Origin of the Felkin–Anh(–Eisenstein) model: a quantitative rationalization of a seminal concept

Abstract

Quantum chemical calculations were carried out to quantitatively understand the origin of the Felkin–Anh(–Eisenstein) model, widely used to rationalize the π-facial stereoselectivity in the nucleophilic addition reaction to carbonyl groups directly attached to a stereogenic center. To this end, the possible approaches of cyanide to both (S)-2-phenylpropanal and (S)-3-phenylbutan-2-one have been explored in detail. With the help of the activation strain model of reactivity and the energy decomposition analysis method, it is found that the preference for the Felkin–Anh addition is mainly dictated by steric factors which manifest in a less destabilizing strain-energy rather than, as traditionally considered, in a lower Pauli repulsion. In addition, other factors such as the more favorable electrostatic interactions also contribute to the preferred approach of the nucleophile. Our work, therefore, provides a different, more complete rationalization, based on quantitative analyses, of the origin of this seminal and highly useful concept in organic chemistry.

Full text

Origin of the Felkin–Anh(–Eisenstein) model:
a quantitative rationalization of a seminal concept†
Daniel Gonz´
alez-Pinardo,
a
F. Matthias Bickelhaupt
bcd
and Israel Fern´
andez *
a
Quantum chemical calculations were carried out to quantitatively understand the origin of the Felkin–
Anh(–Eisenstein) model, widely used to rationalize the p-facial stereoselectivity in the nucleophilic
addition reaction to carbonyl groups directly attached to a stereogenic center. To this end, the possible
approaches of cyanide to both (S)-2-phenylpropanal and (S)-3-phenylbutan-2-one have been explored
in detail. With the help of the activation strain model of reactivity and the energy decomposition analysis
method, it is found that the preference for the Felkin–Anh addition is mainly dictated by steric factors
which manifest in a less destabilizing strain-energy rather than, as traditionally considered, in a lower
Pauli repulsion. In addition, other factors such as the more favorable electrostatic interactions also
contribute to the preferred approach of the nucleophile. Our work, therefore, provides a different, more
complete rationalization, based on quantitative analyses, of the origin of this seminal and highly useful
concept in organic chemistry.
Introduction
The rationalization and prediction of the p-facial stereo-
selectivity in the nucleophilic addition reaction to a carbonyl
group (typically aldehydes and ketones) directly attached to
a stereogenic center has been (and still is) essential in organic
synthesis. To this end, during the 1950s and 60s, various
empirical models were introduced, basically differing in the
orientation of the substituents at the a-chiral carbon with
respect to the carbonyl group as the nucleophile approaches,
i.e., the conformation adopted by the carbonyl reactant. Among
them, the Felkin model,
1
introduced aer the work of Cram,
2
Cornforth,
3
and Karabatsos,
4
is nowadays generally accepted, in
particular, when steric effects become signicant. This model,
which was later supported and modied by the pioneering
calculations of Anh and Eisenstein,
5,6
mainly involves that the a-
carbon adopts a staggered conformation where its ‘large’(L)
group is oriented perpendicular to the carbonyl bond. This
places the ‘medium’(M) group at ca. 30° to the carbonyl bond so
that the incoming nucleophile passes close to the ‘small’(S)
group following a Bürgi–Dunitz (BD) trajectory
7
(Fig. 1).
Although the Felkin–Anh(–Eisenstein) (FA) model continues
to be widely used
8
and presented in most organic chemistry
textbooks,
9
it does not always provide accurate predictions. In
particular, when a metal ion binds to both the nucleophile and
the carbonyl oxygen atom, the so-called Cram's chelation model
is preferred. For this reason, alternatives to the FA model have
been proposed,
10
although they have not been generally
accepted.
11
Despite its limitations,
12
the FA model's core
concept –that the addition pathway with the least steric
hindrance leads to the major diastereomer (approach shown in
black in Fig. 1) –remains valuable.
