Lewis Acid‐Catalyzed Diels‐Alder Reactions: Reactivity Trends across the Periodic Table

Abstract The catalytic effect of various weakly interacting Lewis acids (LAs) across the periodic table, based on hydrogen (Group 1), pnictogen (Group 15), chalcogen (Group 16), and halogen (Group 17) bonds, on the Diels‐Alder cycloaddition reaction between 1,3‐butadiene and methyl acrylate was studied quantum chemically by using relativistic density functional theory. Weakly interacting LAs accelerate the Diels‐Alder reaction by lowering the reaction barrier up to 3 kcal mol−1 compared to the uncatalyzed reaction. The reaction barriers systematically increase from halogen<hydrogen<chalcogen<pnictogen‐bonded LAs, i. e., the latter have the least catalytic effect. Our detailed activation strain and Kohn‐Sham molecular orbital analyses reveal that these LAs lower the Diels‐Alder reaction barrier by increasing the asynchronicity of the reaction to relieve the otherwise destabilizing Pauli repulsion between the closed‐shell filled π‐orbitals of diene and dienophile. Notably, the reactivity can be further enhanced on going from a Period 3 to a Period 5 LA, as these species amplify the asynchronicity of the Diels‐Alder reaction due to a stronger binding to the dienophile. These findings again demonstrate the generality of the Pauli repulsion‐lowering catalysis concept.


Introduction
The Diels-Alder (DA) cycloaddition reaction is of paramount importance in synthetic organic chemistry. [1] Since its discovery in 1928, [2] it has paved the way for a convenient procedure to create six-membered rings, with up to four stereocenters, becoming the gold standard for many applications ranging from the synthesis of natural products to the industrial production of relevant compounds in the pharmaceutical field. [3] A striking number of organocatalysts have been developed over the years to increase the reactivity and selectivity of the DA reaction. For example, Lewis acids (LAs) are able to greatly accelerate the DA via binding to the dienophile. [4] Interestingly, LAs can also reverse the regiochemical course of the DA reaction leading to products that otherwise would be impossible to synthesize: [5] a pioneering example has been shown by Kishi et al. on the total synthesis of the tetrodotoxin. [6] In analogy with conventional Lewis acids, hydrogen-bonded organocatalysts are also able to significantly modify both the reactivity and selectivity of the DA reaction. For example, hydrogen-bonded solvents can activate ketones to undergo a DA reaction, [7] or bifunctional hydrogen bond donor organocatalysts, such as differently substituted thioureas, are able to increase both the reaction rate as well as the endo/exoselectivity of DA reactions between a diene and α, βunsaturated carbonyl compounds. [8,9a] Similar catalytic effects were also reported using catalysts featuring similar weak interactions such as pnictogen, [10] chalcogen, [11] and halogen bonds (Scheme 1). [12,13] Moreover, in our previous work, we have shown that Lewis acidic alkali cations can also exert a remarkable catalytic effect on the generally slow aromatic DA reaction: the archetypal aromatic cycloaddition reaction be-tween benzene and acetylene can be effectively accelerated by up to 5 orders of magnitude. [9b] Thus, in general, weakly interacting Lewis acids play a crucial role in the reactivity of organic reactions, and hence it is highly important to understand the driving force behind this class of catalysis.
The catalytic ability of Lewis acids, such as hydrogen, halogen, chalcogen, and pnictogen bonded species, is traditionally attributed to the lowering of the LUMO of the activated dienophile, resulting in a smaller, i. e., more favorable, HO-MO diene -LUMO dienophile energy gap and hence stronger orbital interaction. [14] Recently, however, we have shown that this rationale is incomplete. Our analyses revealed that, although the LUMO of the dienophile becomes indeed stabilized upon binding to the LA, the increase in reaction rate is determined by a significant reduction of Pauli repulsion between the occupied π-molecular orbitals of the two reactants. [9] Binding of a LA to the dienophile not only polarizes the occupied π-orbital density on the C=C double bond of the dienophile away from the incoming diene, but it also introduces an asymmetry in this orbital, amplifying the asynchronicity of the DA reaction. Both effects contribute to diminishing the Pauli repulsion, however, the latter effect also results in less pressure on the reactants to deform and hence a less destabilizing activation strain in the transition state. We argue that the concept of Pauli repulsionlowering catalysis is also operative in LA-catalyzed Diels-Alder reactions where the Lewis acid is weakly bonded to the dienophile via hydrogen, halogen, chalcogen, or pnictogen bonds.
To this end, we have investigated the periodic reactivity trends of the hydrogen (Group 1), pnictogen (Group 15), chalcogen (Group 16), and halogen (Group 17) bond mediated Diels-Alder (DA) cycloaddition reaction between 1,3-butadiene (B) and methyl acrylate (MA) (Scheme 2), exclusively following the more favorable endo reaction pathway, [15] by means of the activation strain model and quantitative Kohn-Sham molecular orbital theory. This computational methodology has been proven to be reliable for the understanding of fundamental processes in organic chemistry. [9,15] First, we quantitatively examine the bonding between the Lewis acid AF n (A = H with n = 1, A = Cl/Br/I with n = 1, A = S/Se/Te with n = 2, A = P/As/Sb with n = 3) and MA leading to the activated dienophile (LA-MA). Secondly, we analyze the catalytic effect of the Lewis acidic hydrogen, halogen, chalcogen, and pnictogen bonds on the DA reactivity of B and the LA-MA complex. At last, we study how the reactivity changes upon going from Period 3 to Period 5 Lewis acids.

