Stepwise or concerted? A DFT study on the mechanism of ionic Diels–Alder reactions of chromanes J. Serb. Chem. Soc. 81 (1) 67–80 (2016) UDC 577.161.3+547.972.2:519.677:66.095.252+ JSCS–4828 547.538:543.637 Original scientific paper 67 Stepwise or concerted? A DFT study on the mechanism of ionic Diels–Alder reactions of chromanes MINA HAGHDADI*, SEYEDEH SOGHRA MOUSAVI and HASSAN GHASEMNEJAD Department of Chemistry, Islamic Azad University, P.O. Box 755, Babol branch, Babol, Iran (Received 20 April, revised 26 September, accepted 5 October 2015) Abstract: The stepwise and concerted ionic Diels–Alder reactions between phenyl(pyridin-2-ylmethylene)oxonium and styrene derivatives were explored theoretically. The results support the use of a computational method via per- sistent intermediates. The DFT method was essential to reproduce a reasonable potential energy surface for these challenging systems. Keywords: styrene; ionic Diels–Alder reaction; stepwise; concerted; DFT study; reactivity indices. INTRODUCTION The chromane skeleton appears in a number of natural products, such as tocopherols1 and flavans.2 They display a diverse array of biological activities, including antioxidant,3 antiestrogens,4 antiviral,5 antihypertensive6 and antican- cer7 activity. Common approaches to prepare the chromane skeleton8 are Diels−Alder reactions of o-quinone methides (1-oxadienes),9 additions of O- hydroxy acetophenones10 and intramolecular nucleophilic substitution of phenols.11 Alternative approaches to the chroman skeleton are of considerable interest for the formation of substituted chromanes. Diels−Alder (DA) reactions and their formal equivalents provided a power- ful means for the rapid construction of heterocyclic scaffolds. Oxa- and aza-DA variants were developed in which the dienophile and/or dienes could incorporate the heterocomponents.12 One such aza-variant is the Povarov reaction,13,14 ori- ginally developed 50 years ago, which has considerable utility. These DA reac- tions, classified as ionic DA reactions (I-DA), in which positively or negatively charged ionic species can participate in these reactions. In I-DA type of reactions, the reagents, transition states (TSs), feasible intermediates and cycloadducts rem- ain charged during the cycloaddition reaction.15 I-DA reactions could be clas- sified as anionic and cationic DA reactions. However, while cationic DA reac- * Corresponding author. E-mail: mhaghdadi2@gmail.com doi: 10.2298/JSC150420089H 68 HAGHDADI, SOGHRA MOUSAVI and GHASEMNEJAD tions occur rapidly at very low temperatures,16 usually at –78 °C, due to the high electrophilic character of cationic species, there are few anionic DA reactions because, in spite of the high nucleophilic character of anionic species, these reac- tions do not occur easily in the absence of strong electrophiles.17 The authors performed a series of experiments in order to establish the mechanism of these I-DA reactions. Several theoretical studies were devoted to I-DA reactions.18–21 The theo- retical studies of Domingo et al. on I-DA reactions of iminium cations indicated that both one-step and stepwise mechanisms could be found.18 The presence of the strong electron withdrawing pyridinium substituent in the iminium cation enabled the stabilization of a feasible intermediate once the first C–C single bond had completely formed, making corresponding process stepwise.19 Recently, Batey et al. reported the synthesis of chromanes via the I-DA reaction of O-aryl oxonium species with some alkenes, including cyclopentene and styrene, yield- ing the formal [4+2] cycloadducts, which by one rapid loss of a proton afford chromanes.22a Their results showed that such oxonium ion species are more reactive than the corresponding iminium ions and capable of undergoing either direct I-DA reaction or the equivalent stepwise Prins addition/intramolecular electro- philic aromatic substitution reaction to give chromans. Moreover, in 2014, a theoretical study on the mechanism of oxa-Povarov reactions was reported by Domingo et al.22b They studied the stereoselectivity of the I-DA reaction of O-aryl oxonium with cyclopentene and styrene at the B3LYP/6-31G* level in the gas phase and solvent, which was not in agreement with the experimental results. In the present study, the