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\DOI{10.5802/crchim.298}
\datereceived{2024-01-27}
\daterevised{2024-02-01}
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\dateposted{2024-03-06}
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\begin{noXML}

%\makeatletter
%\def\TITREspecial{\relax}
%\def\cdr@specialtitle@english{French Women in Chemistry in 2024}
%%\def\cdr@specialtitle@french{Les chimistes fran\c{c}aises en 2024}
%\makeatother

\CDRsetmeta{articletype}{research-article}

\title{Nucleophilic addition to carbonyl groups from qualitative to
quantitative computational studies. A~historical perspective}

\alttitle{Addition nucl\'{e}ophile sur le groupe carbonyle. Historique
de la contribution de la chimie th\'{e}orique, du qualitatif au
quantitatif}

\author{\firstname{Odile} \lastname{Eisenstein}\CDRorcid{0000-0001-5056-0311}}
\address{ICGM Universit\'{e} de Montpellier, CNRS, ENSCM, Montpellier, France}
\address{Department of Chemistry and Hylleraas Center for Quantum Molecular Science 0315 University of Oslo, Norway}
\email{odile.eisenstein@umontpellier.fr}

\keywords{\kwd{Reaction mechanism}
\kwd{Stereochemistry}
\kwd{Nucleophile}
\kwd{Carbonyl}
\kwd{Computational chemistry}
\kwd{Analysis of intramolecular interactions}}

\altkeywords{\kwd{M\'{e}canisme r\'{e}actionnel}
\kwd{St\'{e}r\'{e}ochimie}
\kwd{Nucl\'{e}ophile}
\kwd{Carbonyle}
\kwd{Mod\'{e}lisation quantique}
\kwd{Analyse des interactions}}

\thanks{French National Center for scientific Research (CNRS), Center
of Excellence Hylleraas Center for Quantum Molecular Science (Grant
262695), Pioneer Research Grant MetalSynergy (Grant 314009), Norwegian
Supercomputing Program (NOTUR) (Grant NN 4654K)}

\begin{abstract}
Nucleophilic addition to carbonyl groups is one of the most important
reactions in organic synthesis. In the case of a prochiral carbonyl
group, the preference for the addition of a nucleophile to one face of
the ${\rmpi}$ system leads to unequal amounts of the two possible
diastereoisomers. The mechanism of this reaction for various
nucleophiles (especially the early main group hydride and the Grignard
reagents) and the various noncyclic and cyclic aldehydes or ketones has
fascinated computational chemists for nearly 40 years. This article
describes the research that has been done on this topic, the incentive
for the present author being that she started her research with this
topic and is returning to it in recent years. 
\end{abstract}

\begin{altabstract}
L'addition d'un nucl\'{e}ophile sur un compos\'{e} carbonyl\'{e}
est une des r\'{e}actions essentielles en synth\`{e}se organique. Si le
groupe carbonyle est prochiral, l'addition sur les deux faces du
syst\`{e}me ne sont pas \'{e}quivalentes et la r\'{e}action conduit
\`{a} un exc\`{e}s d'un des deux diast\'{e}r\'{e}oisom\`{e}res. Le
m\'{e}canisme de ces r\'{e}actions pour les divers nucl\'{e}ophiles
(hydrures des \'{e}l\'{e}ments du groupe principal et r\'{e}actifs de
type Grignard en particulier) sur divers ald\'{e}hydes ou c\'{e}tones
cycliques et non cycliques a attir\'{e} l'attention de nombreux
th\'{e}oriciens depuis pratiquement 40 ans. Cet article d\'{e}crit
l'historique des recherches dans ce domaine. L'auteure s'est
int\'{e}ress\'{e}e \`{a} ce sujet car elle est entr\'{e}e en recherche
avec un sujet dans ce domaine et elle y est revenue ces toutes
derni\`{e}res ann\'{e}es.
\end{altabstract}

\maketitle

\vspace*{.5pc}

\twocolumngrid

\end{noXML}


\section{Introduction}\label{sec1}

Nucleophilic addition to unsaturated organic molecules is an essential
reaction for the formation of new bonds and, in particular new
carbon--carbon bonds. It has been a key reaction in organic synthesis
since Victor Grignard discovered the so-called Grignard reagent in
1900. This groundbreaking achievement, published in a concise two-page
single-author communication in the `Comptes-Rendus de l'Acad\'{e}mie
des sciences'~\cite{1} earned \mbox{Grignard} the Nobel Prize in 1912.~The
citation reads ``for his discovery that has greatly advanced the
progress of organic chemistry''.  The prize was shared with Paul
Sabatier for the discovery of the hydrogenation reaction in presence of
metal~\cite{2}. The discovery of the Grignard reaction is described in
detail together with the author's life in a review article by Bram
et~al.~published in 1997~\cite{3}.

Subsequently, numerous methods of forming new bonds have been
discovered and studied using both experimental and various theoretical
methods. This short review aims to outline a subset of this extensive
body of research. Specifically, it focuses on describing the
theoretical studies related to the reaction mechanism of nucleophilic
addition to carbonyl groups and to the understanding of its
\mbox{stereoselectivity,} a very important aspect of this reaction. Given the
importance of the topic, considerable work was done. Therefore, this
review gives the opportunity to illustrate the evolution of
computational methods applied to reaction mechanism in organic
chemistry. It is remarkable that the earlier studies using very simple
computational methods and models were able to capture the essence of
this reaction. Recently, computations with elaborated methods have
provided information that could not be obtained from experiments.
Moreover, this reaction is of particular interest to the author as it
was the subject of her early research and she has returned to it in the
most recent years. A fuller description of this author's scientific
work, with a different focus than this article, can be found in a
Perspective article~\cite{4}. 


\section{Directionality of the nucleophilic addition from crystal
structures and early calculations}\label{sec2}

\subsection{B\"{u}rgi--Dunitz reaction path and Felkin--Anh rule}\label{sec21}

In the mid-1970s, Hans-Beat B\"{u}rgi and Jack Dunitz proposed to use a
structure correlation method, extracted from the Cambridge data base,
to obtain information about the molecular potential energy hypersurface
which is itself informative about chemical reaction dynamics~\cite{5}.
The basic assumption is that the observed structures tend to
concentrate on the low-lying regions of the potential energy surface.
This also implies that the crystalline environment has little influence
on the molecular structure. By collecting a series of related species
and by looking for correlations between the relevant structural
parameters, B\"{u}rgi and Dunitz established the pathways for several
reactions, namely the nucleophilic substitution, the nucleophilic
addition to an aldehyde or a ketone, and the Berry rotation on
phosphorus. The same method was later used by Crabtree et~al.~to propose
the pathway for C--H bond activation by an unsaturated metal
complex~\cite{6}. This input, derived from crystal structures, is very
useful although it was only applied to few reactions.  