Computational details
All calculations were performed using the Amsterdam Density Functional (ADF2018.105) software package. [16] The generalized gradient approximation (GGA) functional BP86 was used for the optimizations of all stationary points as well as the analyses. [17] The basis set employed, denoted TZ2P, [18] is of triple-ζ quality and is augmented with two sets of polarization functions on each atom. Scalar relativistic effects are accounted for using the zeroth-order regular approximation (ZORA). [19] This level of theory has been proven to be accurate in calculating the relative trends in reaction barriers and energies as well as performing the activation strain and energy decomposition analyses for cycloaddition reactions. [9b,20] The accuracies of the fit scheme (Zlm fit) [21a] and the integration grid (Becke grid) [21b] were set to VERYGOOD. In addition, geometries and energies were recomputed using ZORA-BP86-D3(BJ)/TZ2P [22] to access the effect of dispersion on the reactivity trends. Equilibrium and transition state geometries were verified by means of vibrational analysis, to assess the nature of all structures: for minima, no imaginary frequencies were found, whereas transition states present a single imaginary frequency. Besides, the character of the normal mode associated with the imaginary frequency was analyzed to ensure that the correct transition state was found, i. e., the formation of the two CÀ C bonds between the reactants. The potential energy surfaces of the studied Diels-Alder reactions were obtained by utilizing intrinsic reaction coordinate (IRC) calculations. [23] The acquired potential energy surfaces were analyzed by using the PyFrag 2019 program. [24] Optimized structures were illustrated using CYLview. [25]

Activation Strain Model and Energy Decomposition Analysis
The activation strain model of chemical reactivity (ASM, [26] also known as the distortion/interaction model [27] ), is a fragmentbased approach based on the idea that the energy of a reacting system, i. e., the potential energy surface, is described with respect to, and understood in terms of the characteristics of, the original reactants. It considers their rigidity and the extent to which the reactants must deform during the reaction plus their capability to interact as the reaction proceeds. In this model, we decompose the total energy, ΔE(ζ), into the respective total strain and interaction energy, ΔE strain (ζ) and ΔE int (ζ), and project these values onto the reaction coordinate ζ [Eq. (1)].

