S26
Supplementary Material
A Molecular Electron Density Theory study of [3+2] cycloaddition reactions of chiral azomethineylides with β-nitrostyrene
Lilia Nasria, Mar Ríos-Gutiérrez, bAbdelmalek Khorief Nacereddine a,c,Abdelhafid Djerourou,a Luis R. Domingob
aLaboratoire de Synthèse et Biocatalyse Organique, Département de Chimie, Faculté des Sciences, Université Badji Mokhtar Annaba, BP 12, 23000 Annaba, Algeria.
bDepartment of Organic Chemistry, University of Valencia, Dr. Moliner 50, E-46100 Burjassot, Valencia, Spain.
cDépartement de Physique et Chimie, Ecole Normale Supérieure d’Enseignement Technologique de Skikda, Azzaba, Skikda, Algeria
Index
S2 1. Analysis of the strong stabilities of MCb and TSmn-b
S6 2. ELF topological analysis of the formation of the new C-C single bonds along the most favourable meta/endo/anti reaction channel of the 32CA reaction involving methyl-substituted AY 11b.
S11 3. Theoretical background
S12 3.1.Topological analysis of the electron localisation function (ELF)
S13 3.2. Bonding Evolution Theory (BET)
S14 3.4. Quantum Theory of Atoms in Molecules (QTAIM)
S14 3.3. Non-Covalent interactions (NCIs)
S15 4.References
S17 Table S3. Gas phase MPWB1K/6-31G(d) and MPWB1K/6-311G(d,p)//MPWB1K/6-31G(d) total and relative energies of the stationary points involved in the anti diastereoisomeric pathways associated with the 32CA reaction of AY 11b with NS 7.
S18 Table S4. MPWB1K/6-31G(d) thermodynamic data computed at 110 ºC and 1 atm in toluene of the stationary points involved in the antidiastereoisomeric pathways associated with the 32CA reaction between AY 11b and NS 7.
S19 Table S5. MPWB1K/6-31G(d) total and relative energies of the stationary points involved in the meta/anti pathways of the 32CA reaction of AY 11a with NS 7.
S20 Table S6. MPWB1K/6-31G(d) thermodynamic data computed at computed at 110 ºC and 1 atm in toluene of the stationary points involved in the meta/anti pathways of the 32CA reaction between AY 11a and NS 7.
S21 Table S7. Valence basin populations calculated from the ELF of the intrinsic reaction coordinate (IRC) points, P1 – P10, defining the eleven phases characterising the molecular mechanism of the polar pdr-type 32CA reaction between AY 11b and NS7.
S22 MPWB1K/6-31G(d) computed total energies and Cartesian coordinates in gas phase of the structures involved in the anti diastereoisomeric pathways associated with the 32CA reaction of AY 11b with NS 7, and in the meta/anti pathways of the 32CA reaction of AY 11a with NS 7.
1. Analysis of the strong stabilities of MCb and TSmn-b.
The very low relative energies of MCband TSmn-b suggest that some type of electrostatic or non-covalent interactions may be strongly stabilising both structures. The analysis of the geometries of MCb and TSmn-b shows that one oxygen atom of the nitro group of NS 7 is oriented towards the AY H6 hydrogen atom, due to the acidic character of the latter. The O···H6 distances are 2.37 at MCb and 2.25Å and TSmn-b, respectively. These short distances suggest the formation of an HB between these atoms, which might justify the strong stabilisation of MCb and TSmn-b.
In order to confirm the presence of an O···H6 HB in these species, a topological analysis of the favourable Non-Covalent Interactions (NCIs)[1] taking place at MCb and TSmn-b was performed. Bonding NCI gradient isosurfaces are shown in Figure S1, while thereduced density gradients are represented in Figure S2. The topological analysis of the favourable NCIs at MCb and TSmn-b shows the presence of several small and green surfaces between the two AY and NS frameworks, associated with weak, favourable non-covalent interactions such as Van der Waals interactions or HBs. Particularly noteworthy is the small circular surface observed between one of the oxygen atoms of the nitro group of the NS fragment and the acidic H6 hydrogen of the AY moiety, confirming the existence of a weak O···H6 HB at both MCb and TSmn-b.
In order to verify the low strengh of these HBs, a Quantum Theory of Atoms in Molecules (QTAIM)[2]topological analysis of the electron density in the O···H6 region at MCb and TSmn-b was carried out. The QTAIM parameters of the critical points (cps) found in the O···H6 regions are presented in Table S1, while the representation of the contour line maps of the Laplacian of the electron density on the molecular plane defined by the O···H6-C atoms is shown in Figure S3.
Figure S1. Favourable NCI gradient isosurfacesof MCb and TSmn-b, represented at an isovalue of 0.5 a.u., together with the representation of the contour line maps of the Laplacian of the electron density Ñ2r of both structures on the molecular plane defined by the O···H6-C atoms. Bonding critical points (bcps) with Ñ2rbcp< 0 are coloured in blue, while bcps with Ñ2rbcp> 0 are coloured in red.
