How Bases Catalyze Diels‐Alder Reactions

Abstract We have quantum chemically studied the base‐catalyzed Diels‐Alder (DA) reaction between 3‐hydroxy‐2‐pyrone and N‐methylmaleimide using dispersion‐corrected density functional theory. The uncatalyzed reaction is slow and is preceded by the extrusion of CO2 via a retro‐DA reaction. Base catalysis, for example, by triethylamine, lowers the reaction barrier up to 10 kcal mol−1, causing the reaction to proceed smoothly at low temperature, which quenches the expulsion of CO2, yielding efficient access to polyoxygenated natural compounds. Our activation strain analyses reveal that the base accelerates the DA reaction via two distinct electronic mechanisms: i) by the HOMO‐raising effect, which enhances the normal electron demand orbital interaction; and ii) by donating charge into 3‐hydroxy‐2‐pyrone which accumulates in its reactive region and promotes strongly stabilizing secondary electrostatic interactions with N‐methylmaleimide.


Introduction
Base-catalyzed Diels-Alder reactions are vital in organic synthesis. [1,2] One typical example is the base-catalyzed Diels-Alder reaction between 2-pyrone, acting as a diene, and a dienophile. [1] The analogous uncatalyzed Diels-Alder reaction of 2-pyrone was first described by O. Diels and K. Alder in 1931 [3a] and later found wide applications in the synthesis of complex molecules and natural products. [3b,c] This uncatalyzed reaction is found to be slow, even at a high temperature, and is generally followed by a retro-Diels-Alder reaction expulsing CO 2 (Scheme 1a). [4] In 1995, Okarnura et al. improved the Diels-Alder reaction of 2-pyrone by using a base as a catalyst. [1a] They revealed that the Diels-Alder reaction between 3-hydroxy-2pyrone and N-methylmaleimide catalyzed by triethylamine (Et 3 N) achieved a 100 % yield in 10 minutes at 0°C (Scheme 1b), while its uncatalyzed analog had not been completed after 12 h at room temperature. [1a] Interestingly, the base-catalyzed reaction was not accompanied by the retro-Diels-Alder reaction at such a low temperature, making it a useful strategy for synthesizing polyoxygenated natural products. [1] 3-Hydroxy-2pyridone and several electron-deficient dienophiles have been found suitable for this reaction. [1a-c] Chiral bases such as alkaloid cinchonine, on the other hand, have been utilized in basecatalyzed asymmetric Diels-Alder reactions. [1d-m] However, a thorough understanding of base-catalyzed Diels-Alder reactions is lacking. One can envisage a catalytic mechanism that hinges on enhancing the normal electron demand (NED) HOMOÀ LUMO orbital interaction whereby a catalytic amount of base (electron-donating molecule) binds to the diene and destabilizes the HOMO (HOMO-raising) (Scheme 2), leading to a reduced NED orbital-energy gap and hence an enhanced HOMOÀ LUMO orbital interaction. This resembles the catalytic process proposed in earlier studies on Lewis acid (LA)-catalyzed Diels-Alder reactions: [5] Complexation of a LA to the dienophile stabilizes the LUMO of the dienophile (LUMO-lowering) and, therefore, reduces the NED orbital-energy gap (Scheme 2), thereby enhancing the HOMOÀ LUMO orbital interaction. Recently, however, we have shown that this rationale behind the rate acceleration of LA-catalyzed Diels-Alder reactions is, in general, incorrect. We, in fact, found via our activation strain and Kohn-Sham molecular orbital analyses that LAs promote the Diels-Alder reaction by reducing the Pauli repulsion between the π-systems of the diene and dienophile, and not due to the enhanced donorÀ acceptor interactions. [6] In this work, we aim to expand the scope of our investigations and study base-catalyzed Diels-Alder reactions, with the goal of determining the underlying physical mechanism of the rate-enhancement of base-catalyzed Diels-Alder reactions (Scheme 1).
To this end, we have investigated the archetypal basecatalyzed Diels-Alder reaction between 3-hydroxy-2-pyrone (Py) and N-methylmaleimide (NMM) (Scheme 3) [1a] using dispersioncorrected density functional theory (DFT) calculations at BLYP-D3(BJ)/TZ2P. We concentrated on deciphering the catalytic effect of triethylamine (Et 3 N), which is typically used in experiment. [1] For comparison, we have also evaluated the performance of other bases, such as the related base trimethylamine (Me 3 N) and the weaker base water (H 2 O). The activation strain model (ASM) [7] with a matching canonical energy decomposition analysis (EDA) and quantitative molecular orbital theory [8] were applied to reveal the physical factors behind the origin of the catalysis.