The nucleophilic addition of an amine to a carbonyl group was studied
by looking at the relative arrangement of the amino and carbonyl groups
in the crystal structures of 14 molecules and by showing the
correlation between the N(amino)${\cdots}$C(carbonyl) distance and the
$\mathrm{N}{\cdots}\mathrm{C}{=}\mathrm{O}$ angle
(Figure~\ref{fig1})~\cite{7}. 

\begin{figure}
\includegraphics{fig01}
\caption{\label{fig1}Structural variables used by B\"{u}rgi and Dunitz
to define the reaction path of the nucleophilic addition to a carbonyl
group~\cite{5,7}.}
\end{figure}

This study suggested that the amino group approaches the carbonyl group
from the back of the molecule ($\alpha > 90\text{\textdegree}$).
This trajectory was later confirmed by {ab
initio} calculations performed by Lehn and Wipff et~al.~\cite{8,9}. The
theoretical model was incredibly simple. The nucleophile was an
isolated hydride and the substrate was formaldehyde, with all species
in the gas phase. Optimization of the whole system using the
Hartree--Fock method and a small basis set (the state of the art at the
time) for different distances between the hydride and the carbon
mirrored the path established by the crystal\break structures. 

\begin{figure*}
\includegraphics{fig02}
\caption{\label{fig2}Cram--Cornforth, Karabatsos and Felkin models for
the nucleophilic addition to an ${\alpha}$ substituted carbonyl
compound. Only the approach leading to the major diastereoisomer is
shown. The nucleophile is represented by a circle with 2 orange dots. The
${\alpha}$ angle is shown to be equal to 90\textdegree~as assumed in
the original models. In the calculations R ${=}$ H, X ${=}$ Cl,
L ${=}$ CH$_{2}$CH$_{3}$,  M ${=}$ CH$_{3}$, S ${=}$ H, the nucleophile is H$^{-}$,
${\uptheta}$ was rotated by 30\textdegree~steps and ${\alpha}$ was
optimized for each ${\uptheta}$ value (average value around
105\textdegree).}
{\vspace*{2pt}}
\end{figure*}

This first computational study identified the most important feature of
the nucleophilic addition to a carbonyl group, namely that the
nucleophile does not add perpendicularly to the C${=}$O bond. This feature
was important because it provided information about the short contacts
that could occur during the addition.  Indeed, this pathway contributed
to a more robust interpretation of 1,2-asymmetric induction. The
preferred face for the addition of a nucleophile to an aldehyde or a
ketone, bearing an ${\alpha}$ chiral carbon (with small S, medium M
and large L or polar X substituents), has been a topic of great
interest for organic synthesis. Several empirical rules, proposed by
Cram, Cornforth, Karabatsos and Felkin, have been used to rationalize
the formation of the major diastereoisomer. In these models, the
nucleophile preferentially attacked the less hindered face of the
carbonyl with a given conformation of the chiral carbon. The problem
was that each author had chosen a \mbox{different} conformation resulting in
different rules (Figure~\ref{fig2}). The purpose of the computational
study was to establish which conformation determines the
diastereoisomeric preference. 

The substrates chosen were Cl(CH$_{3}$)HC--CH${=}$O and
(CH$_{3}$CH$_{2}$)(CH$_{3}$)HC--CH${=}$O to mimic systems with polar (Cl) or
large (CH$_{2}$CH$_{3}$), small  (H), medium (CH$_{3}$) and small (H)
groups~\cite{10}. A naked hydride was positioned at 1.5~\AA{}~from the
carbon with an optimized H${\cdots}$C${=}$O ${\alpha}$ angle (average
value around 105\textdegree). The Hartree--Fock/STO-3G energies were
calculated as a function of the conformation of the chiral carbon
described by the ${\uptheta}$ dihedral angle, X--C--C--O, (X ${=}$ Cl or
CH$_{3}$CH$_{2}$) (Figure~\ref{fig2}) without further geometry
optimization. There was a clear preference for the Felkin model,
especially when the ${\alpha}$ angle was greater than 90\textdegree.
Thus, the nucleophile prefers to add antiperiplanar to the substituent
that is either polar (Cl) or the largest (CH$_{3}$CH$_{2}$) on the face
containing the smallest substituent (H). 

This conformational preference is rationalized by being associated with
the largest interactions between the highest occupied orbital (HOMO) of
the nucleophile (the doubly occupied 1s orbital of the hydride) and the
lowest unoccupied molecular orbital LUMO ${\rmpi}^*_{\mathrm{CO}}$ of
the carbonyl group (Figure~\ref{fig3}). The stabilizing interaction
between these two \mbox{frontier} \mbox{orbitals} increases as the energy gap between
them decreases and the overlap increases. Thus, lowering the energy of
${\rmpi}^*_{\mathrm{CO}}$ and increasing the overlap between H$^{-}$ and
${\rmpi}^*_{\mathrm{CO}}$ is favorable. Interestingly, the energy of the
${\rmpi}^*_{\mathrm{CO}}$ orbital depends on the conformation of the
chiral carbon especially in the case of a polar X group or an atom such
as Cl. In fact, the polar C--Cl bond is associated with a low-lying
unoccupied  ${\upsigma}^*_{\mathrm{C}\ndash\mathrm{Cl}}$ orbital. When this
orbital is parallel to the ${\rmpi}^*_{\mathrm{CO}}$ orbital
(${\uptheta} = 90$\textdegree~or 270\textdegree), the two orbitals
overlap and form a low-lying in-phase combination of
${\rmpi}^*_{\mathrm{CO}}$ and ${\upsigma}^*_{\mathrm{C}\ndash\mathrm{X}}$
(Figure~\ref{fig3}). This interaction between the ${\rmpi}$ and
${\upsigma}$ orbitals is known as hyperconjugation. The best overlap
between the hydride and ${\rmpi}^*_{\mathrm{CO}}$ is obtained for an
obtuse ${\alpha}$ angle to reduce the overlap of the hydride with the
oxygen. Some direct overlap of the hydride with
${\upsigma}^*_{\mathrm{C}\ndash\mathrm{X}}$ could also contribute. This
obtuse ${\alpha}$ angle brings the hydride in close proximity to
either the S or M group, with a natural preference for the former. This
explains why the nucleophile enters antiperiplanar to the X group and
on the side containing the smallest group, as suggested by Felkin.

\begin{figure}
{\vspace*{2pt}}
\includegraphics{fig03}
\caption{\label{fig3}The H$^{-}$ occupied orbital (purple) stabilized
by the substrate LUMO in the Felkin conformation. The substrate LUMO is
the in-phase combination of ${\rmpi}^*_{\mathrm{CO}}$ (red) and
${\upsigma}^*_{\mathrm{C}\ndash\mathrm{Cl}}$ (blue). The main in-phase
interactions are indicated by wiggly lines. See ref~\cite{10} for
further details.}
{\vspace*{2pt}}
\end{figure}

It should be emphasized that the Felkin rule was associated with the
best conformation for the nucleophile addition and not with the most
stable conformation of the isolated substrate. However, the transition
state was not really determined but assumed by following the
B\"{u}rgi--Dunitz studies. This approach was acceptable until
methodological advances made it possible to locate a transition state
on a potential energy surface. Naturally, the first studies that
included a transition state determination used highly simplified models
of the reacting partners. Remarkably, these simplified models were
\mbox{useful} and \mbox{encouraged} further studies with better representation of the
chemical systems and higher levels of computation. 

