Mechanism and Kinetics in Homogeneous Catalysis …
303
The problem encountered here can be expressed in a more formal way: The
correct mechanism simply cannot be represented on the potential energy surface
of the [Pd, Cl 2 , ligand, alkene] model system (the ligand was acetonitrile solvent)
initially built. No amount of exploration of the potential energy surface of this model
could possibly generate the correct mechanism. Extension to variants such as [Pd,
Cl 2 , ligand, alkene, nucleophile] was tested, but the extension to [Pd 2 , Cl 4 , ligand n ,
alkene] was only made after the experimental evidence supporting dimers was found.
As it happens, the initial calculations were performed on a model system with two
palladium atoms and one additional solvent ligand (n 1), and this model too is
unable to account for the reactivity, but optimization of one candidate structure did
hint that perhaps a species with n 2, as shown in Fig. 7, might be favorable, and then
calculations with that model confirmed this hint, leading to the correct mechanism.
Note that the n 1 potential energy surface is a lower-dimensional manifold on the n
2 surface, and the monomeric palladium surface is a lower-dimensional manifold
of the dimeric surface, so species and TSs with effectively lower stoichiometry can
be discovered when exploring the surface of the species with higher stoichiometry,
but in both cases the reverse is not true.
The impossibility to represent the correct reaction mechanism in a given model
system is a major challenge for computational mechanistic studies, since there does
not appear to be a systematic yet affordable theory-based approach to generate the correct model stoichiometry. Systematic approaches for exploring the potential energy
surface for a given assumed model stoichiometry are undergoing major expansion
[22] and are already very computationally demanding. Approaches requiring addition of additional fragments to the starting reaction model can also be formulated,
but on the one hand, they do usually require setting a maximum stoichiometry initially, and on the other hand, they rapidly lead to exponentially increasing computing
costs. Model building remains the area where the computational chemist’s chemical
intuition (or rather, that of their experimental collaborators, etc) remains essential
in many cases. To close this section, I will point out that had we been unlucky, and
had the mismatch between the calculated free energy barrier for the initially studied
mechanisms and the experimentally observed rates been somewhat smaller, then we
might have been led to publish this incorrect mechanism.
3.4 Morita–Baylis–Hillman Reaction
Our fourth case study is a reaction mechanism that we have been interested in for
some years now, the coupling of an acrylic ester with an aldehyde with catalysis by
an amine to form a new carbon–carbon bond. This particular variant of the Morita–Baylis–Hillmann reaction has received a lot of synthetic interest, with synthetic
chemists being interested in developing catalysts and conditions that maximize reactivity, and optionally that allow enantioselective formation of one or other of the
mirror-image products. An experimental colleague initiated the collaboration, with
the view of obtaining insight into the structure of key rate-limiting TSs so as to be
303
The problem encountered here can be expressed in a more formal way: The
correct mechanism simply cannot be represented on the potential energy surface
of the [Pd, Cl 2 , ligand, alkene] model system (the ligand was acetonitrile solvent)
initially built. No amount of exploration of the potential energy surface of this model
could possibly generate the correct mechanism. Extension to variants such as [Pd,
Cl 2 , ligand, alkene, nucleophile] was tested, but the extension to [Pd 2 , Cl 4 , ligand n ,
alkene] was only made after the experimental evidence supporting dimers was found.
As it happens, the initial calculations were performed on a model system with two
palladium atoms and one additional solvent ligand (n 1), and this model too is
unable to account for the reactivity, but optimization of one candidate structure did
hint that perhaps a species with n 2, as shown in Fig. 7, might be favorable, and then
calculations with that model confirmed this hint, leading to the correct mechanism.
Note that the n 1 potential energy surface is a lower-dimensional manifold on the n
2 surface, and the monomeric palladium surface is a lower-dimensional manifold
of the dimeric surface, so species and TSs with effectively lower stoichiometry can
be discovered when exploring the surface of the species with higher stoichiometry,
but in both cases the reverse is not true.
The impossibility to represent the correct reaction mechanism in a given model
system is a major challenge for computational mechanistic studies, since there does
not appear to be a systematic yet affordable theory-based approach to generate the correct model stoichiometry. Systematic approaches for exploring the potential energy
surface for a given assumed model stoichiometry are undergoing major expansion
[22] and are already very computationally demanding. Approaches requiring addition of additional fragments to the starting reaction model can also be formulated,
but on the one hand, they do usually require setting a maximum stoichiometry initially, and on the other hand, they rapidly lead to exponentially increasing computing
costs. Model building remains the area where the computational chemist’s chemical
intuition (or rather, that of their experimental collaborators, etc) remains essential
in many cases. To close this section, I will point out that had we been unlucky, and
had the mismatch between the calculated free energy barrier for the initially studied
mechanisms and the experimentally observed rates been somewhat smaller, then we
might have been led to publish this incorrect mechanism.
3.4 Morita–Baylis–Hillman Reaction
Our fourth case study is a reaction mechanism that we have been interested in for
some years now, the coupling of an acrylic ester with an aldehyde with catalysis by
an amine to form a new carbon–carbon bond. This particular variant of the Morita–Baylis–Hillmann reaction has received a lot of synthetic interest, with synthetic
chemists being interested in developing catalysts and conditions that maximize reactivity, and optionally that allow enantioselective formation of one or other of the
mirror-image products. An experimental colleague initiated the collaboration, with
the view of obtaining insight into the structure of key rate-limiting TSs so as to be