Chemistry-A European Journal
Full Paper doi.org/10.1002/chem.202100522 In this equation, the total strain energy, ΔE strain (ζ), is the penalty that needs to be paid to deform the reactants from their equilibrium structure to the geometry they adopt during the reaction at point ζ of the reaction coordinate. On the other hand, the interaction energy, ΔE int (ζ), accounts for all the chemical interactions that occur between the deformed fragments along the reaction coordinate.
The interaction energy between the deformed reactants is further analyzed in terms of our canonical energy decomposition analysis (EDA). [28] The EDA decomposes the~E int (ζ) into the following three physically meaningful energy terms [Eq. (2)]: Herein, ΔV elstat (ζ) is the classical electrostatic interaction between the unperturbed charge distributions of the (deformed) reactants and is usually attractive. The Pauli repulsion, ΔE Pauli (ζ), comprises the destabilizing interaction between occupied closed-shell orbitals of both fragments due to the Pauli principle. The orbital interaction energy, ΔE oi (ζ), accounts for polarization and charge transfer between the fragments, such as HOMO-LUMO interactions. A detailed, step-by-step, guide on how to perform and interpret the ASM and EDA can be found in Ref. 26 f. Note that the concepts of Pauli repulsion and orbital interaction that feature in our canonical EDA also have been successfully applied to reactions that were studied using other decomposition schemes such as DFT-SAPT [29] or valence bond (VB) theory. [30] In both the activation strain and energy decomposition diagrams in this study, the energy terms were projected onto the shortest of the two newly forming C···C bond between the 1,3-butadiene and (LA-)methyl acrylate. This critical reaction coordinate undergoes a well-defined change during the reaction from the reactant complex via the transition state to the cycloadduct and is shown to be a valid reaction coordinate for studying cycloadditions. [9,31]

Lewis acid-methyl acrylate binding and trends in reactivity
First, we analyzed the nature and strength of the interaction between methyl acrylate (MA) and the various Lewis acids (LAs) across the periodic table, that is, the hydrogen, pnictogen, chalcogen, and halogen bond, using the activation strain model (ASM) [26] of reactivity and energy decomposition analysis (EDA) [28] schemes (Table 1). The binding energies of the LAs become increasingly more stabilizing from pnictogen to chalcogen, halogen, and hydrogen bonds. This trend is exclusively dictated by the interaction energies, which are stabilizing and become increasingly so along this series. Not surprisingly, the inclusion of dispersion in our calculations (ZORA-BP86-D3(BJ)/TZ2P level) makes the computed interaction energies slightly more stabilizing (associated with slightly shorter LA···O=C distances, see Table S1 in the Supporting Information). Despite that, the above-commented trend is identical, therefore, validating our selected computational method for the present study (ZORA-BP86/TZ2P). The corresponding LA···O=C distance follows the same trend and becomes systematically shorter. As previously shown in the literature, [9] the interaction consists of both electrostatic interactions and orbital (i. e., covalent) interactions, which becomes increasingly more stabilizing along the series. The latter of these two attractive interactions is, as we will show later, of significant importance for the catalytic ability of the Lewis acid. Surprisingly, the ratio between these two types of interactions changes drastically when going from pnictogen to chalcogen to halogen to hydrogen bonds. In the pnictogen bond, the electrostatic interaction is 2.5 times as large as the orbital interactions, indicating the large electrostatic character of this bond. For the Table 1. Energy decomposition analysis terms (in kcal mol À 1 ) and LA···O=C distance (in Å) computed on LA-methyl acrylate adducts. [