\subsection{The Felkin--Anh and the Cieplak model, the two visions of
the antiperiplanarity rule}\label{sec22}

Interpreting the results in a language that chemists could understand
was considered as important by many computational chemists.  Explaining
the stereoselectivity of the nucleophilic addition to cyclic ketones
was particularly challenging. One of the first reviews that attempted
to discuss the stereoselectivity of the nucleophilic addition to
acyclic and cyclic carbonyls was published by Nguyen Trong Anh, the
author's PhD supervisor~\cite{11}.  The Felkin--Anh model was not easy
to apply. Therefore, an alternative interpretation of the
stereoselectivity was presented by Cieplak~\cite{12,13,14}. This author
presented an interpretation in which the bond antiperiplanar to the
incoming nucleophile acts as a donor towards the incipient
${\upsigma}^*_{\mathrm{C}\ndash\mathrm{Nu}}$ empty orbital that is formed when the
nucleophile interacts with the carbon of the carbonyl group. The
preferred stereoselectivity would be associated with the stronger donor
\textit{trans} to the incoming nucleophile. This was a rather heterodox
\mbox{proposal} as it was pointed out by Frenking et~al.~\cite{15} and by
Tomoda~\cite{16}. It does not follow the rules of orbital interactions,
as established by the frontier orbital theory derived from quantum
chemistry~\cite{17}. It is also unclear how the C--Nu bond would be
formed by the delocalization of electrons into its
${\upsigma}^*_{\mathrm{C}\ndash\mathrm{Nu}}$ orbital. Although the Cieplak rule
has been shown to account for the observed stereoselectivity in some
cases~\cite{18,19,20,21}, it will not appear any longer in the most recent
studies because it contradicts basic principles of quantum chemistry.
In contrast, the Felkin--Anh rule, which obeys the frontier orbitals
theory, gives a qualitative interpretation of how the electron density
of the nucleophile is best transferred to the carbonyl substrate and
thus contributes to the formation of the incipient bond. It has been
used extensively and is still a subject of debate, as illustrated by
selected recent literature~\cite{22,23,24,25,26}. A publication, in the 2023
issue of Helvetica Chimica Acta, dedicated to the memory of J. D.
Dunitz, used the crystallographic method of B\"{u}rgi and Dunitz to
rationalize the diastereoselectivity in a \textit{peri}-naphthalene
derivative~\cite{27}. However, these antiperiplanarity rules were not
sufficient to explain the stereoselectivity of the nucleophilic
addition to carbonyl groups and the numerous studies described in the
following sections, show the other effects that need to be considered.

\subsection{The case of the 1,3-asymmetric induction}\label{sec23}
The stereoselectivity of 1,3-asymmetric induction was considered in the
case of ${\upbeta}$-ketoester with NaBH$_{4}$. The hypothesis in this
work was that the transition state is reactant like in non-chelating
conditions. Consequently, the preferred conformations of the substrates
were considered to determine the selectivity. This proposal gave
results in good agreement with experimental data. This is a rare case
where the nucleophile was not included in the study~\cite{28}. 

\subsection{Energetic aspects of the nucleophilic addition to
carbonyl}\label{sec24}

Ion cyclotron resonance studies and Hartree--Fock calculations for the
reaction of alkoxy anions with B$_{2}$H$_{6}$ provided information on
the thermochemical factors that are determining in these reaction
pathways~\cite{29}. Later, the affinity of the carbonyl groups for
anions was calculated with the MP2 method \mbox{(currently} used in the 1990s
for organic species) for hydride to XYC${=}$O (X, Y ${=}$ H, CH$_{3}$,
NH$_{2}$, OH, and F) and selected additional electrophilic compounds
(${\upalpha}$,${\upbeta}$-unsaturated carbonyl, cycloalkanone,
heterocarbonyl molecular compounds) with data in good agreement with
available experimental data~\cite{30}. This study was extended with the
calculation of the affinity of various anions Z$^{-}$ (Z ${=}$ H, CH$_{3}$,
NH$_{2}$, OH, F, CH${=}$CH$_{2}$, CH${=}$O, C${\equiv}$CH, C${\equiv}$N) for a
large variety of carbonyl systems~\cite{31}.

The interpretation of the obtuse ${\alpha}$ angle for the
nucleophilic addition to a carbonyl, currently called the
B\"{u}rgi--Dunitz angle, has recently been reconsidered and quantified
using energy decomposition analysis (EDA)~\cite{32} and the activation
strain model~\cite{33} in the case of the addition of CN$^{-}$ to
(CH$_{3}$)$_{2}$C${=}$O. With the EDA analysis, Bickelhaupt et~al.~showed
that the obtuse bond angle results from the combination of three
effects: the Pauli repulsion between the HOMO of the nucleophile and
the occupied ${\rmpi}$ orbitals of the substrate, the stabilizing
interaction between the HOMO of the nucleophile and the LUMO,
${\rmpi}^*_{\mathrm{CO}}$, of the substrate and the electrostatic
interaction between the nucleophile and the substrate. Combining the
strain and the EDA analyses, it was found that the preference for an
obtuse ${\alpha}$ angle results from a delicate balance between the
strain and the stabilizing energies. The strain energy, associated with
the deformation of the different chemical species prevents the
${\alpha}$ angle from becoming too large. In contrast, the
stabilizing energy, dominated by the Pauli repulsion, prevents the same
angle from getting smaller (i.e.\ ${<}$ 90\textdegree).
These recent studies demonstrate the importance of quantitative
analysis tools to determine the relative importance of the attractive
and repulsive interactions. This enriches and quantifies the earlier
qualitative analyses. 

\begin{figure*}
\vspace*{-2pt}
\includegraphics{fig04}
\vspace*{-1pt}
\caption{\label{fig4}5-Substituted adamantanones (left) and substituted
7-norbornanones (right) and labels of the isomers resulting from the
addition of a nucleophile to the two faces of the carbonyl group.}
\vspace*{-1pt}
\end{figure*}

\section{Early studies of the reaction pathway}\label{sec3}

\subsection{Early studies with non-cyclic carbonyls}\label{sec31}

A quantitative computational study of the reaction mechanism requires a
reasonable representation of all the reagents and the environment, in
particular the solvent, as well as an extensive exploration of the
chemical spaces and a proper calculation of the thermodynamics of the
chemical systems in solution. These features have been slowly achieved
over the years and this section describes, through selected examples,
the information that has been gained about the nucleophilic addition to
carbonyls and illustrates the improvements in modeling and computation.

