Friedel-Crafts Reaction: Theoretical Study of the Mechanism of Benzene Alkylation with Isopropyl Chloride Catalyzed by AlCl3 and Al2Cl6

The classical alkylation reaction of benzene with isopropyl chloride catalyzed by the species AlCl3 and Al2Cl6 was studied using reliable calculations at M06-2X/def2-TZVPP//X3LYP/def2/SVP level of theory and SMD model for solvent effect. We evaluated the formation of dimers, trimers, tetramers, and pentamers and showed that Al2Cl6 dimers exist in greater proportion, in agreement with experimental observations. The experimental solubility of Al2Cl6 in benzene was also included in the theoretical kinetics analysis. The reaction catalyzed by AlCl3 species presents the highest barrier, in part due to unfavorable dissociation of the Al2Cl6 species. The mechanism via Al2Cl6 catalysis is more effective and even considering its low solubility, the calculated observed DG‡ is only 20.6 kcal mol-1, indicating a fast reaction rate. The mechanism involves the formation of the CH3CHCH3+…Al2Cl7- ion pair, which reacts with benzene to form a Wheland intermediate and this carbon-carbon bond formation step corresponds to the rate-determining one.


Introduction
2][3][4][5][6] In the case of alkylation, the methodology consists of using a Lewis acid, such as AlCl 3 , to activate the alkyl halide (RX), forming an active intermediate (R + or R−X⋅⋅⋅AlCl 3 ) able to promote an electrophilic substitution reaction with the aromatic compound. 1,2,5,6The reaction involves the Wheland or σ intermediate, which loss a proton, leading to the formation of the alkylated product and regeneration of the catalyst. 1,2,5This process is depicted in Scheme 1 for the benzene alkylation reaction catalyzed by AlCl 3 .8][9] This kind of methodology has been used in applications from petroleum chemistry to drug synthesis. 3,6though the Friedel-Crafts reaction is practical and very useful, some aspects make your application limited, especially with classical catalysts such as AlCl 3 .For example, AlCl 3 leads to isomerization of primary alkyl halides, resulting in different isomers in the product. 10,11]5,6 Another unfavorable point is that AlCl 3 can often form complexes with reactants and products, requiring the use of stoichiometric amounts of the catalyst. 6[14][15] Scheme 1. Usual mechanism of Lewis acid-catalyzed alkylation of benzene found in textbooks.0][21][22][23][24][25][26] In particular, the mechanism of the Friedel-Crafts alkylation is not as simple as the Scheme 1 suggests.Indeed, Yamabe and Yamazaki 19 have reported a detailed theoretical study of this reaction, with important contributions for our understanding of its mechanism.They have reported a mechanism involving the dimeric Al 2 Cl 6 species, rather the monomeric AlCl 3 .It is worth to say that the monomeric pathway was not analyzed, neither the dimerization equilibrium, which is critical to decide on the mechanism.In addition, they have reported that the carbon-carbon bond formation step, leading to the Wheland intermediate, is not the rate-determining one.Rather, they have found that a rearrangement of the formed product was the rate-determining step, an unexpected result.Therefore, this reaction should be investigated more deeply.Thus, the aim of this work is to perform a detailed study of the mechanism of a model Friedel-Crafts alkylation reaction and to obtain a reliable free energy profile.The system investigated is the reaction of isopropyl chloride (iPrCl) with benzene catalyzed by aluminum chloride in an apolar solvent, benzene (Scheme 2).Although many Lewis acid catalysts such as AlCl 3 , AlBr 3 , SbCl 5 , FeCl 3 , ZnCl 2 , etc. are known, the aluminum chloride is among the most active and is a classical Lewis acid for this reaction. 11ecause the reaction takes place in apolar medium, the different aggregates of AlCl 3 were investigated, and the solubility in benzene included in order to make an adequate comparison with experiments.It is worth to observe that classical electrophilic aromatic substitution reactions have been recently reinvestigated by reliable theoretical methods, 22,[27][28][29][30][31][32][33][34][35][36][37] providing more insights on these reactions.

