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Journal of Molecular Modeling

, 24:228 | Cite as

Confinement induced catalytic activity in a Diels-Alder reaction: comparison among various CB[n], n = 6–8, cavitands

  • Manas Ghara
  • Debdutta ChakrabortyEmail author
  • Pratim K. Chattaraj
Original Paper
  • 170 Downloads
Part of the following topical collections:
  1. International Conference on Systems and Processes in Physics, Chemistry and Biology (ICSPPCB-2018) in honor of Professor Pratim K. Chattaraj on his sixtieth birthday

Abstract

The impact of the size of the confining regime on the thermodynamic and kinetic outcome of a representative Diels-Alder reaction between ethylene and 1,3 butadiene has been investigated in silico. To this end, two organic hosts namely cucurbit[6]uril (CB[6]) and cucurbit[8]uril (CB[8]) have been considered in order to impose confinement on the reactants/transition state/product of the concerned reaction. The obtained results have been compared with the recently reported (Chakraborty et al. ChemPhysChem 18:2162–2170, 2017) corresponding case of the same reaction happening inside cucurbit[7]uril (CB[7]). Results indicate that as compared to the reaction of ethylene and 1,3 butadiene inside CB[7], both CB[6] and CB[8] cavitands slow down the same reaction at 298.15 K and 1 atm. It appears that the size of the cavitand plays a crucial role in affecting the kinetic outcome of the considered reaction. While CB[7] can enforce productive alignment of the reactants inside its cavity thereby facilitating the reaction, neither CB[6] nor CB[8] can perform the same task as effectively. This situation bears qualitative resemblance with the cases of enzyme catalyzed reactions.

Keywords

Confinement Kinetic facilitation Cucurbit[n]uril Host-guest complex Partial covalent bond 

Introduction

It is well established in the scientific literature that the effect of geometrical confinement can have a profound impact on the physicochemical properties of atoms and molecules [1]. Over the course of the last several years, extensive computational, as well as experimental investigations, have been undertaken in order to understand the impact of confinement on the changes in reactivity of molecules. Recently reported results indicate that due to the effect of confinement, reactivity of atoms/molecules can undergo substantial enhancement as compared to their corresponding free state counterparts [2, 3, 4, 5, 6, 7, 8, 9]. This increment in reactivity of molecules (placed in a confined space) could be utilized in order to promote chemical reactions. This fact has been borne out by several experimental and computational studies [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]. Mock and coworkers were able to demonstrate apparently for the first time, that due to the effect of confinement imposed by the organic cavitand cucurbit[6]uril (CB[6]), the alkyne-azide cycloaddition reaction can undergo substantial kinetic acceleration [15]. Later on, several other thermal and photochemical reactions were studied by different research groups under the effect of confinement imposed by organic/inorganic macrocyclic moieties and several such reactions were shown to get catalyzed [17, 18]. These processes are often referred to as supramolecular catalysis in the literature. The most significant aspect of these processes could be gauged from the fact that they offer an efficient and alternative pathway toward catalyzing chemically important reactions. It has been pointed out that when two reacting molecules are placed in a confined space, appropriate preorganization of the reacting molecules inside the cavitand can take place. Therefore, the entropic cost associated with the reaction gets reduced as compared to their corresponding free state reaction leading to kinetic facilitation of the concerned reaction. Supramolecular catalysis has some physical similarity with enzyme catalyzed reactions. Mock and coworkers pointed out that during the course of supramolecular catalysis, the Pauling principle (operative during the course of several enzyme catalyzed reactions) might provide some physical rationale [15]. Therefore, the relative size of the cavitand and the reactants should play a determining role in supramolecular catalysis. Despite the huge dividends associated with these processes from the point of view of several applications, there seems to be certain bottlenecks associated with the aforementioned processes. Despite recent development in this field, it has also been demonstrated that any confinement regime is not necessarily a sufficient condition as far as promoting a chemical reaction is concerned [22]. A crucial factor in this regard is the nature of the confining regime itself as different cavitands offer different sizes and shapes thereby affecting the outcome of the reaction. Therefore, identifying suitable confinement conditions for a given set of reactions is of pertinent interest.