Soon after the very first studies, the naked hydride was replaced by
more realistic model of the nucleophile. Borohydride was one of them
but the cation and the solvent were not yet included. The Hartree--Fock
study of the reaction of $\mathrm{BH}_{4}^{-}$ with formaldehyde showed that
the formation of the anionic $\mathrm{CH}_{3}\mathrm{OBH}_{3}^{-}$ was
thermodynamically favored and led to the localization of a transition
state. The reaction was found to be concerted although significantly
non-synchronous with the C--H bond being essentially formed while the
O${\cdots}$B bond was not. The two-step pathway was also identified
and found to be at higher energy than the concerted pathway. Both
mechanisms were associated with high energy barriers probably due to an
overly simplistic modeling of the chemical species which neither
included the cation nor the solvent~\cite{34}. A related study using
B$_{2}$H$_{6}$ as nucleophile showed that a BH$_{3}$ coordinates the
oxygen~\cite{35}. Calculations showed that the addition of AlH$_{3}$ to
formaldehyde proceeds via a 4-centered transition state and forms an
energetically favorable aluminum methoxide product~\cite{36}. 

A computational model still using a naked hydride was proposed in the
1990s to analyze the face selectivity in the case of sterically
unbiased ketones. Using also semi-empirical method (MNDO), the authors
were able to consider large molecules like substituted norbornanones
and other bicyclic ketones. The experimental selectivity was well
reproduced. The authors point out that the geometrical details of the
transition state seemed unimportant but the presence of a hydride was
necessary in the calculations~\cite{37}.

\subsection{Early studies with cyclic ketones}\label{sec32}
Considerable efforts have been devoted to the study of the face
selectivity for the addition of various nucleophiles to substituted
cyclohexanones. These 6-membered ring ketones posed a great
computational challenge due to their ring flexibility. The studies were
all based on the determination of the reaction pathway by identifying
the transition states with different nucleophiles that were modeling as
well as possible those used in the experiments. The solvent also began
to be included in the computational studies, usually by means of a
continuum method, although not yet systematically. This improved the
representation of the electrostatic contribution. The studies were
aimed at finding the facial preferences and also at understanding, at
least in a qualitative way, the various factors that determine these
preferences.\looseness=-1


The study of the addition of AlH$_{3}$ to 5-substituted adamantanones
(Figure~\ref{fig4}) confirmed the involvement by hyperconjugation of the
bond that is antiperiplanar to the incoming nucleophile (the essence of
the Felkin--Anh model) and pointed out the importance of torsional
effects in the face selectivity~\cite{38}. A study of the reduction of
substituted 7-norbornanones (Figure~\ref{fig4}) using the AM1 method
emphasized the importance of determining the transition state and not
just looking at the electrostatic properties of the substrate. Using
AlH$_{3}$ to model the reactivity of NaAlH$_{4}$ reproduced the
stereoselectivity for a whole series of substituted
norbornanones~\cite{39}.\looseness=1

LiH was shown to be associated with a 4-centered transition state and a
preference for addition of the hydride to the axial face of the
cyclohexanone (Figure~\ref{fig5}). This preference, established for a
small nucleophile, was related to a distortion of the
${\rmpi}^*_{\mathrm{CO}}$ orbital, which was more developed toward the
axial face. This distortion was shown to be due to the \mbox{hyperconjugation}
with the neighboring C--H and \mbox{C--C} orbitals. Large nucleophiles had a
preference for the equatorial approach due to steric hindrance on the
axial face~\cite{15}. Around the same time, the relative importance of
torsional strain and electrostatic interactions was studied, with LiH
and NaH as nucleophiles and cyclohexanone and related substituted
cyclic carbonyl molecules. Some general trends have emerged. Torsional
strain at the transition state disfavors the equatorial attack, steric
effects often disfavor the axial attack and the electrostatic
interactions can dominate when polar substituents are present on the
ring. Substituents have stronger effects at the axial site than at the
equatorial site~\cite{40,41}, and for substituted
7-norbornanones~\cite{42}. In 1992, Li and le Noble considered all the
rules that have been proposed and favored a rational that mixes the
torsional effects, the Felkin--Anh and Cieplak rules in different
amounts for each system~\cite{43}. 

\begin{figure}
{\vspace*{3pt}}
\includegraphics{fig05}
{\vspace*{3pt}}
\caption{\label{fig5}The two non-equivalent faces of
4-\textit{tert}-butylcyclohexanone and the numbering of the carbon
atoms.}
\end{figure}

Ion mass spectrometry studies showed that pentacoordinated silicon
hydride is also a \mbox{nucleophile} that can add to cyclohexanone and related
molecules~\cite{44}. This was of interest for the computational studies
because gas phase and solution chemistry could be compared.  Using
$\mathrm{SiH}_{5}^{-}$ as a simplified model of the experimental
pentacoordinated alkoxide silicon hydride, the selectivity of the
reduction of several cyclohexanone derivatives was studied using
Hartree--Fock and MP2 methods in the gas-phase and the
solution~\cite{45}. The transition state is dominated by the hydride
transfer and very little Si--O bond formation. Axial reduction is
preferred for the cyclohexanone but the equatorial reduction is
preferred for dithianone, the preferences being similar in the gas
phase and in solution. However, for dioxanone, the gas phase favors the
equatorial addition and the solution (methanol) favors the axial
addition. These computational results were consistent with the observed
selectivity of the reactions with NaBH$_{4}$, LiAlH$_{4}$ and Grignard
reagents in solution. They were qualitatively rationalized as coming
from a balance between electrostatic interactions which disfavors the
axial approach and torsional strain which disfavors the equatorial
attack. Further studies with hindered cyclohexanones and various
nucleophiles (hydride, methyl, acetylenic Grignard and lithium
reagents) were performed. The reaction of CH$_{3}$Li or HC${\equiv}$CLi
with non-substituted cyclohexanone was carried out with an ab-initio
Hartree--Fock study but the same method could not be applied for
hindered cyclohexanones. In this latter case an adapted MM2 force field
method was used.  This approach led to a good reproduction of the
observed selectivity. In this case also, the selectivity resulted from
a balance between steric and torsional effects~\cite{46}. The intrinsic
diastereoselectivity of the reduction of a large series of cyclic
ketones by pentacoordinated silicon hydride ions was investigated in
the gas phase using the flowing afterglow-triple quadrupole
technique~\cite{47}. The percent axial reduction was determined by
collision-induced dissociation experiments. The trend observed
in the condensed phase is consistent with the results observed in the
gas phase suggesting that environmental effects are either unimportant
or cancel each other out. Consequently, the diastereoselectivity was
proposed to be related to the intrinsic nature of the substrate and
rationalized as resulting from a competition between steric, torsional
and \unskip\break electrostatic effects.\looseness=1