Chemistry-A European Journal
Full Paper doi.org/10.1002/chem.202100522 halogen bond, on the other hand, both interactions have an equal contribution to the overall halogen bond strength. The binding energy becomes further enhanced when going from Period 3 to Period 4 and Period 5 LAs, due to (i) a lower-lying σ* acceptor orbital, which, in turn, engages in a more stabilizing (i. e., smaller) HOMO-LUMO gap with MA and (ii) the more electropositive nature of the heavier atoms involved in the interaction with MA, amplifying the stabilizing electrostatic interactions.
After analyzing the bonding situation in the LA-MA complexes, we focused on the Diels-Alder reaction of these activated species with B. As expected, in all cases, the cycloaddition reaction occurs in a concerted manner through the corresponding six-membered transition state (see Figure S1 in the Supporting Information). The electronic reaction barriers (ΔE � ) and the reaction energies (ΔE rxn ) of the uncatalyzed (MA) and LA-catalyzed DA reaction between B and LA-MA are provided in Table 2. Two clear periodic reactivity trends can be observed. In the first place, binding of a LA catalyst significantly accelerates the DA reaction between B and MA. As expected, the uncatalyzed reaction has the highest reaction barrier (13.2 kcal mol À 1 ), which, for Period 3 systematically decreases going from a pnictogen (PF 3 -MA; 12.5 kcal mol À 1 ) to chalcogen (SF 2 -MA; 11.7 kcal mol À 1 ) to hydrogen (HF-MA; 11.0 kcal mol À 1 ) to halogen (ClF-MA; 10.3 kcal mol À 1 ) bond-catalyzed Diels-Alder reaction. The reactivity trends for the Period 4 and 5 Lewis acids are slightly different, namely, MA > AsF 3 -MA > HF-MA > SeF 2 -MA > BrF-MA for Period 4 and MA > HF-MA > SbF 3 -MA > TeF 2 -MA > IF-MA for Period 5, because the pnictogen, chalcogen, and halogen bonds involving Period 4 and 5 atoms engage in a stronger donor-acceptor interaction with MA, which is, as we will show later, crucial for the catalytic effect of the Lewis acids, than the hydrogen-bonded analog. Secondly, the Diels-Alder reaction between B and LA-MA catalyzed by a Period 5 LA goes with a 0.3 to 2.3 kcal mol À 1 lower barrier than those promoted by their Period 3 analogs. Interestingly, however, all reactions studied in this work, both uncatalyzed and catalyzed, are similarly exergonic. Note that the computed trends in reactivity at ZORA/BP86/TZ2P agree well with those calculated at the dispersion-corrected ZORA-BP86-D3(BJ)/TZ2P level, see Table S2 in the Supporting Information.

Catalytic effect of weakly interacting Lewis acids
First, we examine the physical factors leading to the computed periodic reactivity trend upon going, along a period, from the uncatalyzed to the hydrogen, halogen, chalcogen, and pnictogen bond-catalyzed Diels-Alder reactions by applying the activation strain model (ASM) of reactivity. [26] To this end, we have analyzed and compared the reactivity trend involving the uncatalyzed (MA), and Period 3-catalyzed (PF 3 , SF 2 , HF, and, ClF) DA reactions, which has the largest, and hence clearest, differences along the various catalysts ( Figure 1a). Note that the activation strain diagrams (ASDs) of the DA reaction catalyzed by Period 4 and Period 5 Lewis acids can be found in Figures S2 and S3 (Supporting Information). The enhanced reactivity, i. e., lower reaction barrier, of the LA-catalyzed reactions originates predominantly from a less destabilizing strain energy along the entire reaction coordinate. The interaction energy, on the other hand, is for all reactions, in the transition state region, nearly identical and hence not responsible for the observed trend in reactivity. [32] The trend in strain energy, which becomes increasingly less destabilizing from MA > PF 3

