Theoretical Study on the AzaâDielsâAlder Reaction Catalyzed by

Article pubs.acs.org/JPCA

Cite This: J. Phys. Chem. A XXXX, XXX, XXX−XXX

Theoretical Study on the Aza−Diels−Alder Reaction Catalyzed by PHCl2 Lewis Acid via Pnicogen Bonding Fereshteh Yaghoobi*,† and Mahdi Sohrabi−Mahboub†,‡ †

School of Chemistry, Department of Science, University of Nahavand, P.O. Box 65931-39565, Hamadan, Iran Department of Chemistry, Isfahan University of Technology, P.O. Box 84156-83111, Isfahan, Iran

‡

S Supporting Information *

ABSTRACT: The reaction mechanism of the Aza−Diels−Alder (A− D−A) cycloaddition reaction between X2CNNH2, where X = H, F, Cl, Br, and 1,3-butadiene catalyzed by a PHCl2 Lewis acid was characterized using density functional theory calculations. The influences of various substituents of X on the studied reaction were analyzed using the activation strain model (ASM), which is also termed as the distortion− interaction model. Calculations showed that the smallest and largest values of the activation energies belong to the substituents of F and Br, respectively. The activation energy of the studied reactions was decreased within 8.6 kcal·mol−1 in the presence of PHCl2 catalyst. Investigations showed that the pnicogen bonding is adequately capable of activating the A−D−A reaction. The quantum theory of atoms in molecules (QTAIM) and natural bond orbital (NBO) analysis were implemented to understand the nature of C4,Cbut···CXIm and C1,Cbut···NXIm bonds at the TS structures. Additionally, the energy decomposition analysis (EDA) based on the ETS-NOCV scheme was used to characterize the nature of C4,Cbut···CXIm and C1,Cbut···NXIm bond. The results of the study mirror the fact that the PHCl2 Lewis acid may be suggested as a simple suitable catalyst for experimental studies on the A−D−A reactions. stereoselectivity.13 Moreover, Huber et al. showed that the halogen-bond donor can act as an organo-catalyst in the D−A reaction as well.14 The Aza−Diels−Alder reaction or simply “A−D−A” reaction is a modification of the D−A reaction in which the dienes and imines (dienophile) convert to the unsaturated N-hexacycles. The A−D−A reaction, which is classified as a [4π+2π] cycloaddition, proceeds through including a nitrogen (N) atom in the dienes and imines (dienophile). It should be mentioned that the N atom can be part of the dienes and/or the dienophile in this reaction.15 Up to now, the numerous theoretical and experimental investigations have been carried out to understand the catalytic effects of Lewis acids or organocatalysts on the A−D−A reactions.9,16−19 Investigations have shown that the catalytic effects of Lewis acids and organocatalysts in the A−D−A reaction are similar those of the D−A reaction. Over the last years, extensive studies have been done on the noncovalent interactions between catalysis and substrate and also on the net effect of them on the D−A and/or A−D−A reactions. The noncovalent interaction encompasses different bonding types including the hydrogen and halogen bonds. Some recent studies showed that the hydrogen and halogen

1. INTRODUCTION The Diels−Alder (D−A) reaction is drastically of importance in organic chemistry. The D−A reaction has been considered as one of the important methodologies for designing and synthesizing six-membered ring structures.1 After the D−A reaction catalyzed with Lewis acids such as AlCl3 was reported by Yates and Eaton,2 the reaction has received a lot of attention in organic synthesis. Due to the unique characteristics of Lewis acids in the D−A reaction such as boosting the reaction rates, enhancing the regio- and stereoselectivities with respect to the uncatalyzed reactions,3 the D−A reactions may be considered as potential synthesis strategies in modern organic chemistry. In the last years, numerous theoretical simulations and experimental determinations have been carried out to understand the effects of the Lewis acid catalysts on the D−A reactions.4−7 Studies have been indicated that the D−A reactions can be progressed by making use of organo-catalysts where they interact with their substrate through noncovalent bond.8 It is noteworthy that the hydrogen (HB) or halogen bonds (XB) play a key role in the noncovalent organo-catalysis.9−11 MacMillan et al. introduced the D−A reaction catalyzed by an organic catalyst in which the formation of hydrogen-bond reaction was documented, for the first time.12 In another study, Zhou and co-workers investigated the D−A reaction in the absence and presence of hydrogen-bonding catalyst bisthiourea. They clearly showed that the catalyst can be successfully used to increase the rate of the D−A reaction and also the origin of © XXXX American Chemical Society

Received: December 18, 2017 Revised: February 4, 2018

A

DOI: 10.1021/acs.jpca.7b12400 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

fully optimized at the M06-2X39 and BP86 level of theories with def2-TZVPP basis set.40 The energies of each structure were also calculated by making use of the same density functional method including zero-point vibrational energy (ZPE) corrections. All of the optimized structures were followed via the harmonic vibrational frequency calculations to verify the equilibrium geometries at the true local minima on the potential energy surface without the imaginary frequencies. It should be also mentioned that the harmonic vibrational spectrum of the TS is merely characterized by one imaginary frequency. Furthermore, to confirm that each of the TS structures links a given reactant and product, the intrinsic reaction coordinate (IRC)41 calculations were also performed at the M06-2X/def2-TZVPP level used in geometrical optimizations. The coordinates of the optimized structures were utilized to perform other calculations (Supporting Information). Furthermore, natural bonding orbital (NBO) analysis42 at the same level of theory was performed to determine the charge of TS structures and to characterize the nature of the catalytic effect. Moreover, the activation strain or the distortion-interaction model43 was then used to calculate the fragment distortion-interaction energies with the M06-2X/ def2-TZVPP level of theory in the gas phase. Additionally, the role of dispersion energy in the stabilization of complexes in the presence and/or the absence of catalyst was evaluated for imines (XIm) with different substituents of X using the M062X-D3/def2-TZVPP level of theory. The AIM 2000 package was used to characterize the bond properties involved in TS states by the bond critical points (BCPs) analysis in the framework of the quantum theory of atoms-in-molecules (QTAIM) theory. For this purpose, the wave function files were obtained from the Gaussian output files at the M06-2X/def2-TZVPP level of theory.44 Meanwhile, the energy decomposition analysis to the bond analysis was performed using the program package ADF2009.0145 at the M06-2X/TZ2P(ZORA)//M06-2X/def2-TZVPP level of theory with C1 symmetry.

