DFT Study of Solvent Effects in Acid-Catalyzed DielsâAlder

Article pubs.acs.org/JPCA

DFT Study of Solvent Effects in Acid-Catalyzed Diels−Alder Cycloadditions of 2,5-Dimethylfuran and Maleic Anhydride Taha Salavati-fard,†,‡ Stavros Caratzoulas,‡ and Douglas J Doren*,‡,§ †

Department of Physics and Astronomy, ‡Catalysis Center for Energy Innovation (CCEI), Department of Chemical and Biomolecular Engineering, and §Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware 19716, United States S Supporting Information *

ABSTRACT: Density functional theory electronic structure calculations were used to explore the mechanism for the Diels− Alder reaction between 2,5-dimethylfuran and maleic anhydride (MA). Reaction paths are reported for uncatalyzed and Lewis and Brønsted acid-catalyzed reactions in vacuum and in a broad range of solvents. The calculations show that, while the uncatalyzed Diels−Alder reaction is thermally feasible in vacuum, a Lewis acid (modeled as Na+) lowers the activation barrier by interacting with the dienophile (MA) and decreasing the HOMO−LUMO gap of the reactants. A Brønsted acid (modeled as a proton) can bind to a carbonyl oxygen in MA, changing the reaction mechanism from concerted to stepwise and eliminating the activation barrier. Solvation effects were studied with the SMD model. Electrostatic effects play the largest role in determining the solvation energy of the transition state, which tracks the net dipole moment at the transition state. For the uncatalyzed reaction, the dipole moment is largely determined by charge transfer between the reactants, but in the reactions with ionic catalysts, there is no simple relationship between solvation of the transition state and charge transfer between the reactants. Nonelectrostatic contributions to solvation of the reactants and transition state also make significant contributions to the activation energy.

1. INTRODUCTION During the past few years, there has been a great deal of research on biomass conversion to fuels and platform chemicals.1−6 Various aromatic molecules can be produced through Diels−Alder cycloaddition between renewable chemicals and suitable counterparts. The Diels−Alder reaction is an efficient way to synthesize complex molecular structures by forming a pair of carbon−carbon bonds in a single step.7 There have been a number of previous studies of Diels−Alder reactions between maleic anhydride (MA) and furans, which are examples where renewable feedstocks can be used to produce higher-value chemicals.8−18 The reaction is usually run in solvents, such as acetonitrile,12,13 tetrahydrofuran,14 and diethyl ether.15−17 In this paper we focus on the role of catalysts and solvent effects in the reaction of 2,5-dimethylfuran (DMF) and MA to produce 3,6-dimethylphthalic anhydride by dehydrative aromatization of the Diels−Alder product (Scheme 1).11 Brion showed that Diels−Alder reactions with furans are catalyzed by Lewis acids,18 and a number of such reactions have been investigated computationally in the gas phase and also in solvents.19−32 The Lewis acid effect on the reaction rate can be understood by making use of Fukui’s frontier molecular orbital (FMO) theory:33 reducing the energy gap between the highest occupied molecular orbital (HOMO) of the electron-rich © 2015 American Chemical Society

reactant and the lowest unoccupied molecular orbital (LUMO) of the electron-poor reactant leads to a smaller activation energy. Assuming that the FMOs have the same symmetry, coordinating the Lewis acid to the electron-poor reactant (MA in the present case) lowers the LUMO energy and reduces the HOMO−LUMO energy gap. Recently, Nikbin et al. studied Lewis and Brønsted acids as catalysts in the cycloaddition between DMF and ethylene and in the subsequent dehydration of the cycloadduct to produce pxylene.34 They modeled the active sites of zeolites with alkali ions as Lewis acids and a proton as a Brønsted acid. They have shown that, while only Lewis acids are able to catalyze the Diels−Alder cycloaddition, both Brønsted and Lewis acids can catalyze the dehydration reaction. Experimental measurements in zeolites with Lewis and Brønsted activity are consistent with predictions based on these simple models.34 Solvent effects were not considered in that work, but Nikbin and co-workers have also studied models that include the zeolite framework.35 Using cluster models, they showed that charge transfer from the oxygen atoms of the zeolite structure to cations weakens their electron withdrawing ability. As a consequence, Diels−Alder Received: May 27, 2015 Revised: August 10, 2015 Published: September 2, 2015 9834