Chemistry-A European Journal
Full Paper doi.org/10.1002/chem.202100522 Δr TS C···C = 0.51 Å, where Δr TS C···C refers to the difference between the newly forming C···C bond lengths in the TS, see Figure S1). The higher degree of asynchronicity of HF-MA leads to a lower degree of deformation of the reactants since the C B ···C α bond forms behind of the C B ···C β bond, resulting in a less destabilizing strain energy. To understand why the interaction energy does not play a prominent role in the catalysis of the herein studied reactions, we apply the energy decomposition analysis (EDA) (Figure 1b). Contrary to the commonly accepted view that LAs enhance the orbital interactions of LA-catalyzed Diels-Alder reactions, [14] we find that not only the orbital interactions but also the electrostatic interactions, show a trend opposite to the trend in reaction barriers, that is, the uncatalyzed DA reaction has a more stabilizing ΔE oi and ΔV elstat than the LA-catalyzed analogs. The Pauli repulsion follows, in line with our previous work on LA-catalyzed Diels-Alder, Michael addition, and ringopening reactions, [9] the trend in reaction barrier, namely, the uncatalyzed reaction exhibits the most destabilizing Pauli repulsion while the halogen bond mediated reactions has the least destabilizing Pauli repulsion. The reduction of stabilizing orbital and electrostatic interactions and the decrease in destabilizing Pauli repulsion for the LA-catalyzed DA reactions effectively cancel each other, leading to an interaction energy that is nearly identical to the uncatalyzed DA reaction. [32] As prior discussed, the degree of asynchronicity is the key factor in the reactivity of these Diels-Alder reactions. We, therefore, want to understand the origin of the asynchronicity of the herein studied reactions, which ultimately results in the catalytic effect of weakly interacting LAs by allowing for less reactant deformation and hence activation strain. To this end, we compare, in analogy with our work on iminium-catalyzed Diels-Alder reactions, [9d] the actual concerted asynchronous Diels-Alder reaction to the analogous process which is artificially constrained to be concerted synchronous. In Figure 2a Figure S5-S7). Both uncatalyzed and catalyzed synchronous DA reactions proceed with a higher barrier compared to their asynchronous counterpart (ΔΔE � MA = 0.2 kcal mol À 1 ; ΔΔE � ClF-MA = 0.9 kcal mol À 1 ), even though the synchronous DA reactions experience a more stabilizing interaction energy. The strain energy, on the other hand, is the most destabilizing for the synchronous DA reaction pathway, because both newly forming C···C bonds between B and (ClF-) MA are formed simultaneously, leading to more deformation and hence more strain since all involved carbon atoms are pyramidalizing at the same time. The strain energies of both the asynchronous and synchronous DA at the product side are eventually identical because the reactions yield the same cycloadduct and are, therefore, deformed to the same extent.
Next, we turn to the energy decomposition analysis (EDA) [28] to get a better understanding of why the interaction energy is more stabilizing for the synchronous compared to the asynchronous DA reaction (Figure 2c and 2d). In contrast with the widely accepted view that the asynchronicity originates from enhanced orbital interactions due to a larger LUMO-coefficient on the β-carbon, [33] we find that the asynchronous pathway goes with a less stabilizing orbital interaction. Instead, what drives the system away from synchronicity is a significantly more destabilizing Pauli repulsion in the synchronous reaction mode, originating from a larger occupied-occupied orbital overlap of the synchronous DA reaction. To reduce this occupied-occupied overlap and thus the Pauli repulsion, the reaction mode becomes asynchronous, even though this results in the aforementioned loss of the favorable orbital and electrostatic interactions. Thus, it is the interplay between this

Chemistry-A European Journal
Full Paper doi.org/10.1002/chem.202100522 reduction of destabilizing Pauli repulsion and loss of stabilizing orbital and electrostatic interactions that determine the degree of asynchronicity of a Diels-Alder reaction. Note that we do find, as previously reported in the literature, [14] a larger 2p z -coefficient on the β-carbon of the MA and Cl-MA LUMO than on the αcarbon ( Figure S8). This, however, does not result in a stronger orbital interaction, as prior discussed, because the orbital overlaps of both the normal and inverse electron demand are larger and hence more stabilizing for the synchronous reaction pathway (see Figure S9).
The origin of the less destabilizing Pauli repulsion along the asynchronous reaction pathway was further investigated by performing a Kohn-Sham molecular orbital (KS-MO) analysis (Figure 3a). [28b,34] The occupied molecular orbitals of B, as well as, MA and ClF-MA were quantified at consistent geometries with a C B ···C β bond length between B and LA-MA of 2.128 Å. Performing this analysis at a consistent point along the reaction coordinate (near all transition structures), rather than the transition state alone, ensures that the results are not skewed by the position of the transition state. [26,20] The most important occupied orbitals of LA-MA are the HOMO-1 and HOMO-2 of MA and ClF-MA, respectively, where the 2p z atomic orbitals located on the C=C double bond are in-phase. The participating occupied orbital on B is the HOMO-1, where all 2p z atomic orbitals, located on the reacting C=C double bonds, are inphase (Figure 3b). For both MA and ClF-MA, the synchronous reaction pathway experiences a larger orbital overlap between the filled orbitals of B and LA-MA compared to the asynchro-   (Figure 4). The MOcoefficient of the 2p z atomic orbital on the α-carbon of HOMO-1 and HOMO-3 of MA and ClF-MA, [35] respectively, lead to a larger orbital overlap and, therefore, more Pauli repulsion with the filled orbital of the incoming B than the β-carbon, which has a smaller MO-coefficient and hence less orbital overlap, i. e., less Pauli repulsion, with B. To avoid the otherwise more destabilizing Pauli repulsion of B with the α-carbon of LA-MA, the formation of the new C B ···C α bond between LA-MA and B lags behind the formation of the C B ···C β bond, resulting in an asynchronous DA reaction.

