Journal of Molecular Modeling (2018) 24:33 https://doi.org/10.1007/s00894-017-3563-x
ORIGINAL PAPER
Solvent effect on the degree of (a)synchronicity in polar Diels-Alder reactions from the perspective of the reaction force constant analysis Diana Yepes 1 & Jorge I. Martínez-Araya 1 & Pablo Jaque 1 Received: 14 November 2017 / Accepted: 3 December 2017 # Springer-Verlag GmbH Germany, part of Springer Nature 2017
Abstract In this work, we computationally evaluated the influence of six different molecular solvents, described as a polarizable continuum model at the M06-2X/6–31+G(d,p) level, on the activation barrier/reaction rate, overall energy change, TS geometry, and degree of (a)synchronicity of two concerted Diels-Alder cycloadditions of acrolein (R1) and its complex with Lewis acid acrolein···BH3 (R2) to cyclopentadiene. In gas-phase, we found that both exothermicity and activation barrier are only reduced by about 2.0 kcal mol−1, and the asynchronicity character of the mechanism is accentuated when BH3 is included. An increment in the solvent’s polarity lowers the activation energy of R1 by 1.3 kcal mol−1, while for R2 the reaction rate is enhanced by more than 2000 times at room temperature (i.e., the activation energy decreases by 4.5 kcal mol−1) if the highest polar media is employed. Therefore, a synergistic effect is achieved when both external agents, i.e., Lewis acid catalyst and polar solvent, are included together. This effect was ascribed to the ability of the solvent to favor the encounter between cyclopentadiene and acrolein···BH3. This was validated by the asymmetry of the TS which becomes highly pronounced when either both or just BH3 is considered or the solvent’s polarity is increased. Finally, the reaction force constant κ(ξ) reveals that an increment in the solvent’s polarity is able to turn a moderate asynchronous mechanism of the formation of the new C-C σ-bonds into a highly asynchronous one. Keywords Reaction force . Reaction force constant . Diels-Alder reactions . Lewis acid catalysts . Solvent effect . Synchronicity . DFT calculations . Reaction mechanisms
Diels-Alder mechanism: the influence of solvents Experimental chemists have been trying to unveil the riddle of the influence of solvents on the reaction rate, mechanism, and product distribution in numerous organic reactions for many years [1, 2]. Meanwhile, theoretical chemists have been developing several computational and conceptual tools aimed to gain insights into the above-mentioned issues at the molecular level [3]. In this regard, the simplest approaches proposed to tackle molecular systems embedded in condensed solution phase are
This paper belongs to Topical Collection P. Politzer 80th Birthday Festschrift * Pablo Jaque
[email protected] 1
Departamento de Ciencias Químicas, Facultad de Ciencias Exactas, Universidad Andres Bello, Av. República 498, Santiago, Chile
the so-called polarizable continuum (or implicit) solvation models [4–9], which are parameterized in order to compute activation and overall solvation free energy changes. They have been successfully applied in a variety of chemical reactions and processes highlighting the prediction of reduction potentials [10–15], pKa’s [16–19], vertical detachment energies [13, 20–22], rate constants, and reactivity [23–26] in different solvents. An emblematic example where the stepwise mechanism transitions into the concerted pathway as a function of the solvent’s ability to stabilize an intermediate or enhance the nucleophilicity of a ligand corresponds to the nucleophilic substitution at the saturated carbon, namely SN1 and SN2. While the former is highly promoted in polar protic solvents the later easily proceeds in polar aprotic solvents [1, 27–29]. The solvent-reagents interaction has also been shown to play a significant role in reaction rates and product ratio in Diels-Alder cycloadditions. Interest in the influence of solvents in this important and powerful [4 + 2] addition of a diene to a dienophile grew particularly after the study reported by Rideout and Breslow [30–32], where a noticeable catalytic effect exerted by water was evidenced. In this