stereoselectivity, regioselectivity and conform- ational analysis on the stepwise and concerted mechanism of the oxa-Povarov reaction leading to distereosynthesis of 2,4-substituted chromane22a were inves- tigated by theoretical methods. In addition, the influence of substituents on sty- rene was analyzed in these reactions. Herein, the I-DA reactions between cationic aryl oxonium 1 and styrene derivatives 2a–c are analyzed (Scheme 1) using the DFT method. Several pathways were analyzed in an attempt to elucidate the energetic difference between the stepwise mechanism and the concerted one. The calculations support the experimental finding of a two-step mechanism, as pro- posed by Batey et al.22a In order to evaluate fully the possible reaction pathways, several TSs and intermediates were optimized at the B3LYP/cc-pVDZ and MPWB1K/aug-cc-pVTZ level of theory. CALCULATIONS The ubiquitous B3LYP23 hybrid functional has been the workhorse of quantum chemical studies on organic molecules for years.24 It is well-known that B3LYP could describe inter- actions in Diels–Alder reactions. Recently, some functionals such as the MPWB1K,22b,25 were proposed to investigate the reaction energies, barrier heights and intermediates for Diels– DFT STUDY ON MECHANISM OF DIELS–ALDER REACTION OF CHROMANES 69 –Alder reactions. For a comprehensible comparison of geometries, we were prompted to the optimization of all species in the mentioned I-DA reactions using both B3LYP and the MPWB1K exchange–correlation functional. The cc-pVDZ basis set was used for full optimiz- ation using the B3LYP method and a single point with aug-cc-pVTZ basis set of the MPWB1K method. Energies were then recalculated at the MPWB1K/aug-cc-pVTZ level, using the polarizable continuum model (PCM) as developed by the Tomasi group26 within the framework at the self-consistent reaction field (SCRF).27 Dichloromethane (ɛ = 8.93) was selected as a moderately polar organic solvent. The electronic energies were corrected with ZPE at the B3LYP/cc-pVDZ level. All calculations were performed using the Gaussian 09 program.28 The electronic structures of the stationary points were analyzed by the natural bond orbital (NBO) method.29 Global reactivity indexes were estimated according to the equations recommended by Parr and Yang.30 The global electrophilicity index, ω, is given by the fol- lowing expression:31 2 2     (1) where μ is the electronic chemical potential and η is the chemical hardness. Both quantities may be approached in terms of the one-electron energies of the frontier molecular orbitals HOMO and LUMO, ɛH and ɛL, respectively: 32 H L 2      (2) H L    (3) Recently, Domingo introduced an empirical (relative) nucleophilicity index,33 based on the HOMO energies obtained within the Kohn Sham scheme,34 that were defined as: HOMO HOMO(NU) (TCE)  (4) Nucleophilicity is referred to tetracyanoethylene (TCE), because it presents the lowest HOMO energy in a large series of molecules already investigated in the context of polar cyc- loadditions. This choice allows a nucleophilicity scale of positive values to be conveniently handled. Recently, Domingo proposed two new electrophilic, +kP , and nucleophilic, - kP , Parr functions based on the atomic spin density distribution at the radical anion and cation of a neutral molecule.35 The electrophilic, +kP , and nucleophilic, - kP , Parr functions were obtained through the analysis of the Mulliken atomic spin density of the radical anion and cation by single-point energy calculations over the optimized neutral geometries using the unrestricted UB3LYP formalism for radical species. The local electrophilicity indices, ωk, 36 and the local nucleophilicity indices, Nk, 34 were calculated using the following expressions: +k k  P (5) -k kN NP (6) where +kP and - kP are the electrophilic and nucleophilic Parr functions, 35 respectively. RESULTS AND DISCUSSION Experimentally, two concerted and a stepwise mechanism were suggested for these I-DA reactions of which the stepwise mechanism may be preferred to 70 HAGHDADI, SOGHRA MOUSAVI and GHASEMNEJAD the concerted,22a because the reaction is not stereospecific with respect to alkene geometry and the oxa-Povarov reaction must proceed through stepwise pathways. Therefore, two possible mechanisms for these reactions, concerted and