Chemistry-A European Journal
In addition, we want to understand why the DA reaction involving ClF-MA is significantly more asynchronous than MA (ClF-MA: Δr TS C···C = 0.52 Å; MA: Δr TS C···C = 0.38 Å), which, ultimately, is the driving force behind the catalytic effect of the herein studied LAs on the Diels-Alder reaction (vide supra). In order to understand this difference, we need to compare the MO-coefficients of the 2p z atomic orbitals on the αand βcarbon of the key π-MOs of ClF-MA and MA ( Figure 4). As prior discussed, the HOMO-3 of ClF-MA has a larger MO-coefficient on the αthan on the β-carbon. In addition, the MO-coefficients on the αand β-carbon of the HOMO-4 are identical, due to a strong donor-acceptor interaction between ClF and MA (ΔE oi,ClF-MA = À 21.6 kcal mol À 1 ), which effectively polarizes the π-density away from the C=C double bond equalizing the originally asymmetric π-orbital of MA (vide infra). Thus, the net effect of both occupied orbitals works in favor of an asynchronous reaction mode. On the contrary, the MO-coefficients of the key HOMOs of MA do not both point towards the observed asynchronous reaction mode. In line with ClF-MA, the MOcoefficient of the α-carbon of HOMO-1 MA is larger than on the β-carbon, driving the reaction towards the observed asynchronous reaction mode. But, this effect gets partially countered by the asymmetry in the MO-coefficients of the HOMO-2 MA , which has a larger orbital amplitude on the β-carbon than on the α-

