addition reaction.Initially, we investigated as the first possibility the formation of nitrogen-carbon bond through the nucleophilic attack of BnNH 2 to the b-carbon of crotonaldehyde and protonation of a-carbon of crotonaldehyde, catalyzed by CH 3 SO 2 OH.The transition state obtained, (TS3ct, not presented) has a free energy barrier of 29.5 kcal mol -1 in relation to reagents and 34.3 kcal mol -1 in relation to MS1PI, kinetically unfeasible.
Finally, as a second possibility, we consider that following the formation of enol MS1cc, it can form a complex with CH 3 SO 2 OH, resulting in MS2sc with free energy in solution of 6.9 kcal mol -1 .This complex can go through two different transition states in the position where CH 3 SO 2 OH is found, but similar in the transfer of a proton from the oxygen atom of the enol to the nitrogen atom.In the first transition state (TS2sc) there is a transfer of a proton from the oxygen atom to the nitrogen atom and CH 3 SO 2 OH transfers a proton to the oxygen atom, leading to the formation of an ion pair between the protonated enol (in the nitrogen atom) and CH 3 SO 3 -.The transition state (TS2sc) has a free energy of 7.0 kcal mol -1 and the ion pair MS3sc has a free energy in solution of 5.4 kcal mol -1 .In the second transition state (TS5sc), simultaneously with the transfer of a proton from the oxygen atom to the nitrogen atom, CH 3 SO 2 OH protonates the a-carbon of the enol, leading to the formation of an ion pair between CH 3 SO 3 -and 1,4-addition product protonated in the nitrogen atom.The transition state TS5sc has a free energy of 13.6 kcal mol -1 and the ion pair MS6sc has a free energy in solution of -8.0 kcal mol -1 .The dissociation of this complex to form the 1,4-additon product MS2ct is unfavorable, with this species having a free energy of 1.4 kcal mol -1 .

General kinetics analysis of the reaction between benzylamine and crotonaldehyde
We started our kinetics analysis with the 1,4-addition reaction, whose product (MS2ct) is thermodynamically less favorable for its formation when compared to the product of the 1,2-addition reaction.In this case, the rate-determining step takes place with the nucleophilic attack of benzylamine to the s-cis conformation of crotonaldehyde (TS1cc), in the absence of a catalyst.Thus, the rate law ignoring backward reaction can be written as: (3)  With a free energy barrier of 26.0 kcal mol -1 , the corresponding rate constant has a value of 5.3 × 10 -7 L mol -1 s -1 , limiting the formation of MS2ct to trace amounts at room temperature.In this analysis, we are considering the initial concentration of the crotonaldehyde and amine reactants as 0.25 mol L -1 .
On the other hand, the 1,2-addition reaction can be catalyzed by AcOH or CH 3 SO 2 OH, with the rate-determining step in both cases being the dehydration of carbinolamine.Considering AcOH catalysis as a first case and the species involved in this step, the rate law can be written as: The transition state TS3bt has a free energy barrier of 21.4 kcal mol -1 .If AcOH is present at a concentration of 1 mol% (2.5 × 10 -3 mol L -1 ), we can write that the product k[AcOH] = 3.4 × 10 -6 L mol -1 s -1 .This is a pseudo-secondorder rate constant with = 24.9kcal mol -1 , allowing a slow formation of MS2bt.
On the other hand, when CH 3 SO 2 OH catalyzes the 1,2-addition reaction, it initially forms an ionic pair (MS1PI) with the BnNH 2 , whose higher stabilization than the free species implies its predominance in solution.Thus, the rate law can be written as: (6) (7)   The transition state TS4bt has a free energy barrier of 14.3 kcal mol -1 in relation to MS1PI.Considering a concentration of only 0.01 mol% of CH 3 SO 2 OH (2.5 × 10 -5 mol L -1 ), we can write that the product k[CH 3 SO 2 OH] = 5.2 × 10 -3 L mol -1 s -1 .This is a pseudofirst-order rate constant with = 20.6 kcal mol -1 .This finding indicates that even an undetectable trace amount of sulfonic acid is able to promote the catalysis and the formation of a 1,2-addition product.
In the experiments, there is a conversion of 90% of reagents in 310 min, and concentrations of 0.25 mol L -1 for the reagents. 25The experimental rate constant (k obs ) can be estimated as a value of 1.2 × 10 -4 s -1 considering equation 6, a pseudo-first-order rate constant, which corresponds to the observed ∆G ‡ = 22.8 kcal mol -1 .This analysis suggests that if sulfonic or similar acid indeed catalyzes the reaction (if they are present in the solution), then an even lower concentration of this acid would be present.Thus, it would be a hidden catalyst of the reaction.