bonds are capable of activating a substrate in the D−A reaction. For example, Jungbauer and co-workers20 investigated the catalytic activity of the dicationic halogen−bond donors on activating a neutral organic substrate. One of the newest members of the noncovalent interactions’ family is the pnicogen bonding.21−23 This type of noncovalent interaction is of comparable characteristics with respect to other noncovalent bonds. It means that the pnicogen bond is of the similar strength to chalcogen and halogen bonds for a given electron-withdrawing substituent. Therefore, it may be considered as the reaction of a Lewis acid with a Lewis base where a pnicogen atom such as an N, P, or As atom and a Lewis base accept and donate pairs of electrons, respectively.24−26 Historically, the pnicogen bonding was introduced by Hill and Silva-Trivino27,28 when analyzing the NMR spectra of orthocarbaborane-phosphino derivatives. Subsequently, Hey-Hawkins and co-workers22 demonstrated that the P···P bonds established by Hill and Silva-Trivino27,28 are in the same order of magnitude of the H-bonds. For this reason, these types of bonds are of adequate strength to connect the molecules together so that they may be termed as “molecular-linker” in the literature. A study by Eskandri and Mahmoodabadi focused on the pnicogen bond based on the Laplacian of electron density exhibited that the pnicogen bonding may be classified as lump−hole interactions.29 It is noteworthy to mention that the pnicogen bonding has also been observed by making use of the experimental charge density analysis upon the organic molecules.30 Aside from these efforts, several theoretical investigations on the pnicogen bonding have been reported in the literature.30−36 In the most recent theoretical study, Del Bene et al.37 investigated the potential of pnicogen bonding for catalysis. They showed that the model pnicogen-bond donors used in their study are certainly not suitable for experimental scopes and also for more investigations. Because for these scopes, the knowledge of the stability and manageability of the phosphorus-based compounds is undoubtedly required. Considering the above explanations, the purpose of the present work is to concentrate on studying and/or understanding the effect of pnicogen bonding as a noncovalent bonding catalyst upon the activation energy of the A−D−A reaction. For this purpose, the reaction of between the X2C NNH2 (Im) with different substituents including X = H, F, Cl, Br (which is termed “XIm” hereafter) and cis-1,3-butadiene (which is termed “Cbut” hereafter) was chosen. In this reaction, as an example of the A−D−A reaction catalyzed by a PHCl2 compound as a Lewis acid, an unsaturated six-membered ring is generated. It should be mentioned that the six-membered ring forming reaction is progressed through the formation of the intermolecular P···N pnicogen bonding between the P atom of PHCl2 and the N atom of imine. It is noteworthy to mention that the reason for choosing the PHCl2 Lewis acid as an electron-acceptor catalyst follows from the fact that PHCl2 compound is of the manageable and well-known features both for the experimental and for the theoretical studies. So, by making use of this compound in the A−D−A reaction, the scheme of pnicogen-bond donors can be reasonably modeled through the computational studies.

3. RESULTS AND DISCUSSION The mechanism of the A−D−A reaction between the XIm of different X (=H, F, Cl, and Br) and Cbut in the absence and the presence of PHCl2 Lewis acid as an electron-pair acceptor was investigated. The geometries of the cycloaddition reaction of the XIm and Cbut were fully optimized with and without PHCl2 catalyst at the M06-2X/def2-TZVPP level of theory in the gas phase. 3.1. Uncatalyzed A−D−A Reaction. The geometries of the cycloaddition reaction of the XIm and Cbut in the absence of PHCl2 Lewis acid as an electron-pair acceptor were optimized at the M06-2X/def2-TZVPP level of theory39,40 in the gas phase. Scheme illustration of the mechanism of the uncatalyzed A−D−A reaction between the XIm and Cbut has been depicted in Figure 1. As can be seen, after approaching the Cbut and XIm molecules to each other, a Cbut···XIm complex is formed and then the reaction passes through the TS state to generate a nitrogen-containing six-membered ring compound. Figure 2 represents the equilibrium geometries of the molecular structures of IC, TS, and products (p) involved in the ringforming cycloaddition process during the A−D−A reaction pathway in the absence of PHCl2 Lewis acid. As can be seen in Figure 2, the interaction among the Cbut molecule with four different molecules of imine have been investigated, separately. Note that the intermediate complexes (IC-Cbut···XIm)

2. COMPUTATIONAL DETAILS The Gaussian 09 package38 was used to perform all the calculations reported in the present work. Equilibrium geometries corresponding to all local minima and transition states (TS), intermediate complexes (IC), and products were B


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Table 1. Values of C4,Cbut···CXIm and C1,Cbut···NXIm Bond Distances (Å) in the Absence of PHCl2 (Un-CA) and in the Presence of PHCl2 (CA) for IC, TS, and Product Structures in the Gas Phase at the M06-2X/def2-TZVPP Level of Theory C4,Cbut···CXIm

Figure 1. Scheme illustrations of the uncatalyzed Aza−Diels−Alder reaction between cis-1,3-butadiene (Cbut) and X2C = NNH2 (XIm), (X = H, F, Cl, Br) with the transition state (TS) of reaction.