Cucurbit[n]uril moieties constitute an effective confining ‘vessel’, when compared with other host organic molecules, due to their high selectivity in binding organic guest molecules [26, 27]. We have recently demonstrated through density functional theory (DFT) based calculations [22, 23], the efficiency of cucurbit[7]uril (CB[7]) in accelerating several Diels-Alder reactions (in the gaseous phase). In this work, we would like to investigate whether the structural homologues of CB[7], namely CB[6] and CB[8], can also promote the same from a kinetic point of view or not. Due to their structures, CB[6] and CB[8] present two different confining conditions as compared to that in CB[7]. Therefore, the orientation of the reactants and the transition states involved in the course of the reaction should be different inside both CB[6] and CB[8] as compared to that inside CB[7]. How does this factor affect the kinetic outcome of a given Diels-Alder reaction? It is well understood through previous studies reported in the literature that inside a cavitand the reactants can often orient themselves in a ‘nonproductive’ alignment. As a result of this, reaction rates should get slowed down considerably as substantial thermodynamic cost is required in order to bring the reactants into a ‘productive’ alignment. This implies that during the course of a model [4 + 2] thermal Diels-Alder reaction, any cavitand that facilitates the supra-supra mode of interaction [28] between the reactants should also facilitate the reaction from a kinetic and thermodynamic view point. Nonetheless, it becomes difficult to a priori guess which member among the series of cucurbit[n]uril moieties could maximize the propensity of ‘suitable’ orientation of the reactants as other than a purely geometrical confinement effect; the nature of host-guest interaction should also play a pivotal role in affecting the outcome of the reaction. Therefore, in this work we have considered the [4 + 2] cycloaddition reaction between ethylene and 1,3 butadiene as a representative test case and investigated the kinetic outcome of the aforementioned reaction inside CB[6] and CB[8] as compared to that inside CB[7]. For this purpose we perform DFT based calculations at the same level of theory as employed in our previously reported results (inside CB[7]). The nature of bonding and host-guest interactions have been understood on the basis of atoms-in-molecules (AIM) and noncovalent interaction (NCI) methodologies.

Computational details

In this work, all molecular modeling have been carried out with the aid of GaussView 5.0.8 software package [29]. Geometries of all the species involved, viz., reactants, transition states (TS), and products of the reaction have been optimized at the wb97xd/6-311G(d,p) level of theory. No constraints have been added while carrying out the geometry optimization calculations. Associated vibrational frequencies have been obtained in order to ascertain the nature of the obtained stationary points along a given potential energy surface. All the reactants and products reported herein comprise only real vibrational frequencies (NIMAG = 0), whereas the TS structures contain one imaginary vibrational frequency (NIMAG = 1). Since we would like to compare our present results with that in the case of CB[7], we have carried out our calculations at the same level of theory as reported by us in our previous work (wb97xd/6-311G(d,p) level of theory) [22] in order to have a veritable reference point. It is well appreciated in the literature that the chosen functional wb97xd can perform accurately while dealing with problems that involve noncovalent interactions [30, 31]. All the electronic structure calculations have been carried out with the help of Gaussian 09 software package [32]. The nature of bonding has been understood based on the AIM theory [33]. To this end, Multiwfn software [34] has been utilized. Details of the AIM theory can be found elsewhere [33]. Finally, in order to characterize the nature of interaction between the hosts CB[6]/CB[8] and the guests, NCI analysis has been done with the help of NCIPLOT software [35]. In this analysis, electron density (ρ) and reduced density gradient (s) are used to map localized binding and they are related as follows:
$$ s=\frac{1}{2{\left(3\pi \right)}^{1/3}}\frac{\mid \nabla \rho \mid }{\rho^{4/3}} $$
(1)
Attractive and repulsive interactions are distinguished by the second derivative of electron density (∇2ρ). Here ∇2ρ is decomposed into the eigenvalues λi of electron density Hessian matrix along the three principle axes of the maximal variation as:
$$ {\nabla}^2\rho ={\uplambda}_1+{\uplambda}_2+{\uplambda}_3 $$
(2)
where λ2 < 0 for H-bonding, λ2 > 0 for steric repulsion, and λ2 ~ 0 for van der Waals interaction. Thus, the different types of weak interactions can be distinguished from the analysis of the sign of λ2, and the strength of interactions are assessed from the value of ρ. For the purpose of visualization of the gradient isosurfaces, the following color coding has been used:
  1. a)

