Friedel-Crafts Reaction of N,N-Dimethylaniline with Alkenes Catalyzed by Cyclic Diaminocarbene-Gold(I) Complex

In general, Friedel-Crafts reaction is incompatible with amines due to the Lewis acidity of the catalysts. Recently, we reported that cyclic diaminocarbene-Gold(I) can be used as catalyst for the Friedel-Crafts alkylation between aromatic amines and alkenes. Herein, a systematically theoretical research was performed on this rare Friedel-Crafts reaction. The adopted calculation method is accurate enough to reproduce the crystal structure of the catalyst. It was found that the reactions followed the electrophilic aromatic substitution mechanism. The gold cation can activate the C=C double bond and generate the electrophilic group which can be attacked by the aromatic ring. The para-product is more energy favorable which agrees well with the experimental results. The reaction of α-methylstyrene follows the Markovnikov rule, and the activation energy to generate the branched product of methylstyrene is lower than that producing the linear product. However, the reaction of butanone follows the anti-Markovnikov rule, and the activation energy to generate the branched product of butanone is higher than that producing the linear product. These calculation results reveal the mechanism of this new Friedel-Crafts reaction. It can well explain the high para-selectivity and the substrate-dependent of the product structures in the experiment.


Results and Discussion
The structure of the catalyst. To examine the reliability of the theoretical method, the structure of the catalyst 1 was fully optimized with both B3LYP and M06-2X methods. The calculated results were compared with the x-ray experiment data ( Table 1). The calculated structure parameters match well with the experiment data. Most of the calculation errors for the bond length and angle are smaller than 1.0% and the maximum error is 1.7%. It suggests that the calculation method used here is accurate enough to reproduce the crystal structure even though the catalyst contain gold atom. Indeed, methods based on DFT using pseudopotential basis set have    been widely used for the calculation of compound containing gold [41][42][43][44][45][46][47][48][49][50][51] . Our previous experimental results on the hydration of alkynes catalyzed by gold(I) isocyanide were successfully explained by theoretical calculation based on DFT 41 . According to the experimental results, the conversion of the hydroarylation between N,N-diethylaniline and α-methylstyrene is zero when only 1 is used as catalyst. However, the conversion is 97% when chlorine scavenger reagent KBArF was added in the presence of 1 33 . It suggests that the active center in the reaction should be The pathway 1 to produce 5a by the Friedel-Crafts reaction between 2 and 3 without the assistance of aromatic amine (Energy in kcal/mol). Energies out of parenthesis were obtained at M06-2X (6-311 + G*/ LANL2DZ). Energies in parenthesis were obtained at M06-2X (6-311 + G*/LANL2DZ) by PCM calculation. (b) The structures of the optimized transition states (Bond length in Å). All hydrogen atoms (except the transferred H) have been omitted for clarity.
anti-Bredt carbene-Au + cation 1 + (Fig. 2). Similarly, other kinds of carbene-Au + cations have been proposed to be the active catalytic species in a series of reactions 52-55 . The reaction between 2 and 3. 5a is the main product in the reaction between N,N-Dimethylaniline 2 and alkene 3 33 . There has two possible pathways to produce 5a (Fig. 3). Pathway 1: the gold cation activates As we known, FC reaction is a kind of electrophilic aromatic substitution reactions, in which the hydrogen atom of aromatic ring is replaced by an electrophile 1,56-59 . The complex 1 +… 3 can serve as the electrophilic reagent (Fig. 2). It has been known that the gold cation has strong ability to bind alkene 60,61 . The binding between alkene 3 and catalyst 1 + is highly exothermic (33.6 kcal/mol). The C=C bond length of alkene 3 was increased from 1.347 to 1.391 Å, which indicates that the C=C bond was activated after binding with 1 + .
For pathway 1, both C c and C d of alkene 3 attacking the C a of N,N-dimethylaniline 2 were taken into consideration, which can produce branched and linear product (5a and 5b) respectively. In the case of C c attacking, the activation energy for the C a -C c bond formation (TS1 A-1 ) is 27.4 kcal/mol and the C a -C c bond length in TS1 A-1 is 1.998 Å (Energies obtained at M06-2X (6-311 + G*/LANL2DZ) by PCM calculation were discussed if not mentioned) (Fig. 4). At the same time, the C=C double bond of alkene 3 becomes almost single bond (bond length increases from 1.391 to 1.517 Å) in TS1 A-1 . An unstable intermediate (Int1 A-1 ) is produced via TS1 A-1 and the C a -C c bond length of Int1 A-1 is further reduced to 1.647 Å. The formation of C a -C c bond makes the C a -H bond active. Meanwhile, the C c -C d bond becomes single bond in Int1 A-1 (length: 1.562 Å). Though TS2 A-1 can lead to the final product 5a, a direct proton transfer from C a to C d is not energy favorable due to the high overall activation energy (40.8 kcal/mol).
