Understanding the mechanism of the Povarov reaction . A DFT study

The molecular mechanism of the Povarov reaction in acetonitrile has been studied at the MPWB1K/6-311G** level of theory. This reaction follows a domino process that comprises two sequential reactions: (i) a Lewis acid catalysed aza-Diels–Alder (A-DA) reaction between a N-aryl imine and a nucleophilic ethylene yielding a formal [4 + 2] cycloadduct; (ii) a stepwise 1,3-hydrogen shift at this intermediate affording the final tetrahydroquinoline. At this computational level, the Lewis acid catalysed A-DA reaction presents a two-step mechanism as a consequence of the large stabilisation of the corresponding zwitterionic intermediate. Our study allows establishing that the N-aryl substituent has no remarkable incidence in the activation energy, but the presence of a second C-aryl substituent has a relevant role in the reaction rate. Analysis of the DFT-based reactivity indices of the reagents provides further explanation of the behaviours of the mechanism of the A-DA reaction involved in the Povarov reaction.

In order to establish the role of the Lewis Acid (LA) catalyst in Povarov reactions, the A-DA reaction between the simplest N-aryl imine 13a and the electron-rich (ER) 2methylene-1,3-dioxolane 16 was studied.Interestingly, the uncatalysed reaction presents also a two-step mechanism.Consequently, two TSs, an intermediate and the corresponding cycloadduct were characterised (see Scheme S1).The total and relative energies of the stationary points involved in the A-DA reaction between the simplest Naryl imine 13a and the ER ethylene 16 are gathered in Table S3.

Scheme S1
The activation energy associated with the nucleophilic attack of the ER ethylene 16 on the C1 carbon of N-aryl imine 13a, via TS1-13a, is 12.0 kcal/mol; formation of the corresponding intermediate IN1-13a is endothermic by 9.4 kcal/mol.Finally, this intermediate with a very low activation energy, 2.2 kcal/mol, yields the formal [4+2]   cycloadduct 20, via TS2-13a.Formation of 20 is exothermic by -17.7 kcal/mol.A comparison of these relative energies with those of the LA catalysed process allows drawing some appealing conclusions: i) coordination of the BF 3 catalyst to the imine nitrogen of N-aryl imine 13a accelerates considerably the A-DA reaction through a strong decrease of the activation energy of 15.3 kcal/mol, ii) this larger acceleration is a consequence of the high electrophilic character of the LA complex 18 when compared with N-aryl imine 13a (see reactivity index analysis section in the main manuscript); iii) while formation of intermediate IN1-13a is endothermic by 9.4 kcal/mol, formation of intermediate IN1-18 is exothermic by 19.0 kcal/mol.This behaviour can be understood as a strong stabilisation of the zwitterionic intermediate IN1-18 through the electronwithdrawing BF 3 LA.Note that the charge separation at IN1-18 is 0.86e (see main manuscript); iv) the activation energy associated with TS1-13a, 12.0 kcal/mol, is 16.1 kcal/mol below that that associated with the A-DA reaction between N-aryl imine 13a and ethylene 14a, 1 28.1 kcal/mol, as a consequence of the low nucleophilic character of ethylene 14a.Table S3.MPWB1K/6-311G** total (E, a.u.) and relative (E, kcal/mol) energies, in acetonitrile, of the stationary points involved in the A-DA reaction between the simplest N-aryl imine 13a and 2-methylene-1,3-dioxolane 16.The geometries of the TSs associated with A-DA reaction between the simplest Naryl imine 13a and the nucleophilic activated ethylene 16 are given in Figure S1.At TS1-13a, associated with the nucleophilic attack of the C6 carbon of the ER ethylene 16 on the C1 carbon of N-aryl imine 13a, the distance between the C1 and C6 carbons is  In order to establish the role of the substituents (H, Ph, or CO 2 Me) present in the C1 carbon of the imine C=N double bond in Povarov reactions, the endo reactive channel associated with the nucleophilic attack of MVE 23 on the BF 3 complex of Nphenyl-C-methoxycarbonyl imine 26, BF 3 :imine complex 27, was studied (see Scheme S2).The total and relative energies are given in Table S4.A schematic representation of the energy profile for the BF 3 catalysed A-DA reactions of N-phenyl-Cmethoxycarbonyl imine 26 with MVE 23 is given in Figure S2.