DOI: 10.1021/acs.jpca.5b05060 J. Phys. Chem. A 2015, 119, 9834−9843

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The Journal of Physical Chemistry A Scheme 1. Diels−Alder Cycloaddition Followed by Dehydrative Aromatization

and transition states, and intrinsic reaction coordinate calculations were performed for all transition states. To calculate partial charge transfer between reactants at the transition state, we utilized natural bond orbital (NBO) analysis.55,56 Gibbs free energies were calculated at standard temperature and pressure, that is, T = 298.15 K and P = 100 kPa. Solvent effects were modeled with the SMD model, which is based on the solute electron density, a continuum model of the solvent, and atomic surface tensions.57 For FMO analysis, we calculated Hartree−Fock FMOs for comparison, to confirm that they have the same ordering as DFT FMOs.58,59

reaction paths where DMF interacts with the Lewis acid site have activation barriers similar to those where ethylene interacts with the Lewis acid. For the Diels−Alder reaction in Scheme 1, mechanisms for acid catalysis are available that have no analogue in the reaction of DMF and ethylene. In particular, protonation of MA is much more favorable than protonation of ethylene, so that the Diels− Alder reaction of MA and DMF can be catalyzed by a Brønsted acid, even though the reaction of ethylene and furan cannot. Within the context of FMO theory, the rationale for Brønsted acid catalysis follows the same logic as for a Lewis acid, when protonation is feasible. There are many prior examples where a Brønsted acid catalyzes Diels−Alder reactions,36−39 though this mechanism has not been utilized in biomass conversion. In the study presented here, we use density functional theory (DFT) to investigate the mechanisms of uncatalyzed and acidcatalyzed Diels−Alder reactions between DMF and MA in vacuum. We then employ a continuum model of solvent effects to understand how a broad range of solvents affects the reacting molecules and changes the reaction profiles. There have been a number of theoretical and experimental studies of solvent effects on the Diels−Alder reaction.20,31,32,40−51 While solvent effects for the uncatalyzed Diels−Alder reaction are expected to be small in aprotic organic solvents, there may be significant effects when a cationic catalyst is involved in the reaction, especially in polar solvents. In the models of Lewis and Brønsted acid catalysts studied here, we find that both electrostatic and nonelectrostatic contributions are important. Moreover, the electrostatic effects are subtle and not related simply to charge transfer between the reactants. As a result, the impact of solvent cannot be predicted from properties of the reactants alone, such as the FMO approach or conceptual DFT.31 Except for the case of water, the solvents studied are aprotic, and we focus on the impact of varying dielectric constants over a wide range. Water is a special case, with a pronounced effect on the rate and selectivity of the Diels−Alder reaction due to hydrogen bonding and the hydrophobic effect.40−44 It is not our intention to explore detailed effects of specific solvent interactions, such as those in water, though we use the continuum model of water to observe the impact of a high-dielectric environment. In the next section, we provide a brief description of the computational methods and models. In the Results and Discussion section we first present the predicted reaction mechanisms for uncatalyzed and catalyzed reactions in vacuum, then describe the effects of solvent on these reactions. Finally, we summarize the findings of this study.