\subsection{The relative importance of the effects influencing
selectivity}\label{sec33}

Calculations were clearly able to reproduce the observed
stereoselectivity but they were not easy to interpret. The energy
difference between the approach to the two faces of the carbonyl group
is small (usually less than 1 kcal/mol) and it is a real challenge to
identify the driving effect (if there is one) among the several
competing interactions. The following factors have been mentioned:  (i)
the charge transfer of the nucleophile to the substrate also called
delocalization or hyperconjugation ({i.e.}\ the Felkin--Anh or
Cieplak rules), (ii) the electrostatic interaction, (iii)~the
steric~\cite{48} and strain energies, and (iv) the chelation. Another
indicator of stereogenicity has been proposed. It is intrinsic to the
prochiral substrate and can be derived from its molecular orbitals. The
determination of the transition state of the nucleophilic addition can
thus be avoided. In a prochiral carbonyl group, the two faces of the
${\rmpi}$ bond are not equivalent. It means that the occupied ${\rmpi}$
orbital as well as the LUMO ${\rmpi}^*_{\mathrm{CO}}$ have greater
extension toward one of the two faces of the carbonyl. Authors have
analyzed these distortions focusing on the carbon contribution. These
different extensions result from the mixing of the 2p and 2s carbon
orbitals (Figure~\ref{fig6}).  An earlier version of this indicator was
used to justify the Cram rule~\cite{49}. This dissymmetry in the
occupied or empty orbitals has been considered by Klein in particular
for 5- and 6-membered ring ketones~\cite{50, 51}. An elaborate
quantitative evaluation of the expansion of the LUMO
${\rmpi}^*_{\mathrm{CO}}$ orbital was developed by Tomoda~\cite{16}.
\looseness=-1

\begin{figure*}
\vspace*{2pt}
\includegraphics{fig06}
\vspace*{2pt}
\caption{\label{fig6}Qualitative illustration of the mixing of 2p and
2s orbitals for C and O when the carbonyl group is prochiral. The
mixing at carbon was the focus of attention.}
\vspace*{1pt}
\end{figure*}

The relative importance and validity of these various criteria were the
subject of an entire issue of \textit{Chem.~Rev.}\ in 1999, indicating how
important these criteria were to the community of chemists. For
example, in this issue, Dannenberg nicely discussed the pros and cons
of electronic criteria that were used in those years~\cite{52}. He
pointed out that it was unlikely that a single rule could rationalize
all cases. Ohwada described how to use orbitals to rationalize the face
selection in sterically unbiased cyclic systems~\cite{53}. Cieplak
presented his interpretation of the effect of substituents on
${\rmpi}$-face selection~\cite{14}. Wipf and Jung discussed the role of
dipole effects~\cite{54}, Mehta and Chandrasekhar discussed various
electronic effects for sterically unbiased ketones and
olefins~\cite{55}. \mbox{Adcock} and Trout discussed the case of rigid
saturated model substrates and in particular the influence of the
substituents~\cite{56}. 

A study by Rosenberg et~al.~is notable by the number of systems studied
experimentally and computationally and by the careful consideration of
a large number of factors~\cite{57}. These authors considered a series
of 2-X-4-\textit{tert}-butylcyclohexanones (X ${=}$ H, CH$_{3}$, OCH$_{3}$,
F, Cl, Br; with X equatorial or axial), studied their reactivity with
LiAlH$_{4}$ and, performed computational studies of the face
selectivity. They used the simplified model of the hydride that was
currently selected in the early 2000s (LiH, NaH, BH$_{3}$, AlH$_{3}$).
They determined the transition states for all the systems and obtained
a calculated selectivity which correctly identified the main isomer.
The experimental trends were better reproduced by the calculations when
the X substituent was equatorial than axial. The controlling factors
appeared to be the electrostatic interactions between the nucleophile
and the substituent X. When X was axial, the electrostatic effect or
the Felkin--Anh rule rationalized the results but the Cieplak model
failed.  

Thus, in the early 2000s, it was clear that a large number of factors
were controlling the face selectivity and that none was dominant. It
was also encouraging that calculations were successful to determine the
major isomer, although the observed trends were sometimes difficult to
reproduce. Given the very small energy difference between the
transition states of the addition of the nucleophile on the two faces
of the carbonyl, this was very encouraging. Thus, in the following
years, improved \mbox{calculations} were performed. This includes a more
realistic \mbox{modeling} of the nucleophile, the presence of the counter
cation, the almost systematic inclusion of the solvent which was
represented either implicitly (by a continuum) or explicitly by the
presence of one or two solvent molecules. This also includes the use of
more elaborate computational methods, in particular DFT methods that
were successful at representing together the strong covalent bonding
{and} the weak non covalent interactions. The determination of
the reaction pathway (transition states and intermediates) was
systematic. This ``static approach'' was the state of the art for many
years. It was powerful, relatively inexpensive and usually successful
in calculating selectivity in good agreement with the experimental
data. However, with this static approach, the ability to accurately
represent the thermodynamics of a very complex system of solute and
solvent could be limited. 