Computational details
All calculations were performed with ADF2019. [9] The geometries and energies were computed using dispersion-corrected density functional theory at BLYP-D3(BJ)/TZ2P. This approach comprises the GGA functional BLYP [10] augmented by Grimme's D3 dispersion correction [11] using the damping function proposed by Becke and Johnson. [12] The basis set TZ2P is of triple ζ quality augmented with polarization functions. [13] Our previous benchmark on the DFT method for various cycloaddition reactions has proven that this method performs excellently in calculating the trends in reactivity for cycloaddition reactions when weak interactions are involved in the systems. [14] The accuracies of the fit scheme (Zlm fit) [15a] and the integration grid (Becke grid) [15b] were set to VERYGOOD. Frequency calculations were performed to characterize the nature of the stationary points where local minima presented real frequencies while transition structures had one imaginary frequency associated with the transition vector (the vibrational normal mode associated with the reaction and with a negative force constant). The potential energy surface (PES) was calculated using the intrinsic reaction Scheme 1. a) Uncatalyzed Diels-Alder reaction of 2-pyrone and b) base-catalyzed Diels-Alder reaction of 3-hydroxy-2-pyrone.

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Research Article doi.org/10.1002/chem.202203121 coordinate (IRC) method [16] and was further analyzed with the aid of the PyFrag 2019 program. [17] The influence of chloroform, a common solvent used in experiment, [1] was evaluated by the conductor-like screening model (COSMO). [18] All structures were visualized using CYLview. [19]

Activation strain model and energy decomposition analysis
Quantitative analyses of the potential energy surfaces (PESs) associated with the studied reactions were obtained by means of the activation strain model (ASM) of reactivity. [7] The PES, that is, ΔE(ζ), was decomposed into the strain energy, ΔE strain (ζ), and interaction energy, ΔE int (ζ) [Equation (1)]: The ΔE strain (ζ) is associated with the rigidity and the structural deformation of the reactants from their equilibrium structure to the geometry they adopt at the coordinate of ζ during the reaction. The ΔE int (ζ) is related to the electronic structure of the reactants and their spatial orientation and takes the mutual interactions between the deformed reactants into account.
To obtain a deeper insight into the physical mechanism behind ΔE int (ζ), we employed our canonical energy decomposition analysis (EDA), [8] which decomposes the ΔE int between the deformed reactants, within the framework of Kohn-Sham DFT, into four physically meaningful terms [Equation (2)]: The electrostatic interaction, ΔV elstat (ζ), corresponds to the classical electrostatic interaction between the unperturbed charge distributions of deformed reactants. The Pauli repulsion, ΔE Pauli (ζ), comprises the repulsion between closed-shell orbitals and is, therefore, destabilizing. The orbital interaction, ΔE oi (ζ), accounts for the stabilizing orbital interactions, such as, charge transfer, namely, the interactions between the occupied orbitals of one reactant and the unoccupied orbitals of the other reactant, and polarization, that is, the occupied-unoccupied orbital mixing within one reactant due to the presence of the other reactant. The dispersion term ΔE disp corresponds to the dispersion corrections as introduced by Grimme et al. [11] Voronoi deformation density analysis The electron density distribution is analyzed using the Voronoi deformation density (VDD) method [20] for computing atomic charges. The VDD atomic charge on atom A (Q A VDD ) is computed as the (numerical) integral of the deformation density in the volume of the Voronoi cell of atom A [Equation (3)]. The Voronoi cell of atom A is defined as the compartment of space bounded by the bond midplanes on and perpendicular to all bond axes between nucleus A and its neighboring nuclei.
Here, 1(r) is the electron density of the molecule, and � B 1 B (r) the superposition of atomic densities 1 B of a fictitious promolecule without chemical interactions that is associated with the situation in which all atoms are neutral. The interpretation of the VDD charge Q A VDD is rather straightforward and transparent: instead of measuring the amount of charge associated with a particular atom A, Q A VDD directly monitors how much charge flows, due to chemical interactions, out of (Q A VDD > 0) or into (Q A VDD < 0) the Voronoi cell of atom A.