3. RESULTS AND DISCUSSION 3.1. Gas Phase. Table 1 reports FMO gaps for normal and inverse electron demand for the uncatalyzed and acid-catalyzed Table 1. Transition State Free Energy (Relative to the Energy of Noninteracting Reactants R1 and R2) and FMO Gaps for Uncatalyzed and Catalyzed Diels−Alder Reactions between DMF and MAa reactant index

1

a b

MA (MA +Na+) MA

c d e

(MA +H+) MA

FMO gaps (Hartree) 2

G(TS) − (G(R1) + G(R2)) (kcal/mol)

normal

inverse

DMF DMF

24.1 11.3

0.17594 0.02609

0.44639 0.58921

(DMF +Na+) DMF

33.5

0.35141

0.2703

−7.1

−0.04007

0.64696

32.6

0.38802

0.22928

(DMF +H+)

a

FMO gaps are shown for normal (LUMO(R1)−HOMO(R2)) and inverse (LUMO(R2)−HOMO(R1)) electron demand, between orbitals of proper symmetry. The smaller gap in each pair is in bold face. Indices for the reaction in the first column correspond to the labels on the structures in Figure 3.

Diels−Alder reactions in the gas phase. In cases where the HOMO (LUMO) of a reactant does not have the right symmetry for reaction, the next orbital down (up) in energy that possesses the right symmetry is considered. Figures 1 and 2 show the FMOs of the isolated reactants, each shown with and without the Lewis and Brønsted acid. The transition state (TS) geometries for each reaction path are shown in Figure 3, and Figure 4 shows free energy profiles. The uncatalyzed Diels−Alder reaction of DMF and MA is expected to be a case of normal electron demand: DMF is the more nucleophilic reactant, owing to the conjugated π electrons, while MA is more electrophilic because of the electron-withdrawing carboxyl groups. This is confirmed in Table 1, which shows that the FMO gap is smaller for normal electron demand. The Gibbs free energy barrier with respect to

2. COMPUTATIONAL METHODS AND MODELS All calculations were performed with the Gaussian09 software package52 using the M06-2X hybrid DFT53,54 with the 6311+G(d,p) basis set. The Berny optimization algorithm was used, and all structures were fully relaxed. Vibrational frequencies were calculated to confirm the character of minima 9835


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The Journal of Physical Chemistry A

Figure 1. FMOs of isolated MA, Lewis acid-coordinated MA, and protonated MA.

Figure 4. Gibbs free energy profile of Diels−Alder cycloaddition reaction of DMF with MA in vacuum, with and without a Lewis or Brønsted acid. (1) Separated reactants; (2) cation coordinated to one molecule, infinitely separated from the other molecule; (3) interacting complex of reactants; (4) transition state; (5) intermediate (H+-MA path only); (6) transition state (H+-MA path only); (7) Diels−Alder product (coordinated to cation in acid-catalyzed cases). The zero of energy for the uncatalyzed and Lewis acid-catalyzed reactions corresponds to state (1). However, for the Brønsted acid-catalyzed reactions, State (1) cannot be included on this scale, and the reference state corresponds to H+-MA infinitely separated from DMF.

the infinitely separated reactants is 24.1 kcal/mol. The transition state geometry is shown in Figure 3a. To understand the role of the catalysts, we found minima for the Lewis acid (Na+) and Brønsted acid (H+) interacting with each reactant (Figures 1 and 2) and followed the lowest-barrier reaction paths from these configurations. Transition state geometries are shown in Figure 3. To illustrate the correlation between the transition state energy and the FMO gaps, Table 1

Figure 2. FMOs of isolated DMF, Lewis acid-coordinated DMF, and protonated DMF.

Figure 3. Selected geometrical properties of the transition states of the uncatalyzed, Lewis acid-catalyzed, and Brønsted acid-catalyzed Diels−Alder reactions in vacuum. 9836


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The Journal of Physical Chemistry A Scheme 2. Mechanism of Diels−Alder Reaction with Protonated MA

Figure 5. Uncatalyzed Diels−Alder reaction in solvent. (a) Gibbs free energy of activation at STP vs solvent dielectric constant. Free energies are reported with respect to the infinitely separated species in each solvent. (b) Direct and indirect FMO gaps. (c) Negative charge transferred to dienophile at TS (solid curves) and dipole moment of the TS (dashed curves). Arrows near each curve indicate the corresponding scale. (d) Gibbs free energy of solvation for infinitely separated reactants (R), TS, and their difference (TS-R).