X H F

between Cbut and XIm (X = H, F, Cl, Br) were formed through the strong intermolecular interactions. As has been indicated in Figure 2, due to the large distances between two C4,Cbut···CXIm and C1,Cbut···NXIm bonds, i.e., 3.378 and 3.273 Å for C4,Cbut···CXIm and C1,Cbut···NXIm, respectively, in the Cbut··· HIm, the IC structure should be generated via the electrostatic interactions. The values of C4,Cbut···CXIm and C1,Cbut···NXIm bond distances at the IC, TS, and P structures have been tabulated in Table 1. As shown in the table, the values of the

Cl Br

Un-CA CA Un-CA CA Un-CA CA Un-CA CA

C1,Cbut···NXIm

IC

TS

P

IC

TS

P

3.378 3.216 3.149 3.167 3.250 3.184 3.287 3.213

2.050 1.988 1.896 1.861 1.983 1.946 1.966 1.908

1.522 1.520 1.510 1.509 1.521 1.522 1.520 1.522

3.273 3.299 3.574 3.288 3.254 3.332 3.230 3.318

2.125 2.252 2.437 2.524 2.242 2.318 2.272 2.377

1.453 1.457 1.461 1.462 1.464 1.466 1.466 1.468

C4,Cbut···CXIm bond distance range from 3.149 Å (for X = F) to 3.378 Å (for X = H) in IC and from 1.896 Å (for X = F) to

Figure 2. Optimized structures of the intermediate complexes (IC), transition states (TS), and products (P) in the absence of PHCl2 catalyst. C


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Figure 3. Optimized structures of the intermediate complexes (IC), transition states (TS), and products (P) in the presence of PHCl2 catalyst.

3.2. Catalyzed A−D−A Reaction by PHCl2. In this section, the catalytic activity effect of PHCl2 Lewis acid as an electron-pair acceptor in the A−D−A reaction was investigated. The results of these investigations showed that in the presence of the PHCl2 catalyst (CA), the first step is the formation of the IC structures between the PHCl2 catalyst and XIm. It is worthwhile to mention that the catalytic pathway proceeds through the formation of P···N bonding between the P atom of PHCl2 catalyst and the N atom of XIm. In other words, in the A−D−A reaction catalyzed by PHCl2, the IC structures can be generated by pnicogen bonding through the P···N noncovalent interaction. It is noteworthy to mention that the pnicogen bonding is merely formed as a result of the electron-donor capability of the N atom to generate the noncovalent bonding due to its highly concentrated electron density. Additionally, the halogen bonding between the PHCl2 catalyst and XIm were also observed between them. The second step is the formation of the IC structures between Cbut and XIm···CA, which is presented as IC-Cbut···XIm···CA. A more detailed discussion about the role of halogen bonding in this reaction, which is beyond the scope of this paper, is indispensable and will be addressed in future works. The optimized geometries of all stationary points of structures for the catalyzed A−D−A reaction by PHCl2 Lewis acid including intermediate complexes (IC-Cbut···XIm···CA),

2.050 Å (for X = H) in TS and also from 1.510 Å (for X = F) to 1.522 Å (for X = H) in products, respectively. A comparison of the CCbut···CXIm bond lengths of the IC structures with X = F, Cl, and Br shows that the bond distance in the FIm molecule is relatively smaller than those of ClIm and BrIm molecules. In other words, the orders of CCbut···CXIm bond length in the FIm, ClIm, and BrIm molecules are C4,Cbut···CFIm < C4,Cbut···CClIm < C4,Cbut···CBrIm, respectively. The decreasing trend observed may be related to the size and electronegativity of halogen atoms that these chemical properties increases and decreases from the F atom to the Br atom, respectively. Also, the longer bond length of C4,Cbut···CHIm pertains to the smaller electronegativity of H atom connected to the C atom in the HIm molecule. A similar trend can be also observed for the C4,Cbut···CXIm bond length in the TS and P structures. The value of C1,Cbut···NXIm bond distance listed in Table 1 illustrates that the C1,Cbut···NXIm bonds are of longer length compared to the C4,Cbut···CXIm bonds in the TS structure. However, they are roughly close each other in the product structures. So, it can be seen that the C1,Cbut···NXIm bond distances for the uncatalyzed reaction follow the order C1,Cbut···NFIm > C1,Cbut···NHIm > C1,Cbut···NClIm > C1,Cbut···NBrIm in the IC structure, C1,Cbut···NFIm > C1,Cbut··· NBrIm > C1,Cbut···NClIm > C1,Cbut···NHim in the TS structure, and C1,Cbut···NBrIm > C1,Cbut···NClIm > C1,Cbut···NFIm > C1,Cbut···NHIm in the product structure, respectively. D