Base-substrate complexation and trends in reactivity
First, we analyze the binding of various bases to the diene, 3hydroxy-2-pyrone (Py). The electronic and Gibbs free energies, relative to the infinitely separated base B and diene Py, of the base-Py complex (B-Py) and the infinitely separated protonated base cation [B + H] + (B gains a proton and becomes a cation) with deprotonated Py anion [PyÀ H] À (Py loses a proton and becomes an anion) were computed at BLYP-D3(BJ)/TZ2P in the gas phase (Table 1) and in chloroform (Table S1). Table 1 shows that the B-Py complex involves an interaction between the base and Py, which becomes increasingly more stabilizing from À 10.4 to À 12.5 to À 13.0 kcal mol À 1 for H 2 O to Et 3 N to Me 3 N, respectively. We find that the formal deprotonation of Py by the base ([B + H] + + [PyÀ H] À ) is highly unlikely with respect to both the separated reactants and B-Py complex. Thus, we can conclude that the B-Py complex will be a likely intermediate in

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Research Article doi.org/10.1002/chem.202203121 the base-catalyzed Diels-Alder reaction with N-methylmaleimide (NMM). Next, we employ the activation strain model (ASM) and energy decomposition analysis (EDA) to understand the nature of the interaction between the base and Py in the B-Py complexes ( Table 2). The strain energy (ΔE strain ) associated with the formation of B-Py complex becomes more destabilizing as the base goes from H 2 O to the stronger nitrogen bases Me 3 N and Et 3 N. Nevertheless, the interaction energy (ΔE int ) is the primary contributor to the ΔE, and it becomes steadily more stabilizing from H 2 O to Me 3 N to Et 3 N, ranging from À 13.0 to À 18.1 kcal mol À 1 . For all bases, the electrostatic interaction (ΔV elstat ) is the major contributor to the ΔE int and shows, together with the dispersion energy (ΔE disp ), the same trend as the interaction energies. The orbital interactions (ΔE oi ), on the other hand, do roughly recover the trend in interaction energies in that they become more stabilizing from H 2 O to the nitrogen bases Et 3 N and Me 3 N. They are chiefly the result of the interaction between the donating lone-pair orbital of the base and the accepting σ* OÀ H orbital of Py. Note that Et 3 N is more basic than Me 3 N [21] but has a slightly less favorable orbital interaction than Me 3 N upon complexation to Py. This is because the Et 3 N-Py complex has a longer B···HÀ OR bond (1.68 Å) than Me 3 N-Py (1.64 Å) induced by the sterically more encumbered ethyl groups, and therefore has a weaker orbital interaction than Me 3 N-Py. Importantly, binding a base to Py, due to the above-mentioned σ-electron donation from the base to Py, leads to a more negative potential on the latter moiety and thus to a destabilization of its HOMO from À 5.6 eV for HOMO Py to À 5.4 eV for HOMO H2O-Py to À 4.9 eV for HOMO Et3N-Py and HOMO Me3N-Py . This HOMO-raising effect is, as we will show later, crucial for the rate-enhancement of base-catalyzed Diels-Alder reactions.
After analyzing the binding between the base and Py, we examine how the base catalyzes the Diels-Alder (DA) reaction between the activated diene B-Py and NMM. We focus on the uncatalyzed DA reaction and the Et 3 N-catalyzed DA reaction, since Et 3 N is most frequently used to catalyze DA reactions in experiments. [1a] The reaction profiles of other catalysts possess the same features and are provided in Figure S1 of the Supporting Information. The trends in reactivity on the electronic potential energy surface (PES) are the same as those on the Gibbs free energy PES ( Figure S3) and those fully optimized and calculated in chloroform at COSMO(chloroform)-BLYP-D3(BJ)/TZ2P (Figures S4 and S5). Figure 1 shows the PES of the uncatalyzed and the Et 3 N-catalyzed DA reaction between (B-)Py and NMM, together with the transition state structures, following the endo pathway. The exo pathway shares the same reactivity trend but is, in accordance with experimental findings, disfavored relative to the endo-pathways (Figures S2 and S8). [1,4] The reactions proceed via the reactant complex (RC) and the DA transition state (TS DA ) towards the cycloadduct (P DA ), which, in turn, can undergo a retro-DA reaction expulsing CO 2 via a transition state (TS retro-DA ) to the final product (P retro-DA ). The uncatalyzed DA reaction (Py) has the highest activation barrier, with TS DA at 10.1 kcal mol À 1 , and a concerted asynchronous reaction mode (Δr TS C···C = 0.58 Å, where Δr TS C···C refers to the difference in length between the newly forming C···C bonds in the transition state [22] ). Binding the base Et 3 N to Py lowers the DA activation barrier by 10 kcal mol À 1 , to only 0.1 kcal mol À 1 , and increases the degree of asynchronicity of the reaction to Δr TS C···C = 0.89 Å. In contrast, the base imparts only a small effect on the retro-DA (i. e., dissociation of CO 2 ) reaction barrier. With respect to the preceding DA cycloadduct P DA , the retro-DA reaction barrier increases from 17.5 kcal mol À 1 for the uncatalyzed to 18.9 kcal mol À 1 for the base-catalyzed reaction. Our computed PES nicely correlates with experimental observations where the uncatalyzed DA reaction between Py and NMM proceeds at an elevated temperature, which is needed to overcome the rate-determining DA activation barrier and hence continues directly over the retro-DA reaction which has a lower activation barrier (Scheme 1a). [4] The Et 3 N-catalyzed reaction, on the other hand, takes place at a low temperature owing to the relatively lower DA activation barrier, and can effectively be trapped prior to the kinetically unfavorable retro-DA reaction, yielding a polyoxygenated product (Scheme 1b). [1] If the Et 3 Ncatalyzed reaction would be performed at elevated temperatures, it is likely that the retro-DA reaction would become feasible as in the case for the uncatalyzed reaction.