step- wise mechanism were investigated herein to evaluate the energy differences between them by theoretical methods. Then, the present study was divided into three parts: first, a mechanistic study of the I-DA reactions of (E)-phenyl(pyridin- -2-ylmethylene)oxonium (1) and styrene derivatives 2a–c, to yield the chromane derivatives 7–10, was performed along the concerted and stepwise mechanisms. Thereafter, an analysis of the geometrical and electronic structure of the stationary points was undertaken and finally, an analysis of the DFT reactivity indices of the reactants was performed. I) Study of I-DA reaction of (E)-phenyl (pyridin-2-ylmethylene)oxonium (1) and the styrene derivatives 2a–c along the concerted mechanism The reaction of aryl oxonium 1 species and styrene derivatives 2a–c com- prises two consecutive steps (Scheme 1): i) an I-DA reaction between 1 and 2a–c to yield the corresponding intermediates 3–6 and ii) the elimination of hydrogen to give chromans 7–10. The relative energies and Gibbs free energies for the sta- tionary points are given in Table I, and Table S-I of the Supplementary material to this paper. Scheme 1. The calculated possible reaction pathways for the concerted mechanism of the I-DA reaction between phenyl (pyridin-2-ylmethylene)oxonium (1) and styrene derivatives 2a–c. DFT STUDY ON MECHANISM OF DIELS–ALDER REACTION OF CHROMANES 71 TABLE I. The calculated activation energies (ΔE#), activation free energies (∆G#) and reac- tion energies (∆Er), all in kJ mol -1, of the I-DA reactions between phenyl(pyridin-2-ylmethyl- ene)oxonium (1) and styrene derivatives 2a–c for the concerted mechanism (for a full com- parison of energies see the Supporting material) Species TS ∆E#a ∆E#b ∆G#a ∆Er a ∆Er b 1+2a→3a-endo TS1a 15.12 –10.29 67.95 –87.26 –174.75 3a→7a-endo TS2a –75.23 –163.30 –12.55 –261.17 –328.57 1+2a→4a-exo TS3a 14.10 –9.13 66.00 –88.14 –179.91 4a→8a-exo TS4a –63.76 –146.07 –0.39 –245.93 –313.21 1+2b→3b-endo TS1b 21.21 –2.55 72.74 –78.60 –165.50 3b→7b-endo TS2b –74.93 –162.44 –10.71 –261.36 –337.05 1+2b→4b-exo TS3b 20.59 –1.95 72.31 –79.26 –170.15 4b→8b-exo TS4b –64.83 –147.09 –1.32 –246.50 –322.51 1+2c→3c-endo TS1c 5.53 –16.39 55.63 –90.62 –178.37 3c→7c-endo TS2c –74.66 –163.47 –10.23 –260.63 –337.13 1+2c→4c-exo TS3c 4.27 –17.67 61.47 –91.68 –182.74 4c→8c-exo TS4c –63.22 –145.42 0.30 –245.17 –321.63 aOptimization was performed at the B3LYP/cc-pVDZ level of theory; b calculated at MPWB1K/aug-cc- -pVTZ//B3LYP/cc-pVDZ level Due to the asymmetry of the two reagents, four competitive pathways are feasible for the I-DA reaction between aryl oxonium ion 1 and styrene deri- vatives 2a–c. They are related to the two stereoisomers corresponding to the endo and exo approach modes of the styrene aryl group relative to the phenyl group of the oxonium ion, and the two regioisomeric possibilities, ortho and meta (Scheme 1). TS1, TS3, TS5 and TS7 were used to indicate the transition states (TSs) of the first step, TS2, TS4, TS6 and TS8 are the TSs for the second step, 3–6 are intermediates and 7–10 are cycloadducts of each pathway. The structures of the TSs and intermediates are displayed in Figs. S-1–S-3 of the Supplementary material. As can be seen from the results of the calculations presented in Tables I and S-I, the transition states of the first step (cycloaddition reaction), TS1, TS3, TS5 and TS7, are more energetic than the second step (elimination of a proton), TS2, TS4, TS6 and TS8, which suggests that the cycloaddition step is the rate-deter- mining step. Then in ortho-endo pathway, the energy barriers for two transition states, TS1a and TS2a are 15.12 and –75.23 kJ mol–1 for the B3LYP geometries, and –10.29 and –163.30 kJ mol–1 for the MPWB1K geometries, respectively, and the first step with TS1a could be the rate-controlling one. The energy barriers of the first step for ortho and meta pathways are 15.12, 14.10, 42.10 and 59.85 kJ mol–1 for the B3LYP geometries, and –10.29, –9.13, 19.20 and 31.81 kJ mol–1 for the MPWB1K geometries, respectively, which are higher than of the second steps and the intermediate 3a with –87.26 kJ mol–1 could be a stable compound. In order to obtain a quantitative estimate of the conformational energies in such systems, conformational analyses of the chromane ring were performed for 72 