Chemistry-A European Journal
Full Paper doi.org/10.1002/chem.202100522 carbon, resulting in a DA reaction that has a smaller degree of asynchronicity and hence a higher reaction barrier than ClF-MA.
After having established the origin of the different degrees of asynchronicity and, thus, the reason why hydrogen, halogen, chalcogen, and pnictogen bonds are able to catalyze Diels-Alder reactions, we want to understand why these Lewis acids are able to reduce the Pauli repulsion (Figure 1b). The less destabilizing Pauli repulsion for the LA-catalyzed Diels-Alder reaction derives from the reduced occupied-occupied orbital overlap between B and LA-MA. The occupied molecular orbitals of B and LA-MA were quantified at consistent geometries with a C B ···C β bond length between B and the dienophile of 2.128 Å ( Figure 5). The most important occupied π-MOs of LA-MA involved in the two-center four-electron interaction are the HOMO-1 of MA and the HOMO-2 of ClF-MA and SF 2 -MA. Notably, the π-MOs of LA-MA are the same π-orbital located on the C=C double bond of the dienophile. The contributing occupied orbital of B is the HOMO-1, where all 2p z AOs located on both reacting C=C double bonds are in-phase. The orbital overlap between the HOMO-1 B and the occupied π-MO LA-MA of the dienophile is the largest and, therefore, most destabilizing (S = 0.18) for MA (uncatalyzed reaction) and smallest and least destabilizing for ClF-MA (S = 0.13) (Figure 5a). Binding of a Lewis acid to MA polarizes, due to the strong donor-acceptor interaction (Table 1), the occupied π-MO LA-MA located on the C=C double bond of the dienophile away from the incoming B (Figure 5b), which, in turn, decreases the occupied-occupied orbital overlap and hence the Pauli repulsion. In addition, the above-discussed larger degree of asynchronicity also plays a role in the reduction of the occupied-occupied orbital overlap. A more asynchronous reaction, i. e., the DA reaction catalyzed by a LA, has, due to the longer C B ···C α bond, less orbital overlap at the α-carbon of LA-MA, manifesting in less Pauli repulsion between B and LA-MA. We have observed these exact phenomena also in our analysis of Lewis acid and iminium ioncatalyzed Diels-Alder, Michael addition, and ring-opening reactions, [9] which again demonstrates that the concept of Pauli repulsion-lowering catalysis is a broader phenomenon and independent of how the Lewis acid is bound to the dienophile.
At last, we address why the orbital interactions for the uncatalyzed DA reaction are more stabilizing than for the LAcatalyzed counterpart, which effectively compensates the observed trend in Pauli repulsion and hence results in a nearly identical interaction energy for the uncatalyzed and LAcatalyzed reactions (Figure 1). In line with the current textbook rationale, [14] binding a Lewis acid to MA strengthens the normal electron demand (NED) orbital interaction by lowering the LUMO LA-MA energy, but, simultaneously, the LA catalyst suppresses the inverse electron demand (IED) orbital interaction since it also lowers the π-MO LA-MA and hence increases the LUMO B -π-MO LA-MA energy gap. The latter effect overrules the former, resulting in orbital interactions for the LA-catalyzed reaction between B and LA-MA which are less favorable than the uncatalyzed analog. By performing a Kohn-Sham molecular orbital (KS-MO) analysis on consistent geometries with a C B ···C β bond length between B and LA-MA of 2.128 Å, [28b,34] we found that the NED orbital energy gap between HOMO B -LUMO LA-MA decreases from 2.5 eV for the uncatalyzed reaction to 1.8 eV for the ClF-catalyzed reaction (Figure 6a). This reduction of the orbital energy gap is significant enough to overcome the minor loss of orbital overlap, which results from the more asynchronous reaction mode, and hence results in a more favorable NED interaction. However, binding of a LA stabilizes all orbitals of LA-MA, thus also the key occupied π-MO LA-MA , which effectively   (Figure 6b). This, in conjunction with a significantly reduced orbital overlap as a result of the more asynchronous reaction mode, leads to a weaker IED interaction for the LA-catalyzed compared to the uncatalyzed DA reaction.

Transitioning from Period 3 to Period 5-based Lewis acid catalysts
In the next section, we want to establish the periodic reactivity trend upon descending a group, that is, why Period 5-based LAs accelerate the Diels-Alder (DA) reaction between B and LA-MA to a larger extent than their Period 3-based analogs. Figure 7a shows the activation strain diagrams (ASDs) from the separate reactants to the transition states for the Diels-Alder reaction between B and LA-MA catalyzed by the Group 15 LAs: PF 3 , AsF 3 , and SbF 3 of Periods 3, 4, and 5, respectively. The DA reaction catalyzed by the Group 16 and Group 17 LAs show the same, but less pronounced characteristics ( Figure S10 and S11). The enhanced reactivity of the DA reaction catalyzed by the Period 5 LA SbF 3 originates exclusively from a less destabilizing strain energy. On the other hand, the interaction energy is, in the transition state region, identical and hence not responsible for the observed trend in reaction barriers.
The less destabilizing strain energy for SbF 3 -MA can be ascribed to the larger degree of asynchronicity compared to  (Figure 7b). The HOMO-1 of PF 3 -MA has a larger MO-coefficient on the αthan on the β-carbon inducing an asynchronous reaction mode. However, this effect gets partly compensated by the HOMO-3 of PF 2 -MA, because it shows the opposite characteristics, that is, a smaller MO-coefficient on the α-carbon compared to the βcarbon, making the reaction moderately asynchronous. The same effect, only less pronounced due to a more asymmetric HOMO-1, can also be seen for the AsF 3 -LA, making this reaction slightly more asynchronous. The reaction involving SbF 3 -MA, on the contrary, follows a more asynchronous reaction mode, due to (i) a larger asymmetry in the MO-coefficients of the HOMO-1 compared to PF 3 -MA; and (ii) a symmetric HOMO-3 which does not counter the asynchronicity induced by the HOMO-1. Both of these effects are initiated by the stronger donor-acceptor interaction between SbF 2 and MA compared to the interaction between PF 3 or AsF 3 and MA (Table 1; ΔE oi,PF 3 -MA = À 2.2 kcal mol À 1 , ΔE oi,AsF 3 -MA = À 6.8 kcal mol À 1 , and ΔE oi,SbF 3 -MA = À 10.7 kcal mol À 1 ), which results in a more significant polarization of the π-MOs away from the C=C double bond of SbF 3 -MA, amplifying the asymmetry in the MO-coefficients of the 2p z atomic orbitals on the αand β-carbon atoms of SbF 3 -MA and hence making the reaction more asynchronous.