Origin of base catalysis
The physical factors leading to the enhanced reactivity of the base-catalyzed compared to the uncatalyzed DA reaction are examined by applying the activation strain model (ASM) of reactivity, [7] where the interacting fragments are the diene, (B-)Py, and the dienophile, NMM. In both the activation strain and energy decomposition analysis diagrams, the intrinsic reaction coordinate (IRC) is projected onto the shorter of two newly forming C···C bonds between (B-)Py and NMM. This critical reaction coordinate undergoes a well-defined change during the reaction from the reactant complex via the transition state to the cycloadduct and has been shown to be a valid reaction coordinate for studying cycloadditions. [6,14,23] Figure 2a shows the activation strain diagrams from the reactants to the transition states for the uncatalyzed and Et 3 N-catalyzed DA reactions (see Figures S6 and S7 for all transition state structures and analyses). The accelerated reactivity of the Et 3 N-catalyzed reaction originates exclusively from a more stabilizing interaction energy. The strain energy, on the other hand, follows a trend that is opposite to the activation barriers and is, therefore, not responsible for the observed rate enhancement. To pinpoint the origin of the more stabilizing interaction energy, we applied the energy decomposition analysis (EDA) (Figure 2b). [8] We find that both the orbital and electrostatic interactions are responsible for the observed trend in interaction energy because both these energy terms are more stabilizing for Et 3 N-Py compared to Py. The Pauli repulsion shows an opposite trend, i. e., the Et 3 N-catalyzed DA reaction goes with more destabilizing Pauli repulsion than the uncata-  lyzed analog and, hence, is not responsible for the observed reactivity trend. These findings demonstrate the difference in the underlying electronic mechanism between base-catalyzed Diels-Alder reactions (HOMO-raising catalysis) and Lewis acidcatalyzed Diels-Alder reactions (Pauli-lowering catalysis). Next, we address why the Et 3 N-catalyzed DA reaction experiences a more stabilizing orbital interaction compared to the uncatalyzed analog. In line with the textbook rationale behind base-catalysis, [2h-j] the binding of Et 3 N to Py destabilizes the orbitals of Py and consequently strengthens the normal electron demand (NED) interaction, i. e., the donorÀ acceptor interaction between the filled molecular orbitals of (B-)Py with virtual molecular orbitals of NMM. This effect, however, gets partly compensated, as Et 3 N simultaneously weakens the inverse electron demand (IED) interaction, i. e., the donorÀ acceptor interaction between the virtual molecular orbitals of (B-)Py with filled molecular orbitals of NMM. By performing a Kohn-Sham molecular orbital (KS-MO) [8b,24] analysis on the consistent geometries where the shorter forming bond between (B-)Py and NMM is 1.95 Å, [25] we find that the NED interaction energy becomes more stabilizing, going from À 46.5 kcal mol À 1 for the uncatalyzed to À 58.5 kcal mol À 1 for the Et 3 N-catalyzed reaction (ΔΔE oi NED = À 12 kcal mol À 1 ), while the IED interaction energy gets less stabilizing and goes from À 35.1 kcal mol À 1 for the uncatalyzed to À 28.0 kcal mol À 1 for the catalyzed case (ΔΔE oi IED = 7.1 kcal mol À 1 ). Note that the strength of the NED interaction is obtained by performing EDA computations while having artificially removed all virtual orbitals on (B-)Py, and the IED interaction is obtained by performing EDA computations while having artificially removed all virtual orbitals on NMM. It is apparent that the loss of IED interaction is small and cannot completely counteract the gain in NED interaction.
Moreover, we inspect the key NED interaction of HOMO (B-)Py À LUMO NMM and find that the strengthening of the NED interaction for the Et 3 N-catalyzed reaction comes exclusively from a raised HOMO (B-)Py . The HOMO (B-)Py is raised in energy from À 6.3 eV for the uncatalyzed to À 4.6 eV for the catalyzed reaction, leading to a smaller and thus more favorable orbital energy gap (Figure 3a). An inspection of the key IED interaction of LUMO (B-)Py À HOMOÀ 1 NMM shows that the weakening of the IED interaction along with the Et 3 N-catalyzed reaction comes from a smaller energy gap induced by a destabilized LUMO (B-)Py with a reduced overlap (Figure 3b). Thus, we conclude that the enhanced orbital interactions associated with the Et 3 N-catalyzed DA reaction between Py and NMM is solely the result of the HOMO-raising effect of the base.
To understand the origin of the more stabilizing electrostatic interactions for the Et 3 N-catalyzed DA reaction (Figure 2b), we analyze how, in B-Py, coordinating the base to the diene Py has changed the charge density distribution of the Py moiety, using the Voronoi deformation density (VDD) method [21] and the molecular electrostatic potential (MEP). This has been done for the uncoordinated reactant Py and for B-Py, each at consistent TS-like geometries. The latter are defined as the structures near the saddle-point in which, for both reactions, the shorter of the newly forming C···C bonds between (B-)Py and NMM assumes the exact same value of 1.95 Å. Our analyses reveal that the enhanced stabilization of the electrostatic interactions for the Et 3 N-catalyzed DA reaction originates from the promoted secondary electrostatic interaction between the interacting reactants. During the DA reaction, (B-)Py and NMM can engage in two attractive electrostatic interactions: [26] i) the primary electrostatic interaction between the bond-forming atoms, that is, of C 1 and C 4 in (B-)Py with C 5 and C 6 of NMM, respectively; and ii) the secondary electrostatic attraction between C 2 and C 3 in (B-)Py with C 7 and C 8 in NMM. For the uncatalyzed DA reaction between Py and NMM, the positively charged C 1 and C 4 atoms and the negatively charged C 2 and C 3 atoms of Py have a stabilizing electrostatic interaction with the negatively charged C 5 and C 6 atoms and the positively charged C 7 and C 8 atoms, respectively (Figure 4a and c). Binding Et 3 N to Py has a profound effect on the magnitude and distribution of the electron density of the Py moiety in Et 3 N-Py, as electrons flow from Et 3 N to Py via the donorÀ acceptor interaction between the donating lone pair orbital of Et 3 N and the accepting σ* HÀ O orbital of Py (Table 2). Accordingly, C 1 , C 2 , and C 3 of Et 3 N-Py become more negatively charged (Figure 4b and  d). As a result, the secondary electrostatic interaction becomes significantly stronger, whereas the primary electrostatic interaction gets slightly weakened, ultimately yielding a more stabilizing electrostatic interaction for the Et 3 N-catalyzed compared to the uncatalyzed DA reaction.

