Supplementary Material A Molecular Electron Density Theory study of [3+2] cycloaddition reactions of chiral azomethineylides with β-nitrostyrene Lilia Nasri a , Mar Ríos-Gutiérrez, b Abdelmalek Khorief Nacereddine a,c ,Abdelhafid Djerourou, a Luis R. Domingo b a Laboratoire de Synthèse et Biocatalyse Organique, Département de Chimie, Faculté des Sciences, Université Badji Mokhtar Annaba, BP 12, 23000 Annaba, Algeria. b Department of Organic Chemistry, University of Valencia, Dr. Moliner 50, E-46100 Burjassot, Valencia, Spain. c Département 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.
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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-bS6 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 backgroundS12 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.ReferencesS17 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.
S2
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···H6C
atoms is shown in Figure S3.
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 of both structures on the molecular plane defined by the O···H6C atoms. Bonding critical points (bcps) with bcp< 0 are coloured in blue, while bcps with bcp> 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,
bcp, with the increase of the kinetic energy electron density, Gbcp, the decrease of the potential
S4
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,bcp, 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, bcp(1) = 0.013 a.u.
and bcp(1) = 0.048 a.u., and that associated to bcp(2) at TSmn-b, bcp(2) = 0.016 and bcp(2)
= 0.060, presents similar values. The low values of bcp< 0.06 and the positive sign of
Laplacian 2bcp> 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 bcp
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 bcp, its Laplacian bcp and the total electron energy density Hbcp.
bcp bonding region cbcp bcp Hbcp
MCb (1) O···H6 0.013 0.048 0.00
1
TSmn-b (2) O···H6 0.01
6 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 C3H 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.
S5
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.
S6
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 CC
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 CC 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 CC 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
CC single bonds are shown in Figures S3and Figure 6of the manuscript, respectively.
At MCb, d(C1C5) = 2.929 Å and d(C3C4) = 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 C1N2 and N2C3 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 C4C5 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(C1C5) = 2.216 Å and d(C3C4) = 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
CC 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
S7
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(C1C5) = 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(C1C5) = 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 CC single bond formation,
demand an energy cost of 5.7 kcal·mol-1.
At P7, d(C1C5) = 2.141 Å and d(C3C4) = 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 CC single bonds, the GEDT has
slightly increased to 0.30e.
At P8, d(C1C5) = 2.019 Å and d(C3C4) = 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
S8
change indicates that the formation of the new C1C5 single bond begins at a C1C5 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 C1C5 single bond, the GEDT
reaches the maximum value along the reaction path, 0.34e.
At P9, d(C1C5) = 1.687 Å and d(C3C4) = 2.095 Å, the second most relevant
topological change along the reaction path takes place; likewise to what happens at P8, the
two V(C3) and V(C4) monosynaptic basins previously present have merged into a new
V(C3,C4) disynaptic basin integrating an initial population of 1.36e (see P9 in Figure S3).
This significant topological change indicates that the formation of the second C3C4 single
bond begins at a C3C4 distance of ca. 2.10 Å through the C-to-C coupling of two C3 and C4
pseudoradical centers. At P9, situated 27.1 kcal·mol-1 below the separated reagents, the
GEDT has decreased to 0.28e as the consequence of a retro-donation process from the NS
towards the AY moieties.
Finally, at 12n-b, d(C1C5) = 1.549 Å and d(C3C4) = 1.546 Å, the two V(C1,C5) and
V(C3,C4) disynaptic basins have reached populations of 1.87e and 1.88e, and the V(C1,N2),
V(N2,N3) and V(C4,C5) disynaptic basins integrate 1.68e, 1.77e and 1.97e. The presence of
two V(N2) and V’(N2) monosynaptic basins characterising the non-bonding N2 nitrogen lone
pair, with electron populations of 2.14e and 0.28e, which is indicative of a more or less planar
arrangement, is noteworthy. The great difference between the populations of both V(N2) and
V’(N2) monosynaptic basins accounts for an inexact planar configuration. At 12n-b, situated
61.8 kcal·mol-1 below the separated reagents, the GEDT is again very low, 0.07e.
Table S2. Valence basin populations calculated from the electron localisation function (ELF) of the stationary points MCb, TSmn-b and 12n-b, and the IRC points P7 – P9defining Phases VIII – X involved in the formation of the new C1C5 and C3C4 single bonds along the polar pdr-type 32CA reaction between AY 11b and NS 7. Distances are given in angstroms, Å, GEDT values and electron populations in average number of electrons, e, and relativea energies in kcal·mol-1.
a Relative to the separated reagents AY 11b and NS 7.
Figure S2. ELF attractor positions of TSmn-b and the points of the IRC defining Phases VII – IX involved in the formation of the new C1C5 and C3C4 single bonds along the polar pdr-
S10
type 32CA reaction between AY 11b and NS7. The electron populations, in e, are given in brackets.