Conclusion
Our study quantifies and pinpoints the catalytic effect of various weakly interacting Lewis acids, across the periodic table, on the Diels-Alder (DA) reaction between 1,3-butadiene (B) and methyl

Chemistry-A European Journal
Full Paper doi.org/10.1002/chem.202100522 acrylate (MA). Lewis acids (LAs), binding via hydrogen, halogen, chalcogen, and pnictogen bonds, efficiently catalyze the DA reaction by lowering the reaction barrier up to 3 kcal mol À 1 . This catalytic effect decreases going, along a period, from halogen to hydrogen to chalcogen to pnictogen-bonded Lewis acids. In addition, the Period 5-based Lewis acids catalyze the DA reaction to a larger extent than the corresponding Period 3 and Period 4-based counterparts.
Our activation strain and Kohn-Sham molecular orbital analyses uncovered that the enhanced reactivity of the Lewis acid-catalyzed compared to the uncatalyzed DA reaction originates from a larger degree of asynchronicity, which yields a less destabilizing activation strain since one newly forming C···C bond forms later than the other. The asynchronicity of these DA reactions are caused by the asymmetry in the MO-coefficients of the 2p z atomic orbitals on the αand β-carbon of the occupied π-orbitals of the dienophile, namely, the MO coefficient on the α-carbon is larger than on the β-carbon, inducing more occupied-occupied orbital overlap between B and the α-carbon of LA-MA. To circumvent this repulsive interaction, the formation of the new C B ···C α bond between LA-MA and B lags behind that of the C B ···C β bond, resulting in an asynchronous DA reaction. The stronger the Lewis acid interacts with the dienophile, going from halogen to hydrogen to chalcogen to pnictogen bonds, the larger the asymmetry in the MO-coefficients of the occupied π-orbitals of the dienophile, which leads to a more asynchronous reaction mode and hence less repulsion between the reactants and a lower reaction barrier.
The increased rate enhancement upon descending a group from Period 3 to Period 5 is exclusively caused by the reduced activation strain, originating from the increased degree of a synchronicity. The Period 5 LA catalysts enter in a stronger donor-acceptor interaction with MA, due to the higher polarizability and more electropositive nature of the heavier atoms of the LA involved in this interaction. Consequently, the asymmetry in the MO coefficients of the occupied π-orbitals of the dienophile is more prominent for the Period 5 LAs, making the reaction more asynchronous. The work presented herein demonstrates, once again, the more general applicability of the Pauli repulsion-lowering catalysis concept. Despite that, and different to our previous works on related catalyzed processes, [9] the Pauli repulsion lowering induced by these weakly bonded catalysts is not translated into a stronger interaction between the deformed reactants but is mainly manifested in a more asynchronous reaction mode, which constitutes the causal actor behind the catalytic effect of these Lewis acids in the considered DA reactions.