\subsection{Studies with improved representation of the nucleophilic reagent}\label{sec34}

Calculations were performed with LiBH$_{4}$, NaBH$_{4}$ or LiAlH$_{4}$
as reagents. This allowed to understand how the cation and the element
(B or Al) carrying the hydride cooperate to transfer the hydride to the
carbonyl carbon. The solvent was often but not always included although
its presence seemed necessary in presence of charged species. Besides
the determination of the reaction pathway, the stereoselectivity for
acyclic and cyclic carbonyl remained the main goal of these studies. 

\begin{figure*}
{\vspace*{-2pt}}
\includegraphics{fig07}
{\vspace*{-2pt}}
\caption{\label{fig7}Transition states for the addition of LiAlH$_{4}$
to formaldehyde. Similar transition states were located with
cyclohexanone~\cite{58}.}
{\vspace*{-2pt}}
\end{figure*}

The computational study of the reaction of LiAlH$_{4}$ with
formaldehyde and cyclohexanone was carried out in the gas
phase~\cite{58}. The authors stated that neglecting the solvent was
justified because similar stereoselectivity had been observed in the
gas phase and in solution~\cite{47}. Under these conditions, the
calculations were performed with the DFT method with the widely popular
B3LYP functional and a \mbox{6--31G$^{**}$}\ basis set (a good level of calculation
in the early 2000s). Two types of transition states with either
bidentate (preferred) or tridentate Li/AlH$_{3}$ bonding were
identified (Figure~\ref{fig7}). All transition states yielded the same
intermediate where Li is still bound to the oxygen.  It rearranges to
the more stable Al--O bound final product. 

The calculations carried out for the cyclohexanone show a preference
for an axial approach, which has already been found with nucleophiles
such as LiH, $\mathrm{SiH}_{5}^{-}$, BH$_{3}$ etc. The strain energy is again
mentioned as disfavoring the equatorial attack. The hyperconjugation
effect is suggested to be small since the C--H and C--C ${\upsigma}$
bonds, next to the reactive carbonyl group, do not lengthen or contract
significantly.  Thus, the greater extension of the ${\rmpi}^*_{\mathrm{CO}}$ LUMO
towards the axial face was suggested to be a favorable factor for the
attack on this face. A similar study was carried out on the reduction
of 2-X-substituted cyclohexanones (X ${=}$ OMe, SMe, SeMe) with LiAlH$_{4}$
in the gas phase~\cite{59}. To interpret the results, the extension of
the ${\rmpi}^*_{\mathrm{CO}}$ LUMO towards one of the faces of the carbonyl and the
electrostatic potential were considered. However, this was not
sufficient because the conformations of the 6-membered ring and the
complexation of X by lithium (Li) had a determining role in the
stereoselectivity. To study cases where the X${\cdots}$Li interactions
did not exist, calculations were also performed for  X ${=}$ CH$_{3}$ and
CH(CH$_{3}$)$_{2}$ ~\cite{60}. The conformational preferences of the
2-X-substituted cyclohexanones in the transition state gave a
preference for the \textit{trans}-isomer (Figure~\ref{fig8}). 

\begin{figure*}
{\vspace*{-3pt}}
\includegraphics{fig08}
{\vspace*{-3pt}}
\caption{\label{fig8}Products resulting from the reaction of
LiAlH$_{4}$ with 2-alkylcyclohexanones.}
\end{figure*}

The reaction mechanisms for the addition of LiBH$_{4}$ and LiAlH$_{4}$
to formaldehyde were compared with the CAM-B3LYP/Aug-cc-pVTZ level for
geometry optimization and with single point calculations at the
CCSD(T)/Aug-cc-pVTZ level~\cite{61}. The solvent (THF) was represented
by an SCRF/PCM continuum and selected calculations included an explicit
molecule of THF. The energy barrier was significantly higher for
LiBH$_{4}$ than for LiAlH$_{4}$. Thus, in agreement with the Hammond
postulate, the transition state is product like for LiBH$_{4}$ and
reactant like for LiAlH$_{4}$. In the product, O--B or O--Al bonds are
formed and Li interacts either with the oxygen only (case of
LiAlH$_{4}$) or with the oxygen and the hydride (case of LiBH$_{4}$).
From, the evolution of the charge density along the reaction pathway,
the authors suggested that the reaction started with an electron
transfer from the hydride to the carbon of the carbonyl and is followed
by the hydrogen transfer. This mechanism has not been suggested in
other studies. 

\begin{figure*}
\includegraphics{fig09}
{\vspace*{-3pt}}
\caption{\label{fig9}6-Membered ring ketones whose reactivity with
small and large hydride species were studied by calculations.}
{\vspace*{-3pt}}
\end{figure*}

The experimental conditions were well represented in the relatively
recent computational study of the face selectivity for reactions of
small and large hydride species to 4-\textit{tert}-butylcyclohexanone,
\textit{cis}-2,6-dimethyl \textit{N}-acylpiperidone and
\textit{N}-acyltropinone (Figure~\ref{fig9})~\cite{62}. The substrates
were considered in full and, small and large hydrides were represented
by LiAlH$_{4}$ and by LiBH(CH$_{3}$)$_{3}$, respectively.
LiBH(CH$_{3}$)$_{3}$ was used as a model for the experimental lithium
tri-\textit{sec}-butylborohydride, L-Selectride, whose conformational
complexity was beyond the reach of calculations. The geometry
optimization was carried out at the B3LYP/6-31(d,p) and the energies
were refined by single point calculations with a larger basis set and
implicit solvent effect represented with a recently developed powerful
continuum method (SMD). These were high level calculations for such
systems 10 years ago. The calculated free energies of activation
(${\Updelta}\mathrm{G}^{\neq}$) for the addition of the nucleophile to
the two faces of the carbonyls differ by less than 1~kcal/mol and
systematically, the transition state that yields the observed major
isomer is calculated to have the lower energy. Thus, small
diastereoisomeric excesses were correctly calculated.  Small hydride
species preferentially added to the axial face of the substituted
cyclohexanones and tropinone. However, an equatorial attack to a twist
boat conformation was preferred for the piperidone. In the case of the
bulky hydride, the equatorial face was preferred in all systems.
Torsional strain and steric effects control the selectivity and steric
effects dominate in the case of large hydride.  