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The Journal of Physical Chemistry A transition states (TS-Cbut···XIm···CA), and products (P− Cbut···XIm···CA) have been shown in Figure 3. As can be seen, in all these species, the nitrogen atom of imine in the XIm is bonded to the phosphorus atom of the PHCl2 catalyst. In addition, in all IC structures, a halogen bond between the chlorine atom of the PHCl2 catalyst and the hydrogen atom of imine can be clearly observed in Figure 3. It should be noted that the geometry of the PHCl2 catalyst remains with no change when the catalyst is coordinated to the XIm. In TS-Cbut···XIm···CA complex, the bond is formed between C1,Cbut and NXIm with X = H, F, Cl, and Br are 2.252, 2.524, 2.318, and 2.377 Å, respectively. Also, the formed bond between C4,Cbut and CXIm with X = H, F, Cl, and Br are 1.988, 1.861, 1.946, and 1.908 Å, respectively, at the corresponding level of theory used in geometrical optimizations. A detailed comparison of the IC, TS, and P structures in the absence of PHCl2 catalyst with the corresponding structures in the presence of PHCl2 catalyst can help to understand how the catalytic effect of PHCl2 through the pnicogen bonding acts upon C1,Cbut···NXIm and C4,Cbut···CXIm bond formation in the studied A−D−A reaction. By more precise inspection of the geometric features of species in the TS state, it was found that the forming C4,Cbut··· CXIm bonds in TS-Cbut···HIm···CA, TS-Cbut···FIm···CA, TSCbut···ClIm···CA, and TS-Cbut···BrIm···CA are of the bond lengths 1.988, 1.861, 1.946, and 1.908 Å, respectively, while the forming C1,Cbut···NXIm bonds in these species are all around 2.300 Å. It means that the C4 atom of Cbut is first bonded to the C atom of XIm in the TS state. It is also interesting to compare the TS structures of the A−D−A reaction catalyzed by PHCl2 with those of the uncatalyzed A−D−A reaction. For this purpose, it can be clearly seen from Figures 2 and 3 that the length of C4,Cbut···CXIm bonds in the catalyzed A−D−A reaction are slightly shorter than those of the uncatalyzed reaction. Opposite trend can be also seen for the C1,Cbut···NXIm bonds where they are of the higher bond lengths in the catalyzed A− D−A reaction compared to those of the uncatalyzed A−D−A reaction. By comparison of the values of the bond distance calculated for the C4,Cbut···CXIm and C1,Cbut···NXIm bonds for the catalyzed reaction with those for the uncatalyzed reaction, it could therefore be concluded that the PHCl2 catalyst leaves its effect upon the bond length of C4,Cbut···CXIm more than C1,Cbut···NXIm in the TS state. In addition to, the bond angles of the noncovalent interactions evaluated for all structures of the catalyzed and uncatalyzed A−D−A reactions studied in this work have been tabulated in Table S1. The results demonstrate that the ∠CXImC4,butC3,but bond angles of TS and IC structures in the uncatalyzed A−D−A reaction are slightly smaller than the corresponding angles in the catalyzed A−D−A reaction. Similar behavior can be observed for the bond angles ∠NXImC1,butC2,but, as well. It should be mentioned that the three bond angles of∠CXImC4,butC3,but, ∠NXImC1,butC2,but, and ∠PCANXImC1,but in TS structures are higher than those of IC structures. 3.3. Energy Diagrams. To analyze in more detail the role of catalytic effects of PHCl2 through forming the pnicogen bonding on the A−D−A reaction, the values of energies of the uncatalyzed and catalyzed reaction paths via TS-Cbut···XIm and TS-Cbut···XIm···CA complexes, respectively, were investigated in this section. The potential energy surfaces (PES) with the geometries of the stationary points for the reaction of Cbut with XIm without and with the PHCl2 catalyst (CA) in the A− D−A reaction have been depicted in Figure 4a,b, respectively.

Figure 4. Potential energy surfaces (PES) with the geometries of the stationary points for the reaction of Cbut with XIm (a) without and (b) with the PHCl2 catalyst (CA) in the A−D−A reaction studied in this work.

From the Figure 4a, it is seen that the ZPE-corrected energy barriers for the uncatalyzed A−D−A reaction between Cbut and XIm with X = H, F, Cl, and Br are 25.86, 25.26, 31.36, and 31.45 kcal/mol, respectively. It should also be mentioned that these IC structures were found to be stable thermodynamically, which are lower in energy by 1.87, 3.09, 2.97, and 3.25 kcal/mol than the reactants for Cbut···HIm, Cbut···FIm, Cbut···ClIm, and Cbut···BrIm, respectively. After passing through the TS state, the reaction would yield one nitrogen-containing sixmembered ring compound depends on the type of X atom used in XIm molecule. Considering the explanations above, it can be seen that the activation energies for the A−D−A reaction in the absence of the PHCl2 catalyst follow the order TS-Cbut···FIm < TS-Cbut···HIm < TS-Cbut···ClIm < TS-Cbut···BrIm. Therefore, it could be concluded that the uncatalyzed A−D− A reaction between Cbut and FIm is most likely favorable with respect to other XIms with X = H, Cl, and Br. It means that the A−D−A reaction between Cbut and XIm with no catalyst is the favorable reaction when the X atom linked to imine is of the small atomic size and the high electronegativity. In Figure 4b, the effect of PHCl2 catalyst on the A−D−A cycloaddition reaction has been shown. As can be seen, the A− D−A reaction will proceed through a stepwise mechanism to produce an IC compound after passing the TS state including TS-Cbut···XIm···CA where X is H, F, Cl, and Br, respectively. A comparison between the PES calculated using two different DFT methods including M06-2X and BP86 with the same basis set of TZVPP was carried out. Typically, the result of comparison has been shown for the reaction of Cbut with HIm in the absence and the presence of PHCl2 catalyst (CA) in Figure S1. It can be seen that the obtained results from M06-2X and BP86 are adequately of the similar trend. Moreover, the similar results were observed for other A−D−A reactions studied in this work including those of different substituents of XIm. Tables 2 and S2 list all the calculated values of energy belong to the IC, TS, and P structures studied in this work. For example, it can be seen in Table 2 that the values of energy of the IC structures of HIm···CA and FIm···CA, at the M06-2X/ def2-TZVPP level of theory, are −6.200 and −5.060 kcal/mol, respectively. The results show that the energy of IC-XIm···CA with different substituents decreases after binding to the Cbut E


