On the Question of Stepwise [4+2] Cycloaddition Reactions and Their Stereochemical Aspects

: Even at the end of the twentieth century, the view of the one-step [4+2] cycloaddition (Diels-Alder) reaction mechanism was widely accepted as the only possible one, regardless of the nature of the reaction components. Much has changed in the way these reactions are perceived since then. In particular, multi-step mechanisms with zwitterionic or diradical intermediates have been proposed for a number of processes. This review provided a critical analysis of such cases.


Introduction
The history of the [4+2] cycloaddition reaction began in 1928, when Otto Diels and his student, Kurt Alder, published the work in which they described the cycloaddition of cyclopentadiene (1) to quinone (2) (Scheme 1) [1]. Since then, the number of literature reports dealing with the most diverse aspects of [4+2] cycloaddition has been steadily increasing. Scheme 1. The "original" Diels-Alder reaction between cyclopentadiene (1) and quinone (2).
According to the classical school of organic chemistry, the course of the [4+2] cycloaddition reaction was usually interpreted on the basis of the FMO theory and the rules of the conservation of the symmetry of orbitals [15,16]. At present, this "philosophy" based on the analysis of molecular orbitals seems to be quite outdated as it does not always provide adequate information [17]. Instead, nowadays, the parameters of global and local electrophilicity and nucleophilicity, defined within the Conceptual DFT (CDFT), are used [18]. Moreover, Domingo generally challenges the term "pericyclic reaction" in relation to most [4+2] cycloaddition processes [19]. In the light of the current state of knowledge, the [4+2] cycloaddition reactions should be classified according to the nature of intermolecular interactions in the elementary reaction. These interactions may be polar or non-polar, depending on how much the global electrophilicities/nucleophilicities of the reaction components will differ [20]. The nature of these interactions, however, does not impose in advance the one-or two-step nature of cycloaddition. In the case of both polar and non-polar processes, two-step reactions are possible. However, while in polar reactions the intermediates are zwitterionic species [21], in non-polar reactions, they are diradical ones [22] (Scheme 2).  Even in the 1960s, the one-step "concerted" mechanism of [4+2] cycloadditions was adopted as dogma [23]. Such a mechanism implies the retention of the original addends stereoconfiguration (cis-stereospecificity), since in this case the formation of new sigmabonds occurs simultaneously with the destruction of the pi bonds. The situation becomes more complicated, however, when we allow the possibility of the acyclic intermediate appearing in the reaction environment. Then, both cis-stereospecific products and those with a relative configuration of the substituents other than in the addends may appear in the post-reaction mixture [24]. This is possible as a consequence of free rotation around single bonds within the intermediate (Scheme 3). Thus, the reaction mechanism is crucial for the number and configuration of products for [4+2] cycloadditions. Scheme 3. The influence of the [4+2] cycloaddition reaction mechanism on its stereochemistry.
Nowadays, various techniques, both experimental and quantum-chemical, are used to study the mechanistic aspects of the cycloaddition reaction. The first information about the reaction mechanism can be obtained from thorough analysis of the reaction mixture. In particular, the two-step mechanism may suggest the loss of stereoconfiguration due to addends (Scheme 3), but also the presence of acyclic products with a conformation suggesting that they were transformed from the originally formed zwitterions and/or diradicals. The presence of this first group of intermediates in the reaction mixture can be proved independently by spectral analysis using NMR or UV/VIS techniques [25]. Investigation of the reaction course with kinetic methods can, in turn, provide data on the substituent and solvent effects and activation parameters, which shed light on the nature of the reaction transition states [26][27][28][29]. In turn, measurements of kinetic isotope effects make it possible to estimate the degree of advancement of new, specific chemical bonds [30][31][32]. On the other hand, data on the process step may be provided by thermogravimetric studies of retro-cycloaddition processes [33]. In the literature, some [4+2] cycloaddition reaction cases can be found, in which the presence of zwitterionic/diradical intermediate can be proposed based on research using the above-mentioned methods. However, these studies are very diverse in nature and practical value.

