Theoretical Insight into the Reversal of Chemoselectivity in Diels-Alder Reactions of α,β-Unsaturated Aldehydes and Ketones Catalyzed by Brønsted and Lewis Acids

Experimentally, a reversal of chemoselectivity has been observed in catalyzed Diels–Alder reactions of α,β-unsaturated aldehydes (e.g., (2E)-but-2-enal) and ketones (e.g., 2-hexen-4-one) with cyclopentadiene. Indeed, using the triflimidic Brønsted acid Tf2NH as catalyst, the reaction gave a Diels–Alder adduct derived from α,β-unsaturated ketone as a major product. On the other hand, the use of tris(pentafluorophenyl)borane B(C6F5)3 bulky Lewis acid as catalyst gave mainly the cycloadduct of α,β-unsaturated aldehyde as a major product. Our aim in the present work is to put in evidence the role of the catalyst in the reversal of the chemoselectivity of the catalyzed Diels–Alder reactions of (2E)-but-2-enal and 2-Hexen-4-one with cyclopentadiene. The calculations were performed at the ωB97XD/6-311G(d,p) level of theory and the solvent effects of dichloromethane were taken into account using the PCM solvation model. The obtained results are in good agreement with experimental outcomes.

In order to make the cycloaddition feasible, various catalysts are introduced in reactions. Lewis acid (LA) and Brønsted acid (BA) catalysts [38][39][40][41][42] considerably extend the useful scope of DA reactions, enhancing the reaction rate and leading to significant changes in chemo-, regio-, and stereo-selectivities in comparison with the uncatalyzed process [43,44]. A large number of experimental works has been carried out to understand the effects of LA catalysts on the selectivity and the nature of molecular mechanisms of DA Scheme 2. Competitive chemoselective pathways of the BA-/LA-catalyzed DA reactions of (2E)-but-2-enal 1 and 2-hexen-4-one 2 with Cp.

Computational Details
All DFT calculations were carried out with the DFT/ωB97XD functional [60] combined with the 6-311G(d,p) basis set [61] implemented in the Gaussian 09 suite of programs [62]. This level of theory has shown to be suitable for geometry optimization and electronic property analysis of (3+2) cycloaddition and (4+2) DA reactions [17,63,64]. Optimizations were performed using the Berny analytical gradient optimization method [65,66] and the stationary points were characterized by frequency computations in order to verify that the transition states had one and only one imaginary frequency. Solvent effects were analyzed by optimizing the geometries in dichloromethane (DCM) through the polarizable continuum model (PCM) developed in the framework of the self-consistent reaction field (SCRF) [67][68][69][70]. The global electron density transfer (GEDT) [71] was computed as a sum of the natural atomic charge, obtained by a natural population analysis (NPA) [72,73] of the atoms belonging to each framework (f) at the TSs, i.e., GEDT (f) = q f q ∈  . Global reactivity indices derived from CDFT [74][75][76][77][78][79][80][81], namely the electrophilicity index ω and the nucleophilicity index N, were calculated using the following expressions [74]: where TCE = tetracyanoethylene. Scheme 2. Competitive chemoselective pathways of the BA-/LA-catalyzed DA reactions of (2E)-but-2-enal 1 and 2-hexen-4one 2 with Cp.

Computational Details
All DFT calculations were carried out with the DFT/ωB97XD functional [60] combined with the 6-311G(d,p) basis set [61] implemented in the Gaussian 09 suite of programs [62]. This level of theory has shown to be suitable for geometry optimization and electronic property analysis of (3 + 2) cycloaddition and (4 + 2) DA reactions [17,63,64]. Optimizations were performed using the Berny analytical gradient optimization method [65,66] and the stationary points were characterized by frequency computations in order to verify that the transition states had one and only one imaginary frequency. Solvent effects were analyzed by optimizing the geometries in dichloromethane (DCM) through the polarizable continuum model (PCM) developed in the framework of the self-consistent reaction field (SCRF) [67][68][69][70]. The global electron density transfer (GEDT) [71] was computed as a sum of the natural atomic charge, obtained by a natural population analysis (NPA) [72,73] of the atoms belonging to each framework (f) at the TSs, i.e., GEDT (f) = ∑ q∈ f q. Global reactivity indices derived from CDFT [74][75][76][77][78][79][80][81], namely the electrophilicity index ω and the nucleophilicity index N, were calculated using the following expressions [74]: where TCE = tetracyanoethylene.