HAGHDADI, SOGHRA MOUSAVI and GHASEMNEJAD intermediates in all pathways at B3LYP/cc-pVDZ level, which adopts two conformers, distorted half-chair and boat conformations. The conformational analysis showed that the distorted boat conformers are more stable than the chair conformers for the ortho-endo and meta-endo pathways by 16.73 and 27.28 kJ mol–1, respectively, while in the ortho-exo and meta-exo pathways, the distorted chair conformers are the more stable ones by 15.21 and 11.33 kJ mol–1, respect- ively. Similar to the ortho-endo pathway, a common intermediate, 4a, is formed in the ortho-exo pathway, via TS3a with an energy barrier of 14.10 kJ mol–1 at the B3LYP/cc-pVDZ and –9.13 at the MPWB1K/aug-cc-pVTZ level. Then, 4a loses a proton (as AcOH) to form the cycloadduct of 8a via TS4a, the barrier height of which is –63.76 kJ mol–1 at the B3LYP method and –146.0 kJ mol–1 at the MPWB1K method (in Fig. S-1, AcO– is not shown in all structures but it was considered in all of the calculations). As mentioned above, the energy barrier of the ortho-endo pathway is lower than those of the others are, and should be the most favorable pathway from the kinetic viewpoint. The processes are extremely exothermic and the corresponding cyclo- adducts, 7a and 8a, are stable because their energies are lower than their corres- ponding reactants by –261.17 and –245.93 kJ mol–1 with B3LYP calculations, and –328.57 and –313.21 kJ mol–1 with MPWB1K calculations, respectively. The most favorable product 7a was also confirmed, suggesting that the ortho- -endo pathway is the favorable pathway from the thermodynamic viewpoint. The transition states of the meta pathways, TS5a, TS6a, TS7a and TS8a, have higher energy than those of the ortho ones, indicating that the ortho pathways are expected to be the dominant reaction pathways. Therefore, the meta pathways were ignored due to their high potential energies and focus was directed to the ortho pathways, see more information about meta pathways in Table S-I and Fig. S-3 of the Supplementary material. To understand the effects of electron donating (methyl) and electron with- drawing substituents (chloro) on the styrene ring on the I-DA reaction, the reac- tions of the aryloxonium ion 1 with 4-chlorostyrene (2b) and 4-methylstyrene (2c) were investigated. These two I-DA reactions also take place in the same way as mentioned earlier (I-DA reaction of 1+2a). Then, the two ortho pathways dominated the reaction pathways. As shown in Table I, along the ortho pathway, the chloro group on styrene slightly increased the activation energies of TS1 and TS3, while the methyl group decreased the energy barriers (10 kJ mol–1), relative to the parent (styr- ene). The activation energies associated to the regioisomeric pathways (ortho and meta) indicated a large regioselectivity in the I-DA reaction of 1 with 2b and 2c. Thus in this section, for the I-DA reactions of 1 with 2b and 2c, the main focus DFT STUDY ON MECHANISM OF DIELS–ALDER REACTION OF CHROMANES 73 was on the two ortho pathways and meta ones were ignored due to the high potential energies (Tables I and S-I). If the easy equilibrium between all stereoisomers is considered, the most favorable reaction pathway corresponds to the formation of 7c via TS1c, by 5.53 kJ mol–1 at the B3LYP level and –16.39 kJ mol–1 at the MPWB1K level. A comparison of the activation energies for all the I-DA reactions indicated that the energy of the transition states associated with the ortho-endo pathway were slightly lower than those of the ortho-exo ones; which is in agreement with the experimental results.22 When the solvent effects of CH2Cl2 were considered, the activation energies increased. For example, the activation barrier for the first step of the I-DA reaction of 1 with 2a becomes 15.52 kJ mol–1 with MPWB1K calculations, which is 25.81 kJ mol–1 higher than that in gas phase (–10.29 kJ mol–1). In addition, the relative energy of 3a is reduced (by about 30 kJ mol–1) in gas phase, which shows that it becomes more stable than in the solvent. Fur- thermore, the predicted stereoselectivity in the solvent remains almost the same as in the gas phase (the ortho-endo pathway is preferred). Thus, it is apparent that in this work geometry optimization in the continuum solvent does not offer any direct