Diels-Alder Reactions
The simplest "prototype" case of the [4+2] cycloaddition reaction between buta-1,3-diene 4 and ethene 5 (Scheme 4) was the subject of both experimental and theoretical studies of various research groups. In experimental conditions, this reaction is carried out at a temperature of 175 • C and a pressure of 6000 bar [34]. Quantum chemistry studies at various theoretical levels have shown that the path leading to the product follows one high-synchronic transition state, which is confirmed by experimental determinations of kinetic isotope effects [35][36][37][38]. Quantum-chemical studies have shown that a path passing through two transition states and an intermediate (7) of a radical nature is theoretically possible [37,38]. This path, however, regardless of the level of theory applied, must be considered insurmountable from a kinetic perspective. Similar studies were also carried out for the analogous reaction with cyclopentadiene 1, leading to very similar conclusions [39][40][41]. In an analogous reaction with the participation of perfluorinated ethylene analogue 8, apart from the expected norbornene 9, perflurocyclobutane 11 is also formed (Scheme 5), which, as the authors suggest, testifies to the formation of a diradical intermediate undergoing various cyclisation processes along competing paths [42,43]. The diradical nature of the postulated intermediate was confirmed based on the quantum-chemical calculations at UB3LYP/6-311G(d) [44]. At the same time, the conversion of diradical 10 to cyclobutane 11 is the only possible path of cyclisation. The conformation excludes cyclisation of the diradical 10 to adduct 9. The gradual rotation around the C(F 2 )-CF 2 bond occurs simultaneously with the gradual dissociation of the bond between the tetrafuoroethene 8 and cyclopentadiene 1 substructures. As a result, it led to the reconstruction of the original addends, which are converted to 9 according to the aforementioned one-step mechanism. The cycloadditions of cyclopentadiene 1 to nitroalkenes having the CF 3 group in the 2-position of the nitrovinyl fragment are clearly polar. This is due to the presence of two electron-withdrawing groups (EWG) groups adjacent to the reaction centres of the 2-π-electron component. These processes lead to mixtures of appropriate, stereoisomeric nitronorbornenes 14 + 15 differing endo/exo in the location of the nitro group (Scheme 6) [45]. The DFT calculations showed that the isomer with the exo orientation 15 of the nitro group was formed by an asynchronous but one-step mechanism, while the isomer with the endo orientation 14 of the nitro group was formed by a two-step mechanism with the heterocyclic intermediate 13 [46]. At the same time, in the case of reactions involving nitroalkenes additionally functionalised in position 1, a third, competitive path to the zwitterion 16 with an "extended" conformation is possible. Cycloadditions of cyclopentadiene 1 to 2-arylonitroethenes 16 took place at elevated temperature and led to mixtures of endoand exo-isomeric nitronorbornenes, and their one-step nature is not in doubt regardless of the reaction conditions [47][48][49]. Analogous reactions with the participation of 2-aryl-1-cyano-1-nitroethenes 17 (Scheme 7), despite the greater concentration of substituents at the reaction centres, take place very easily even at 0 • C [50,51]. The reason is the strongly polar nature of the cycloaddition, determined by the extremely π-deficient nature of the nitroalkene. The data on the mechanism of this transformation is provided by the DFT computational study data [52]. In "conventional" solvents (such as dichloromethane or toluene), exo-nitronorbornenes 20 are formed by a one-step mechanism through highly asynchronous transition states, whereas endo-nitronorbornenes 19 are formed by a two-step mechanism with a heterocyclic intermediate 18. The introduction of an ionic liquid into the reaction medium causes, on the path leading to final exo-nitronorbornene 20, a change of the one-step mechanism into a two-step mechanism with zwitterionic intermediate 21. This is a consequence of the interaction of the ionic liquid cations with the 2-π-component of the analysed reaction [53]. It should be noted that, for analogous reactions involving the less β-deficient 2-π-components, a similar catalytic effect accelerates the cycloaddition but does not promote the stepwise mechanism [54].
DFT calculations suggest that, according to the two-step mechanism with heterocyclic intermediate, a similar reaction of cyclopentadiene 1 with methyl p,β-dinitrocinnamate 22 The cycloaddition reactions of cyclopentadiene 1 with fumaric acid esters 26 (Scheme 9) have been the subject of detailed studies by many research groups. Such studies have been carried out with the retention of the stereoconfiguration of the dienophile, and the one-step character has been confirmed by kinetic studies [23,[56][57][58]. However, in a similar reaction with the participation of perchlorocyclopentadiene 28, together with the cycloadduct (31) presenting an identical stereoconfiguration to that brought in from the dienophile, a product with the different Z/E stereoconfiguration (32) was formed with the yield of 27% [59] (Scheme 10). This suggests the stepwise nature of the analysed cycloaddition. Taking into account the non-polar nature of the addends interactions, this reaction is most likely occurring through the stereoisomeric diradical intermediates 30. The cycloadditions of the same diene with other E-1,2-disubstituted ethene analogues 29 are similar.
As is well known, arenes generally do not show the properties typical of alkenes or conjugated dienes. Sometimes, however, they can participate in [4+2] cycloaddition reactions as diene analogues [60]. For example, the reaction of anthracene 33 with 1,2-disubstituted nitroalkene 34 leads to the expected cycloadduct 35, and additionally, small amounts of the Michael adduct 37 [61] (Scheme 11). The presence of the latter product in the reaction mixture indicates that the zwitterionic intermediate 37 must have arisen in the course of the addends interactions. However, detailed DFT studies have shown that it is not a common intermediate for 35 and 37 formation processes, and that the cycloaddition leading to the Diels-Alder adduct is carried out according to the one-step mechanism [62].   The reaction between 4,6-dinitrobenzofuroxan (50) and 1-trimethylsilyloxybuta-1,3diene (48/49) (Scheme 14) has been the subject of comprehensive mechanistic studies. According to the analysis of the nature of electrophile-nucleophile interactions, the authors suggested [65] a polar nature for the cycloaddition, which prompted them to perform experimental tests to confirm the presence of zwitterionic intermediate in the reaction environment. These studies were performed in two ways, studying the kinetics of the reaction and monitoring the cycloaddition environment with spectroscopic methods. Both of these techniques confirmed the formation of the zwitterionic intermediate product, which, according to the authors, undergoes competitive cyclisation to the cyclohexene analogue (52) or to the HDA-type adduct (54). Later DFT studies showed that, in fact, the course of this reaction is even more complex [66]. In the first step of the reaction, two different zwitterions (51 and 53) can form, one of which is cyclised to cyclohexene 52 and the other to its heterocyclic analogue 54. In addition, there is a possibility of free rotation within zwitterionic intermediates, which puts both possible isomeric forms of the intermediate in a certain balance with each other.