Fig. 1 Schematic illustration of the Felkin–Anh(–Eisenstein), Cram–
Cornforth and Karabatsos models of the stereochemical course of
nucleophilic addition to a carbonyl group next to a stereogenic center.
a
Departamento de Qu´
ımica Org´
anica, Centro de Innovaci´
on en Qu´
ımica Avanzada
(ORFEO-CINQA), Facultad de Ciencias Qu´
ımicas, Universidad Complutense de
Madrid, Ciudad Universitaria, 28040-Madrid, Spain. E-mail: israel@quim.ucm.es
b
Department of Chemistry and Pharmaceutical Sciences, AIMMS, Vrije Universiteit
Amsterdam, The Netherlands
c
Institute for Molecules and Materials (IMM), Radboud University, Nijmegen, The
Netherlands
d
Department of Chemical Sciences, University of Johannesburg, South Africa
†Electronic supplementary information (ESI) available: Fig. S1–S3, Cartesian
coordinates and energies of all the species discussed in the text. See DOI:
https://doi.org/10.1039/d4sc03176h
Cite this: Chem. Sci.,2024,15,12380
All publication charges for this article
have been paid for by the Royal Society
of Chemistry
Received 15th May 2024
Accepted 7th July 2024
DOI: 10.1039/d4sc03176h
rsc.li/chemical-science
12380 |Chem. Sci.,2024,15,12380–12387 © 2024 The Author(s). Published by the Royal Society of Chemistry
Chemical
Science
EDGE ARTICLE

The FA model, therefore, implies that Pauli repulsion
between the nucleophile and the carbonyl reactant constitutes
the main factor controlling the p-facial stereoselectivity of the
nucleophilic addition. However, this explanation has never
been quantitatively veried accurately and, therefore, the actual
origin of the FA behavior remains unknown. Steric (Pauli)
repulsion was also traditionally used to explain the origin of the
Bürgi–Dunitz (BD) angle adopted by the nucleophile.
7
However,
we recently found, by applying the Activation Strain Model
(ASM)
13
and energy decomposition analysis (EDA) method,
14
that the obtuse BD angle originates from not only a reduced
Pauli repulsion between the reactants but also from a more
stabilizing HOMO(nucleophile)–p*(C]O) molecular orbital
interaction as well as a more favorable electrostatic attrac-
tions.
15
We also found that the latter factor (i.e. electrostatic
interactions), and not Pauli repulsion, is decisive in dening the
intrinsic electrophilicity of carbonyl groups.
16
The importance
of our results, which provide a complementary rationalization
to the widely accepted textbook explanations, has been very
recently highlighted by Eisenstein: “.These recent studies
demonstrate the importance of quantitative analysis tools to
determine the relative importance of the attractive and repulsive
interactions. This enriches and quanties the earlier qualitative
analyses.”
17
Indeed, in a different context, our ASM-EDA
approach has been key to unraveling that the catalysis of
various fundamental transformations, such as Diels–Alder,
Michael additions or Alder-ene reactions, is not, as widely
accepted, caused by enhancing frontier molecular orbital (FMO)
interactions (i.e.,“LUMO-lowering catalysis”) but by a signi-
cant reduction in the Pauli repulsion between key occupied
molecular orbitals of the reactants (i.e.,“Pauli repulsion-
lowering catalysis”).
18,19
Herein, we apply our ASM-EDA approach to identify the so
far not fully understood mechanism behind the FA model and
quantify the importance and role of the various physical factors
controlling the p-facial stereoselectivity in the nucleophilic
addition reaction to carbonyl groups.
Results and discussion
We rst explored the addition of cyanide (CN
−
)to(S)-2-phe-
nylpropanal (L =Ph, M =Me and S =H). This particular
nucleophile was selected because it is a potent nucleophile (N=
16.27 on Mayr's scale)
20
and mainly because its contribution to
the total strain is practically negligible. The 2-dimensional
potential energy surface (2D PES) associated with the addition
of cyanide to the aldehyde was extensively explored at the ZORA-
M06-2X/TZ2P//M06-2X/6-311+G(d) level for any possible route of
approach of the nucleophile leading to the syn (experimentally
preferred) and anti diastereoisomers (see Fig. 2). This 2D PES
was constructed from two principal geometrical descriptors,
namely the NC/C(]O) bond-forming distance, ranging from
the separate reactants (rim of circle) up to the corresponding
transition states (close to center of circle) and the OCCCPh
dihedral angle in the aldehyde (494 structures computed for
each reaction product); we use a color code to indicate energy
values relative to the initially formed reactant complex which
lies −8.3 kcal mol
−1
below the separate CN
−
and the most
stable conformation of (S)-2-phenylpropanal (for the corre-
sponding conformational study, see Fig. S1 in the ESI†).