increases the electrophilicity of MA, decreases the normal electron demand FMO gap (relative to the uncatalyzed case), and lowers the activation free energy so that it is below the energy of the separated reactants (Figure 4). A sodium ion interacting with DMF sits above the plane of the furan ring at the transition state (Figure 3c). This makes DMF less nucleophilic, and the FMO gap indicates that inverse electron demand would be operative. Relative to the separated reactants, the barrier for this reaction is lower than the uncatalyzed case, though the activation barrier is higher than when Na+ interacts with MA, so this pathway is not likely to be important in the gas phase.

reports the energy difference between the transition state and the initial state where the cation is coordinated to either the diene or dienophile. This is not the activation barrier that would be observed experimentally. The FMO gaps are shown for each combination of cation and molecule, and the ordering of transition state energy, relative to this reference state, follows the order of the lowest FMO gap for each reactant pair. Note that, while the geometries of Na+-MA and H+-MA are not symmetric, the frontier orbitals remain similar to those of MA. When a sodium ion (Lewis acid) is coordinated to MA, the minimum free energy configuration has Na+ in the plane of the MA ring, coordinated to the central oxygen atom and one of the carbonyl oxygen atoms (Figure 3b). As expected, this 9837


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Figure 6. Lewis acid-catalyzed Diels−Alder reaction. Two arrangements, with Na+ coordinated to DMF and Na+ coordinated to MA, are considered. (a) Gibbs free energy of activation at STP vs solvent dielectric constant, relative to DMF, MA, and Na+ at infinite separation. (b) Direct and indirect FMO gaps when Na+ is coordinated to one of molecules. (c) Negative charge transferred to dienophile (Na+-MA or MA) at TS (solid curves) and dipole moment of the TS (dashed curves). Arrows near each curve indicate the corresponding scale. (d) Solvation energy contributions to activation energy eq 1.

this study. Finally, when the proton interacts with DMF (Figure 3e), the mechanism follows inverse electron demand, but the activation barrier increases dramatically, and this mechanism is not likely to be important. 3.2. Solvent Effects. 3.2.1. Uncatalyzed Reaction. The activation barrier for the uncatalyzed reaction (Figure 5a) shows a modest influence of solvent, decreasing by a few kilocalories per mole across the range of examples shown. This is the opposite of the direction expected from FMO theory, as the normal electron demand gap (which is smaller than the inverse demand gap in all cases) increases with the solvent polarity (Figure 5b), while the activation energy shows a generally decreasing trend. Charge transfer to the dienophile at the transition state increases smoothly with solvent dielectric (Figure 5c). This also contrasts with the expectation from FMO theory, which predicts that a larger gap leads to less orbital mixing and less charge transfer at the transition state.31 Thus, despite its success in the gas phase, FMO theory does not predict the correct trends in solvent. The fact that charge transfer at the TS increases with solvent dielectric suggests that the solvent lowers the activation barrier by stabilizing a dipole at the transition state (Figure 5c).

For the Brønsted acid-catalyzed reaction, the proton interacts with an oxygen atom of one reactant. When the proton interacts with MA, through a carbonyl oxygen, the asymmetry leads to a stepwise reaction mechanism, namely, it proceeds through two transition states (Scheme 2, Figure 3d). The proton makes MA more electrophilic, and the transition state is lower in energy than the protonated reactants (Figure 4). Note that we used protonated MA (H+-MA) and isolated DMF as the reference state for the free energy changes. This is a matter of convenience, as the difference in energy between this state and the state with an isolated proton is large, being equal to the proton affinity of the organic molecule. The cycloaddition of H+-MA with DMF follows normal electron demand. For this stepwise reaction we searched for unrestricted DFT solutions for the intermediate but found only the restricted wave function. We note that the proton can also attach to the ring oxygen of MA, which is higher in energy than the protonated carbonyl by ∼10 kcal/mol and higher than the transition state for the Diels−Alder reaction with a protonated carbonyl. Moreover, protonation at the ring oxygen opens the MA ring and does not lead to the Diels−Alder product. This alternate path may lead to side products, but this is outside the scope of 9838