Scheme S3
Thus, the anti reaction channel shown in Scheme S3 was studied in order to explain Whiting's results.Interestingly, the TS associated with the anti approach mode of MVE 23 to BF 3 :imine complex 27, TSa-26, was located 6.7 below the reagents (see Table S4).Such as in the BF 3 catalysed A-DA reaction of the simplest N-aryl imine 13a, the IRC from TSa-26 to reagents allowed finding the molecular complex MC-26, which is 6.6 kcal/mol more stable than BF   Table S5.MPWB1K/6-311G** Total and relative enthalpies (H, in au, and H, kcal/mol), entropies (S, in cal/mol .K and S, in cal/mol .K), Gibbs free energies (G, in au, and G, in kcal/mol), computed at 25.0 °C and 1.0 atm, and scaled by a factor 0.96, in acetonitrile, of the stationary points involved in Schemes 7, 9 and S2.Several theoretical studies have shown that the electron localisation function (ELF) topological analysis along a reaction path can be used as a valuable tool to understand the bonding changes along the reaction path. 3After an analysis of the electron density, the ELF provides basins, which are the domains in which the probability of finding an electron pair is maximal. 4The basins are classified as core basins and valence basins.The latter are characterized by the synaptic order, i.e., the number of atomic valence shells in which they participate.Thus, there are monosynaptic, disynaptic, trisynaptic basins and so on. 5Monosynaptic basins, labeled V(A), correspond to the lone pairs or non-bonding regions, while disynaptic basins connect the core of two nuclei A and B and, thus, correspond to a bonding region between A and B and are labeled V(A,B).This description recovers the Lewis bonding model, providing a very suggestive graphical representation of the molecular system.
Recently, Domingo et al. have shown that the C-C single bond formation in organic reactions begins in the short C-C distance range of 1.9 -2.0 Å by merging two monosynaptic basins, V(Cx) and V(Cy), into a new disynaptic basin V(Cx,Cy) associated with the formation of the new Cx-Cy single bond. 6The Cx and Cy carbons characterized by the presence of the monosynaptic basins V(Cx) and V(Cy) have been called pseudoradical centres. 7 order to understand the C-C bond formation in Povarov reaction, an ELF topological analysis of the MPWB1K/6-31G(d) wavefunctions of some relevant points of the IRCs of the two-step reaction between BF3:imine complex 18 and ER ethylene 16 was carried out.For this ELF topological study, eight structures were selected: the stationary points 18 + 16, TS1-18, IN1-18, TS2-18, and the formal [4+2] cycloadduct 19, plus three relevant points of the IRCs, namely P-I, P-II and P-III.ELF valence basin populations N calculated at the eight structures are given in Table S6.
Starting from the reagents, the most remarkable feature is the topological representation of the C1=N2 and C5=C6 double bonds.In this way, the C1=N2 double bond of BF 3 :imine complex 18 is topologically represented by two disynaptic basins, S10 V(C1,N2) and V'(C1,N2), integrating a total of 3.18e.On the other hand, the C5=C6 double bond of the ER ethylene 16 is also depicted by two disynaptic basins, V(C5,C6) and V'(C5,C6), integrating a total of 3.93e.Note that the integration of the C1=N2 double bond basins is lower than that of the C5=C6 one as a consequence of presence of the electron-withdrawing BF 3 catalyst at the N2 nitrogen.
Table S6.ELF valence basin populations N calculated at some selected points of the IRCs of the two-step A-DA reaction between the BF 3 :imine complex 18 and the ER ethylene 16. d(A-B) is the distance between A and B atoms (in Angstroms).practically formed, any monosynaptic basin at the C4 and C5 carbons is observed.In addition, the monosynaptic V(N2) basin has almost doubled its integration at the expense of the disynaptic basin V(C1,N2).
On going from IN1-18 to TS2-18, d1=1.556 and d2=2.291Å, the V(N2) basin starts to behave as an electronic pump, providing the necessary electronic density to promote the appearance of V(C4) monosynaptic basin.Note that this is just the phenyl ring position where the ring closure will take place.In fact, V(N2) diminishes its integration from 1.38e to 1.03e, a difference which almost covers the 0.44e of monosynaptic basin V(C4).The phenyl ring attached at N2 nitrogen, which has been almost inert towards electronic changes along the reaction path, starts to practice some interesting changes.Until IN1-18, the electronic picture of the phenyl ring was those of an aromatic structure with almost a symmetrical charge distribution and integration of the disynaptic V(Cphenyl,Cphenyl) basins, but from IN1-18, some disynaptic basins start to accumulate charge (V(C7,C8) and V(C9,C10)) while others start to lose electronic density (V(C3,C10), V(C4,C7) and V(C3,C4)).Note that at the location of those basins which accumulate charge end up being a formal double bond at the final formal [4+2] cycloadduct 19 while those that lose charge, will have a single C-C bond.

S12
After to pass TS2-18, at P-II, d1=1.538 and d2=2.019Å, a second monosynaptic basin appears at C5 carbon, V(C5), with a population of 0.50e.This electronic density comes partially from the disynaptic basin V(C5,C6) and from the V(C5,Ox) ones.Note that the location of this second monosynaptic basin corresponds to one of the carbon atoms participating in the formation of the second C4-C5 single bond.Furthermore, the monosynaptic basin V(C4) has increased its integration to reach 0.76e.

1 .
884 Å, while the distance between the C4 and the C5 carbons, which do not participate in the nucleophilic addition, is 3.151 Å.At intermediate IN1-13a, the length of the C1-C6 single bond is 1.602 Å, while the distance between the C4 and the C5 carbon remains at 3.012 Å.Finally, at TS2-13a, associated with the ring-closure, the distance between the C4 and C5 carbons is 2.377 Å.
of bonding changes along the A-DA reaction between BF 3 :imine complex 18 and ER ethylene 16.A topological characterization of the C-C bond formation in the Povarov reaction.

Table S1
2ust as the LA catalysed A-DA reaction model between imine 13a and ER ethylene 16 (see Scheme 7), the nucleophilic attack of MVE 23 on BF 3 :imine complex 27 has a low activation barrier, 5.1 kcal/mol from MC-26; formation of the zwitterionic intermediate INn-26 is exothermic by -12.8.The subsequent ring-closure via TS2n-26 has a unappreciable barrier, 0.8 kcal/mol.Formation of the formal [4+2] cycloadduct 28 ).Thus, the fast ring closure found in INn-26 does not allow to justify the formation of intermediate 12 as proposed by Whiting for the formation of product 11(see Scheme 4 in the main manuscript).2
Most P-DA reactions, taking place along high asynchronous TSs, are associated with two centre reactions characterised by the most favourable nucleophile-electrophile interaction.Although usually the most favourable reaction channel is that involving the formation of the new C-C bond in a gauche conformation, the anti approach mode yielding an anti intermediate is also feasible, requiring a further bond rotation to yield the formal [4+2] cycloadduct (see Scheme S3).
MPWB1K/6-311G** computed total energies, unique imaginary frequency, and cartesian coordinates in acetonitrile of the stationary points involved in the studied Povarov reactions.