Methodology
The calculations were carried out in four steps: first, the optimized geometries of the minima and transition states (TS) were obtained using the X3LYP functional 38 in conjunction with the def2-SVP basis set 39 for C, Al and H atoms, and the ma-def2-SVP basis set 40 for the O and Cl atoms.This is a reliable functional for determining geometries. 41These geometries were characterized as minima or transition states by harmonic frequency calculations.This calculation was also used to obtain the vibrational, rotational and translational contributions to the free energy (G vrt ) through the use of standard equations of statistical thermodynamics. 42Because we are describing reactions in condensed phase, the standard state of 1 mol L -1 was used to obtain the standard chemical potential in solution phase for all species by adding 1.89 kcal mol -1 to the free energy contribution obtained from frequency calculations.The third step was performing the single point energy calculation of the electronic energies (E ele ) using higher level of theory, the M06-2X functional and the def2-TZVPP basis set for the C, Al and H atoms, and ma-def2-TZVPP for the atoms of O and Cl. 43The M06-2X functional is a very reliable method for barrier height, staying in the top 10% best functionals in a recent benchmarking study involving 200 functionals. 44The forth step was determining the solvation free energy for each species (ΔG solv ) from the single point calculation using the continuum SMD model 45 with the X3LYP/6-31(+)G(d) electron density (benzene solvent).The final free energy for each species in the benzene solvent (G sol , 25 ºC, 1 mol L -1 ) corresponds to a composite approach and were calculated by: [51]

Formation of (AlCl 3 ) n complexes
The AlCl 3 catalyst can form dimers (dim, Al 2 Cl 6 ). 19,52urthermore, it is important to evaluate the possibility of the formation of larger complexes such as trimers (trim, Al  S1, Supplementary Information (SI) section).The ΔG for formation of these aggregates for each monomeric unit is equal to −8.38, −6.87, −6.53, and −5.98 kcal mol -1 , respectively.Thus, stabilization for each monomer unit is greater for the dim.To make this point clear, the formation of tetramer from dimer can be written as: Therefore, aggregates larger than the dimer can be formed in a small proportion and only AlCl 3 and Al 2 Cl 6 were considered in the description of the reaction mechanism in this work.The predominance of the dimer in solution phase is in agreement with experiments. 52

AlCl 3 catalyzed reaction
In this process, we have considered the initial Al 2 Cl 6 species as reference, because the monomer is less stable.In this analysis, we have used ∆G for each step (process) and also taking the initial reactants as reference (relative).Thus, the free energy profile in the Figure 1 points out that the monomer is 8.4 kcal mol -1 above of the dimer.The monomeric AlCl 3 species can interact with benzene (BZ), forming the BZ-AlCl 3 complex.The value of ΔG referring to this process is equal to −4.2 kcal mol -1 (Table S1), indicating that it is less favorable than the dimerization of AlCl 3 .As a result, the ΔG of this species in the free energy profile is 4.2 kcal mol -1 .In the case of the complexation of AlCl 3 with iPrCl to form iPrCl-AlCl 3 , the value of ∆G for the process is equal to −6.2 kcal mol -1 , also indicating that the Al 2 Cl 6 dimer is more stable, because the relative ∆G for this complex becomes 2.2 kcal mol -1 .These results point out that in solution phase, the catalyst is present in the form of dimers and the reactants do not form stable complexes with AlCl 3 in appreciable extension.
The alkylation of benzene must occur via the previously formed iPrCl-AlCl 3 complex.Next, the nucleophilic attack of BZ to this complex must take place via TS1 and forming the Wheland intermediate.The ∆G ‡ for this step calculated in benzene is 19.6 kcal mol -1 .When the free energy for the iPrCl-AlCl 3 complex is included, the value of ∆G ‡ for TS1 becomes 21.8 kcal mol -1 .This is the effective ∆G ‡ barrier.

Kinetic model for monomeric AlCl 3 catalysis
The kinetic model of a reaction is useful for a correct comparison between mechanisms, because the free energy profile alone may not be enough. 53 Equations 3 and 4 leads to the kinetic law: with k obs related to an observed free energy barrier of: The next step is quick and involves deprotonation of the intermediate.The details of all reaction steps were done only for the case of the mechanism involving the Al 2 Cl 6 , which is the most favorable reaction pathway.
The rate law in equation 6 does not take in account the solubility of the Al 2 Cl 6 in benzene, which has low solubility and can limit the reaction rate.Indeed, the experimental solubility of the Al 2 Cl 6 in benzene is only 3.6 × 10 -4 mol L -1 at 25 ºC. 52Considering this solubility in equation 5 leads to: with k' obs related to a new ∆G obs ‡ ' = 24.1 kcal mol -1 .This case corresponds to the use of higher amount of the catalyst, which has the reaction rate limited by its solubility.