advantage over the single-point calculations on the gas phase geometries. II) Study of I-DA reaction of (E)-phenyl(pyridin-2-ylmethylene)oxonium (1) and the styrene derivatives 2a–c along the stepwise mechanism Experimentally, these reactions were not stereospecific with respect to the alkene geometry and scrambling was observed, thus the oxa-Povarov reaction must proceed through a stepwise path. Hence, the second suggested mechanism is a stepwise one. The TSs structures, suggested intermediates, products and rel- ated energies are provided in Scheme 2, Table II and Table S-II of the Supple- mentary material. The computational results indicated that these I-DA reactions could be achieved by a stepwise mechanism along four competitive pathways, two stereo- selective (endo and exo) and two regioselective pathways (ortho and meta). The initial stepwise Prins-type addition of the styrene derivatives 2a–c to the oxo- nium 1 generates carbocation intermediates, 11, 14, 17 and 20 via TS9, TS13, TS17 and TS21. The relative stereochemistry of the C1–C5 or C1–C6 bond form- ation could be compared to the addition of styrene to the oxonium ion. The com- putational study revealed that I-DA reactions between styrene derivatives and the oxonium ion occurred preferentially to give the syn carbocation intermediate. These observations were rationalized comparing the energy barriers of all TSs, of which the lowest energy barrier as starting points were predicted for TS9 or TS13 in the ortho pathways. Next, the newly attached bond C–C undergoes a rotation to form 12, 15, 18 and 21 via TS10, TS14, TS18 and TS22. Then a rotation along the newly formed  bond in the intermediates yields new inter- 74 HAGHDADI, SOGHRA MOUSAVI and GHASEMNEJAD mediates 13, 16, 19 and 22 via TS11, TS15, TS19 and TS23, respectively. Now, the latter intermediates having the proper stereochemistry undergo Friedel−Crafts cyclization to form 3–6 via TS12, TS16, TS20 and TS24, respectively. Scheme 2. The calculated possible reaction pathways for the stepwise mechanism of the I-DA reaction between phenyl(pyridin-2-ylmethylene)oxonium (1) and the styrene derivatives 2a–c. A comparison among the activation energies and reaction energies for the I-DA reaction of 1 with 2a in Table II and Table S-II of the Supplementary material indicated that the meta pathways with extremely high potential energies should be ignored and thus attention was focused on the ortho pathways of these reactions. For more information about the meta pathways, see Table S-II of the Supplementary material. In ortho-endo stepwise pathway, first, styrene 2a approaches to 1 through a synclinal orientation to generate the carbocation intermediate 11a via TS9a. The energy barrier for this process is –7.26 kJ mol–1 at the B3LYP level and –29.93 kJ mol–1 at the MPWB1K level with 11a being more stable than reactants by – 37.44 kJ mol–1 according to the B3LYP method and –89.52 kJ mol–1 according DFT STUDY ON MECHANISM OF DIELS–ALDER REACTION OF CHROMANES 75 to the MPWB1K method. Then intermediate 11a must undergo C1–C5 bond rotation to generate intermediate 12a, which is antiperiplanar, via TS10a with an energy barrier of –35.41 and –79.85 kJ mol–1 at the B3LYP and MPWB1K levels, respectively. Next, 12a undergoes rotation around the same C1–C5 bond, with an energy cost of –16.45 kJ mol–1 (–61.79 kJ mol–1 at the MPWB1K level), to yield 13a via TS11a. Subsequently, intermediate 13a undergoes Friedel−Crafts cyclization to produce 3a via TS12a. Finally, 3a loses a proton to produce 7a, as discussed in the concerted section. TABLE II. The calculated activation energies (ΔE#), activation free energies (∆G#) and reaction energies (∆Er), all in kJ mol -1, of the I-DA reactions between phenyl(pyridin-2-yl- methylene)oxonium (1) and styrene derivatives 2a–c for the stepwise mechanism (for a full comparison of the energies, see the Supplementary material) Species TS ∆E#a ∆E#b ∆G#a ∆Er a ∆Er b 1+2a→11a-endo TS9a –7.62 –29.93 42.44 –37.44 –89.52 11a→12a-endo TS10a –35.41 –79.85 30.39 –45.68 –91.18 12a→13a-endo TS11a –16.45 –61.79 43.93 –33.65 –79.52 13a→3a-endo TS12a –21.46 –75.72 40.28 –87.26 –174.75 1+2a→14a-exo TS13a –5.85 –28.31 45.58 –35.77 –88.96 14a→15a-exo TS14a –18.58 –68.66 42.02 –72.32 –118.12 15a→16a-exo TS15a –6.05 –56.07 53.42 –28.89 –75.91 