Detailed microkinetic analysis of the reaction between benzylamine and crotonaldehyde
The reaction between benzylamine and crotonaldehyde was carried out experimentally at room temperature in a toluene solution with a concentration of 0.25 mol L -1 for both reagents, with and without the use of molecular sieves.Based on the experimental value of using molecular sieves in toluene, 41 we have assumed the water concentration to be constant at 8.5 × 10 -6 mol L -1 along the microkinetic modeling.We analyzed the effect of different concentrations of acetic acid (1 and 100 mol%) and methanesulfonic acid (0.01 and 0.1 mol%).The microkinetic model used by us is presented in the SI section, with the rate constants calculated using the transition state theory and kinetic equations integrated with the Kintecus program.
The first system investigated is the catalysis by acetic acid (AcOH) with a concentration of 1 mol% (2.5 × 10 -3 mol L -1 ) and a reaction time of 6 days (Figure 6a).We can observe in the figure a slow decline in the concentration of CrotT (s-trans crotonaldehyde) with the concentration reaching 1.7 × 10 -1 mol L -1 at approximately 6 days.In fact, we can see the predominant formation of imine (MS2bt), but also a minimal amount of MS2ct (1,4 addition product), with the concentration rising slightly to a maximum of 3.6 × 10 -3 mol L -1 in 3 days and 13 h and then starting to decrease.As it is a catalyzed reaction, the concentration of AcOH has a direct impact on the reaction rate (Figure 6b), with the CrotT concentration halving in 13 h when using 100 mol% of AcOH and a reaction time of 1 day.In both cases, the amount of AcOH available for catalysis is lower, due to the formation of dimers.When using 1 mol%, the concentration of free acid is 0.002 mol L -1 , and when using 100 mol%, 0.049 mol L -1 .
In sequence, we evaluated the effect of methanesulfonic acid (CH 3 SO 2 OH), in the concentration of 0.01 mol%, with the use of molecular sieves (Figure 7a) and without the use of molecular sieves (Figure 7b), in the same reaction time of 15 min.As it is a stronger acid, in addition to the formation of dimers, the ionic pairs formed during the reaction were also considered, having a direct impact on the concentration of free acid, which changes throughout the reaction.In the Figure 7a, we have observed a fast formation of MS2bt, with the concentration of CrotT halving in approximately 5 min, and reached a conversion above 92% of the reagents to MS2bt at the end of the 15 min reaction time.Without the use of molecular sieves, the only difference is the lower conversion of reagents to MS2bt, reaching a value of 84.9% (Figure 7b).
We also evaluated the effect of using 0.1 mol% of CH 3 SO 2 OH in the reaction time of 5 min, with the use of molecular sieves (Figure 8a) and without the use of molecular sieves (Figure 8b).In Figure 8a we can see that in less than 3 min, there is an almost complete conversion of CrotT into MS2bt.In Figure 8b, MS2bt reaches a maximum concentration of 0.21 mol L -1 at approximately 2 min and maintains a constant concentration.
Based on these detailed microkinetic analyses, which are in line with a simpler kinetics analysis of the previous section, it is evident that methanesulfonic acid is a very  powerful catalyst for this reaction, and even a trace amount can catalyze imine formation.

Conclusions
In this work, a detailed theoretical investigation of the mechanisms of 1,2-addition and 1,4-addition reactions between benzylamine and crotonaldehyde in a toluene solution was performed.From our results, direct bimolecular and amine-catalyzed mechanisms are unviable due to very high ∆G ‡ , leading to very slow kinetics that cannot explain this reaction.Rather, the formation of the imine is possible by the presence of acids in the solution, which effectively catalyzes the 1,2-addition.The mechanisms by which acetic acid and methanesulfonic acid catalyze the 1,2-addition and 1,4-addition reactions have some differences.While acetic acid catalyzes the transfer of protons and reconstitutes itself after passing through the transition state, methanesulfonic acid also provides proton transfer.However, it forms highly stable ion pairs in solution.In the 1,2-addition reaction, the formation of these stable ion pairs does not compromise the formation of the final product, since the catalyst is present in small amounts.In fact, methanesulfonic acid was found to be a very powerful catalyst, being effective even in a trace amount of 0.0003% in mass in a toluene solution.

Figure 1 .
Figure 1.Free energy profile for s-trans a,b-unsaturated imine (MS2bt) formation from the reaction between crotonaldehyde and BnNH 2 in toluene via direct bimolecular mechanism and amine-catalysis.Units in kcal mol -1 , standard state of 1 mol L -1 for all species, 298 K temperature.

Figure 2 .
Figure 2. Free energy profile for s-trans a,b-unsaturated imine (MS2bt) formation from the reaction between crotonaldehyde and BnNH 2 in toluene catalyzed by acetic acid.Units in kcal mol -1 , standard state of 1 mol L -1 for all species, 298 K temperature.

Figure 3 .
Figure 3. Free energy profile for s-trans a,b-unsaturated imine (MS2bt) formation from the reaction between crotonaldehyde and BnNH 2 in toluene catalyzed by methanesulfonic acid.Units in kcal mol -1 , standard state of 1 mol L -1 for all species, 298 K temperature.

Figure 4 .
Figure 4. Free energy profile for 1,4-addition of BnNH 2 to crotonaldehyde in toluene without catalyst and catalyzed by acetic acid.Units in kcal mol -1 , standard state of 1 mol L -1 for all species, 298 K temperature.

Figure 5 .
Figure 5. Free energy profile for 1,4-addition of BnNH 2 to crotonaldehyde in toluene catalyzed by methanesulfonic acid.Units in kcal mol -1 , standard state of 1 mol L -1 for all species, 298 K temperature.