Al 2 Cl 6 catalyzed reaction
Another possible reaction pathway is the direct involvement of the Al 2 Cl 6 dimer.The reaction via Al 2 Cl 6 catalysis has two pathways before the nucleophilic attack of benzene: the first one involving the previous complexation of the Al 2 Cl 6 dimer with BZ and iPrCl (Al 2 Cl 6 ..iPrCl..BZ) and the second with complexation between Al 2 Cl 6 and iPrCl only (Al 2 Cl 6 ..iPrCl).The calculated free energy profile is presented in the Figure 2 and the thermodynamic data are presented in Table S2 of the SI section.The values in Table S2 are considering the free species as reference, which is used in the discussion of the results.To facilitate the discussion, the processes presented in the Table S2 are numbered, and those related to the path involving Al 2 Cl 6 ..iPrCl..BZ is followed by the letter "a" and those involving Al 2 Cl 6 ..iPrCl are followed by the letter "b".These two pathways have a common intermediate, int1a1.From this point, there is a unique pathway.Because this reaction is very complex, with some subtle changes in the structures, some steps were omitted on the Figure 2, although are presented in the Figures S1 and S2 of the SI section.
Initially, pathway "a" begins with the formation of Al 2 Cl 6 ..iPrCl..BZ (process 1, Table S2) and the ΔG of this step is equal to 6.1 kcal mol -1 .It is important to note that this complex is not the "zero" of the free energy profile, as considered by Yamabe and Yamazaki. 19Next, the int1a1 intermediate is formed with a value of relative ∆G equal to 7.80 kcal mol -1 .This intermediate is very interesting, because there is a clear C−Cl and Cl−Al bonds involving the same chlorine atom (see Figures S1 and S2 in the SI section).At the same time, only one Cl makes the bridge between the Al atoms inside the formed Al 2 Cl 7 − anion.The conversion of int1a1 to int1a2 occurs via TS1a2 (process 4a, Table S2 and Figure S2, omitted in Figure 2).This transition state refers to the stretching of the C−Cl bond and a rearrangement of the complex, leading to a second ion pair, formed by the CH 3 CHCH 3 + carbocation and the Al 2 Cl 7 − anion, interacting with the benzene.In fact, the distance of the positively charged carbon of the carbocation to a carbon of the benzene is only 2.81 Å.The corresponding overall ∆G ‡ = 12.9 kcal mol -1 for TS1a2, an extremely low value, indicating as able the Al 2 Cl 6 is for inducing the formation of the carbocation.It is worth to observe that int1a2 has ∆G = 13.2 kcal mol -1 , slightly above of TS1a2, indicating that the int1a2 minima is a very shallow potential well or could not exist at all at a higher level of the theory used in the single point energy calculation.These structures, omitted from Figure 2, are not kinetically relevant.
The next step taking place is the critical one and involves the transition state TS2, corresponding to the formation of C−C bond via nucleophilic attack of the benzene to the carbocation.The overall ∆G ‡ = 15.9 kcal mol -1 , the highest barrier in the free energy profile, indicating that the solubilized Al 2 Cl 6 catalyst is indeed highly effective to promote the reaction.Further, it indicates that the Al 2 Cl 6 species is more active than AlCl 3 , and is responsible for the catalysis.It is worth to observe that Yamabe and Yamazaki 19 have not reported the step via TS2 as the highest in ∆G.Our results support the usual view that the formation of C−C bond via TS2 is the rate-determining step.
In the case of path "b", the process is similar to path "a".The calculations indicate higher stability of the Al 2 Cl 6 ..iPrCl than the Al 2 Cl 6 ..iPrCl..BZ complex, the former being 2.7 kcal mol -1 more stable than the latter.The reaction proceeds with the respective breaking of the Al−Cl bond, forming int1b1, which consists of the ion pair iPr + …Al 2 Cl 7 − .The respective transition state is TS1b1, which is 1.4 kcal mol -1 more stable than TS1a1.In the next step, the int1b1 ion pair interacts with a benzene, forming the int1a1 complex.We can note that both pathways "a" and "b" that ionize the iPrCl species can take place, because the difference between the barriers referring to TS1a1 and TS1b1 is small.The next step via TS2 has the critical free energy barrier, which determines the kinetics.
Once the system crosses the TS2 transition state, the intermediate int2 is formed (relative ΔG equals 12.5 kcal mol -1 , Table S2, process 7).The next step involves the migration of the proton to a vicinal carbon, and this process takes place through TS3, which has relative ∆G ‡ = 11.4 kcal mol -1 , below of int2.Again, we can note a very shallow well for int2 or even not a minimum at higher level of theory.On the other hand, the free energy profile indicates that int3 is a kinetically more stable intermediate, involving an ion pair.Finally, there is removal of the proton by the Al 2 Cl 7 − species via TS4, with the respective formation of the int4.The overall ΔG ‡ for this transition state is 11.0 kcal mol -1 (process 10, Table S2) and int4 has a free energy of 10.6 kcal mol -1 (process 11, Table S2).This intermediate is a weakly bond complex between the final alkylated benzene and the HAl 2 Cl 7 species.The dissociation forming a free HAl 2 Cl 7 species and the alkylated product (BZiPr) leads to decrease of the free energy value to 1.0 kcal mol -1 .In the last step, the HAl 2 Cl 7 species dissociates, regenerating the Al 2 Cl 6 and releasing the HCl, with the value of ΔG equal to −3.2 kcal mol -1 .Therefore, the reaction is thermodynamically favorable, although the final free energy is slightly negative.This fact indicates that to reach a high yield, the reaction should not be performed in high temperature.