Our data show that the preferred approach is syn (Fig. 2, le),
and that along this syn approach, the most favorable path
coincides with the FA prediction, i.e. the nucleophile passes
close to the small group, following a BD trajectory (computed
O]C/C(N) angle of 112°), and the large substituent is placed
perpendicular to the carbonyl group. Not surprisingly, the
opposite approach, i.e. the nucleophile passing close to the
large group, is strongly disfavored. In addition, the Cornforth
approach (CF, dihedral angle of ca. 180°), which has also been
used to explain the syn-selectivity,
3
is also disfavored over the FA
approximation (DDG
s
=2.4 kcal mol
−1
, at the highly accurate
DLPNO-CCSD(T)/def2-TZVPP//M06-2X-6-311+G(d) level). For
the anti-approach (Fig. 2, right), we found that the expected
anti-FA approach is not the most favorable approximation
(DDG
s
=2.7 kcal mol
−1
with respect to the syn-FA attack) but
the anti-CF addition (DDG
s
=1.1 kcal mol
−1
with respect to the
syn-FA attack). Gratifyingly, this barrier difference between the
FA and anti-CF attacks can be translated into an 86 :14 syn/anti
ratio, matching that observed experimentally in the strongly
related phenylacetylide addition to (S)-2-phenylpropanal (84 :
16)
21
for which a 85 : 15 ratio was computed.
Now that the main features of PES have been explored, we
quantitatively analyze the physical factors behind the prefer-
ence for the FA addition over the alternative approaches of the
nucleophile. First, we compare the FA-pathway with the most
representative alternative additions, namely that for the syn-
approach where the nucleophile passes close to the large group
(FA-hindered) and the two more favorable (albeit unpreferred)
anti-additions, i.e.,anti-FA and anti-CF. To this end, we applied
the Activation Strain Model (ASM) of reactivity,
13
a method that
decomposes the total electronic energy (DE) into two terms: the
strain energy (DE
strain
) that results from the deformation of the
individual reactants and the interaction (DE
int
) between the
increasingly deformed reactants along the reaction coordinate,
dened in this particular case by the NC/C(]O) bond-forming
distance. As commented above, the computed total strain
derives almost exclusively from the deformation of the aldehyde
reactant, as the structure of the cyanide reactant hardly changes
during the transformation. Fig. 3 shows the corresponding
activation strain diagrams (ASDs) for the selected approaches of
the nucleophile from the initial stages of the reaction up to the
corresponding transition states. As readily seen in this gure,
the lower barrier computed for the FA approach (leading to the
preferential formation of the syn-isomer) as compared to the
anti-FA or anti-CF approaches is not at all due to the interaction
energy between the deformed reactants, as the DE
int
term is
rather similar in all cases (and even slightly more stabilizing for
the anti-CF attack). Instead, the sole factor favoring the syn-FA
approach is the strain energy, DE
strain
, which is the least
destabilizing for this pathway along the entire reaction coordi-
nate. This nding, therefore, suggests that the syn/anti selec-
tivity of the nucleophilic addition nds its origin exclusively in
the lower strain required for the FA approach. The strain energy
also plays a key role in dening the preferred addition
© 2024 The Author(s). Published by the Royal Society of Chemistry Chem. Sci.,2024,15,12380–12387 | 12381
Edge Article Chemical Science

approach. Thus, when comparing the unhindered, FA attack
with the FA-hindered approach, it becomes evident that the
latter approximation (where the nucleophile passes close to the
large L group) exhibits a much higher destabilizing strain
energy. In other words, in the FA-hindered approach (and also
in anti-approaches, albeit to a lower extent), the aldehyde must
deform considerably to avoid a signicant increase in the
destabilizing Pauli (steric) repulsion (see below). In addition,
the FA approach also benets from a much more stabilizing
interaction between the reactants as compared to the FA-
hindered attack, once again along the entire reaction coordi-
nate. Therefore, the combined action of a lower strain and
a stronger interaction denes the preferred approach of the
nucleophile in the preferred-syn pathway (i.e., the nucleophile
passing close to the small S group), which suggests that the FA
model cannot be solely rationalized in terms of direct steric
repulsion but rather involves a geometrical adaptation of the
reactant to avoid such a repulsion.