16a→4a-exo TS16a –14.30 –63.82 51.15 –88.14 –179.91 1+2b→11b-endo TS9b –1.66 –23.56 47.84 –33.95 –84.80 11b→12b-endo TS10b –29.54 –72.84 36.64 –42.07 –86.83 12b→13b-endo TS11b –13.33 –57.43 47.45 –25.55 –71.62 13b→3b-endo TS12b –15.36 –69.28 46.97 –78.60 –165.50 1+2b→14b-exo TS13b 0.015 –21.41 51.45 –13.27 –85.59 14b→15b-exo TS14b –15.05 –64.25 46.18 –67.30 –112.17 15b→16b-exo TS15b 7.09 –32.38 70.46 –25.68 –71.94 16b→4b-exo TS16b –8.425 –56.87 29.67 –79.26 –170.15 1+2c→11c-endo TS9c –17.29 –38.26 32.19 –53.23 –106.06 11c→12c-endo TS10c –50.56 –95.89 15.68 –65.38 –112.65 12c→13c-endo TS11c –38.12 –84.02 22.37 –53.65 –101.37 13c→3c-endo TS12c –35.06 –90.43 27.30 –90.62 –178.37 1+2c→14c-exo TS13c –15.12 –35.15 35.51 –56.49 –110.39 14c→15c-exo TS14c –39.28 –91.24 22.13 –88.39 –135.34 15c→16c-exo TS15c –16.54 –59.82 46.21 –50.10 –101.07 16c→4c-exo TS16c –27.07 –79.41 37.93 –91.68 –182.74 aOptimization was performed at B3LYP/cc-pVDZ level of theory; bcalculated at the MPWB1K/aug-cc-pVTZ// B3LYP/cc-pVDZ level From a comparison of the relative energies of the TSs and intermediates in the ortho-endo stepwise pathway, some results could be concluded as follows: i) the formation of the C1–C5 bond (TS9a) is the rate-determining step, ii) as expected, the energy of intermediates are low compared to the surrounding bar- riers (TS9a–TS12a), iii) the low energy of the TSs and intermediates (their ener- 76 HAGHDADI, SOGHRA MOUSAVI and GHASEMNEJAD gies are lower than those of reactants) together with the rotation of the C1–C5 bond may suggest that these processes occur via an reversible stepwise mech- anism, iv) furthermore, the lowest activation and relative energies were seen for TS10a and 3a, respectively. The optimized geometries of TSs and intermediates involved in the domino pathway are given in Figs. S-2 and S-3 of the Supple- mentary material, respectively. Similar results were obtained for the ortho-exo pathway, which are given in Table II. Comparing the ortho pathways with regard to stereochemistry, the endo pathways are usually followed preferentially, as the activation energies in the more stable step (TS10a) are slightly lower than those in the exo addition and the resulting intermediates are more stable. These results confirmed that the ortho- -endo pathway is the most energetically favorable one among the other proposed reaction pathways, in agreement with the experimental results. Moreover, the stepwise pathways were investigated in I-DA reaction of 4-chlorostyrene and 4-methylstyrene (2b and 2c, respectively) with aryl oxonium ion 1 (Scheme 2) along the more favored pathways (ortho ones), and the results of their activation energies and reaction energies, given in Table II, indicated that the ortho-endo pathways are the more favorable ones. The theoretical results proved that the I-DA reaction with the lowest acti- vation barriers involved 4-methyl substituted styrene along the ortho-endo path- way, while 4-chloro substitution increased the activation and reaction energies. As can be seen in Table II, the activation energies varied within the series of dienophiles. Of all the possible stepwise TSs, TS10 is consequently favored over the others. Furthermore, the energy of TSs increased when going from 2a to 2b and became the lowest for 2c. A similar trend was observed for their inter- mediates, i.e., 11c, 12c, 13c and 3c are the most stable intermediates, while the intermediates of I-DA reaction 1+2 appear to be less stable. III) Geometrical parameters Selected geometry parameters of the TSs on the concerted pathways at the B3LYP/cc-pVDZ level are shown in Fig. 1. As can be seen, the lengths of the C1–C5 and C4–C6 bonds (the atom numbering is given in Scheme 1) for the concerted mechanism, at the ortho-endo pathway (TS1), are about 2.23 and 3.89 Ǻ, and at the ortho-exo (TS3), the corresponding values are 2.25 and 3.89 Ǻ, res- pectively. These bond lengths indicated that both TSs structures are with highly asynchronous bond formation processes, where it seems only the C1–C5 bond is being formed. The extent of bond-formation along a reaction pathway is provided by the concept of bond order (BO).37 The BO values of the C4–C6 forming bonds for the concerted mechanism along the most favorable pathway is virtually zero, indicating a stepwise or at