Recent years have seen an improved representation of solvation.
Solvation has been implemented in calculations for many years using a
continuum model which in particular allowed a correct representation of
the electrostatic effects in solution. However, microsolvation was not
present in implicit solvation and its omission was becoming
increasingly questionable because microsolvation is recognized to be
important when polar reagents are used. Thus, the selectivity of the
reduction of 4-\textit{tert}-butylcyclohexanone by LiAl(OR)$_{3}$H 
(R ${=}$ \textit{tert}-butyl for the experiments and methyl for the
calculations) with THF mono- and bi-solvation was studied
computationally with three functionals, B3LYP, B3LYP-D3 and
M06-2X~\cite{63}. Implicit solvation was also included with the SMD
method. Bi-solvation was found to be preferred. A two-step reaction was
identified, with the first step describing the hydride transfer to the
carbonyl carbon and the second step describing the formation of the
Al--O bond. However, the intermediate between the two transition states
is energetically high and close to the two transition states,
questioning the existence of a two-step reaction and a strongly
non-synchronous reaction cannot be ruled out. In fact, a recent
high-level calculation of the reduction of 2-X-substituted
cyclohexanones (X ${=}$ H, Cl, Br) by NaBH$_{4}$ in which the solvent is
explicitly represented by microsolvation and implicitly represented by
a continuum showed a single transition state pathway~\cite{64}. This
recent study highlights the need for this dual representation of the
solvent. The calculations gave a late transition state with an almost
formed C--H bond as actually found in most previous studies. This late
transition state was said to be consistent with the mild reducing power
of NaBH$_{4}$. The observation that 
\mbox{2-halo} \mbox{cyclohexanones} are more
reactive than cyclohexanone was only well represented when both
solvation and microsolvation were considered. Thus, even if the solvent
(ethanol) does not change the face selectivity, its explicit inclusion
is necessary to better model a reaction pathway involving polar
transition states. Today, the need for an explicit representation of
the solvent molecules especially when highly polar or ionic species are
present is fully recognized. The question remains on how to represent
this explicit solvation. For years, calculations were performed with a
reasonably small number of solvent molecules following some
computational tests and chemical intuition. Today, this is an important
issue in the study of reaction pathways and other methods are starting
to be used~\cite{65} (see also below).\looseness=-1

Computational chemists have also been concerned with the quality of the
calculations and in particular with the method and level of calculation
that must be used to represent the strong bonds and the weak
interactions in a balanced way in order to correctly determine the face
selectivity. Such a study has been carried out for substituted
2-X-substituted cyclohexanones (X ${=}$ Me, OMe, SMe, Cl) and LiAlH$_{4}$
with eight different functionals, MP2 and CCSD(T) methods~\cite{66}.
The energy barrier is found to be more sensitive to the calculation
method than the conformational properties of the substrate. MP2 appears
one of the poorest methods in this particular study.  The coordination
mode of AlH$_{4}$ to Li at the transition state was found to depend on
the calculation method but not the face selectivity which is the same
for all methods. An interesting analysis of the strain energy and
steric effects, reinforces the accepted understanding that face
selectivity results from a balance between them. The fact that the
selectivity of the reaction does not vary with these already high-level
computational methods is encouraging for further studies with more
complex substrates and nucleophiles.\looseness=-1

\section{What is in solution? Searching for the structure of the alkali
and alkalino earth complexes}\label{sec4}

\subsection{The metal hydride cases}\label{sec41}
The nature of the solvated species present in ethereal solutions of
LiAlH$_{4}$ has been studied by combining experiments and computations
based on IR spectroscopy. The result of this study is that LiAlH$_{4}$
in ethereal solutions forms contact ion pairs. The dissociated species
are higher in energy than the associated species by about 2.3 kcal/mol
and 4 kcal/mol for THF and dimethyl ether, respectively~\cite{67}. 

Car--Parrinello molecular dynamics simulation of NaBH$_{4}$ in methanol
also suggested a preference for a solvated contact ion pair and found
that the dissociation pair to be more than 4 kcal/mol higher in
energy~\cite{68}. This led the authors to propose a transition state
for the reduction of ketone that incorporates this finding in a set of
static calculations. Using this solvated contact ion pair as reagent
for the reaction with cyclohexanone derivatives dramatically lowers the
activation energy.  It also leads to calculated selectivities in very
good agreement with observed values (4-methylcyclohexanone
axial/equatorial: exp ${=}$  86:14, calc ${=}$ 80.9:19.1;
2-\textit{tert}-butcyclohexanone axial/equatorial: exp ${=}$ 50:50, calc ${=}$
41:59). These results were used to calculate the complete mechanism for
the reduction of resorufin by NaBH$_{4}$ in water~\cite{69}. As
mentioned above, the effect of the solvent (ethanol) on the
stereoselectivity and reactivity was also investigated in the case of
the reduction of 2-X-substituted cyclohexanones (X ${=}$ H, Cl, Br) by
NaBH$_{4}$~\cite{64}.\looseness=-1

\subsection{The Grignard reaction}\label{sec42}
The Grignard reaction is a prominent process in organic synthesis for
the formation of carbon--carbon bonds. Despite extensive experimental
studies, the mechanism of the reaction at the molecular level remains
unknown. This is because the nature of the Grignard reagent in solution
is still unknown. As summarized by Dietmar Seyferth, ``Generally
written as RMgX, the Grignard reagents in ethereal solution are more
complicated than this simple formula indicates''~\cite{70}. It is
currently recognized that the nominal reagent, RMgX is a condensed
representation of numerous mono- and poly-metallic species in rapid
equilibrium and that the exact nature of the species is determined by
the solvent. Thus, unfortunately, most of the studies attempting to
characterize these species by the most advanced and diverse
spectroscopic methods~\cite{71}, and crystallization have identified
them under conditions different from those of the reaction itself.
Traditional static computational methods would also fail because they
cannot properly calculate the free energy changes of the solvent
organization and dynamics at close and intermediate distances from the
organomagnesium species. A method of calculations capable of
representing the thermodynamics of the solute and the solvent, as
accurately as possible, is the {ab initio} molecular dynamics
(AIMD). This method has been used to describe solvated NaBH$_{4}$ as
mentioned above~\cite{68} and has thus been used to uncover the
diversity of species representing the global Grignard reagent in
ethereal solution and to propose a mechanism for the Schlenk
equilibrium (Equation~(\ref{eq1})), for CH$_{3}$MgCl in THF~\cite{72}.
{\begin{equation}\label{eq1}
2\mathrm{RMgX}\rightleftharpoons\mathrm{MgR}_2+\mathrm{MgCl}_2.
\end{equation}}\unskip

It appears that the solvation of the magnesium species is highly
variable and also very dynamic. It takes very little energy to add or
remove a solvent molecule from the coordination sphere of magnesium. As
expected, solvation is higher when Mg is bound to the electron
withdrawing-chloride atom than to the electron-donating methyl group.
Thus, dimethyl magnesium is best solvated by two THF molecules, while
magnesium dichloride prefers three THF molecules in its coordination
sphere. Thus, a higher positive charge on Mg increases the solvation.
Several chloride and methyl-bridged dinuclear magnesium species, which
differ in their solvation, are present in equilibrium,
(Figure~\ref{fig10}). The calculations suggest that the Cl/Me exchange
between the two magnesium centers is initiated by a solvation imbalance
between the two metal centers. The least solvated attracts a bridging
chloride more strongly. The chloride unequally bound to the two
magnesium centers becomes terminal to the closer magnesium promoting
the transfer of a methyl group from the terminal to the bridging
position.  This chloride-methyl-bridged dimer achieves the Cl/Me
exchange. The dynamics of the solvent is thus essential in the Schlenk
equilibrium.