Conclusion
Our computational study furnishes physical insight into the base-catalyzed Diels-Alder (DA) reaction between 3-hydroxy-2pyrone (Py) and N-methylmaleimide (NMM). The uncatalyzed DA reaction is slow and is followed by a retro-DA reaction expelling CO 2 . However, when catalyzed by a base, such as triethylamine, the DA activation barrier is lowered up to 10 kcal mol À 1 , causing the reaction to proceed smoothly at low temperature, thereby quenching the kinetically unfavorable expulsion of CO 2 . In this way, base catalysis affords efficient access to polyoxygenated cycloadducts at a low temperature.
Our quantum chemical analyses based on the activation strain model (ASM) and Kohn-Sham molecular orbital theory identify that the base lowers the DA activation barrier through two mechanisms: i) by enhancing the normal electron demand (NED) interactions via the HOMO-raising effect of the base; and ii) by stabilizing the secondary electrostatic interactions between the reactants. Complexation of a base to Py induces a strong electrostatic interaction and donorÀ acceptor interaction between the donating lone pair of the base and the σ OH * orbital of Py, resulting in a more negative potential on Py. The latter destabilizes the molecular orbitals of Py, in particular the HOMO of Py, and thus reduces the NED energy gap and enhances the stabilizing orbital interactions.
Finally, this work highlights the fundamentally different electronic mechanisms behind base-catalyzed versus Lewis acid-catalyzed DA reactions. Previously, we found that Lewis acids enhance the DA reactivity by reducing the Pauli repulsions between the π-systems of the diene and dienophile, and not due to enhanced donorÀ acceptor orbital interactions. [6] Taken altogether, we find that Lewis acids accelerate DA reactions via Pauli-lowering catalysis, whereas bases accelerate DA reactions via HOMO-raising catalysis.