least highly asynchronous pathway for these reactions. DFT STUDY ON MECHANISM OF DIELS–ALDER REACTION OF CHROMANES 77 The polar nature of the two cyclization modes can be estimated by a charge transfer (CT) analysis at the TSs.29 The CT descriptors (Figs. S-1 and S-3) clearly show that these reactions are polar according to the Domingo classific- ation. Moreover, the important dihedral angles and bond lengths for the TSs and intermediates of stepwise mechanism are presented in Table III, and Table S-III of the Supplementary material. TABLE III. Selected geometrical parameters, bond lengths (r / Ǻ) and dihedral angles (φ / °) for the stationary points of I-DA reactions between phenyl(pyridin-2-ylmethylene)oxonium (1) and styrene (2a) for the ortho pathway of stepwise mechanism at the B3LYP/cc-pVDZ level of theorya (for numbering of atoms, see Scheme 2, and for full comparison of geomet- rical parameters, see the Supporting information to this paper) Species φO-C1-C5-C6 rC1-O rC3-C4 rC4-C6 rC5-C6 1 – 1.28 1.39 – – 2a – – – – 1.34 TS9a 69.15 1.31 1.39 4.93 1.37 11a 53.52 1.41 1.39 5.09 1.47 TS10a 116.23 1.43 1.39 5.74 1.48 12a 172.26 1.41 1.40 5.22 1.46 TS11a 115.01 1.44 1.39 4.93 1.45 13a 45.23 1.43 1.40 4.59 1.47 TS12a 65.20 1.45 1.44 4.51 1.48 3a 26.11 1.48 1.47 1.58 1.55 TS2a 49.10 1.46 1.48 1.58 1.55 7a 62.05 1.43 1.40 1.52 1.54 TS13a 67.86 1.30 1.39 4.55 1.37 14a 60.11 1.40 1.39 5.13 1.47 TS14a 120.32 1.42 1.39 5.52 1.47 15a 177.17 1.40 1.40 4.43 1.46 TS15a 119.75 1.42 1.40 4.89 1.46 16a 41.30 1.42 1.39 4.72 1.47 TS16a 45.52 1.45 1.44 2.49 1.49 4a 53.14 1.47 1.49 1.55 1.54 TS4a 44.33 1.46 1.49 1.57 1.55 8a 53.81 1.43 1.40 1.52 1.54 CONCLUSION The molecular mechanism of I-DA reactions between aryl oxonium 1 species and styrene derivatives 2a–c yielding chromanes 7–10 was studied using the DFT method at the B3LYP/cc-pVDZ level of theory. The formation of cycloadducts 7–10 occurs through two consecutive steps; first, a cycloaddition reaction between 1 and 2a–c occurred to yield the inter- mediates 3–6, then the elimination of hydrogen from these intermediates yielding 78 HAGHDADI, SOGHRA MOUSAVI and GHASEMNEJAD chromanes 7–10. These I-DA reactions are completely regioselective and slightly endo selective. The calculation results suggest that: I. The elimination of hydrogen is kinetically favored over the cycloaddition process (first step). II. The concerted and stepwise mechanism of all the I-DA reactions were investigated, the results of which showed that the stepwise mechanism is more favorable than the concerted ones. III. The ortho-endo pathway with an energy barrier of 15.12 kJ mol–1 for 4-Cl styrene and 5.53 kJ mol–1 for 4-Me styrene, on the concerted mechanism is the most energetically favorable pathway; on the stepwise mechanism these energy barriers are reduced to –13.33 and –38.12 kJ mol–1, respectively. IV. DFT-based reactivity indices clearly predict the regiochemisty of the iso- lated cycloadducts. Moreover, it is reasonable to conclude that the gas-phase geometry optimiz- ation at the B3LYP/cc-pVDZ level can give quite good estimates of the mech- anism and stereoselectivity in I-DA reactions. SUPPLEMENTARY MATERIAL The calculated energies, geometrically optimized transition states and intermediates, as well as selected geometrical parameters are available electronically from http:// //www.shd.org.rs/JSCS/, or from the corresponding author on request. И З В О Д ПОСТЕПЕНО ИЛИ КОНЦЕРТОВАНО? DFT СТУДИЈА МЕХАНИЗМА ЈОНСКЕ ДИЛС–АЛДЕРОВЕ РЕАКЦИЈЕ ХРОМАНА MINA HAGHDADI, SEYEDEH SOGHRA MOUSAVI и HASSAN GHASEMNEJAD Department of Chemistry, Islamic Azad University, P.O. box 755, Babol branch, Babol, Iran Постепене и концертоване јонске Дилс–Алдерове рекције између фенил(пиридин- -2-илметилен)оксонијумских и стиренских деривата изучаване су коришћењем теориј- ских метода. Резултати дају подршку употреби рачунарких метода првенствено на ста- билнијим интермедијерима. DFT метод се показао битним за репродуковање реалис- тичне површине потенцијалне енергије за ове захтевне системе. (Примљено 20. априла, ревидирано 26. септембра, прихваћено 5. октобра 2015) REFERENCES 1. A. KamaI-Eldin, L. A. Appelqvist, Lipids 31 (1996) 671 2. A. R. Tapas, D. M. Sakarkar, R. B. Kakde, Trop. J. Pharm. Res. 7 (2008) 1089 3. a) E. J. Jacobsen, F. J. Van Doornik, D. E. Ayer, K. L. Belonga, J. M. Braughler, E. D. Hall, D. J. House, J. Med. Chem. 35 (1992) 4464; b) K. Terao, E. Niki, J. Free Rad. Biol. Med. 2 (1986) 193; c) J. M. Grisar, M. A. Petty, F. N. Bolkenius, J. Dow, J. Wagner, E. R. Wagner, K. D. Haegele, W. D. Jong, J. Med. Chem. 34 (1991) 257 4. J. Lal, Contraception 81 (2010) 275 DFT STUDY ON MECHANISM OF DIELS–ALDER REACTION OF CHROMANES 79 5. Y.  