Results and Discussion
In order to explain the role of the catalyst on the reversal of the chemoselectivity of the catalyzed DA cycloaddition reaction of the α,β-unsaturated aldehyde 1 and α,β-unsaturated ketone 2 with Cp, all the chemoselective pathways were investigated (Scheme 2). The studied DA reactions were: (i) 1 + Cp in the absence and presence of the BA/LA catalysts; and (ii) 2 + Cp in the absence and presence of the BA/LA catalysts.
The quantum chemical calculations are based on the analysis of CDFT reactivity indices and calculated activation energies and free energies. The polarity of the cycloaddition processes is quantified by GEDT calculations at the located TSs.

Analysis of the Global CDFT-Based Reactivity Indexes
Global indexes defined in the context of the CDFT [34,35], namely, the electronic chemical potential µ, chemical hardness η, global electrophilicity ω, and nucleophilicity N, were calculated in terms of the one electron energies of the HOMO/LUMO frontier molecular orbitals at the ground states of the reactants in gas phase. The following table recapitulates the global reactivity indices for uncatalyzed reactants 1 and 2, BA-catalyzed reactants 1-BA and 2-BA, and LA-catalyzed reactants 1-LA and 2-LA (Table 1). Table 1. ωB97XD/6-311G(d,p) global electronic properties (chemical potential µ, chemical hardness η, electrophilicity ω, nucleophilicity N) of uncatalyzed reactants 1 and 2, BA-catalyzed reactants 1-BA and 2-BA, and LA-catalyzed reactants 1-LA and 2-LA, in gas phase. It turned out that the electronic chemical potential µ [34,82] of Cp, −0.123 eV, was higher than that of the uncatalyzed and catalyzed aldehyde and ketone, indicating that along the cycloaddition reaction the electron density will flux from the diene Cp to the dienophile aldehyde/ketone, being classified as the forward electron density flux (FEDF) [83]. The electrophilicity ω index [35] of Cp, 0.58 eV, being classified as a weak electrophile, was lower than that of uncatalyzed and catalyzed aldehyde and ketone. In the absence of catalysts, aldehyde 1 (ω = 1.02 eV) and ketone 2 (ω = 0.94 eV) can be classified as moderate electrophiles [74]. By introducing the BA catalyst, the electrophilicity of the dienophiles increased. It became 1.52 eV for BA-catalyzed aldehyde 1-BA and 1.40 eV for BA-catalyzed ketone 2-BA. By substituting the BA catalyst by the LA catalyst, the electrophilicities increased and reached 2.05 eV for LA-catalyzed aldehyde 1-LA and 1.89 eV for LA-catalyzed ketone 2-LA, which made them strong electrophiles although the aldehyde was predicted to be more electrophile than the ketone in the absence and presence of BA/LA catalysts.