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The Journal of Physical Chemistry A However, the variation in activation barrier is not as simple as the trend in charge transfer or dipole moment, indicating that other solvation effects are also important. It is a thermodynamic identity that † † ΔGsol = ΔGvac + ΔGsolvation(TS) − ΔGsolvation(R )

(1)

where ΔG†sol and ΔG†vac are the free energies of activation for the reaction in solution and in vacuum, respectively, and the solvation energies ΔGsolvation(TS) and ΔGsolvation(R) are the difference in free energy between the solution and vacuum phase for the transition state and reactant state. This means that the solvent dependence of the activation barrier is equivalent to variation in ΔGsolvation(TS) − ΔGsolvation(R). Figure 5d shows the solvation energy of the transition state and the isolated reactants in the different solvents. Consistent with the expectations based on charge transfer, solvation is more favorable for the transition state than the neutral reactants, and as required, the difference between these solvation energies tracks the variation in activation energy. However, the solvation energy of both the reactants and transition state vary nonmonotonically, and the difference between them does not follow a simple correlation with charge transfer or solvent polarity. There is no significant difference among the optimal geometries in different solvents, so we attribute the nonmonotonicity in solvation energy to nonelectrostatic contributions (cavity formation, dispersion, and solvent structure). 3.2.2. Lewis Acid-Catalyzed Reaction. The lower energy path with a Lewis acid has Na+ is coordinated to MA. The activation energy increases strongly with solvent dielectric, as shown in Figure 6a. This reflects both FMO gaps and solvation energy. The FMO gaps, measured relative to the state with Na+ coordinated to MA, increase with dielectric constant (Figure 6b), and the transition state energy shows a similar increasing trend when measured relative to this state. However, the observable activation energy is measured relative to the three separated reactants (Figure 6a). Solvation energy effects are stronger for this reaction than in the uncatalyzed case, because of the presence of the ion. In fact, charge transfer at the transition state is a small perturbation to the dipole caused by the ion. Thus, even though charge transfer to the dienophile (Na+-MA) at the transition state decreases with solvent polarity, the net dipole at the TS increases (Figure 6c), and the solvation energy of the transition state becomes more favorable (Figure 6d). This effect depends on the geometry of the transition state, and cannot be predicted based on groundstate properties of the separated reactants. While the solvation energy for the transition state becomes more favorable with solvent polarity, the solvation energy of the reactants increases at an even greater rate (Figure 6d). There are again nonelectrostatic contributions to the solvation energy, accounting for some of the variation in solvation energy (Figure 6d), but these are a much smaller part of the total variation than in the uncatalyzed case. The net effect is that the solvation energy contribution to eq 1 is positive, and generally increasing with solvent polarity. Figure 7 is a graphical representation of the reaction profile in the specific case of acetonitrile. In contrast to the gas-phase reaction, the transition state in solvent for this Lewis acid-catalyzed path has a higher free energy than the reactants, though the barrier remains lower than that of the uncatalyzed case and is easily overcome at room temperature. While the lowest-energy pathway for this reaction always has the sodium ion associated with MA, we also explored the path where Na+ is coordinated with DMF (Figure 7). As noted

Figure 7. Free energy profiles of the uncatalyzed and acid-catalyzed reactions in acetonitrile. In this figure, the zero of free energy for the uncatalyzed and Lewis acid-catalyzed reactions corresponds to the case where all of the reacting species are infinitely separated. However, for the Brønsted acid-catalyzed reaction, the reference state corresponds to the case that protonated MA is infinitely far from DMF. (1) Separated reactants; (2) cation coordinated to one molecule, infinitely separated from the other molecule; (3) interacting complex of reactants; (4) transition state; (5) intermediate (H+-MA path only); (6) transition state (H+-MA path only); (7) Diels−Alder product (coordinated to cation in acid-catalyzed cases).