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The activation energies (or energy barrier) diagram, as revealed by the theoretical calculations presented in this work, illustrates that the energies of TS state, TS-Cbut···HIm···CA, TS-Cbut···FIm···CA, TS-Cbut···ClIm···CA, and TS-Cbut··· BrIm···CA, in the presence of catalyst, are 8.622, 8.665, 8.560, and 8.855 kcal/mol, respectively, which are considerably stable compared to the uncatalyzed reaction. To investigate the role of dispersion energy in the stabilization of complexes in the presence and/or the absence of catalyst, the evaluation of them seems to be useful. So, typically, the values of dispersion energy were evaluated for Hand F-substituents of imine using the M062X-D3/def2-TZVPP level of theory. The calculated values of dispersion energy have been tabulated in Table S2. The results show that the dispersion energy is of a relatively similar role in the stabilization of complexes in the presence and/or the absence of PHCl2 catalyst for the A−D−A reaction studied in this work. In other words, the effect of dispersion forces on the stability of complexes is small. 3.4. Activation−Strain Analysis. To see the effects of PHCl2 catalyst on the interactions between the Cbut and XIm molecules at the TS states, the activation-strain (or distortioninteraction) (ASM) model43 was used to perform the fragment analysis. Parts a and b of Figure 5 illustrate the ASM analysis performed for the A−D−A reactions studied in this work with and without PHCl2, respectively. The results compare the TS structures with those of the reactant complexes. It should be mention that the red and black downward arrows, on the left of the ASM diagrams in Figure 5, demonstrate the interaction (ΔΕint) and activation (ΔΕ‡) energies, respectively. Given Figure 5a,b, the strong intermolecular interactions can merely be observed between a substituted imine by the F atom and C but (−13.21 kcal/mol) in the absence of PHCl2, compared to the H-substituted value (−4.78 kcal/mol) at the TS structures, respectively. It is worth mentioning that the deformation (distortion) energies are broken into the distortion energies for Cbut and XIm and are shown in green and blue. The distortion energy of F-substituted XIm is 19.93 kcal/mol whereas the corresponding value for H-substituted imine is 8.62 kcal/mol. A comparison between the ΔΕint and ΔΕdis values show that the interaction and distortion energies, respectively, have a similar trend of for the X-substituted imines. Additionally, the smallest value of Cbut strain (in green) can be observed for the F-substituted imine, which is of the greatest XIm strain (in blue). It is

Table 2. Calculated Values of Energy of All Structure Studied in This Work at the M06-2X/def2-TZVP Level of Theory (kcal/mol) structures IC-Cbut···XIm TS-Cbut···XIm P−X IC-XIm···CA ΔE1, kcal/mol IC-Cbut···XIm···CA TS-Cbut···XIm···CA P−X···CA ΔE2, kcal/mol P−X

X=H

X=F

Without PHCl2 −1.870 −3.090 25.86 25.26 −28.56 −41.03 With PHCl2 −6.200 −5.060 −3.420 −4.990 −9.620 −10.05 17.24 16.60 −38.66 −47.93 10.10 6.910 −28.56 −41.02

X = Cl

X = Br

−2.970 31.36 −32.47

−3.250 31.45 −32.96

−5.510 −4.950 −10.46 22.80 −38.85 6.380 −32.47

−5.700 −5.540 −11.24 22.59 −39.19 6.230 −32.96

molecule. In addition, the value of released energy, ΔE1, of HIm···CA and FIm···CA are −3.42 and −4.99, respectively. It is worthwhile to note that the ZPE-corrected energy barriers for the catalyzed A−D−A reaction studied in this work are 17.24, 16.60, 22.80, and 22.59 kcal/mol for TS-Cbut··· HIm···CA, TS-Cbut···FIm···CA, TS-Cbut···ClIm···CA, and TSCbut···BrIm···CA, respectively. Also, the results showed that the mentioned IC structures (IC-Cbut···XIm···CA) are considerably more stable than the corresponding structures of reactants by 9.62, 10.05, 10.46, and 11.24 kcal/mol. Note that the formation of the P−X···CA is accompanied by releasing energy after passing through the TS state. Meanwhile, the results illustrate that, after separating the PHCl2 catalyst from the product as the last step of the catalyzed A−D−A reaction, the value of released energy, ΔE2, is roughly 6−10 kcal/mol. It should also be mentioned that the energy of the XIm molecule decreases by forming the pnicogen bonding through coordinating the P atom of catalyst to the N atom of imine. Therefore, the activation energies for the A−D−A reaction in the IC state in the presence of PHCl2 catalyst (or through forming pnicogen bonding) follow the order IC-Cbut···HIm··· CA < IC-Cbut···FIm···CA < IC-Cbut···ClIm···CA < IC-Cbut··· BrIm···CA. The order shows that the most favorable pathway to proceed the A−D−A reaction between Cbut and XIm with X = H, F, Cl, and Br atom linked to imine in the presence of the employed catalyst is merely through the H channel, where the hydrogen atom is of the smaller atomic size and electronegativity than other substituents.

Figure 5. Plots of the distortion, interaction, and activation energies for the transition states of the A−D−A reactions (a) without CA, (b) with CA: green, distortion energy of Cbut; blue, distortion energy of XIm; orange, distortion energy of CA; red, interaction energy; black, activation energy. Units are in kcal/mol. F


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Table 3. Wiberg Bond Indices (WBIs) and Natural Population Analysis Corresponding to C4,Cbut···CXIm and C1,Cbut···NXIm Interactions in the Absence of PHCl2 (Un-CA) and in the Presence of PHCl2 (CA) C4,Cbut···CXIm

C1,Cbut···NXIm

X

A−D−A reaction

WBI

C4,Cbut

CXIm

WBI

C1,Cbut

NXIm

H

Un-CA CA Un-CA CA Un-CA CA Un-CA CA

0.448 0.480 0.486 0.512 0.480 0.506 0.509 0.553

−0.444 −0.420 −0.498 −0.500 −0.441 −0.440 −0.437 −0.444

−0.162 −0.164 0.822 0.831 0.109 0.121 0.017 0.034

0.367 0.296 0.242 0.212 0.312 0.279 0.295 0.257

−0.257 −0.251 −0.236 −0.231 −0.237 −0.230 −0.236 −0.230

−0.272 −0.330 −0.351 −0.395 −0.318 −0.362 −0.356 −0.400

F Cl Br

Table 4. NBO Energies (kcal/mol) Corresponding to Possible Pairs of Interacting Molecular Orbitals Studied in This Work at the M06-2X/def2-TZVPP Level of Theory uncatalyzed reaction NBO analysis diene → imine imine → diene π(CXIm−NXIm) → π(CXIm−NXIm) → π(C2,Cbut···C3,Cbut) π(C4,Cbut···C5,Cbut)