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regard, Desimoni and co-workers [33–35] attempted to decode the solvent effect on a specific set of Diels-Alder reactions finding that the acceptor number (which provides a rank of the solvent electron acceptor ability) describes the solvent role in this kind of chemical reaction. In accordance with the solventreagents interactions they classified Diels-Alder reactions into three main classes [34]. The first includes those that exhibited an enhancement of the reaction rates as the acceptor number power increases; this behavior is quite similar to the catalytic effect exerted by Lewis acids. The second group corresponds to solvents with donating ability, which presents a reverse effect and consequently, the reaction rates decrease as the donating power increases. The last group encompasses those DielsAlder reactions where solvent-solvent interactions are more important and concomitantly, the solvent effect can be negligible. Nowadays, the rationalization of the solvent effect on DielsAlder reactions has been extended to ionic liquids [36, 37]. The Diels-Alder reactions classified as multi-bond reactions by Dewar [38] can proceed in a concerted mechanism implying that the two new carbon-carbon σ-bonds form in a single kinetic step, whereas a stepwise mechanism proceeds via either diradical or zwitterion intermediate. Notice that the former can be further classified as synchronous or asynchronous (also known as two-stage [38]) depending on whether the bonds are or are not formed at unison. The issues of concertedness versus nonconcertedness and synchronicity versus nonsynchronicity in Diels-Alder reactions have received much attention [28, 38–48]. In many recent reports we proposed the reaction force constant as a suitable indicator for this purpose [49–55]. Since there is experimental evidence that supports how the solvent can turn a stepwise mechanism into a concerted mechanism and vice versa, our current interest is in revealing how the solvent can transition a synchronous Diels-Alder reaction into a two-stage (or highly asynchronous) reaction. In this paper we investigate the influence of the solvent polarity on the synchronicity/nonsynchronicity of two Diels-Alder reactions depicted in Scheme 1. Note that in both, the diene is cyclopentadiene and the dienophile is acrolein in R1 and the respective intermolecular complex with the Lewis acid BH3 in R2. We have previously studied the gas-phase reactions finding that the presence of the Lewis acid emphasizes the polar character and the asynchronicity of the cycloaddition reaction [53], which is quite meaningful to evaluate the influence of the solvents. For this purpose we take into account six molecular solvents by means of polarizable continuum solvation models.
The reaction force and the reaction force constant From classical physics, in a conservative system the force is the negative gradient of the potential energy U(ξ) while the force constant corresponds to the second derivative.
Scheme 1 Diels-Alder cycloadditions between acrolein (R1) and acrolein···BH3 (R2) and cyclopentadiene
Consistently, the reaction force F(ξ) [56] and the reaction force constant κ(ξ) [57] can be defined for any chemical process along the reaction coordinate ξ (typically the intrinsic reaction coordinate, IRC [58, 59]) as the first and second derivatives of the potential energy profile U(ξ), respectively: FðξÞ ¼ −
∂UðξÞ ∂2 UðξÞ ∂ FðξÞ and κðξÞ ¼ : ¼− ∂ξ ∂ξ ∂ξ2
Notice that both F(ξ) and ξ are vectors directing from reactants (ξR) to products (ξP), while κ(ξ) is a scalar. The details of these properties have already been described in many reports (see references [49–55, 60–75]), and hence here we will briefly refer to the main features of this analysis. The potential energy profile U(ξ) and its derivatives, the so-called F(ξ) and κ(ξ), provide valuable quantitative and qualitative information to fully characterize both the energetics and the degree of synchronicity for a one-step reaction. According to Fig. 1, the activation barrier, ΔEact, and the overall energy change, ΔErxn, can be directly computed from the U(ξ) profile as: ΔEact ¼ UðξTS ÞUðξR Þ and ΔErxn ¼ UðξP ÞUðξR Þ: From the reaction force F(ξ) profile a negative minimum at ξ1 (retarding process) and a positive maximum at ξ2 (driving process) are revealed. Both divide the entire reaction coordinate into three regions: the first (third) known as the reactant (product) region is mainly associated with the structural changes in the reactants (products) such as bond lengthening/shortening, rotations, and torsions; whereas the most significant electronic events, such as bond breaking and bond formation, usually take place in the middle one (coined as the transition region due to its analogy with the continuum of transient, unstable states, described by Zewail and Polanyi on the basis of the transition state spectroscopy [76, 77]) [72]. Thus, the energy barrier can be decomposed into two components along ξ (Fig. 1): ΔEact ¼ ΔEact;1 þ ΔEact;2 ¼ ½Uðξ1 Þ–UðξR Þ þ ½UðξTS Þ–Uðξ1 Þ;