above, in zeolites, the activation barrier is similar whether the diene or dienophile coordinates to the Lewis acid site.35 The activation energy on this path is consistently higher than when the cation is coordinated to MA, but it shows much less dependence on solvent dielectric (Figure 6a). This is in contrast to the strong decrease in FMO gaps (Figure 6b). Note that in every solvent, the normal electron demand FMO gap is lower than the inverse demand gap. On the Na+-DMF pathway, charge transfer to the dienophile (MA in this case) at the TS is weaker than on the Na+-MA path (Figure 6c), as expected from fact that the positive charge is now on the diene. Charge transfer increases with solvent dielectric, consistent with the predictions of FMO theory in this case. However, the TS solvation energy for this path is more favorable (Figure 6d) despite the smaller charge transfer. This again reflects the impact of Na+: the TS has a very large dipole moment (Figure 6c) due to the position of the ion (Figure 3c), resulting in a large solvation energy. The difference between solvation energy of the reactants and TS is small, so the contribution to eq 1 is only a few kilocalories per mole and decreases with solvent polarity (Figure 6d). In this case, the solvation effect counters the decreasing FMO gap to some degree, but the overall effect is that the activation energy on the Na+-DMF pathway in solution gradually declines with increasing solvent polarity. Since solvation raises the barrier on the Na+-MA pathway, the difference in activation barriers between the two paths decreases in solution. As shown in Figure 6a, the barrier on the Na+-DMF path is more than 25 kcal/mol higher than the Na+-MA path in vacuum, but the difference is less than 7 kcal/mol at high dielectric. This illustrates how environmental effects can bring the activation energies on these two paths closer, as observed in zeolites. 9839


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Figure 8. Brønsted acid-catalyzed Diels−Alder reaction. Two arrangements, with H+ coordinated to a carbonyl of MA and H+ coordinated to the ring oxygen of DMF, are considered. (a) Gibbs free energy of activation at STP vs solvent dielectric constant. The reference state is H+ attached to MA, with DMF at infinite separation. Note that this is a different reference than used in Figure 6. (b) Direct and indirect FMO gaps when H+ is coordinated to one of molecules. (c) Negative charge transferred to dienophile (H+-MA or MA) at TS (solid curves) and dipole moment of the TS (dashed curves). Arrows near each curve indicate the corresponding scale. (d) Solvation energy contributions to activation energy eq 1.

3.2.3. Brønsted Acid-Catalyzed Reaction. The low-energy pathway for the Brønsted acid-catalyzed cycloaddition has a proton attached to one of the MA carbonyl oxygens (Figure 3d). The corresponding activation free energies are presented in Figure 8a. Note that we used H+-MA and DMF as the reference state for the free energy changes, as in the gas-phase reactions. The free energy to protonate MA in a given solvent will be proportional to the pKa of H+-MA in that solvent, but accurate calculations of these numbers are beyond the scope of this work. We will limit our conclusions about the effect of solvent to factors that are not affected by this choice of reference state. The activation barrier on the H+-MA path is negligible in every case, so that the rate-limiting step will be the protonation of MA. The normal demand FMO gap between H+-MA and DMF increases with solvent polarity (Figure 8b). The activation energy, relative to this reference state, increases as expected at low dielectric constant, but solvation effects counter this in the higher dielectric examples. Charge transfer at the transition state increases slightly with solvent polarity (Figure 8c), opposite the prediction based on the increasing FMO gap. In this case, the variation in dipole moment is closely correlated

with the variation in charge transfer. However, nonelectrostatic effects appear to play an important role in the solvation energy of the reactants, leading to nonmonotonic behavior in the activation energy (Figure 8d). As in the Na+-MA path for Lewis acid catalysis, both the FMO effect and solvation tend to raise the activation energy relative to the reaction in vacuum, but the net effect here is small due to cancellation between the solvation energy of the reactants and transition state. The alternate path, with protonated DMF, has a much higher activation barrier (Figure 8a), though it shows an interesting solvent dependence. The FMO gap decreases with increasing solvent polarity, and the solvation contribution to the activation barrier is negative. While both effects tend to decrease the activation energy, it remains much higher than the H+-MA path. In contrast to the gas-phase reaction, the interacting complex is not strongly stabilized in solution (Figure 7). In the gas phase, the interacting complex has both reactants in the same plane, with the oxygen atoms in front of each other and interacting with the proton. However, the structure of the interacting complex in solvent looks similar to the transition state, with larger carbon−carbon distances. The more compact 9840