Results above therefore indicate that the extent of the
deformation required by the chiral aldehyde to adopt the
geometry of the corresponding transition state plays a key role
in dening the approximation of the nucleophile to the
carbonyl group. To ensure that this nding is not biased by the
representative approaches selected previously, we analyzed the
relative contribution of both the strain and interaction energies
along the entire 2D-PES explored above. For the syn-approach
(Fig. 4, le), it becomes clear that the FA-hindered region
exhibits both a rather high strain energy and the weakest
interaction between the deformed reactants. At variance, the FA-
region benets from the least destabilizing DE
strain
and much
stronger interaction. There exists a region where the dihedral
angle ranges between 30–60° which exhibits also a strong
interaction; however, this approach is not favored once again
because it requires a higher strain than the preferred FA-addi-
tion. Regarding the anti-pathway, data in Fig. 4 (right) conrm
that the anti-CF region (dihedral angle of ca. 180°) benets from
a comparatively lower strain (albeit higher than that computed
for the FA-approach) along with a stronger interaction as
compared to the anti-FA addition. Therefore, it can be
concluded that (i) the syn/anti selectivity of the nucleophilic
addition nds its origin exclusively in the lower strain energy
required for the FA approach as a consequence of a lower steric
hindrance, and (ii) the nucleophile passes close to the small
group to avoid a signicant increase of the Pauli (steric) repul-
sion which, in turn, leads to a stronger interaction between the
reactants along the transformation.
Fig. 2 Possible cyanide additions to (S)-2-phenylpropanal leading to the corresponding syn (left) and anti (right) reaction products. C/C bond-
forming distances vary from 2.1 Å in the center of the circle (i.e., transition state region) to 2.8 Å on the outer rim of the circle (i.e., separate
reactants region). Energy values refer to electronic energies. All data were calculated at the ZORA-M06-2X/TZ2P//M06-2X-6-311+G(d) level.
Fig. 3 Comparative activation strain diagrams for the addition of
cyanide to (S)-2-phenylpropanal following the FA (black), FA-hindered
(red), anti-FA (blue) and anti-CF (green) approaches projected onto
the C/C(]O) bond-forming distance. All data were computed at the
ZORA-M06-2X/TZ2P//M06-2X-6-311+G(d) level.
12382 |Chem. Sci.,2024,15,12380–12387 © 2024 The Author(s). Published by the Royal Society of Chemistry
Chemical Science Edge Article

The reasons behind the stronger interaction computed for
the FA approach as compared to the FA-hindered deserve
further analysis. To this end, we applied the Energy Decompo-
sition Analysis (EDA) method,
14
which involves decomposing
the total interaction energy (DE
int
) between the deformed reac-
tants into three physically meaningful energy terms, namely the
classical electrostatic interaction (DV
elstat
), the Pauli repulsion
(DE
Pauli
) arising from the repulsion between occupied closed-
shell orbitals of both deformed reactants, and the orbital
interaction (DE
orb
) that accounts for charge transfer and
polarization. Fig. 5 graphically shows the evolution of the EDA
terms along the reaction coordinate (from the beginning of the
processes up to the corresponding transition states) for the
extreme situations represented by the (unhindered)-FA and the
FA-hindered approaches. It is expected that the hindered
approach should exhibit a signicantly higher (i.e. more
destabilizing) Pauli repulsion. However, our EDA calculations
indicate that, although the FA-hindered addition indeed pres-
ents a more destabilizing Pauli repulsion (particularly at the
transition state) region, this term is not the main factor behind
the lower barrier computed for the FA approach. The reason for
this unexpectedly low steric Pauli repulsion for the sterically
more hindered pathway is not the absence of steric factors.