Global Properties (in eV)
The nucleophilicity N index [84,85] of Cp, 3.63 eV, was higher than that of the uncatalyzed aldehyde 1 (N = 2.56 eV) and ketone 2 (N = 2.76 eV), indicating that Cp acted as a nucleophile and dienophiles 1 and 2 acted as electrophiles. In the presence of BA, the nucleophilicity of the catalyzed aldehyde 1-BA and ketone 2-BA was reduced to 1.36 and 1.60 eV, respectively. Contrariwise, in the presence of LA, the nucleophilicity of the catalyzed aldehyde 1-BA and ketone 2-BA was increased to 2.91 and 2.94 eV, respectively. The difference in electrophilicity, ∆ω, for the DA reactions (1 + Cp), (1-BA + Cp), and (1-LA + Cp) were 0.44 eV, 0.94 eV, and 1.47 eV, respectively, indicating the largest polarity of the cycloaddition reaction between the aldehyde 1 and Cp corresponded to the 1-LA + Cp catalyzed reaction. The same trends were found for the DA reactions between the ketone 2 and Cp. In conclusion, compared to the uncatalyzed and BA-catalyzed DA reactions, the LA-catalyzed DA reactions were predicted to be the most polar ones. The competitive DA reactions between α,β-unsaturated aldehyde 1 with Cp and between α,β-unsaturated ketone 2 with Cp (Scheme 1) were studied first in the absence of catalysts. The first DA reaction of 1 with Cp led to the formation of the cycloadduct CA-1 via TS-1 and the second DA reaction of 2 with Cp led to the formation of the cycloadduct CA-2 via TS-2. The gas phase energies and Gibbs free energies in DCM at −40 • C (experimental conditions of BA-catalyzed reaction) and at −20 • C (experimental conditions of LA-catalyzed reaction) are summarized in Table 2 and the chemical structures of the gas phase TSs, drawn using GaussView 5.0 [86], are given in Figure 1a. Organics 2021, 2, FOR PEER REVIEW 7 chemo pathway involving the catalyzed aldehyde was kinetically more favored than the chemo pathway involving the catalyzed ketone, in agreement with experiment. We noted that the calculations performed in gas phase did not reproduce the experimental finding, showing the importance of solvent effects in the calculation of activation barriers. We also noted that the two competitive chemo pathways were exergonic. It is important to note that intrinsic reaction coordinate (IRC) calculations indicated that the studied DA reactions followed a one-step mechanism and the eventuality of a stepwise mechanism was excluded. Indeed, the optimization of the last structures on the IRC curves in the forward direction gave structures identical to those of cycloadducts, indicating the absence of stable reaction intermediates.
To quantify the electronic and steric effects of BA and LA catalysts on the chemoselectivity of the studied DA reactions, we calculated the enthalpic and entropic contributions by partitioning ΔG° into two terms: ΔH° and −TΔS° (Tables 3 and 4). According to the obtained results, we concluded that (i) both the steric and electronic effect are important in BA-and LA-catalyzed DA reactions; (ii) the steric contribution is more important than the electronic contribution in both BA-and LA-catalyzed reactions; (iii) the electronic contributions for LA-catalyzed reactions, 33.3% and 30.4%, are more important than those of BA-catalyzed reactions (17.5% and 14.9%); (iv) for BA-catalyzed reactions, the steric contribution in TS-2-BA is more important than in TS-1-BA; and (v) in LA-catalyzed reactions, there is a decrease of steric contribution and increase of electronic contribution compared to BA-catalyzed reactions.
(a) Uncatalyzed reactions in gas phase.

Relative Activation Free Energies and Boltzmann-Maxwell Populations
for the two equilibriums TS-1-BA ⇌ TS-2-BA and TS-1-LA ⇌ TS-2-LA were also calculated and are recapitulated in Table 5. The calculated activation barriers in gas phase and in DCM show that the second DA reaction (2 + Cp) was kinetically more favored than the first DA reaction (1 + Cp) by 0.9, 0.3, and 0.3 kcal/mol in gas phase, DCM at −40 • C, and DCM at −20 • C, respectively. We also noted that the second DA reaction was found to be more exergonic than the first one by 2.0 and 1.  Table 3 and the chemical structures of TSs in solvent are given in Figure 1b. Table 3. Total energies E and relative energies ∆E in gas phase, and free energies G • and relative free energies ∆G • in solvent for the possible chemo pathways of DA reactions catalyzed by BA. The enthalpy and entropy contributions of ∆G • are included.

Gas Phase
In Introducing Tf 2 NH as BA catalyst, the calculated activation barriers in gas phase and in DCM at −40 • C show that the second DA reaction (2-BA + Cp) was kinetically more favored than the first DA reaction (1-BA + Cp) by 0.5 and 0.7 kcal/mol in gas phase and DCM at −40 • C, respectively. We also noted that the second DA reaction was found to be more exergonic than the first one by 2.8 kcal/mol in DCM at −40 • C, which is in good agreement with experimental outcomes.  Table 4 and the chemical structures of TSs in solvent are given in Figure 1c. Table 4. Total energies E and relative energies ∆E in gas phase, and free energies G • and relative free energies ∆G • in solvent for the possible chemo pathways of DA reactions catalyzed by LA. The enthalpy and entropy contributions of ∆G • are included.