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Fig. 1 Profiles of U(ξ), F(ξ), and κ(ξ) along the intrinsic reaction coordinate ξ for concerted synchronous (left-bottom panel) and asynchronous (right-bottom panel) mechanism
where, ΔEact,1 measures the energy required to overcome the structural rearrangements until the TS is reached and, ΔEact,2 is related to the electronic reorganizations. Notice that even though the terms are not solely structurally or electronically oriented, they have been recognized to be suitable in unveiling
how an external agent, e.g., a solvent or a catalyst, can affect the energy barrier and consequently, the reaction rate [64, 67]. Regarding the reaction force constant κ(ξ), the emphasis will be put upon its fine structure along the transition region, i.e., from ξ1 to ξ2. As can be seen κ(ξ) is negative throughout
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this region. Previous studies have established that the presence of only one minimum therein evidences a fully synchronous mechanism (see left-bottom panel in Fig. 1). Moreover, if the formation of the new bonds is asynchronous enough, then a shoulder in κ(ξ) would arise; while if the asynchronicity increases, the process would be described by two closely spaced minima, separated by a negative local maximum after ξTS (see right-bottom panel in Fig. 1) [49–55], when this local maximum becomes positive the asynchronous concerted mechanism is thus close to turn into a stepwise pathway [51]. Therefore, the analysis of κ(ξ) can be seen as a useful manner to control or modulate the transition of a concerted mechanism into a stepwise path as the reaction conditions (e.g., solvent, catalysts, co-factors, etc.) are changed. Finally, it should be pointed out that the degree of synchronicity cannot be uniquely assessed neither from the TS structure nor from U(ξ)/F(ξ) profiles.
Computational details Full geometry optimization for all stationary states were performed in gas phase and implicit solvent employing both B3LYP [78, 79] and M06-2X [80] (hybrid and hybrid-meta) exchange-correlation functionals combined with a double-ζ basis set augmented with d-type polarization and diffuse functions for carbon, boron, and oxygen atoms and p-type polarization function for hydrogens, i.e., the 6–31+G(d,p) [81]. Harmonic frequency analysis were also done to confirm reactant and product as true local minima and TS as first-order saddle point on the potential energy surface through all positive eigenvalues and only one negative eigenvalue in the Hessian matrices, respectively. The IRC calculations [58, 59] were also carried out at the two KS-DFT levels with a gradient reaction step size of 0.10 amu1/2bohr providing the input U(ξ) profile needed to generate F(ξ) and κ(ξ), these calculations were only performed for the pathway that leads to the isomer preferentially formed, i.e., the endo [28]. The solvent-reagents interaction along the cycloaddition reactions between cyclopentadiene and acrolein in R1 and its complex with BH3 in R2 were described by the polarizable continuum solvation model (PCM) [4, 9] taking into account the following six molecular solvents ordered as the polarity increases: cyclopentane (ε = 1.96), chlorobenzene (ε = 5.70), acetonitrile (ε = 35.69), water (ε = 78.35), formamide (ε = 108.94), and N-methyl formamide mixture (ε = 181.56). All calculations were performed in the Gaussian09 suite of program [82]. Although the B3LYP functional was able to provide reliable results in the Diels-Alder reaction [83–86] there are, however, some studies that unveil its poor description of exothermicity [87] and its tendency to exaggerate the asynchronous character [88, ]. In general, we confirmed these facts and consequently, in the following sections we will refer only to
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the results from the M06-2X/6–31+G(d,p) level, which has been recommended for applications involving main-group thermochemistry, kinetics, and non covalent interactions [80].