Rather, what happens is that the carbonyl-containing reactant
deforms in reaction to the steric clash and, in this way, allevi-
ates much of the enhanced Pauli repulsion. In other words,
Pauli repulsion is absorbed into deformation, and this shows
up as a higher, more destabilizing strain which, however, is less
destabilizing than the Pauli repulsion would have been without
this deformation. As readily seen in Fig. 5, the favored addition
also benets from much more stabilizing electrostatic interac-
tions. For instance, at the same consistent C/C bond-forming
distance of 2.23 Å,
22
the difference in the electrostatic attrac-
tions DDV
elstat
is 4.1 kcal mol
−1
(favoring the FA-approach),
whereas a lower value of 3.5 kcal mol
−1
was computed for the
DDE
Pauli
term. This nding is in line with earlier qualitative
studies by Houk and Paddon-Row,
23
Adcock,
24
or Rosenberg,
25
who anticipated the importance of electrostatic effects in the
nucleophilic additions to different sterically hindered ketones.
At variance, the orbital interactions, mainly deriving from the
HOMO(nucleophile)/p*-LUMO(C]O) molecular orbital
interaction, are comparatively stronger in the FA-hindered
approach (which results from a larger orbital overlap, S=0.302
vs. S =0.273 for the FA-hindered and FA approaches, respec-
tively, at the same consistent C/C bond-forming distance).
Therefore, our quantitative ASM-EDA analysis indicates that the
preference for the Felkin–Anh addition is mainly dictated by
steric factors which, manifest in a less destabilizing strain-
energy rather than, as traditionally considered, in a lower
Pauli repulsion. In addition, other factors such as the more
favorable electrostatic interactions between the reactants along
the reaction coordinate also contribute to the preferred
approach of the nucleophile.
It could be reasonably assumed that the above results might
be biased due to the charged nature of the cyanide nucleophile.
To check this issue, we compared the reaction involving cyanide
with the analogous addition reactions involving the neutral
ylides Me
2
S]CH–CN and Me
2
S]CH–CO
2
Me, which exhibit
similar nucleophilicities as cyanide according to the Mayr's
scale (N=16.23 and N=15.85, respectively).
20
From the data in
Table 1, it is conrmed that the corresponding FA approach is
consistently found as the most favored addition over the alter-
native anti-FA and FA-hindered approaches. In all cases, the
preference for the FA addition nds its origin exclusively in the
higher strain computed for the anti-FA approach (which denes
the selectivity) and particularly, for the FA-hindered addition
(which denes the approach of the nucleophile), therefore
further supporting our previous results. Interestingly, we found
that even when using neutral nucleophiles, the electrostatic
term is stronger than the orbital term, although different from
Fig. 4 2D-activation strain diagrams of the possible cyanide additions
to (S)-2-phenylpropanal leading to the corresponding syn (left) and
anti (right) reaction products. Strain energy (top) and interaction
energy (bottom). All data were computed at the ZORA-M06-2X/
TZ2P//M06-2X-6-311+G(d) level.
Fig. 5 Comparative energy decomposition analyses of the addition of
cyanide to (S)-2-phenylpropanal following the FA (black) and FA-
hindered (red) approaches projected onto the C/C(]O) bond-
forming distance. All data were computed at the ZORA-M06-2X/
TZ2P//M06-2X-6-311+G(d) level.
© 2024 The Author(s). Published by the Royal Society of Chemistry Chem. Sci.,2024,15,12380–12387 | 12383
Edge Article Chemical Science

the data involving the cyanide nucleophile, the DV
elstat
term
seems slightly more stabilizing for the FA-hindered approaches.
To check the generality of our ndings, we extended our
study to the analogous nucleophilic addition of the cyanide to
the related ketone, (S)-3-phenylbutan-2-one. From the data in
Table 2, which gathers the activation barriers associated with
the most representative approximations, it becomes clear that
the FA addition is, not surprisingly, preferred while the anti-
isomer is again produced through the anti-CF addition (in this
case, a higher syn/anti ratio of 97 : 3 is predicted), therefore
conrming the reactivity likeness between the aldehyde and
ketone. Moreover, the shape of the corresponding 2D-PES
(including all the possible pathways) is rather similar to that
involving the aldehyde counterpart (see Fig. S2 in the ESI†).