Figure S2.Plots of the reduced density gradient (RDG) versus the electron density multiplied by the sign of the second Hessian eigenvalue for MCb and TSmn-b. Both quantities are given in a.u.
Numerous studies encountered that the strength of interaction, particularly of HBs, is expressed by the characteristics of the H···X bonding critical point (bcp).[3] The increase of the strength of HBs is associated with the increase of the electron density at the H···X bcp, rbcp, with the increase of the kinetic energy electron density, Gbcp, the decrease of the potential energy (the increase of its modulus), Vbcp,and the decrease of the total electron energy density, Hbcp, at the bcp.[4] The relation between the strength of interaction, and particularly, the H···X distance, and the Laplacian, Ñ2rbcp, is more complicated; starting from the weakest HB, the positive value of the Laplacian increases with the augmentation of the strength of interaction. However, for very strong hydrogen bonds, it decreases and is even negative.[5]
Table S1shows that the electron density associated to bcp(1) at MCb, rbcp(1) = 0.013 a.u. and Ñ2rbcp(1) = 0.048 a.u., and that associated to bcp(2) at TSmn-b, rbcp(2) = 0.016 and Ñ2rbcp(2) = 0.060, presents similar values. The low values of rbcp< 0.06 and the positive sign of Laplacian Ñ2rbcp> 0 indicate that these (3,-1) bcps are associated with weak O···H6 HBs, in agreement with the NCI topological analysis. Note that for some of the weakest HBs rbcp values ≤ 0.03 a.u. and Hbcp values very close to 0 were found,[6] such as those reported for MCb and TSmn-b.
Table S1. QTAIM parameters, in a.u., of the (3,-1) bcps present in the O···H6 regions in MCb and TSmn-b, namely, the electron density rbcp, its Laplacian Ñ2rbcp and the total electron energy density Hbcp.
bcp / bonding region / rcbcp / Ñ2rbcp / HbcpMCb / (1) / O···H6 / 0.013 / 0.048 / 0.001
TSmn-b / (2) / O···H6 / 0.016 / 0.060 / 0.001
Given the weakness of the O···H6 HBs, feasible electrostatic interactions, such as dipole-dipole interactions and local electrostatic interactions, were further analysed in order to explain the strong stabilities of MCb and TSmn-b. On the one hand, the total dipole moments are 5.09 D at AY11b, 5.77 D at NS 7, 3.85 D atMCb and 5.21 D at TSmn-b. As the total dipole moment of MCb is smaller than that of any of the two separated reagents, it can be concludedthat some dipolar interactions stabilising MCb are also feasible. On the other hand, the MEP of MCb given in Figure 5 of the manuscriptshows a favourable electrostatic interaction between the nitro group of NS 7, negatively charged, and the C3-H and H6 hydrogen atoms of AY 11b, positively charged. The fact that these interactions are also present at TSmn-a andTSmx-a (seeSection 3.3.3 of the manuscript) suggests that they are also maintained along the reaction towards the corresponding TSmn-b.
In summary, the strong stabilisation of both MCb and TSmn-b arises from a series of favourable non-covalent (HBs) and electrostatic (dipolar and potential) interactions, confirming that they are responsible for the feasibility of the polar pdr-type 32CA reactions between AYs 11a,b and NS 7, rather than the polar character of the reaction.
2. Electron Localisation function (ELF)topological analysis of the formation of the new C-C single bonds along the most favourable meta/endo/anti reaction channel of the 32CA reaction involving methyl-substituted AY 11b.
In order to confirm the pdr-type reactivity of AYs 11a,b and to understand the C-C single bond formation processes along the polar 32CA reactions of AYs 11a,b with NS 7, an ELF [7] topological analysis of the stationary points as well as of the most relevant points implied in the formation of the new C-C single bonds along the IRC associated with the most favourable meta/endo/anti reaction channel of the 32CA reaction involving methyl-substituted AY 11b, is carried out. A BET procedure was used for the selection of the mentioned points (those defining the phases in which the bond formation takes place and those defining the previous ones). The populations, among other relevant parameters, of the most significant valence basins (those associated with the bonding regions directly involved in the reaction) of the selected points of the IRC, Pi, defining the different topological phases are included in Table S7, while those of the stationary points and the points involved in the formation of the new C-C single bonds are displayed in Table S2. Additionally, the ELF attractor positions as well as ELF localisation domains of the TS and the points involved in formation of the new C-C single bonds are shown in Figures S3and Figure 6of the manuscript, respectively.