Hetero Diels-Alder Reactions Involving Heteroanalogs of Dienes
The vast majority of the [4+2] cycloaddition reactions described in the literature with the participation of nitroalkenes as diene heteroanalogues take place under catalytic conditions [70][71][72]. However, in the case of the more highly deficient nitroalkenes, activated by the presence of an additional EWG group, the reaction may take place under thermal conditions. At the same time, due to the strongly polar nature of interactions in such processes, they can be realised with the participation of a zwitterionic intermediate. Thus, the authors of [73] described a series of cycloadditions of 2-aryl-1-cyano-1-nitroethenes 17 to vinyl ethyl ether 62. These reactions take place at temperatures ranging from 0-25 • C, leading to the expected cycloadducts 63 within a few minutes (Scheme 17). However, comprehensive kinetic studies including the analysis of the substituent and solvent effects in these cycloadditions ruled out the presence of acyclic intermediates 64 on the reaction paths [74]. DFT simulations of the profiles of the reaction paths led to a similar conclusion.  [76]. However, their direct cyclisation to cycloadducts is not possible due to conformation (the bending of the molecule causes the reaction centres to be too far apart). The conversion of zwitterions 67 to cycloadducts 66 is accomplished by the dissociation step into individual addends, followed by a one-step, polar cycloaddition. The reaction of 4,4,4-trifluoro-2-nitrobut-2-ene 68 with 3,3-dimethyl-2-morpholinobutene 69, apart from the expected cycloadduct 71, also yields the acyclic adduct 72 (Scheme 19). This gave the authors of [77] the basis for the statement that the reaction is carried out through a zwitterionic intermediate, which on competing pathways can either cyclise to 71 or convert to 72 via the [1,3]-H-sigmatropic shift step. DFT calculations confirm that heterocyclic ring formation is accomplished via zwitterionic intermediate 70 [78]. However, it is not the same intermediate that appears through the conversion of addends into 72. It is not only nitroalkenes that can be heteroanalogues of diene in stepwise cycloadditions. For example, the reactions between 3,5,6-triphenyl-1,2,4-triazine 77 and 2-cyclopropylidene-1,3-dimethylimidazolidine 78 at −40 • C lead to a relatively stable zwitterion 79, which can be identified by spectroscopic methods [80] (Scheme 21). Due to the significant degree of spatial hindrance, cyclisation of zwitterion 81 requires a higher temperature, at which there is a spontaneous elimination of nitrogen from the resulting cycloadduct 80. Scheme 21. The [4+2] cycloaddition reaction between 3,5,6-triphenyl-1,2,4-triazine 77 and 2-cyclopropylidene-1,3-dimethylimidazolidine 78.