    red color indicates the destabilizing steric interactions

     
  2. b)

    green color denotes the van der Waals interactions

     
  3. c)

    blue color identifies the H-bonding interactions

     

Results and discussion

We first analyze the computed structures of the reactants, as well as that of the TS, in the case of CB[6] (Fig. 1). At the reactant state, only 1,3 butadiene remains inside the cavitand, whereas ethylene stays outside the cavity. It appears that the cavity of CB[6] is not large enough to accommodate both the reactants, although this reactant encapsulated geometry is thermodynamically favorable as given by negative values of enthalpies and free energy changes (Table 1). Although we have carried out several computational attempts, a minimum energy structure could not be located in which both the reactants stay inside CB[6]. Considering the relative orientation of the reactants in the case of CB[6], we can infer that CB[6] does not promote the supra-supra mode of interaction between them. The two reactants, viz., 1,3 butadiene and ethylene stay in an almost perpendicular orientation with respect to each other. Therefore, we can infer that as compared to the case of CB[7] (Fig. 2), where the two reactants stay in proximity as well as in a suitable orientation with respect to one another, CB[6] offers a stark contrast. Also, for the TS structure inside CB[6], the ethylene molecule barely remains inside CB[6] unlike in the case of CB[7] [22]. The product of the reaction, however, remains inside CB[6]. It may be noted that due to the encapsulation of the guests inside CB[6], the geometry of the host does not change much. Considering the corresponding situation in the case of CB[8], it may be inferred that both the reactants can stay inside the cavitand at the minimum energy structure (Fig. 3). Nonetheless, the two reactants stay distant from one another unlike the corresponding situation in the case of CB[7] (Fig. 2). The closest distance between the two C–C atom centers of 1,3 butadiene and ethylene has been found to be 4.73 Ǻ. It seems that two competing factors are operative here. The cavitand due to the geometrical confinement effect helps the two reactants to approach each other. On the other hand, the two reactants also interact with the host through its glycoluril units via host-guest interactions. It appears that this type of interaction dominates over the confinement effects herein as the reactants prefer to stay in proximity of the host rather than each other. Clearly, due to the larger cavity size of CB[8], the reactants experience a greater space to accommodate themselves inside CB[8] as compared to that inside CB[7]. Similarly, at the TS and product states, the corresponding guests stay inside the host. In both the cases, the guests tend to stay in close proximity of the cavitand wall so as to maximize the favorable host-guest interaction. We now analyze the thermochemical results computed at 298.15 K and 1 atm (Table 2) and compare it with that in the case of CB[7] (the corresponding results obtained for the free state reaction have been presented in Table 2). We have presented the change in reaction Gibbs free energies (ΔG), enthalpy (ΔH), the Gibbs free energy of activation (ΔG), and enthalpy barrier (ΔH) in Table 2, whereas the thermochemical results obtained due to the encapsulation of the reactants inside the hosts have been presented in Table 1. It becomes clear that both the hosts can encapsulate the reactants in a thermodynamically favorable way. The rate constants (k) associated with the concerned reactions have been computed (Table 2) according to the Eyring equation [36] at 298.15 K and 1 atm:
$$ k=\frac{k_BT}{h}{e}^{-\Delta {G}^{\ddagger }/ RT} $$
(3)
Fig. 1

Geometrical structures of (a) reactants, (b) TS (it has imaginary harmonic vibrational frequency of 579.18i cm−1), and (c) product for the case of the reaction inside CB[6] respectively