S11
3. Theoretical background
Like many other chemical concepts, chemical bonds are defined in a rather ambiguous
manner as they are not observable, but rather belong to a representation of the matter at a
microscopic level, which is not fully consistent with quantum mechanical principles. To
harmonise the chemical description of matter with quantum chemical postulates, several
mathematical models have been developed. Among them, the theory of dynamical systems
[9], convincingly introduced by Bader through the QTAIM [2], has become a powerful
method of analysis. The QTAIM enables a partition of the electron density within the
molecular space into basins associated with atoms. Another appealing procedure that provides
a more straightforward connection between the electron density distribution and the chemical
structure is the quantum chemical analysis of the ELF of Becke and Edgecombe. [7] ELF
constitutes a useful relative measure of the electron pair localisation characterising the
corresponding electron density [10,11]. Finally, NCIs[1] have a unique fingerprint and their
presence can be revealed solely by means of electron density analysis. They are highly non-
local and manifest in real space as low-gradient isosurfaces with low densities.
3.1. ELF
Within the framework of Density Functional Theory (DFT)[12], ELF is a density-based
property that can be interpreted in terms of the positive-definite local Pauli and Thomas Fermi
kinetic energy densities in a given system. In the validity of such a framework, these
quantities provide key information to evaluate the relative local excess of kinetic energy
density associated to the Pauli principle. ELF presents values in the range [0,1][13]; the
highest values being associated with the spatial positions with higher relative electron
localisation [14-17]. After an analysis of the electron density, ELF provides basins of
attractors, which are the domains in which the probability of finding an electron pair is
maximal. The spatial points in which the gradient of ELF has a maximum value are
designated as attractors [18]. ELF basins are classified as core basins, C(...), and valence
basins, V(...). The latter are characterised 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 [16]. Monosynaptic basins, labelled V(A), correspond to the lone pairs or
non-bonding regions, while disynaptic basins, labelled V(A,B), connect the core of two nuclei
A and B and, thus, correspond to a bonding region between A and B. This description
S12
recovers the Lewis bonding model, providing a very suggestive graphical representation of
the molecular system.
3.2. BET
When trying to achieve a better understanding of bonding changes in organic chemical
reactions, the so-called Bonding Evolution Theory (BET) has proved to be a very useful
methodological tool [19]. BET applies Thom’s Catastrophe Theory (CT) concepts [20-22] to
the topological analysis of the gradient field of the ELF.
Within the BET methodology [19], the structural stability of the critical points of the
ELF gradient field is examined for the system of nuclei and electrons ‘evolving’ along the
Born-Oppenheimer energy hypersurface or a given reduced reaction coordinate, e.g. the
intrinsic reaction coordinate, occurring as a result of the variation in the control space
parameters from reactive to product configurations. The chemical process becomes thus
rationalised in terms of successive structural stability domains (SSDs), also called phases,
comprising structures along the path where the number and type, e.g. synaptic orders, of
critical points of the gradient field of ELF remain without changes [19].
Within the BET context, the turning points between these phases are located and the
discontinuities or bifurcation catastrophes can be identified. BET allows, thus, characterising
unequivocally the behaviour of the dynamical system upon bifurcations associated with the
ELF gradient field changing along the reaction coordinate. The different catastrophes in this
case correspond to the reduction or the increase of the critical points associated with attractors
of electron pairs defining bonding and non-bonding, e.g. lone pairs, domains for electron
(de)localisation.
A detailed examination of the topology of ELF along the IRC pathway for a given
reaction reveals the existence of several catastrophes belonging exclusively to the fold, F and
F†, and cusp, C and C†, elementary types, according to Thom’s classification. The F
catastrophe merges an attractor and a saddle point into a wandering point, i.e. a non-critical
point, decreasing the number of basins by 1, whereas F† splits a wandering point into an
attractor and a saddle point increasing the number of basins by 1. The † superscript is used in
those catastrophes in which either the number of attractors or the synaptic order increase. The
cusp catastrophe C merges two attractors and a saddle point into an attractor decreasing the
number of basins by 1, while C† splits an attractor into two attractors and a saddle point
increasing the number of basins by 1. The symbol of a catastrophe written in bold is used to
S13
mark a catastrophe leading to the formation of the first covalent bond. The analysis of the
changes in the number and type of ELF valence basins for the structures involved along the
IRC of the reaction allows establishing a set of points, Pi, separating the different phases that
characterise the studied molecular mechanism.
Several theoretical studies have shown that the topological analysis of the ELF offers a
suitable framework for the study of the changes of electron density.[23-29] This
methodological approach is used as a valuable tool to understand the bonding changes along
the reaction path and, consequently, to establish the nature of the electronic rearrangement
associated with a given molecular mechanism within the BET perspective.