π*(C2,Cbut···C3,Cbut) π*(C4,Cbut···C5,Cbut) → π*(CXIm−NXIm) → π*(CXIm−NXIm)

catalyzed reaction

X=H

X=F

X = Cl

X = Br

X=H

X=F

X = Cl

X = Br

66.16 31.59 14.21 17.38 55.03 11.13

92.23 30.89 25.29 5.600 87.94 4.290

83.70 31.52 21.41 10.11 74.67 9.050

87.10 31.64 22.59 9.050 79.82 7.320

75.40 26.17 15.89 10.28 67.17 8.290

105.4 30.10 26.30 3.800 102.0 3.440

100.5 30.14 22.70 7.440 85.93 7.270

101.2 31.12 25.05 6.070 95.96 5.170

Table 5. Bond Lengths (Å), Electron Densities (ρ(r), e/a03), Laplacians (∇2(ρr), e/a03), and a Number of Other AIM Topological Parameters at BCPs of the Interactions between the Cbut and XIm (X = H, F, Cl, Br) Molecules at the TS States complexes TS-Cbut···HIm TS-Cbut···FIm TS-Cbut···ClIm TS-Cbut···BrIm TS-Cbut···HIm···CA TS-Cbut···FIm···CA TS-Cbut···ClIm···CA TS-Cbut···BrIm···CA

bond length C1,Cbut···NHIm C4,Cbut···CHIm C1,Cbut···NFIm C4,Cbut···CFIm C1,Cbut···NClIm C4,Cbut···CClIm C1,Cbut···NBrIm C4,Cbut···CBrIm C1,Cbut···NHIm C4,Cbut···CHIm C1,Cbut···NFIm C4,Cbut···CFIm C1,Cbut···NClIm C4,Cbut···CClIm C1,Cbut···NBrIm C4,Cbut···CBrIm

2.125 2.050 2.437 1.896 2.242 1.983 2.272 1.966 2.252 1.988 2.524 1.861 2.318 1.946 2.377 1.908

worthwhile to mention that the values of ΔΕint and ΔΕdis of Cbut increase and decrease, respectively, after binding the PHCl2 catalyst to the XIm. Moreover, the distortion energy of the PHCl2 catalyst (in yellow) is roughly less than 1 kcal/mol in all cases. A comparison between the distortion energies and interaction energies shows that the PHCl2 catalyst linking to the XIm leaves its highest effect upon the ΔΕint values of structures studied in this work. 3.5. Natural Bond Orbital (NBO) Analysis. In this section of the paper, the charge-transfer analysis has been performed on the basis of the natural bond orbital (NBO) method42 to evaluate atomic charges. The natural population analysis corresponding to C4,Cbut···CXIm and C1,Cbut···NXIm interactions has also been reported in Table 3. As can be observed, the value of natural charge of the C atom of imine in C4,Cbut···CXIm bond depends on the nature of the X atom (electron-donating

ρ(rc)

∇2(ρr)

−Gc/Vc

ε

0.064 0.076 0.035 0.110 0.051 0.092 0.048 0.095 0.050 0.085 0.030 0.118 0.044 0.097 0.040 0.106

0.082 0.043 0.068 0.032 0.078 0.016 0.076 0.011 0.078 0.031 0.064 0.054 0.073 0.001 0.070 0.015

0.739 0.611 0.905 0.450 0.801 0.532 0.816 0.523 0.806 0.566 0.951 0.424 0.838 0.502 0.866 0.476

0.051 0.119 0.237 0.049 0.097 0.073 0.107 0.076 0.117 0.105 0.367 0.042 0.154 0.067 0.191 0.065

substituent) on the imine. For instance, as observed in Table 3, the charge value of CXIm atom for the FIm is 0.822 whereas the corresponding value for HIm is −0.162. It is important to note that the charge value of the C atom of imine (q = 0.831 and q = −0.164 for F- and H-substituents, respectively) increases with the connection of PHCl2 to imine as a Lewis acid. Moreover, the Wiberg bond indices (WBIs), which provide a relative scale for comparing the bond densities and also their strengths to predict the activated bonds, have been computed with the NBO analysis. The obtained results through WBIs analysis have been listed in Table 3. As can be seen, the WBIs calculated for the C4,Cbut···CXIm bond in the presence of the PHCl2 catalyst are greater than those in the absence of the catalyst. WBIs indices after connecting the PHCl2 catalyst to imine for the C1,Cbut···NXIm bond are of the decreasing trend. The WBIs and natural charge values of the C and N atoms for G