Table 1

Enthalpy (ΔH, kcal mol−1) and free energy changes (ΔG, kcal mol−1) for encapsulation of the reactants (butadiene and ethylene) with the CB[n] cages at 298.15 K and 1 atm

System

ΔH

ΔG

Reactant@CB[6]

−30.48

−5.13

Reactant@CB[8]

−26.25

−4.40

Fig. 2

Geometrical structures of (a) reactants, (b) TS, and (c) product for the case of the reaction inside CB[7] respectively. Reprinted with permission from Wiley-VCH Verlag GmbH & Co, KGaA, Weinheim (ref. [22])

Fig. 3

Geometrical structures of (a) reactants, (b) TS (it has imaginary harmonic vibrational frequency of 600.59i cm−1), and (c) product for the case of the reaction inside CB[8] respectively

Table 2

Free energy change (ΔG, kcal mol−1) and reaction enthalpy change (ΔH, kcal mol−1) at 298.15 K and 1 atm for the overall reaction at the free and confined states; Free energy and enthalpy of activation (ΔG‡/ΔH‡, kcal mol−1) and the rate constant (k, sec−1) associated with the processes at 298.15 K and 1 atm

System

ΔG

ΔH

ΔG

ΔH

k

Free

−39.37

−46.74

27.32

20.98

5.80 × 10−8

Reaction@CB[6]

−43.31

−50.53

29.58

22.51

1.27 × 10−9

Reaction@CB[8]

−36.41

−41.20

27.76

24.94

2.76 × 10−8

It might be prudent here to mention that the computed values of ΔG, ΔH, ΔG, and ΔH for the corresponding case of CB[7] [22] are as follows: −40.02, −42.75, 24.13, and 21.65 kcal mol−1 respectively. It becomes clear that the considered cycloaddition reaction becomes thermodynamically more favorable inside CB[6] as compared to both CB[7] and CB[8]. It appears that the favorable change in enthalpy drives the reaction inside CB[6] when thermodynamics is considered as compared to both CB[7] and CB[8]. However, when kinetics is considered the reaction between ethylene and 1,3 butadiene gets slowed down considerably inside CB[6] and CB[8] as compared to that in CB[7] as evidenced by the ΔG values. We note that as compared to the reaction at the free state, neither CB[6] nor CB[8] can facilitate the said reaction from a kinetic point of view. One might infer from the above stated results that the probable rationale behind these crucial kinetic outcomes may lie in the relative ability of the cavitands in enforcing a suitable preorganization of the reactants inside the three cavitands considered. While CB[7] facilitates the suitable ‘productive’ alignment of the reactants, neither CB[6] nor CB[8] can achieve this based on our computational results. As a result of this, the kinetic ‘cost’ of bringing the two reactants into suitable position increases inside both CB[6] and CB[8] as compared to that inside CB[7]. Therefore, we may infer that for the case of the reaction between 1,3 butadiene and ethylene, CB[7] offers the optimum cavity size for facilitating the reaction from kinetic considerations. This situation bears qualitative analogy with various enzyme catalyzed reactions as only a suitable cavity size can facilitate such processes. Therefore, we can infer that any confining regime is not a sufficient condition for catalyzing the representative Diels-Alder reaction considered in this work.