\begin{figure*}
\includegraphics{fig10}
\caption{\label{fig10}Methyl magnesium chloride in THF. Species present
in solution and involved in the Schlenk equilibrium proposed by AIMD
calculations. The red (green) arrow represents the loss (addition) of a
molecule of THF from (to) the coordination of the magnesium atoms.
${D}_{ij}^{XY}$ labels the dinuclear species with $i/j$ coordinated THF
molecules on the left/right magnesium center with XY (Cl or Me) are the
bridging atom or group. Adapted from ref~\cite{72}.}
\end{figure*}

The Grignard reaction itself was studied with the AIMD method by
considering the reaction of acetaldehyde with all identified forms of
CH$_{3}$MgCl in THF~\cite{73}. It was found that all forms are
competent in the Grignard reaction as the free energies of activation
are within a narrow energy range. Since the different Grignard species
are in rapid equilibria, they can all contribute to the reaction in
parallel. Therefore, the reaction can occur {via} competing
parallel pathways resulting in unclear kinetic order. Additional
solvation may also be required to achieve the reaction. This is the
case for the monomeric species, of which Mg(CH$_{3}$)$_{2}$ is found to
be the most reactive. A highly solvated ${\mu}^{2}$-Cl
dimagnesium species is the most reactive dinuclear species.
Importantly, the substrate and the nucleophile are initially bound to
different magnesium centers and, in the transition state the
acetaldehyde is strongly electrophilically activated by being
O-coordinated to both magnesium centers (Figure~\ref{fig11}). Previous
studies of the reaction using traditional (static) DFT calculations
also identified dinuclear magnesium complexes as the most
reactive~\cite{74,75,76}. The direct role of the solvent in modulating the
reaction pathway is the main reason for the structural and energetic
differences between the earlier and later studies. Indeed, the AIMD
calculations indicate that the solvent is an essential active partner
in the reaction. 

\begin{figure*}
\includegraphics{fig11}
\caption{\label{fig11}The most reactive species in the Grignard
reaction. The substrate (acetaldehyde) is coordinated to the left-hand
side magnesium, and the nucleophilic methyl group (green color) is on
the right-hand side magnesium. Copyright from~\cite{73}.}
\end{figure*}

This study also clarified the issue of nucleophile {vs} single
electron transfer (SET) mechanism. The SET mechanism has been proposed
for substrates with low reduction potential. Recent studies have shown
that the SET is rare and occurs only with aromatic carbonyl
compounds~\cite{77,78}. The computational study was limited to the
formation of the organic radical and thus to the calculation of the
bond dissociation energy (BDE) of the homolytic cleavage of the
CH$_{3}$--Mg bond (DFT static calculations). The
carbon--magnesium BDE in CH$_{3}$MgCl was calculated to be
high (about 60 kcal/mol) with very little influence of the solvent.
This high BDE would indicate that the radical cannot be formed.
However, when the substrate is bonded to the magnesium, the
carbon--magnesium BDE drops dramatically and the drop is increased as
the energy of the ${\rmpi}^*_{\mathrm{CO}}$ orbital of the substrate
is decreasing. The reason is that the single electron of the magnesium
species remains located on Mg in solvated MgCl species. However, the
MgCl(substrate) species has a low-lying LUMO that is localized on the
${\rmpi}^*_{\mathrm{CO}}$ empty orbital of the coordinated
substrate. Thus, the single electron goes to the coordinated substrate
${\rmpi}^*_{\mathrm{CO}}$ orbital, where it is stabilized compared
to be located on Mg. In other words, the substrate itself assists the
formation of the organic radical and the lowering of its reduction
potential reinforces the assistance. The calculations show that the SET
mechanism becomes competitive with the nucleophilic addition in the
case of fluorenone in excellent agreement with Woerpel's experimental
results~\cite{77,78}.  

\section{Conclusion and perspective}\label{sec5}

This topic was of interest to the author as she was an active member in
the construction of the Felkin--Anh rule. Recently, she returned to the
addition of nucleophiles to carbonyl groups with the Grignard reaction.
The description of important work done in the field of nucleophilic
addition to carbonyl groups by many authors described in this
perspective is well representative of the way in which computational
chemistry has developed and accompanied experimental studies. It is
noteworthy that the direction of approach of a nucleophile to a
carbonyl group has long been correctly captured with very simple
calculations. The attempts to quantitatively reproduce the face
selectivity illustrate the courage of computational chemists to try to
capture small energy differences that are computationally challenging
but chemically significant.  Trying to interpret the factors that
control the selectivity has also been a struggle. Now everyone seems to
accept that many factors contribute and none of them dominate. There
have been great improvements in the representation of chemical systems
and in computational methods over the past 40 years. This has allowed
small diastereomeric excesses can be calculated quite accurately.
Getting it right was not and is still not easy. One of the greatest
difficulties is to decide which species to include in a model.
Unfortunately, there are no entities present in the experimental
systems that should be ignored {a priori} in the modeling. In
particular, it would be a serious mistake to ignore the solvent. None
of the species present in the reactive media are total spectators but
representing the entire media is simply not possible. Computational
chemists will proceed step by step using either (or both) static and
{ab initio} molecular dynamics calculations. Static calculations,
including explicit and implicit solvation, will be useful for
well-identified reactive systems as illustrated by the cases reported
in this article. {Ab initio} molecular dynamics will be needed
to study cases where the dynamics of the solvent plays a role. It will
also be needed to analyze highly complex chemical media with unknown
solvent-dependent reactive systems as illustrated by the Grignard
reaction. This topic is indeed pursued with the study of the
\mbox{synergistic} role of lithium salts~\cite{79} in the so-called Turbo
Grignard~\cite{80}. This author is involved in the exploration of this
subject~\cite{81} in a collaboration with Professor Michele Cascella of
the Hylleraas Center at the University of Oslo. 

\section*{Declaration of interests}
The author does not work for, advise, own shares in or receive funds
from any organization that could benefit from this article, and has
declared no affiliations other than her research organizations. 

\section*{Funding}
Early work by this author was supported by the French National Center
for scientific Research (CNRS). More recent work by this author was
supported by the Research Council of Norway through the Center of
Excellence Hylleraas Center for Quantum Molecular Science (Grant
262695) and the Pioneer Research Grant MetalSynergy (Grant 314009) and
by the Norwegian Supercomputing Program (NOTUR) (Grant NN 4654K).

\CDRGrant[RCN]{262695}
\CDRGrant[RCN]{314009}
\CDRGrant[NOTUR]{NN 4654K}

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