At MCb, d(C1-C5) = 2.929 Å and d(C3-C4) = 3.091 Å, the ELF topological characteristics of the separated reagents, AY 11b and NS 7, are maintained (see Section 3.1 of the manuscript and Table S2). The three V(C1), V(C3) and V’(C3) monosynaptic basins present at AY 11b, which are related to the two C1 and C3 pseudoradicalcenters that allow establishing its pseudodiradical structure,[8] are also observed at the AY framework of MCb integrating 0.63e, 0.31e and 0.23e, respectively. The two V(C1,N2) and V(N2,C3) disynaptic basins associated with the two C1-N2 and N2-C3 bonding regions have populations of 2.45e and 3.00e, while the two V(C4,C5) and V’(C4,C5) disynaptic basins present in the NS moiety with a total electron population of 3.52e are related to the C4-C5 double bond of NS 7. At MCb, stabilised by 12.0 kcal·mol-1 with respect to the separated reagents, the GEDT is negligible, 0.04e.
At TSmn-b, d(C1-C5) = 2.216 Å and d(C3-C4) = 2.524 Å, one of the two monosynaptic basins associated with the C3 pseudoradicalcenter, the V’(C3) one, which is situated on the syn face of the AY fragment, has disappeared. This topological change is the consequence of the loss of the planar C3 environment, which is a change demanded for the C-C bond formation. Note, however, that the corresponding total population has also decreased by ca. a half to 0.30e. This lost electron density has been redistributed into the adjacent V(N2,C3) disynaptic basin, whose population has increased to 3.50e. Otherwise, together with the decrease of the population of the V(C1,N2) disynaptic basin to 2.28e, the V(C1) monosynaptic basin has doubled its population to 0.62e. However, it should be emphasised that coming from MCb to TSmn-b, this monosynaptic basin disappeared at d(C1-C5) = 2.673 Å as a consequence of the delocalisaton of its associated electron density into the adjacent bonding region of the imidazolidine ring, and then again appeared at d(C1-C5) = 2.562 Å. In addition, at TSmn-b, the two V(C4,C5) and V’(C4,C5) disynaptic basins present at the NS moiety have merged into a new V(C4,C5) disynaptic basin integrating only 0.02e less than at MCb. The GEDT at TSmn-b, situated 6.3 kcal·mol-1 below the separated reagents, is 0.27e (see Section 3.3.1 of the manuscript), a high value that allows establishing the strong polar character of this pdr-type 32CA reaction.
The changes in electron density taking place coming from MCb to TSmn-b, which can be mainly associated to the depopulation of the C3 pseudoradicalcenter as well as the loss of the planar sp2 hybridisation of the C3 carbon required for the C-C single bond formation, demand an energy cost of 5.7 kcal·mol-1.
At P7, d(C1-C5) = 2.141 Å and d(C3-C4) = 2.487 Å, two new V(C4) and V(C5) monosynaptic basins, integrating 0.38e and 0.20e, are observed at the NS framework. The electron density of these monosynaptic basins, which correspond to two C4 and C5 pseudoradicalcenters, mainly proceeds from the depopulation of the V(C4,C5) disynaptic basin to 2.96e. The other two V(C1) and V(C3) monosynaptic basins have maintained their populations. Note that the four V(C1), V(C2), V(C3) and V(C4) monosynaptic basins demanded for the formation of the new V(C,C) disynaptic basins are simultaneously present at this point (see P7 in Figure S3). Another noticeable topological change at P7 is the presence of a new V(N2) monosynaptic basin, integrating 0.69e, while the population of the V(N2,C3) disynaptic basin has decreased to 2.79e. This V(N2) monosynaptic basin is associated with an N2 pseudoradical center that will further become a non-bonding N2 nitrogen lone pair at the final pyrrolo imidazole12n-b. At P7, situated 6.6 kcal·mol-1 below the separated reagents, prior to the formation of the new C-C single bonds, the GEDT has slightly increased to 0.30e.
At P8, d(C1-C5) = 2.019 Å and d(C3-C4) = 2.414 Å, the first most relevant topological change along the reaction path takes place; the two V(C1) and V(C5) monosynaptic basins present at the previous point P7 have merged into a new V(C1,C5) disynaptic basin integrating an initial population of 1.19e (see P8 in Figure S3). This relevant topological change indicates that the formation of the new C1-C5 single bond begins at a C1-C5 distance of ca. 2.02 Å through the C-to-C coupling of two C1 and C5 pseudoradicalcenters. Note that the C1 and C5 carbons correspond to the most nucleophilic and electrophilic centers of AY 11b and NS 7, respectively.At the same time, together with the depopulation of the V(C4,C5) disynaptic basin to 2.69e, the population of the V(C4) monosynaptic basin of the NS fragment has increased to 0.52e, while that of the V(C3) monosynaptic basin still remains invariable. Note that the population of this V(C3) monosynaptic basin has remained practically unchanged along the reaction path (see Table S7). At P8, situated 8.5 kcal·mol-1 below the separated reagents, together with the formation of the first C1-C5 single bond, the GEDT reaches the maximum value along the reaction path, 0.34e.