It is worth to notice that there is plenty of aromatic amines in the microenvironment 33 . The aromatic amine is a good proton acceptor. It can abstract the proton of C a -H in Int1 A-1 with a barrier of 22.1 kcal/mol (TS2 A-1′ ) (Fig. 5). Then, the intermediate Int2 A-1′ can re-abstract the proton of ammonium via TS3 A-1′ and the corresponding energy barrier is 14.7 kcal/mol. The re-abstracting proton process is vital for the catalytic cycle. If the catalyst cannot re-abstract the proton from the ammonium, the reaction will be terminated. As an example, when 25 mol% proton-trapping reagent, 2,6-di-t-butyl-4-methylpyridine, was added in the FC alkylation of aniline catalyzed by acid, no any alkylation reaction can be observed 26 . TS3 A-1′ can lead to the final product 5a and the overall energy change from Rea A-1 to Pro A-1′ is −24.6 kcal/mol. As indicated above, N,N-dialkylaniline is not only reactant but also a promoter. It should be the reason why excess N,N-dialkylaniline is necessary for the reaction 33 . The rate determining step is the C a -C c bond formation process via the transition state TS1 A-1 (barrier: 27.4 kcal/mol). This barrier height is reasonable considering that the reaction requires a temperature of 135 °C 33 .
Producing 5a by the pathway that the gold cation activates the N,N-Dimethylaniline 2 and the C a carbon of 2 attacks the C c of alkene 3 is not possible because of the extremely high activation energy (Figs 3 and 6). The binding energy between 2 and 1 + is −35.3 kcal/mol. This binding can increase the positive charge on the C a -H proton from 0.112 to 0.214. It makes the C a -H proton quite active. The external N,N-dialkylaniline 2 can abstract the C a -H proton with quite low activation barrier (12.8 kcal/mol, TS1 A-2 ). However, the following C a -C c bond formation is extremely energy-unfavorable and the corresponding activation barrier is 60.1 kcal/mol. It indicates that producing 5a by gold cation activated N,N-Dimethylaniline 2 is not possible. Hence, this pathway is not taken into consideration for the producing of 5b, 5c, 6a and 6b.
If the alkene terminal carbon C d can attack the C a of N,N-dialkylaniline 2 (Fig. 7), anti-Markovnikov product 5b should be obtained. The activation energy for the C a -C d bond formation is only 22.5 kcal/mol (TS1 B ). Though the barrier height of TS1 B is lower than that of TS1 A-1 , the proton abstracting process via TS2 B is not easy for this anti-Markovnikov reaction. The overall activation energy for the process to produce 5b is 29.5 kcal/mol. Furthermore, the energy change from Rea B to Pro B is only −1.5 kcal/mol. Hence, comparing with the producing of 5a, the generation of the linear product 5b is difficult because the higher activation energy and quite small free energy change. Indeed, no 5b was observed for the FC reaction between 2 and 3 in our previous experiment 33 .
Most of the known FC reactions gave both para-and ortho-products 1,62,63 . Interestingly, for the reaction between N,N-Dimethylaniline 2 and alkene 3, quite high para-selectivity was obtained and 5a was isolated with 93% yield 33 . Due to the steric hindrance of the -N(CH 3 ) 2 group, the C c of alkene 3 attacking the C b carbon of 2 is difficult (Fig. 8). The energy barrier for the C b -C c bond formation is 31.8 kcal/mol (TS1 C ). Furthermore, the access of extra aromatic amine is not easy due to the steric hindrance, which makes the abstracting proton from C b not easy comparing with the process to produce 5a. The free energy change from Rea c to Pro c is −7.9 kcal/mol. Considering that the barrier of the rate determining step to produce 5c is 4.4 kcal/mol higher than that to produce 5a, observing a minute quantity of 5c as byproduct is reasonable 33 . The reaction between 2 and 4. The reaction of olefine ketone 4 is quite different from that of aromatic alkene 3. For aromatic alkene 3, the C a of N,N-Dimethylaniline 2 and C c of 3 forms C-C bond and the producing of 5a follows the Markovnikov rule. However, the reaction of olefine ketone 4 follows the anti-Markovnikov rule. The C-C bond was formed between the C a of 2 and the terminal carbon C d of 4 to produce 6a (Fig. 1) 33 . To fully understand this difference, both C c and C d of 4 attacking the C a of 2 were taken into consideration, which can produce branched and linear product (6b and 6a) respectively. The binding between 4 and 1 + can form the electrophilic group and this process releases 25.5 kcal/mol energy. The C=C bond length of olefine ketone 4 was increased from 1.341 to 1.375 Å during the formation of 1 +… 4 (Fig. 2).