Reaction energetics Table 1 compiles all energetic data computed at M06-2X/6– 31+G(d,p) level for both Diels-Alder reactions, R1 and R2, in gas and solution phases. ΔErxn, the overall energy change, ΔEact, the activation energy and its components, ΔEact,1 and ΔEact,2, were calculated using the above equations and they are given relative to the reactant complexes (also known as van der Waals complexes). Firstly, the exothermicities do not change as the reaction media is altered and the main feature is given by the presence of the BH3 shifting into the endothermic direction by around 2.0 kcal mol−1. Secondly, the effect of the Lewis acid catalyst BH3 on R1 is not highly dramatic in the gas phase as revealed by the calculations at the M06-2X level of theory. The energy barrier is reduced by about 2.3 kcal mol−1 which increases the reaction rate by a factor of 51 at room temperature (rt) (the reaction rates ratios between two conditions were computed 1 using the Arrhenius equation, i.e., kk 2 ¼ eΔΔEact ð21Þ=RT . Both contributions, ΔEact,1 and ΔEact,2, are less than in R1. As can be seen in Table 1, the solvent slightly affects the activation energy and its components for R1. The highest polar solvent lowers the activation energy by only 1.3 kcal mol−1, which implies that the reaction rate can be enhanced by about 10 times at rt. Contrarily, polar solvents can be assigned to accelerate the reaction rate by more than 2000 times at rt. (ΔΔEact = 4.5 kcal mol−1) for R2 as the highest polar media is employed. Therefore, a synergistic effect is achieved when both external agents, i.e., Lewis acid catalyst and polar solvent, are included together. Moreover, the component associated with the structural demand of the overall activation process, ΔEact,1, showed to be more emphasized by the solvent than the component associated with electronic rearrangements, ΔEact,2; thus, the enhancement of the rate is mainly assisted by the solvent probably favoring the encounter between cyclopentadiene and acrolein···BH3.
Transition state geometries: incipient C-C bonds In accordance with previous studies [53, 89], both [4 + 2] cycloadditions considered herein proceed concertedly but through an asymmetric transition state (the distances of the incipient C-C σ-bonds are not equivalent), with the unsubstituted olefinic C-atom more reactive than the substituted one as displayed in Fig. 2. This asymmetry, measured by
J Mol Model (2018) 24:33 Table 1 Computed reaction energetics. All data are given in kcal mol−1
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Reaction media
R1
R2
ΔEact,1
ΔEact,2
ΔEact
Gas phase
10.8
5.2
16.0
−23.4
9.3
4.4
13.7
−20.9
Cyclopentane ChloroBenzene Acetonitrile Water Formamide MethylFormamide
10.5 10.2 10.0 9.4 10.0 9.4
5.0 4.8 4.8 5.3 4.7 5.3
15.5 15.0 14.8 14.7 14.7 14.7
−23.1 −22.6 −22.3 −22.3 −22.3 −22.3
7.7 6.2 5.6 5.5 5.9 5.5
4.4 4.2 3.8 3.8 3.4 3.7
12.1 10.4 9.4 9.3 9.3 9.2
−19.3 −21.0 −20.5 −20.5 −20.5 −20.3
Δd, becomes highly pronounced when either the Lewis acid BH3 is considered or the solvent’s polarity is increased or both external agents are included at the same time. On the other hand, Δd can also be seen as a measure of the extension in which the new C-C bonds are formed. Thus, these values help to understand the above-discussed energetic tendencies: Δd varies slowly with the solvent’s polarity for R1 while it strongly changes when the media becomes more and more polar for R2, due to a shortening of d1 and a lengthening of d2 that favors the encounter between diene and acrolein···BH3 and concomitantly, reduces the required energy associated with structural rearrangements. Certainly, Δd has been a widely used criterion to classify Diels-Alder reactions as synchronous or asynchronous, but it provides a continuum scale of (a)synchronicities making it confusing to rank from fully or slightly synchronous to highly asynchronous (or Btwo-stage^) mechanisms, or even when the latter transitions into a stepwise mechanism [43, 91, 92]. Therefore, the reaction force constant analysis is proposed to overcome this ambiguity since asymmetric TSs can just be seen as a needed condition for certain asynchronicity.
