effects. The solute is placed inside a solvent cavity and the interaction between the
solute and the solvent is calculated at the cavity boundaries (Fig. 15, left). The
current models have been carefully parameterized to reproduce known experimental
solvation Gibbs energies. Continuum models have proved their usefulness to model
organometallic reactions and nowadays its use has become mandatory in the organometallic field even for solvents with low dielectric constant [101].
Despite their success, one should not forget that implicit solvent models describe
poorly specific interactions between solute and solvent. Moreover, these models fail
if solvent molecules take active part in the reaction. For these reasons, in the recent
years the studies using hybrid cluster-continuum models in which several solvent
molecules are incorporated to the quantum mechanical description of the system,
which in turn is placed inside a continuum model, have become increasingly
frequent (Fig. 15, middle) [102]. This approach has been successful in many
cases, but has an important limitation, related with the limited and fixed number of
solvent molecules which can be included. In addition, in the case of a relatively large
number of molecules, the geometrical optimization with a high number of positional
and conformational isomers can make the study intractable. These limitations vanish
using explicit solvent models (Fig. 15, right) in which the solute is placed in a box
containing a sufficiently large number of molecules, and molecular dynamics are
performed for the whole system either at the quantum, hybrid QM/MM, or full MM
levels. However, these calculations may be computationally demanding, and their
uses for the study of organometallic reactions are just starting as described in a recent
review [80] and the examples shown in the next paragraphs.
A recent study has compared explicit and implicit solvent modeling on
non-catalyzed and Ag-catalyzed intramolecular C-O coupling between terminal
alkyne and β-ketoester moieties to yield a furan ring [103]. The reaction takes
place in dimethylformamide (DMF), a highly polar (ε ¼ 36.7) but non-H bond
forming solvent. QM/MM molecular dynamics simulations were performed with the
explicit solvent model. Analysis of the trajectories obtained from QM/MM calculations indicated neither direct solvent participation in the reaction nor any site-specific
reactant–solvent interaction. In this system both solvent approaches give similar
energies, pointing out that when a sufficiently mobile, fluctuating solvent shell is
present it can be efficiently substituted by implicit solvent models with a huge
reduction of the computational costs. A similar approach was employed to compare
explicit and implicit solvation models in modeling the free energy profile of the
reductive elimination step in Suzuki-Miyaura coupling. The reductive elimination of
2 Ph ligands from Pd(PPh 3 ) 2 was modeled in a diverse set of solvents (benzene,
toluene, DMF, ethanol, and water) using both QM/MM molecular dynamics simulations and a continuum model (SMD) [104]. Whereas a reasonable correlation
between both solvent representations was found in aprotic solvents, the correlation
was poor for ethanol and water. The paper stresses the need for considering explicit
solvation for modeling Pd-catalyzed reactions in protic solvents [104]. Indeed, this
can be a rather general conclusion. Ab initio molecular dynamics simulations of the
ruthenium-catalyzed transfer hydrogenation reaction converting formaldehyde into
methanol in an explicit methanol solution showed that methanol solvent molecules
26
O. Eisenstein et al.
solute and the solvent is calculated at the cavity boundaries (Fig. 15, left). The
current models have been carefully parameterized to reproduce known experimental
solvation Gibbs energies. Continuum models have proved their usefulness to model
organometallic reactions and nowadays its use has become mandatory in the organometallic field even for solvents with low dielectric constant [101].
Despite their success, one should not forget that implicit solvent models describe
poorly specific interactions between solute and solvent. Moreover, these models fail
if solvent molecules take active part in the reaction. For these reasons, in the recent
years the studies using hybrid cluster-continuum models in which several solvent
molecules are incorporated to the quantum mechanical description of the system,
which in turn is placed inside a continuum model, have become increasingly
frequent (Fig. 15, middle) [102]. This approach has been successful in many
cases, but has an important limitation, related with the limited and fixed number of
solvent molecules which can be included. In addition, in the case of a relatively large
number of molecules, the geometrical optimization with a high number of positional
and conformational isomers can make the study intractable. These limitations vanish
using explicit solvent models (Fig. 15, right) in which the solute is placed in a box
containing a sufficiently large number of molecules, and molecular dynamics are
performed for the whole system either at the quantum, hybrid QM/MM, or full MM
levels. However, these calculations may be computationally demanding, and their
uses for the study of organometallic reactions are just starting as described in a recent
review [80] and the examples shown in the next paragraphs.
A recent study has compared explicit and implicit solvent modeling on
non-catalyzed and Ag-catalyzed intramolecular C-O coupling between terminal
alkyne and β-ketoester moieties to yield a furan ring [103]. The reaction takes
place in dimethylformamide (DMF), a highly polar (ε ¼ 36.7) but non-H bond
forming solvent. QM/MM molecular dynamics simulations were performed with the
explicit solvent model. Analysis of the trajectories obtained from QM/MM calculations indicated neither direct solvent participation in the reaction nor any site-specific
reactant–solvent interaction. In this system both solvent approaches give similar
energies, pointing out that when a sufficiently mobile, fluctuating solvent shell is
present it can be efficiently substituted by implicit solvent models with a huge
reduction of the computational costs. A similar approach was employed to compare
explicit and implicit solvation models in modeling the free energy profile of the
reductive elimination step in Suzuki-Miyaura coupling. The reductive elimination of
2 Ph ligands from Pd(PPh 3 ) 2 was modeled in a diverse set of solvents (benzene,
toluene, DMF, ethanol, and water) using both QM/MM molecular dynamics simulations and a continuum model (SMD) [104]. Whereas a reasonable correlation
between both solvent representations was found in aprotic solvents, the correlation
was poor for ethanol and water. The paper stresses the need for considering explicit
solvation for modeling Pd-catalyzed reactions in protic solvents [104]. Indeed, this
can be a rather general conclusion. Ab initio molecular dynamics simulations of the
ruthenium-catalyzed transfer hydrogenation reaction converting formaldehyde into
methanol in an explicit methanol solution showed that methanol solvent molecules
26
O. Eisenstein et al.