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The Journal of Physical Chemistry A C4,Cbut···CXIm and C1,Cbut···NXIm bond formations are in good agreement with the calculated bond lengths and the activation energies. To better understand the effect of the P···N bonding upon interaction in the A−D−A reaction, NBO second-order perturbation theory analysis was carried out to evaluate of the charge transfer between the Cbut (diene) and the XIm (imine) at the TS structures. For the catalyzed and uncatalyzed A−D− A reaction studied in this work, Table 4 tabulates the NBO energies corresponding to four pairs possible of interacting molecular orbitals: π(CXIm−NXIm) → π*(C2,Cbut···C3,Cbut), π(CXIm−NXIm) → π*(C4,Cbut···C5,Cbut), π(C2,Cbut···C3,Cbut) → π*(CXIm−NXIm), and π(C4,Cbut···C5,Cbut) → π*(CXIm−NXIm). However, as observed in Table 4, the charge-shifting from Cbut (diene) to XIm (imine) (diene → imine) is the greater amount of the reverse process, namely, imine → diene. Additionally, the charge transfer from diene to imine depends strongly on the nature of substituent on the imine. Comparing interaction energies calculated in this work, one can clearly observe the effect of the substituents including H, F, Cl, and Br on the electron-donor and electron-acceptor capacity corresponds to the XIm. So, the F-substituent and H-substituent of imine are of the maximum and minimum amount of charge transfer from diene → imine, respectively. It means that the electronwithdrawing groups on the C atom of imine strengthen the P··· N interactions. Note that the diene → imine charge-transfer values are relatively high in the presence of PHCl2. On the basis of the tabulated results in Table 4, it can be seen that the imine → diene charge transfer depends strongly on the absence and/ or presence of the PHCl2 catalyst so that these values decrease in the presence of the PHCl2 catalyst. It is consistent with the fact that by linking the PHCl2 catalyst to imine the diene → imine charge transfer increases whereas it decreases for that of the imine → diene charge transfer. 3.6. QTAIM Analysis. To evaluate the nature of the interactions between the Cbut and XIm molecules with different substitutions such as X = H, F, Cl, and Br in TS states, the bond critical points (BCPs) were analyzed by implementing of the quantum theory of atoms-in-molecules (QTAIM) theory.44 Tables 5 and S3 list the quantum topological features of the electron densities and their Laplacian at the analyzed BCPs of TS and IC states, respectively. As can be seen, the electron densities (ρr) and their Laplacian ∇2ρ > 0 are of the small and positive values. The results mirror the fact that the interactions could be reasonably characterized by those of electrostatic. A comparison between the ρr values of C1,Cbut··· NXIm and C4,Cbut ···CXIm bonds in their TS structures, respectively, illustrates that the electron density of C4,Cbut··· CXIm bond is greater than that of C1,Cbut···NXIm bond. The nature of interactions was investigated by making use of the obtained values of ∇2ρ and −Gc/Vc.46 Given the values of ∇2ρ > 0 and −Gc/Vc < 1, it could be concluded that the interactions between the Cbut and XIm tend to be slightly covalent. To determine which bonds (C4,Cbut···CXIm or C1,Cbut···NXIm) in TS structures are most affected by the PHCl2 catalyst, the ellipticity of the electron density at the BCPs, which is computed as a parameter in the framework of the QTAIM analysis,44 was used to evaluate the bond stability. The obtained results show that the C4,Cbut···CXIm bond is of the slightly shorter bond length with respect to the C1,Cbut···NXIm bonds in TS state. This shows that the PHCl2 catalyst affects the bond length of C4,Cbut···CXIm more than C1,Cbut···NXIm in the TS state of A−D−A reaction. Therefore, it could be concluded that

there is a reasonable consistency between the obtained results of AIM analysis and those of other above-mentioned analyses. 3.7. Energy Decomposition Analysis (EDA). To analyze the nature of the bonding, the energy decomposition analysis EDA calculations47 were carried out at the M06-2X/TZ2P(ZORA)//M06-2X/def2-TZVPP level of theory with the Amsterdam Density Functional program package, ADF2009.01. The interaction energy (ΔEint) between the interacting fragments may be divided as follows: ΔE int = ΔEels + ΔE Paul + ΔEorb

(1)

in which the subscripts “els”, “Paul”, and “orb” stand for the classical electrostatic interaction, the repulsive Pauli interaction, and the stabilizing interactions between the occupied and unoccupied molecular orbitals, respectively. The calculated values of three components of ΔEint for all structures obtained in the catalyzed and uncatalyzed A−D−A reaction between Cbut and XIm with the different substituents of X have been tabulated in Table 6. As can be seen, the interaction energies Table 6. Energy Decomposition Results Describing the Bond between Cbut and XIm with X = H, F, Cl, and Br for Both the Uncatalyzed and Catalyzed A−D−A Reaction at the M06-2X/TZ2P(ZORA)//M06-2X/def2-TZVPP Level of Theory complexes

ΔEint, kcal/mol

ΔEPaul, kcal/mol

ΔEels, kcal/mol

ΔEorb, kcal/mol

TS-Cbut···HIm TS-Cbut···FIm TS-Cbut···ClIm TS-Cbut···BrIm TS-Cbut···HIm···CA TS-Cbut···FIm···CA TS-Cbut···ClIm···CA TS-Cbut···BrIm···CA

−7.650 −14.98 −11.83 −12.33 −12.16 −20.22 −14.86 −16.24

131.75 129.93 134.07 137.61 124.85 136.00 137.31 146.26

−64.31 −65.20 −67.14 −68.18 −62.95 −70.11 −70.10 −73.65

−75.09 −79.71 −78.76 −81.76 −74.07 −86.11 −82.07 −88.84

(ΔEint) calculated between the Cbut and XIm reactants in the transition state via the EDA analysis verify the following order for P···N interaction: FIm > BrIm > ClIm > HIm for the catalyzed A−D−A reaction. Note that the similar result can be also observed for ΔEint in the uncatalyzed A−D−A reaction. It should be mentioned that the ΔEels and ΔEorb values increase from −64.31 and −75.09 kcal/mol for HIm···Cbut to −68.18 and −81.76 kcal/mol for BrIm···Cbut complex for the uncatalyzed A−D−A reaction, respectively. It is noteworthy that the similar organized trend can be observed in the catalyzed A−D−A reaction. Therefore, according to Table 6, the orders of ΔEels and ΔEorb values in the catalyzed A−D−A reaction related to the Cbut···XIm···CA complexes with X = H, F, Cl, and Br are Cbut···BrIm···CA > Cbut··· FIm···CA > Cbut···ClIm···CA > Cbut···HIm···CA, respectively. By precise inspection of the ΔEels and ΔEorb values listed in Table 6, the percentage contribution of the mentioned terms in ΔEint can be clearly found for the uncatalyzed and catalyzed A−D−A reaction, separately. The percentage contribution of ΔEels and ΔEorb terms is of a similar trend for both the uncatalyzed and catalyzed A−D−A reaction. As can be seen from Table 6, the contribution of ΔEorb term is greater than the contribution of ΔEels term. The contours of the dominant deformation density contributions, Δρ1 and Δρ2, for the catalyzed and uncatalyzed A−D−A reaction have been depicted in Figure 6. As can be H