The reaction force constant: analysis of synchronicity/asynchronicity Figure 3 comparatively presents the U(ξ), F(ξ), and κ(ξ) profiles computed at M06-2X/6–31+G(d,p) for R1 (left-panels) and R2 (right-panels) in both gas and solution phases, and the latter six solvents that encompass a wide range of polarities
ΔErxn
ΔEact,1
ΔEact,2
ΔEact
ΔErxn
were employed. The present analysis is mainly focused on the shape of κ(ξ) rather than U(ξ) and F(ξ) by paying special attention along the transition region (delimited by the negative minimum of F(ξ), at ξ1, and the positive maximum of F(ξ), at ξ2), since this has been reported as a suitable indicator of the degree of (a)synchronicity in concerted mechanisms of multibond reactions [49–55]. Our main goal is to analyze how the solvent’s polarity can control the (a)synchronicity in the formation of the new C-C σ-bonds, which will be revealed by κ(ξ). At first glance, the profiles of U(ξ), F(ξ), and κ(ξ) for R1 (see left-panels in Fig. 3) clearly evidence a synchronous reaction mechanism (one κ(ξ) minimum) without marked changes on the contours of the profiles. However, a detailed look of κ(ξ) along the transition region (shown at the leftbottom panel) reveals that a small increment of the solvent’s polarity (ε = 1.96, cyclopentane) asynchronizes the formation of the new C-C σ-bonds and concomitantly, a shoulder starts to appear. This effect becomes emphasized as the dielectric constant ε increases until acetonitrile (ε > 35); afterwards, there is no solvent polarity effect (since the curves start to appear superimposed). Regarding R2, the ability of the solvent’s polarity to turn a moderate asynchronous mechanism into a highly asynchronous one is noticeable even from the U(ξ) and F(ξ) profiles (see right-panels in Fig. 3): in the former, the curves significantly broaden and the energy barriers decrease (keeping the same exothermicity), while in the latter the shoulder seen in gas-phase and cyclopentane resolves into a minimum for the other condensed media with the consequent extension of the transition region. Additionally, regardless of the solvent, the
Fig. 2 TS geometries for R1 (left side) and R2 (right side) and differences between the incipient C-C σ-bond lengths (Δd = d1 – d2, in Å) calculated in gas-phase and in six solvents at M06-2X/6–31+G(d,p) level. CYLview was used for structural representations [90]
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Fig. 3 Comparative profiles of U(ξ), F(ξ), and κ(ξ) along ξ for R1 (left-panels) and R2 (right-panels) computed in gas-phase and in six solvents at M062X/6–31+G(d,p) level of theory
κ(ξ) profiles show the typical two minima connected by a maximum that belongs to a highly asynchronous process. Indeed, the maximum (the second minima) turns out to be more and more positive (negative) as ε increases until acetonitrile; thereafter, all the shapes seem to remain constant (there is no solvent polarity effect). Therefore, the more polar the solvent is, the higher the asynchronicity becomes. Finally, it can be concluded that polar solvents enhance the reaction rate of polar Diels-Alder reactions as a consequence of an increase of asynchronicity in the formation of two C-C σ-bonds.
Conclusions The influence of the solvent’s polarity on the reaction energetics, TS geometries, and synchronous/asynchronous character of C-C bond forming processes has been studied for two polar Diels-Alder reactions between cyclopentadiene and acrolein (R1) and its complex with BH3 (R2). A synergistic effect has been found when both external agents, Lewis acid and polar solvent, are taken into account. While the solvent slightly affects the activation process for R1, this is highly marked for R2 reaching a decrease of the barrier energies by 1.3 kcal
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mol−1 and 4.5 kcal mol−1, respectively, when the highest polar solvent is used. Both Δd and κ(ξ) support the idea that polar solvents emphasize the asynchronicity in both cycloadditions increasing the reaction rates (reducing the activation energies). However, while Δd gives a continuum scale of asynchronicities, κ(ξ) allows classification of a one-step mechanism as fully or moderately synchronous (one κ(ξ) minimum) or as highly asynchronous or two-stage (two κ(ξ) minima). Finally, κ(ξ) shows how a fully (moderate) synchronous concerted mechanism turns into a moderate (highly) asynchronous mechanism as the solvent’s polarity increases. Acknowledgments The authors are delighted to dedicate this article to Professor Peter Politzer on his 80th birthday for his important contributions in theoretical chemistry, which have been a continuous inspiration in our career as researchers. The authors also acknowledge FONDECYT through the project numbers 3150249 (DY) and 1140340 (PJ).
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