Kashiwada, K.  Yamazaki,  Y. Ikeshiro, T. Yamagishi,  T.  Fujioka,  K.  Mihashi, K. Mizuki,  L. M.  Cosentino,  K. Fowke, S. L. Morris-Natschke  K.-H.  Lee, Tetrahedron 67 (2001) 1563 6. F. Cassidy, J. M. Evans, M. S. Hadley, A. H. Haladij,  P. E. Leach, G.  Stemp, J. Med. Chem. 35 (1992) 1623 7. a) C. Pouget, C. Fagnere, J. P. Basly, H. Leveque, A. J. Van Doornik, Tetrahedron 56 (2000) 6047; b) N. P. Seeram, H. Jacobs, S. McLean, W. F. Reynolds, Phytochemistry 49 (1998) 1389 8. H. C. Shen, Tetrahedron Lett. 65 (2009) 3931 9. a) R. W. Van de Water, T. R. R. Pettus, Tetrahedron Lett. 58 (2002) 5367; b)  K. A.  Korthals, W. D.  Wulff, J. Am. Chem. Soc. 130 (2008) 2898; c) T.  Inoue, S.  Inoue,  K.  Sato, Bull. Chem. Soc. Jpn. 36 (1990) 1647 10. S. K. Ko, H. J. Jang, E. Kim, S. B. Park, Chem. Commun. 28 (2006) 2962 11. a) P. Kotame, B. C. Hong, J. H. Liao, Tetrahedron Lett. 50 (2009) 704; b) X. Meng, Y. Huang, H. Zhao, P. Xie, J. Ma, R. Chen, Org. Lett. 11 (2009) 991; c) N. R. Mente, J. D. Neighbors, D. F. Wiemer, J. Org. Chem. 73 (2008) 7963 12. a) V. M. Cherkasov, N. A. Kapran, Chem. Heterocycl. Compd. 28 (1992) 1101; b) K. C. Nicolaou, S. A. Snyder, T. Montagnon, G. Vassilikogiannakis, Angew. Chem. Int. Ed. 41 (2002) 1668 13. a) V. I. Grigos, L. S. Povarov, B. M. Mikhailov, Russ. Chem. Bull. Int. Ed. (Engl. Transl.) 12 (1965) 2163; b) L. S. Povarov, V. I. Grigos, B. M. Mikhailov, Russ. Chem. Bull., Int. Ed. (Engl. Transl.) 1 (1966) 144 14. For reviews on the Povarov reaction, see: a) L. S. Povarov, Russ. Chem. Rev. 36 (1967) 656; b) V. A. Glushkov, A. G, Tolstikov, Russ. Chem. Rev. 2 (2008) 137; c) V. V.  Kouznetsov, Tetrahedron 65 (2009) 2721 15. L. R. Domingo, J. A. Saez, Org. Biomol. Chem. 7 (2009) 3576 16. a) D. G. Gassman, D. A. Singleton. J. Org. Chem. 51 (1986) 3075; b) P. G. Gassman, D. A. Singleton, J. Am. Chem. Soc. 109 (1987) 2182 17. M. V. Basaveswara Rao, J. Satyanarayana, H. Ham, H. Junjappa, Tetrahedron Lett. 36 (1995) 3385 18. L. R. Domingo, J. Org. Chem. 66 (2001) 3211 19. L. R. Domingo, M. Oliva, J. Andres, J. Org. Chem. 66 (2001) 6151 20. L. R. Domingo, M. Oliva, J. Andres, J. Mol. Struct. THEOCHEM 544 (2001) 79 21. H. Mayr, A. R. Ofial, J. Sauer, B. Schmied, Eur. J. Org. Chem. (2000) 2013 22. a) A. Batey, R. R. Rivka, J. Org. Chem. 78 (2013) 1404; b) L. R. Domingo, M. J. Aurell, P. Pérez, RSC Adv. 4 (2014) 16567 23. a) A. D. Becke, Phys. Rev., A 38 (1988) 3098; b) C. Lee, W. Yang, R. G. Parr, Phys. Rev., B 37 (1988) 785 24. L. Simon, J. M. Goodman, Org. Biomol. Chem. 9 (2011) 684 25. L. R. Domingo, M. J. Aurell, P. Pérez. Tetrahedron 70 (2014) 4519 26. a) J. Tomasi, M. Persico, Chem. Rev. 94 (1994) 2027; b) B. Y. Simkin, I. Sheikhet, Quantum chemical and statistical theory of solutions – A computational approach, Ellis Horod, London, 1995 27. a) E. Cances, B. Mennucci, J. Tomasi, J. Chem. Phys. 107 (1997) 3032; b) M. Cossi, V. Barone, R. Cammi, J. Tomasi, Chem. Phys. Lett. 255 (1996) 327 28. Gaussian 09 revision A, Gaussian, Inc., Wallingford, CT, 2009 29. A. E. Reed, R. B. Weinstock, F. Weinhold, J. Chem. Phys. 83 (1985) 735 80 HAGHDADI, SOGHRA MOUSAVI and GHASEMNEJAD 30. R. G. Parr, W. Yang, Density functional theory of atoms and molecules, Oxford Univ. Press, New York, 1989, p. 16 31. R. G. Parr, L. Von Szentpaly, S. Liu, J. Am. Chem. Soc. 121 (1999) 1922 32. R. G. Parr, R. G. Pearson, J. Am. Chem. Soc. 105 (1983) 7512 33. L. R. Domingo, P. Pérez, J. Org. Chem. 73 (2008) 4615 34. P. Pérez, L. R. Domingo, M. Duque-Noreña, E. Chamorro, J. Mol. Struct. THEOCHEM 895 (2009) 86 35. L. R. Domingo, P. Pérez, J. A. Saez, RSC Adv. 3 (2013) 1486 36. L. R. Domingo, M. J. Aurell, P. Pérez, J. Phys. Chem., A 106 (2002) 6871 37. K. B. Wiberg, Tetrahedron 24 (1968) 1083 38. H. Chemouri, S. M. Mekelleche, Int. J. Quantum. Chem. 112 (2012) 2294 39. W. Benchouk, S. M. Mekelleche, B. Silivi, M. J. Avrell, L. R. Domingo, J. Phys. Org. Chem. 24 (2011) 611.