organometallic reactions. It is also known that it is preferable to include these effects
at the optimization stage. Schoenebeck et al. proved the crucial role of dispersion as
reactivity-controlling factor in organometallic reactivity. Using methods which
included dispersion correction allowed for the first time to locate the transition states
for the oxidative addition of Pd(0)L 2 (L ¼ phosphine) to aromatic CÀO bonds. In
contrast, DFT methods without dispersion correction indicated a preferred pathway
involving a phosphine dissociation for all cases considered [71].
For the benchmark studies commented above, the energy differences between
functionals incorporating dispersion are usually small, around a few kcal mol
À1 .
This could suggest a small impact of the functional. Unfortunately, this is only true
because all reactions which were considered occur on the closed-shell singlet PES.
However, and despite the success of DFT methods for reactions involving closedshell species, DFT calculations of systems in which more than one spin state can be
involved are much more challenging. In the next subsection we will illustrate the
difficulties encountered in using DFT for describing a reaction where more than one
spin state could be involved and show how we tackle these problems.
5.2 Spin-State Energetics
Usually, the energy profiles obtained with functionals of similar quality only differ in
a few kcal mol
À1 . However, major discrepancies, which can impact on the interpretation of a reaction mechanism, can appear when radical species are involved. This is
a topic of current interest for first-row transition metals where one-electron steps are
frequent. Non innocent redox active ligands or substrates can also favor pathways
via radical species. When two (or more) spin states are close in energy the usual
questions to address are the electronic nature of the ground state and the possible
change of spin state along a reaction pathway. These two issues are important for
chemical understanding, and Chap. 8 presents a detailed account of challenges posed
by spin states in computational organometallic chemistry [72].
The relative energies of different spin states can be obtained from DFT calculations, but the values are very sensitive to the approximation used for the exchange
functional, and particularly to the percentage of Hartree-Fock (HF) exchange in the
functional. Usually pure functionals (0% HF exchange) stabilize low spin states and
high spin states are stabilized by increasing the percentage of exact (HF) exchange
[73]. Due to this effect the relative energies obtained with different functionals may
differ by 10–30 kcal mol
À1 .
The suitability of the local coupled-cluster methods, as DLPNO-CCSD(T), for
describing two-spin-state reactivity is a matter of current discussion [74, 75]. A
recent study concluded that even if these methods are promising the approximations
used are not yet robust enough to enable applications in demanding systems [74].
The difficulties in evaluating spin-state energy gaps can be illustrated by the study
of the mechanism of the cyclohydroamination of primary aliphatic alkenyl-amines
catalyzed by a β-diketiminatocobalt(II) complex (Scheme 6) [60]. The question of
20
O. Eisenstein et al.
at the optimization stage. Schoenebeck et al. proved the crucial role of dispersion as
reactivity-controlling factor in organometallic reactivity. Using methods which
included dispersion correction allowed for the first time to locate the transition states
for the oxidative addition of Pd(0)L 2 (L ¼ phosphine) to aromatic CÀO bonds. In
contrast, DFT methods without dispersion correction indicated a preferred pathway
involving a phosphine dissociation for all cases considered [71].
For the benchmark studies commented above, the energy differences between
functionals incorporating dispersion are usually small, around a few kcal mol
À1 .
This could suggest a small impact of the functional. Unfortunately, this is only true
because all reactions which were considered occur on the closed-shell singlet PES.
However, and despite the success of DFT methods for reactions involving closedshell species, DFT calculations of systems in which more than one spin state can be
involved are much more challenging. In the next subsection we will illustrate the
difficulties encountered in using DFT for describing a reaction where more than one
spin state could be involved and show how we tackle these problems.
5.2 Spin-State Energetics
Usually, the energy profiles obtained with functionals of similar quality only differ in
a few kcal mol
À1 . However, major discrepancies, which can impact on the interpretation of a reaction mechanism, can appear when radical species are involved. This is
a topic of current interest for first-row transition metals where one-electron steps are
frequent. Non innocent redox active ligands or substrates can also favor pathways
via radical species. When two (or more) spin states are close in energy the usual
questions to address are the electronic nature of the ground state and the possible
change of spin state along a reaction pathway. These two issues are important for
chemical understanding, and Chap. 8 presents a detailed account of challenges posed
by spin states in computational organometallic chemistry [72].
The relative energies of different spin states can be obtained from DFT calculations, but the values are very sensitive to the approximation used for the exchange
functional, and particularly to the percentage of Hartree-Fock (HF) exchange in the
functional. Usually pure functionals (0% HF exchange) stabilize low spin states and
high spin states are stabilized by increasing the percentage of exact (HF) exchange
[73]. Due to this effect the relative energies obtained with different functionals may
differ by 10–30 kcal mol
À1 .
The suitability of the local coupled-cluster methods, as DLPNO-CCSD(T), for
describing two-spin-state reactivity is a matter of current discussion [74, 75]. A
recent study concluded that even if these methods are promising the approximations
used are not yet robust enough to enable applications in demanding systems [74].
The difficulties in evaluating spin-state energy gaps can be illustrated by the study
of the mechanism of the cyclohydroamination of primary aliphatic alkenyl-amines
catalyzed by a β-diketiminatocobalt(II) complex (Scheme 6) [60]. The question of
20
O. Eisenstein et al.