Data in Table 2 indicate that the computed barriers involving
the ketone reactant are, regardless of the approach of the
nucleophile, much higher than those involving the analogous
aldehyde. One might expect that this is due to both unfavorable
steric effects showing up in more Pauli repulsion due to the
replacement of the hydrogen atom by the bulkier methyl group
in the ketone and to the lower electrophilicity of the ketone
carbonyl group due to hyperconjugation from the methyl group.
Our quantitative ASM-EDA analyses reveal a somewhat different
picture of the ultimate factors behind the increased barriers in
the CN
−
+ ketone reaction. Thus, we compared the preferred
unhindered FA additions for both reactions. The ASDs in
Fig. 6a, once again showing the evolution of the ASM terms
from the early stages of the transformation up to the corre-
sponding transition states, suggest that the higher barrier
computed for the reaction involving the ketone results mainly
from a more destabilizing strain energy and, to a lesser extent,
also from stronger interactions between the deformed reactants
along the entire reaction coordinate. Our EDA analyses (Fig. 6b)
show that the weakening in the interactions exclusively origi-
nates from the more destabilizing Pauli repulsion between the
occupied HOMO(nucleophile) and p(C]O) molecular orbitals
of the ketone reactant. The most interesting nding is, however,
again that much of the Pauli repulsion is absorbed into the
ketone deformation, which shows up in the signicantly higher
strain energy. Therefore, the enhanced electrophilicity (i.e.
reactivity) of (S)-2-phenylpropanal compared to (S)-3-
phenylbutan-2-one results primarily from a less destabilizing
strain energy and, to a lesser extent, also from less destabilizing
Pauli repulsion between the deformed reactants. This result
further supports our recent ndings on the non-critical role of
orbital interactions in dening the electrophilicity of carbonyl
groups,
16
which in this particular case are nearly identical for
both processes (Fig. 6b).
Although data in Table 2 strongly suggest that the nucleo-
philic addition in the process involving (S)-3-phenylbutan-2-one
resembles that involving (S)-2-phenylpropanal, we nally
applied the ASM-EDA method to the complete 2D-PES for the
CN
−
+(S)-3-phenylbutan-2-one reaction to conrm whether the
conclusions reached for the reaction involving the aldehyde can
be safely extended to its methyl-ketone counterpart. From the
data in Fig. 7, which shows the relative contribution of both the
strain and interaction energies in the 2D-PES, it is conrmed
that the FA addition benets, once again, from the lowest (i.e.
least destabilizing) strain of all possible nucleophilic
approaches. Thus, again, steric repulsion is largely absorbed
into deformation and thus reactant strain along the more
hindered trajectory. In comparison with the FA-hindered
approach, the FA approach benets also from a stronger
Table 1 Computed reaction barriers (DG
s
, computed at the DPLNO-CCSD(T)/def2-TZVPP//M06-2X/6-311+G(d) level) and EDA terms
(in kcal mol
−1
, computed at the ZORA-M06-2X/TZ2P//M06-2X/6-311+G(d) level)
a
of the reactions of (S)-2-phenylpropanal with different
nucleophiles
Nucleophile DG
s
DE
strain
DE
int
DE
Pauli
DV
elstat
DE
orb
CN
−
FA 9.1 6.4 −20.5 56.9 −40.2 −37.2
aFA 11.8 8.5 −20.1 58.4 −41.0 −37.5
FA-hind 18.1 11.3 −15.8 59.4 −36.0 −39.2
Me
2
S]CH–CN FA 15.1 7.6 −5.9 67.7 −45.1 −28.5
aFA 18.2 11.5 −7.4 70.7 −47.6 −30.5
FA-hind 19.3 15.9 −10.4 74.5 −49.5 −32.1
Me
2
S]CH–CO
2
Me FA 17.9 7.2 −5.8 67.9 −45.6 −28.0
aFA 23.5 11.5 −6.5 66.9 −44.5 −29.0
FA-hind 24.0 15.5 −7.3 73.6 −49.1 −31.9
a
Computed at the same consistent C/C bond-forming distance of 2.23 Å.