3.3. QTAIM
QTAIM analysis of the electron density provides a series of critical points (cps),
which are points of the molecular space where (r) = 0.[2] The presence of a (3,-1) cp
appears to provide the boundaries between the basins of neighbouring atoms, being called a
bonding cp (bcp). Thus, the existence of a (3,-1) bcp and its associated atomic interaction line
indicates that electron density is accumulated between the nuclei linked in such a manner. The
Laplacian of the electron density in a cp, bcp, is a very appealing property that determines
where bcp is locally concentrated, bcp< 0, and locally depleted,bcp> 0. Thus, the sign of
bcp determines which of these two competing effects is dominant, allowing the
characterisation of (3,-1) bcps associated with covalent bonds, bcp< 0 and high bcp values,
and those associated with ionic bonds or weak non-covalent interactions such as hydrogen
bonds or van der Waals interactions, bcp> 0 and low bcp values.
3.4. NCIs
The sign of the Laplacian of the density, , is a widely used tool to distinguish
between different types of strong interactions.[1] To analyse bonding in more detail, the
Laplacian is often decomposed into a sum of contributions. These components are the three
eigenvalues λi of the electron density Hessian matrix, such that = λ1 + λ2 + λ3. Analysis of
these components has been widely applied to chemical bonding. The sign of λ2can be used to
distinguish bonding (λ2< 0) from non-bonding (λ2> 0) interactions.
The gradient isosurfaces provide a useful visualisation of NCIs as broad regions of real
space, rather than simple pairwise contacts between atoms, and are coloured according to the
corresponding values of sign(λ2). Analysis of the sign of λ2 thus helps to differentiate
S14
between different types of NCIs, whereas the density itself provides information about their
strength. Surfaces with very low density values (< |0.005| a.u.) generally represent weaker
dispersion interactions, while surfaces with slightly higher density values (|0.005| << |0.05|
a.u.) represent stronger NCIs, including both attractive HBs and steric clashes. On the other
hand, large negative values of sign(λ2) are indicative of strong attractive interactions and are
coloured in blue, while if the sign(λ2) is large and positive, the interactions are non-bonding
and are coloured in red; values near zero indicate weak Van der Waals interactions, and are
coloured in green.
S15
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Table S3.Gas phaseMPWB1K/6-31G(d) and MPWB1K/6-311G(d,p)//MPWB1K/6-31G(d) total (E, in au) and relativea (E, in kcal·mol-1) energies of the stationary points involved in the anti diastereoisomeric pathways associated with the 32CA reaction of AY 11b with NS 7.
a Relative to the separated reagents AY 11b and NS 7.
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Table S4. MPWB1K/6-31G(d) enthalpies (H, in a.u), entropies (S, cal·mol−1·K−1) and Gibbs free energies (G, in a.u.), and relativea enthalpies (H, in kcal·mol−1), entropies (S, cal·mol−1·K−1) and Gibbs free energies (G, in kcal·mol−1), 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.
a Relative to the separated reagents AY 11b and NS 7.
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Table S5. MPWB1K/6-31G(d) total (E, in au) and relativea (E, in kcal·mol-1) energies of the stationary points involved in the meta/anti pathways of the 32CA reaction of AY 11a with NS 7.
a Relative to the separated reagents AY 11b and NS 7.
S20
Table S6. MPWB1K/6-31G(d) enthalpies (H, in a.u), entropies (S, cal·mol−1·K−1) and Gibbs free energies (G, in a.u.), and relativea enthalpies (H, in kcal·mol−1), entropies (S, cal·mol−1·K−1) and Gibbs free energies (G, in kcal·mol−1), 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 NS7.
Structure H H S S G G11a -767.581023 149.9 -767.6725277 -513.745913 106.1 -513.810683MCa -1281.341005 -8.8 204.7 -51.2 -1281.465991 10.8TSmn-a -1281.334391 -4.7 201.9 -54.0 -1281.457679 16.0TSmx-a -1281.329324 -1.5 198.1 -57.8 -1281.450292 20.712n-a -1281.418162 -57.2 200.6 -55.4 -1281.540638 -36.012x-a -1281.410617 -52.5 201.9 -54.1 -1281.533880 -31.8a Relative to the separated reagents AY 11b and NS 7.
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Table S7. Valence basin populations calculated from the electron localisation function (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. The stationary points MCb, TSmn-b and 12n-b are also included. Distances are given in Å, GEDT values and electron populations in average number of electrons, e, and relativea energies in kcal·mol-1.
a Relative to the separated reagents AY 11b and NS7.
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S23
MPWB1K/6-31G(d) computed electronic 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.