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the reactants cannot capture this effect. We have illustrated this within the FMO approach, but even an approach like conceptual DFT, which resolves some shortcomings of the FMO theory, will not account for differential solvation. The present work also suggests that Brønsted acid catalysis may be a promising avenue for Diels−Alder reactions to produce some platform chemicals from renewable furans. If this can be accomplished with practical Brønsted acid catalysts, the same catalyst could likely be used for the following dehydration step as well.

structure preferred in solvent is not stabilized to the same degree as in the gas-phase complex.

4. CONCLUSION We have presented DFT calculations for the Diels−Alder cycloaddition of DMF and MA in vacuum and solution with simple models of Lewis and Brønsted acid catalysts. The uncatalyzed reaction can occur at a reasonable rate in vacuum, and the barrier is slightly reduced in solution. However, the reaction is strongly accelerated by acid catalysts. With Na+ coordinated to MA, there is no barrier to reaction in vacuum, with the transition state lower in energy than the reactants. In solution, there is a barrier to reaction, though it is 6−20 kcal/ mol lower than the uncatalyzed reaction in the examples that we have considered. With Na+ coordinated to DMF, the barrier in vacuum is lower than the uncatalyzed case, but in solvent the barrier is close to the uncatalyzed barrier, and in some cases is higher. However, the activation barrier on the Na+-DMF path decreases with increasing solvent polarity, while the barrier on the Na+-MA path increases. Thus, increasing solvent polarity makes Lewis acid catalysis less effective but brings the activation barriers on the two paths closer together. In the Brønsted acid case, with H+ coordinated to MA, the transition state energy in the gas phase is lower than the energy of the protonated reactants. It remains below that level in solvent, with only three examples of slightly positive barriers. This is a stronger catalytic effect than with the Lewis acid, though protonation may be rate-limiting. When H+ is coordinated to DMF, the activation barrier is so high that the reaction is unlikely to occur by this path. The difference in activation barriers on these two paths has a generally decreasing trend with solvent polarity, reminiscent of the Lewis acid case. However, the difference remains much larger for the Brønsted case. This reflects the fact that the difference in FMO gaps for the two paths is much larger in the Brønsted acid case, while the difference in solvation energies is much smaller. In other words, the FMO gap on the Na+-DMF path is not much greater at high dielectric than on the Na+-MA path, and the Na+-MA path is strongly destabilized by solvent. These results give qualitative insight into the impact that environment can have on acid catalysis of the Diels−Alder reaction. When ionic species are involved, charge transfer at the transition state does not always correlate with the solvation energy of the transition state. For example, on the Na+-MA path, charge transfer decreases, while TS solvation becomes more favorable; and, for both the Lewis and Brønsted acidcatalyzed cases, the path with less charge transfer has the more favorable TS solvation energy. However, the dipole moment of the TS correlates well with TS solvation. This reflects the fact that in ionic species, the geometry of a charged site relative to the rest of the molecule will have a large impact on charge distribution. While charge transfer is a good proxy for net dipole with neutral reactants (as in the uncatalyzed case), this is not so for ionic reactants. The electrostatic contribution to the solvation energy of ionic species is much greater than for neutral species, and solvent polarity is an important variable. However, there is often a great deal of cancellation between the solvation energies of reactants and the transition state, and non-electrostatic contributions can make an important contribution as well. The examples studied here show that differences in solvation energy between the reactants and transition state can either increase or decrease the activation barrier. Qualitative predictions based on properties of

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b05060. Tabulated data including FMO gaps and Gibbs free energy profiles. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +1 302 831 2793. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This material is based upon work supported as part of the Catalysis Center for Energy Innovation, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award No. DE-SC0001004.

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REFERENCES

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