Table 2 Computed free activation barriers (in kcal mol
−1
)
a
for the
most representative cyanide additions to (S)-2-phenylpropanal and
(S)-3-phenylbutan-2-one
Addition
(S)-2-Phenylpropanal
(S)-3-Phenylbutan-2-
one
DG
sa
DDG
sb
DG
sa
DDG
sb
FA 9.1 0.0 13.1 0.0
FA-hindered 18.1 8.9 25.5 12.4
CF 11.5 2.4 17.0 3.9
anti-FA 11.8 2.7 16.8 3.7
anti-CF 10.2 1.1 15.3 2.1
a
Free activation energies (DG
s
) computed as DG
s
=G(transition state)
−G(reactant complex).
b
Free energy barrier difference with respect to
the favored FA approach. All data were computed at the DLPNO-
CCSD(T)/def2-TZVPP//M062X-6-311+G*level.
12384 |Chem. Sci.,2024,15,12380–12387 © 2024 The Author(s). Published by the Royal Society of Chemistry
Chemical Science Edge Article

interaction between the deformed reactants, which according to
the EDA (see Fig. S3 in the ESI†) originates from a less desta-
bilizing Pauli repulsion and, to a higher extent, from more
favorable electrostatic interactions. Similarly to the reaction
involving the aldehyde, the preferred addition for the unfavored
anti-addition is dominated by the anti-CF approach, mainly
because of a stronger interaction between the deformed reac-
tants. Therefore, our calculations conrm the generality of the
origin of the preferred FA approach regardless of the nature of
the carbonyl reactant.
For completeness and to check the inuence of the nature of
the substituents at the chiral carbon atom on the process, we
replaced the phenyl group in (S)-3-phenylbutan-2-one with
a chlorine atom. The corresponding ASDs for the FA and anti-FA
pathways are rather similar to those computed for the reaction
involving the phenyl-substituted counterpart (see Fig. S4 in the
ESI†), therefore conrming the crucial role of the strain term
(i.e. sterics) in dictating the syn/anti selectivity.
Conclusions
The syn-selectivity of the nucleophilic addition to the carbonyl
group in chiral aldehydes and ketones (over the alternative anti
addition) originates, as follows from our activation strain
analyses, exclusively from the lower deformation energy
required by the carbonyl reactant to adopt the transition state
geometry in the Felkin–Anh approach. This is a direct conse-
quence of the higher steric clash that goes with the anti-addi-
tion (and other even less favorable trajectories), which is largely
absorbed into the deformation of the carbonyl-containing
reactant. In addition, the preferred approach of the nucleo-
phile, i.e., passing close to the small group of the carbonyl
reactant, cannot be solely explained in terms of steric interac-
tions, as widely accepted, because the FA approach also benets
from a stronger interaction between the reactants along the
entire reaction coordinate. This, according to our canonical
EDA calculations, derives from slightly less destabilizing Pauli
repulsion (which is expected) together with more stabilizing
electrostatic interactions. Our nding therefore diverges from
more traditional explanations based solely on a weakening of
the interaction between reactants due to the steric clash.
Furthermore, our analyses conrm that chiral aldehydes are
more reactive than the corresponding ketones. Reasons behind
the higher electrophilicity of the aldehyde, at least in the reac-
tion with cyanide as a nucleophile, are directly related once
again to the required lower strain of the carbonyl reactants and,
to a lesser extent, also to a reduced Pauli repulsion and not, as
widely considered, to a more favorable orbital (mainly,
HOMO(CN
−
)/p*(C]O)) interactions.
Our work not only demonstrates the usefulness of the ASM-
EDA approach to understanding fundamental processes in
Fig. 6 Comparative activation strain diagrams (a) and energy decomposition analysis (b) for the addition of cyanide to (S)-2-phenylpropanal
(black) and (S)-3-phenylbutan-2-one following the preferred FA approach projected onto the C/C(]O) bond-forming distance. All data were
computed at the ZORA-M06-2X/TZ2P//M06-2X-6-311+G(d) level.
Fig. 7 2D-activation strain diagrams of the possible cyanide additions
to (S)-3-phenylbutan-2-one leading to the corresponding syn (left)
and anti (right) reaction products. Strain energy (top) and interaction
energy (bottom). All data were computed at the ZORA-M06-2X/
TZ2P//M06-2X-6-311+G(d) level.