Hetero Diels-Alder Reactions Involving Heteroanalogs of Dienophiles
Reactions of 1,3-butaliene 4 with formaldehyde and thioformaldehyde (82) were the subject of theoretical studies using the CASSCF(8,7)/6-31(d,p) and CASSCF(6.6)/6-31G(d,p) theory levels [81]. These studies revealed optimised geometries of diradicals 84 that could be formed in the course of these reactions (Scheme 22). At the same time, the process of their formation should be considered forbidden from the kinetic point of view in the conditions of competition with one-step [4+2] cycloaddition. In addition,1-phenyl-1-tosyl-azine-ethene 85 reactions with thioketones 86, 88 were investigated [82]. These reactions, regardless of the structure of the thioketone, always take place in a completely regioselective manner (Scheme 23). DFT calculations showed, however, that their mechanism may be completely different. In particular, cycloadditions involving diarylthioketones 86 follow an asynchronous but one-step mechanism. In contrast, analogous processes involving 1-thioxo-2,2,4,4-tetramethylcyclobutan-3-one 88 take place in a two-step mechanism with zwitterionic intermediate 89. Reactions of isomeric hexa-2,4-dienes 91 and 92 with diarylselenoketones 93 take place in a regioselective manner [83] (Scheme 24). However, regardless of the initial geometric configuration of the diene, identical stereoisomeric products 94 and 95 were detected in the post-reaction mixture. This observation prompts us to assume the presence of acyclic intermediates in the reaction environment, which through isomerisation are responsible for the presence of non-stereospecific cycloadducts. Unfortunately, there are no other premises indicating a two-step reaction mechanism [83]. Neither are there hints as to the nature of the hypothetical intermediates 96. Based on similar premises, a two-step mechanism of the reaction of 2,3-dimethyl-buta-1,3-dienes with diarylthioketones is predicted [84]. Carbon dioxide 97, as it is commonly known, is not a very highly reactive molecule [85,86]. Even with a relatively active nucleophile, which is cyclopentadiene 1, it does not undergo the cycloaddition reaction. DFT calculations have shown that, in the gas phase, such a process would be carried out according to a one-step mechanism, through a transition state of relatively high synchronicity (Scheme 25) [87]. However, the energy of this transition state is so high that it excludes the likelihood of effective conversion of the reaction components under normal conditions. The introduction of a solvent and catalysts in the form of Lewis acids (LA) with boron core into the reaction medium lowers the activation barrier to such an extent that the [4+2] cycloaddition process can be carried out at room temperature. Moreover, the one-step mechanism observed in the gas phase gives way to the two-step mechanism with zwitterionic intermediate.

Conclusions
Even 30 years ago, the discussion on examples of stepwise [4+2] cycloaddition reactions took the form of an analysis of incidental cases that elude the "classic" rule. Today, many examples of such reactions can be found in the literature. It is no longer possible to treat them marginally anymore. It is significant that the vast majority of such processes are carried out with the participation of zwitterionic-type intermediates. The processes in which it is possible to look for intermediates with diradical nature type belong to the minority. Sometimes the presence of an acyclic intermediate does not affect the stereochemistry of the reaction. This happens, for example, when intermediates with the "extended" conformation are formed, which, due to their conformation, cannot be converted into cycloadducts in one step. In the literature one can find such cases relating to both zwitterionic and diradical intermediates. It should also be mentioned that the collected material regarding the analysed class of reactions has a different value. There are cases where the stepwise mechanism is postulated on the basis of an ambiguous stereochemical criterion. There are also cases where the results of kinetic studies have been collected that allow for the indirect observation of transition states and/or rapid spectroscopic studies that allow to look for signs of labile intermediates in the reaction environment. Much of the existing work is supported by quantum-chemical computation data. Finally, there are incidental cases where acyclic intermediates can be isolated under certain conditions as relatively stable connections. Overall, the number of postulated stepwise [4+2] cycloaddition cases is constantly increasing and the coming years should bring significant progress in this area.

Conflicts of Interest:
The author declares no conflict of interest.