Kinetic model for dimeric Al 2 Cl 6 catalysis
5][56] Usually, this reaction takes place very quickly in solution phase and only catalytic quantities of the catalyst is needed for alkyl halide reactions catalyzed by aluminum chloride.Further, because the Al 2 Cl 6 species can interact with solvents having Lewis base groups such as nitrobenzene, the kinetic law can be different in different solvents.In the present case, because the reaction takes place in low polarity benzene solution, the Al 2 Cl 6 species predominates in solution phase.In addition, the experimental solubility of the Al 2 Cl 6 in benzene, which is only 3.6 × 10 -4 mol L -1 at 25 ºC, 52 needs be taken in account.This solubility leads to the equilibrium: where T is the temperature and R the gas constant.Based on the free energy profile of Figure 2, the reaction rate is determined by the process: Al 2 Cl 6 + BZ + iPrCl → TS2 ∆G 2 ‡ = 15.9 kcal mol -1 (10)   And the rate law is: with k 2 related to equation 10.This rate law corresponds to the use of the catalyst with concentration below of its solubility limit.When the solution is saturated, we can combine equations 9 and 11, which leads to the observed rate law: with k obs related to an observed free energy barrier of: This low ∆G ‡ corresponds to quick reaction rate in solution phase, in agreement with experimental observations of the small reaction time at room temperature for isopropyl bromide reactant. 56The ∆G ‡ also agrees with longer reaction time (5 h at −6 ºC, 41% conversion) for the less reactive chloride. 10In addition, under this low polarity condition, the system could not be homogenous, as the limited solubility of Al 2 Cl 6 indicates.Thus, we have not found experimental ∆G ‡ for this system, only a related one in more polar, homogeneous medium. 54ndeed, DeHaan et al. 54 have reported the isopropylation reaction of benzene with isopropyl chloride in nitromethane solution and have found a third order kinetics with rate constant of 5.2 × 10 -2 L 2 mol -2 s -1 , which translate to ∆G ‡ = 19.2kcal mol -1 at 25 ºC.Although the agreement with our value is very good, the reaction in nitromethane has a different mechanism and should involve the soluble AlCl 3 −O 2 NCH 3 complex (present in the rate law).Such polar solvent could be able to generate solvated carbocation instead of the ion pair in low polarity medium.

Conclusions
The mechanism of benzene alkylation with isopropyl chloride using the aluminum chloride as catalyst was studied in detail in apolar benzene solution using theoretical methods.A reliable free energy profile was obtained, and the calculations were followed by a kinetics analysis, including the low solubility of the catalysts.It was found that the catalyst exists as Al 2 Cl 6 dimers, and this species is the active one in the catalysis.The reaction proceeds via formation of the CH 3 CHCH 3 + …Al 2 Cl 7 − ion pair, which reacts with benzene to form the carbon-carbon bond.This step is the rate-determining one, supporting the usual view of this reaction whose kinetics is determined by the carboncarbon bond formation step.

Scheme 2 .
Scheme 2. Reaction investigated in this work.

Figure 1 .
Figure 1.Free energy profile (ΔG) of the benzene alkylation reaction by isopropyl chloride using AlCl 3 as the catalytic species determined by theoretical calculations in benzene solution.Units in kcal mol -1 , 25 ºC, and 1 mol L -1 standard state.The optimized structures were obtained at X3LYP/def2-SVP level (see Figure S1 in the SI section).Single point energy calculation at M06-2X/ma-def2-TZVPP level.Wheland intermediate not included.

Figure 2 .
Figure 2.Free energy profile (ΔG) of the benzene alkylation reaction by isopropyl chloride using Al 2 Cl 6 as the catalytic species determined by theoretical calculations in benzene solution.Units in kcal mol -1 , 25 ºC, and 1 mol L -1 standard state.The optimized structures were obtained at X3LYP/def2-SVP level (see FigureS1in the SI section).Single point energy calculation at M06-2X/ma-def2-TZVPP level.Some structures were omitted for clarity.More complete mechanism in the SI section (FigureS2).Brackets were used for ion-pair and van der Walls complexes.