In order to analyze the nature of bonding present in the TS structures involved in the cases considered herein, the results of the AIM analysis (Table 3) are now considered. It is well known that within the purview of AIM theory [33, 37], the electron density (ρ(rc)), Laplacian of electron density (∇2ρ(rc)), and local electron energy density (H(rc)) computed along a given bond critical point (BCP) could be utilized in order to gain insight into the nature of bonding. If H(rc) < 0 and ∇2ρ(rc) > 0, then the pertinent bond could be classified as having partial covalent nature. Considering this aspect, we can argue that in both the cases of the TS structures, the two forming C–C bonds have partial covalent character. It is to be noted that inside CB[6], the two developing C–C bonds are almost equivalent in nature from the perspective of bonding characteristics. However, inside the CB[8] host, the two developing C–C bonds are slightly asymmetric in nature as compared to each other and one of the bonds has slightly greater covalent nature as evidenced by the various electron density descriptors. We would like to mention the corresponding values of the electron density descriptors at the two developing C–C bonds in the TS structure in the case of CB[7]. The computed values of ρ(rc), (∇2ρ(rc)), and H(rc)) in the case of the TS inside CB[7] are as follows: 0.0499/0.0541, 0.0452/0.0445, and −0.0088/−0.0107 respectively [22]. Therefore, it becomes evident that inside CB[7], the developing C–C bonds in the TS structure can obtain greater covalent character. This factor might well be a crucial driving force behind the observed kinetic acceleration of the concerned reaction inside CB[7] as compared to that in the cases of CB[6]/CB[8]. This further highlights the fact that CB[7] can enact the role of a suitable confining ‘vessel’ for the concerned reaction in a better way as compared to either CB[6] or CB[8].
Table 3

Electron density descriptors (in a.u.) at the bond critical points (BCP) present in between the reacting moieties at the TS state at the confined state

Systems

BCP

ρ(rc)

2ρ(rc)

H(rc)

TS@CB[6]

C–C(forming)

0.0490

0.0469

−0.0085

TS@CB[6]

C–C(forming)

0.0489

0.0469

−0.0085

TS@CB[8]

C–C(forming)

0.0498

0.0469

−0.0088

TS@CB[8]

C–C(forming)

0.0519

0.0464

−0.0097

In order to understand the nature of interaction between the hosts and guests, the results of the NCI analysis (Fig. 4) are now considered. In all the cases, the guests interact with the hosts CB[6] and CB[8] through noncovalent interactions as evidenced by the green colored isosurfaces present between the hosts and guests. Considering the volume of the isosurfaces, we can clearly note that the reactants, TS, and products involved in the concerned reaction interact with CB[6] in a more facile manner as compared to CB[8]. This is primarily due to the geometrical proximity of the guests with all the available glycoluril fragments of CB[6] with whom they take part in favorable attractive interactions. CB[8], however, interacts with the guests through only a couple of glycoluril segments. It may be concluded therefore that in both the cases, the host-guest complexes are mainly stabilized by van der Waals interactions (Fig. 4).
Fig. 4

NCI isosurfaces of (a) reactant@CB6, (b) TS@CB6, (c) product@CB6, (d) reactant@CB8, (e) TS@CB8, and (f) product@CB8

Conclusions

In quest of identifying an appropriate confining vessel so that a model Diels-Alder reaction between 1,3 butadiene and ethylene could be facilitated from a kinetic point of view, an in silico investigation has been undertaken in this work. Results indicate that neither CB[6] nor CB[8] could accelerate the chosen reaction as compared to their structural analogue CB[7] at ambient conditions. The crucial factor that determines the outcome of the reaction inside the hosts is the nature of the confining regime itself. It appears that while the cavity of CB[6] is too small to enforce an appropriate confining condition on the reactants thereby facilitating the reaction, CB[8] has a much bigger cavity than what might be suitable (as in CB[7]). Therefore, as a proof of concept, one might note that any confining condition cannot facilitate any given reaction kinetically. It appears that the preorganization of the reactants inside the cavitands play a determining role in deciding the outcome of the process. Therefore, the relative size of the cavity vis-a-vis that of the reactants should be of prime importance. Given the importance of confinement induced kinetic facilitation of chemical reactions from the point of view of various applications, it might be prudent to consider several other reactions inside various organic cavitands so as to enrich our knowledge in this regard. We hope to address these issues in our future course of work.

Notes

Acknowledgments

P.K.C. would like to thank DST, New Delhi for a J. C. Bose National Fellowship. MG thanks CSIR, New Delhi for his senior research fellowship.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Chemistry and Center for Theoretical StudiesIndian Institute of Technology KharagpurKharagpurIndia
  2. 2.Department of ChemistryIndian Institute of Technology BombayMumbaiIndia

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