© 2024 The Author(s). Published by the Royal Society of Chemistry Chem. Sci.,2024,15,12380–12387 | 12385
Edge Article Chemical Science

chemistry but also provides a denitive (i.e., quantitative)
explanation for one of the most widely used models in organic
chemistry.
Computational details
Geometry optimizations of the molecules were performed
without symmetry constraints using the Gaussian16 (RevB.01)
suite of program
26
at the M06-2X
27
/6-311+G(d) level. Reactants
were characterized by frequency calculations and have positive
denite Hessian matrices. Transition states show only one
negative eigenvalue in their diagonalized force constant
matrices, and their associated eigenvectors were conrmed to
correspond to the motion along the reaction coordinate under
consideration using the Intrinsic Reaction Coordinate (IRC)
method,
28
with the exception of the constrained transition
states (hindered approach), were another negative eigenvalue
related to the rotation of the system may appear. Energy
renements were carried out by means of single-point calcula-
tions at the Domain Based Local Pair-Natural Coupled-Cluster
(DLPNO-CCSD(T), using NormalPNO)
29
with the Orca 5.0.3
(ref. 30) program using the def2-TZVPP
31
basis set on the M06-
2X/6-311+G(d) geometries. This level is denoted DLPNO-
CCSD(T)/def2-TZVPP//M06-2X/6-311+G(d).
The computed thermochemistry data were corrected
following Grimme's quasi-harmonic (QHA) model for entropy
32
with a frequency cutoffvalue of 100.0 cm
−1
using the Good-
Vibes
33
program at 298.15 K.
Activation strain model (ASM) of reactivity and energy
decomposition analysis (EDA) methods
Within the ASM method,
13
the potential energy surface DE(z)is
decomposed along the reaction coordinate, z, into two contri-
butions, namely the strain DE
strain
(z) associated with the
deformation (or distortion) required by the individual reactants
during the process and the interaction DE
int
(z) between these
increasingly deformed reactants:
DE(z)=DE
strain
(z)+DE
int
(z)
Within the EDA method,
14
the interaction energy can be further
decomposed into the following chemically meaningful terms:
DE
int
(z)=DV
elstat
(z)+DE
Pauli
(z)+DE
orb
(z)
The term DV
elstat
corresponds to the classical electrostatic
interaction between the unperturbed charge distributions of the
deformed reactants and is usually attractive. The Pauli repul-
sion DE
Pauli
comprises the destabilizing interactions between
occupied orbitals and is responsible for any steric repulsion.
The orbital interaction DE
orb
accounts for bond pair formation,
charge transfer (interaction between occupied orbitals on one
moiety with unoccupied orbitals on the other, including
HOMO–LUMO interactions), and polarization (empty-occupied
orbital mixing on one fragment due to the presence of another
fragment).
The program package ADF
34
was used for EDA calculations
using the optimized M06-2X/6-311+G(d) geometries at the same
DFT level in conjunction with a triple-z-quality basis set using
uncontracted Slater-type orbitals (STOs) augmented by two sets
of polarization functions with a frozen-core approximation for
the core electrons.
35
Auxiliary sets of s, p, d, f, and g STOs were
used to t the molecular densities and to represent the
Coulomb and exchange potentials accurately in each SCF
cycle.
36
Scalar relativistic effects were incorporated by applying
the zeroth-order regular approximation (ZORA).
37
This level of
theory is denoted ZORA-M06-2X/TZ2P//M06-2X/6-311+G(d).
Data availability
The data supporting this article have been included as part of
the ESI.†
Author contributions
D. G.-P. investigation. F. M. B. discussion and manuscript
writing. I. F. conceptualization, funding acquisition, and
manuscript writing.
Conflicts of interest
There are no conicts to declare.
Acknowledgements
This work was supported by the Spanish MCIN/AEI/10.13039/
501100011033 (Grants PID2022-139318NB-I00 and RED2022-
134287-T) and the Dutch Research Council (NWO).
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© 2024 The Author(s). Published by the Royal Society of Chemistry Chem. Sci.,2024,15,12380–12387 | 12387
Edge Article Chemical Science