Gas Phase
In In opposition to the Tf 2 NH-catalyzed DA reactions, the B(C 6 F 5 ) 3 -catalyzed DA reactions led to a reversed chemoselectivity. Indeed, in DCM at −20 • C, the calculated activation barriers indicate that the activation free energy for the DA reaction 1-LA + Cp, 15.7 kcal/mol, was lower than that of the DA reaction 2-LA + Cp, 16.5 kcal/mol, indicating that chemo pathway involving the catalyzed aldehyde was kinetically more favored than the chemo pathway involving the catalyzed ketone, in agreement with experiment. We noted that the calculations performed in gas phase did not reproduce the experimental finding, showing the importance of solvent effects in the calculation of activation barriers. We also noted that the two competitive chemo pathways were exergonic. It is important to note that intrinsic reaction coordinate (IRC) calculations indicated that the studied DA reactions followed a one-step mechanism and the eventuality of a stepwise mechanism was excluded. Indeed, the optimization of the last structures on the IRC curves in the forward direction gave structures identical to those of cycloadducts, indicating the absence of stable reaction intermediates.
To quantify the electronic and steric effects of BA and LA catalysts on the chemoselectivity of the studied DA reactions, we calculated the enthalpic and entropic contributions by partitioning ∆G • into two terms: ∆H • and −T∆S • (Tables 3 and 4). According to the obtained results, we concluded that (i) both the steric and electronic effect are important in BA-and LA-catalyzed DA reactions; (ii) the steric contribution is more important than the electronic contribution in both BA-and LA-catalyzed reactions; (iii) the electronic contributions for LA-catalyzed reactions, 33.3% and 30.4%, are more important than those of BA-catalyzed reactions (17.5% and 14.9%); (iv) for BA-catalyzed reactions, the steric contribution in TS-2-BA is more important than in TS-1-BA; and (v) in LA-catalyzed reactions, there is a decrease of steric contribution and increase of electronic contribution compared to BA-catalyzed reactions.   Table 5.

GEDT Analysis and Polarity
The global electron density transfers (GEDTs) [71] were estimated from natural population analysis (NPA) [72,73] at the located TSs. The calculated GEDTs for uncatalyzed and BA/LA-catalyzed DA reactions are summarized in Table 6. Table 6. GEDT (given in e) of the uncatalyzed and BA-/LA-catalyzed DA reactions. In the absence of catalysts, the GEDT values at TS-1 (0.13e) and TS-2 (0.12e) showed electron density fluxes from Cp to aldehyde 1 and ketone 2. The flux was two times greater in the presence of the BA catalyst and three times greater in the presence of the LA catalyst. These results clearly reveal that both the uncatalyzed and catalyzed studied DA reactions can be classified as polar processes. We noted that the calculated GEDTs (Table 6) correlated well with the calculated activation barriers (Tables 2-4). Indeed, when passing from the uncatalyzed reactions to BA-and LA-catalyzed reactions, an increase in the polarity led to a decrease in activation energies and free energies. We also noted that the calculated GEDTs (Table 6) also correlated well with the calculated electrophilicity differences ∆ω (Table 1). Indeed, when passing from the uncatalyzed reactions to BA-and LA-catalyzed reactions, the increase of ∆ω values led to an increase in polarity and consequently a decrease in activation barriers.

Conclusions
The chemoselectivity of the (un)catalyzed DA reactions of α,β-unsaturated aldehyde 1 and ketone 2 with Cp was investigated at the ωB97XD/6-311G(d,p) level of theory. The obtained results show that the most favored chemo pathway depends strongly on the type of the catalyst (Brønsted acid vs. bulky Lewis acid).
(i) In the case of the uncatalyzed DA reactions, the 2 + Cp reaction was found to be kinetically more favored than the 1 + Cp reaction both in gas phase and in DCM. (ii) In the case of the DA reactions catalyzed by BA, the 2-BA + Cp reaction was found to be kinetically more favored than the 1-BA + Cp reaction both in gas phase and in DCM at −40 • C. Moreover, the calculated activation barriers, GEDTs at TSs, and electrophilicity differences (∆ω) indicated that the BA-catalyzed reactions were predicted to be more polar and faster compared to the uncatalyzed reactions. (iii) In the case of the DA reactions catalyzed by LA, the 1-LA + Cp reaction was found to be kinetically more favored than the 2-LA + Cp reaction in DCM at −20 • C. In addition, the LA-catalyzed reactions were predicted to be more polar and faster compared to the uncatalyzed and BA-catalyzed reactions. (iv) The relative free energies and Maxwell-Boltzmann populations of the competitive TSs, calculated in DCM, put in evidence the reversal of the chemoselectivity when the BA catalyst Tf 2 NH -was replaced by the bulky LA catalyst B(C 6 F 5 ) 3 , in agreement with the experimental findings.