In the case of C d attacking, the activation energy for the C a -C d bond formation (TS1 D ) is only 15.2 kcal/mol and the C a -C d bond length is 2.117 Å in TS1 D (Fig. 9). During the C a -C d bond formation, the C=C double bond of 4 was increased from 1.375 to 1.439 Å. For the reaction of aromatic alkene 3, this bond was increased by 0.126 Å (from Rea A-1 to TS1 A-1 ). As we know, the structure distortion can induce energy change and enhance the reaction barrier 64 . Correspondingly, the energy barrier of TS1 D is 12.2 kcal/mol lower than that of the same process to produce 5a (TS1 A ). The smaller structure change is responsible for the low barrier of TS1 D . Similarly, proton abstracting by aromatic amine and re-abstracting the proton of ammonium happen for the producing of 6a. The proton re-abstracting process from the ammonium is the rate determining step and the corresponding activation energy is 21.1 kcal/mol (TS3 D ).
If the C c of olefine ketone 4 can attack the C a of N,N-dialkylaniline 2 (Fig. 10), Markovnikov product 6b should be observed in the experiment. In the case of C c attacking, the activation energy for the C a -C c bond formation is quite high (TS1 E : 30.8 kcal/mol). At the same time, the C=C double bond of 3 becomes almost single bond in TS1 E (increasing from 1.375 to 1.461 Å). The proton abstracting by the aromatic amine and re-abstracting from the ammonium is easy to achieve in this pathway. However, the producing 6b is not competitive to 6a. The activation energy of the rate determining step to produce 6b is 9.7 kcal/mol higher than that of 6a. That is why the anti-Markovnikov linear product 6a was observed in the experiment 33 .

Conclusion
The Friedel-Crafts alkylation of N,N-dimethylaniline with alkenes catalyzed by cyclic diaminocarbene-Gold(I) complex were theoretically investigated. The calculation method adopted here is accurate enough to reproduce the crystal structure of the catalyst. The gold cation can activate the C=C double bond to produce the electrophilic [R-C=C … Au-L] + . Then, the [R-C=C … Au-L] + attacks the aromatic ring, following the electrophilic aromatic substitution mechanism. Being different from previous result that alkaline arenes will trap the proton and the reaction will be terminated as result 26 , herein, it was found that the alkaline N,N-dimethylaniline can assist the reaction. Based on the obtained reaction mechanism, we can well understand why the reaction was high para-selevtivity, and why branched and linear products were obtained for different substrates: (1) Producing the para-product is more energy favorable comparing with the ortho-product. (2) The reaction of α-methylstyrene follows the Markovnikov rule. The activation energy to generate the branched product of α-methylstyrene is lower than that producing the linear product. Besides, the reaction leading to branched product is highly exothermic. (3) The reaction of butanone follows the anti-Markovnikov rule. The activation energy to generate the branched product of butanone is higher than that producing the linear product.
These theoretical results are quite useful for designing more effective catalysts for this rare FC reaction using alkaline arenes as substrates. Based on the understanding of the reaction mechanism, the development of none-noble metal catalyst for this FC reaction is on going in our group.
Computational Methods. All the structures were fully optimized with B3LYP based on Density Functional Theory (DFT) (See SI for structure details). This method is a good choice for the calculation of organometallic systems [65][66][67][68][69][70][71][72][73][74][75] . The following combination of basis sets were used for geometric configuration optimization and frequency calculation: 6-31G basis set for all atoms except Au and LANL2DZ basis set for Au (abbreviated as 6-31G/LANL2DZ) 41,75 . LANL2DZ basis set includes the relativistic effect of the heavy element 65,76 . The calculation method adopted here can well reproduce the crystal structure of the carbene-gold used for the FC reaction of basic arenes with alkenes (Table 1). Because B3LYP method often suffers from incorrect energies, especially for systems containing non covalent bonds. A higher level method M06-2X was used to generate more accurate energies. The energy calculations were performed using 6-311 + G* basis set for all atoms except Au and LANL2DZ basis set for Au (abbreviated as 6-311 + G*/LANL2DZ). The influence of solvent was performed in condensed phase with the Polarizable Continuum Model (PCM) using 6-311 + G*/LANL2DZ basis set. This method creates the solute cavity via a set of overlapping spheres. Aniline was used as solvent to simulate the environment of N,N-dimethylaniline.
The computed stationary points have been characterized as minima or transition states by diagonalizing the Hessian matrix and analyzing the vibrational normal modes. In this way, the stationary points can be classified as minima if no imaginary frequencies are shown or as transition states if only one imaginary frequency is obtained. The particular nature of the transition states has been determined by analyzing the motion described by the eigenvector associated with the imaginary frequency. All calculations were performed with the Gaussian 03 suite of programs 77 .