Article


Figure 6. Dominating contributions to the deformation density Δρ describing the bond between Cbut and phosphorus-based fragments and the most important orbital interactions (kcal/mol). The contour value is |Δρ| = 0.003 au.

electron density, respectively. Additionally, it can be observed from the contour of Δρ1, in the TS state, the new π-bonding between C2,Cbut and C3,Cbut is being formed, which corresponds to an early stage of cycloadduct process. It is worth mentioning that the transferred electrons make stable the TS-XIm···Cbut and TS-Cbut···XIm···CA in the uncatalyzed and catalyzed A−

seen, two C−C and C−N bonds between imine and Cbut molecules are formed in the transition state. It indicates an outflow of electrons from the occupied π-orbital of imine and an accumulation of electron density in the bonding regions of CCbut···CXIm and CCbut···NXIm. Note that the blue and red contours correspond to the accumulation and depletion of I


Article

The Journal of Physical Chemistry A D−A reaction, respectively. For example, ΔEorb(Δρ1) = −37.96 kcal/mol for TS-HIm···Cbut in the uncatalyzed reaction, ΔEorb(Δρ1) = −41.46 kcal/mol for TS-CA···HIm···Cbut in the catalyzed reaction. The second contribution of deformation density, Δρ2, which demonstrates the electron-depleting from the π-bonding orbitals of Cbut and the electron-accumulating inside the C1,Cbut···CXIm, C4,Cbut···CXIm, and π*(CXIm−NXIm) bonding regions have also been observed in Figure 6. A comparison between the ΔEorb(Δρ2) values of the catalyzed and uncatalyzed A−D−A reaction shows that the corresponding stabilization ΔEorb(Δρ2) for both A−D−A reaction are definitely of less importance than ΔEorb(Δρ1). For instance, the ΔEorb(Δρ2) is −32.23 and −28.99 kcal/mol for Cbut··· HIm and Cbut···HIm···CA structures, respectively, whereas the corresponding values of the ΔEorb(Δρ1) for the mentioned structures is −38.44 and −41.05 kcal/mol. On the basis of the results obtained in this section, it could be concluded that the total orbital interaction, ΔEorb, and the electrostatic, ΔEels, terms are responsible to increase the stabilization of the TS complexes. Note also that the existence of the activation barrier in the studied reactions in this work originating from the Pauli repulsion contribution, ΔEPaul (Table 6). It means that the ΔEPaul term is more important in the destabilization with respect to the distortion energy contribution, ΔEdis.

stabilization of the TS complexes and also the ΔEPaul leads to the activation barrier in the studied reactions.

4. CONCLUSION Quantum mechanical calculations (M06-2X density functional theory with the def2-TZVPP basis set) were used to study the intermolecular noncovalent interactions in the A−D−A reaction between X2CNNH2 (as a dienophile), where X = H, F, Cl, Br, and 1,3-butadiene (as a diene) in the absence and presence of a catalyst. The PHCl2 Lewis acid was chosen as the simplest catalyst consistent with the experimental scope for theoretical investigating of the catalytic effects of electrophiles on the activation free energies of A−D−A reaction. The ASM (or distortion-interaction) model was utilized to characterize the origins of the differences in reactivity of the diene and dienophile studied in this work. The pnicogen bonding through the P···N noncovalent interaction was shown to have more effective roles in the catalytic activity of PHCl2 catalyst in the A−D−A reaction. Therefore, in the presence of a catalyst, the activation barriers were approximately calculated to be 8.6 kcal/ mol less than those in the absence of a catalyst. It was found that the enhanced stability may be attributed to the formation of the favorable pnicogen bonding. The charge-transfer analysis was performed on the basis of the NBO method to evaluate the atomic charges. The NBO analysis showed that the value of natural charge of the C atom of imine (dienophile) in C4,Cbut··· CXIm bond depends on the nature of X atom (electron− donating substituent) on imine. To predict the activated bonds, the WBIs analyses were computed using the NBO analysis. The nature of the interactions between the Cbut and XIm molecules in TS states was investigated by analyzing the BCPs by recourse of QTAIM theory. The ellipticity of the electron density at the BCPs illustrated that the PHCl2 catalyst affects the bond length of C4,Cbut···CXIm more than C1,Cbut···NXIm in the TS state. The electronic structures at characteristic points on the PES surface were analyzed on the basis of the EDA analysis at the M06-2X/ TZ2P(ZORA)//M06-2X/def2-TZVPP level of theory. Additionally, to analyze the nature of the bonding, the ADF calculations were performed. These calculations showed that the ΔEels and ΔEorb terms are responsible to increase the

Notes

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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.7b12400. Cartesian coordinates of all structure studied in this work at the M06-2X/def2-TZVPP level of theory, bond angles of the noncovalent interactions for the structures studied (Table S1), the values of energy of some selected structure studied at the M062X-D3/def2-TZVPP level (Table S2), AIM topological parameters at BCPs of the of the IC states (Table S3), and the comparison between the PES calculated using M06-2X and BP86 (Figure S1) (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*Fereshteh Yaghoobi. Email: [email protected]. Tel: (+98) 813 3493003. ORCID

Fereshteh Yaghoobi: 0000-0002-8880-8690 Mahdi Sohrabi−Mahboub: 0000-0003-3171-6362 The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We are indebted to the Research Council of the University of Nahavand for their support of this work. The authors thank Prof. S. Salehzadeh from Bu-Ali Sina University for their helpful suggestions.

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REFERENCES

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