Keywords Catalysis · Density functional approximations · High-valent metals ·
Oxidation chemistry · Spin states · Transition metals
Abbreviations
DFAs
Density functional approximations
DFT
Density functional theory
IPEA
Ionization potential, electron affinity
MECP Minimum energy crossing point
SCO
Spin cross-over
1 General Introduction
Chemistry can (or should) be defined as the discipline of transformation, where
molecules meet, interact, and then depart completely reshaped; these processes can
be enhanced or made more selective through the implication of (transition) metals.
The first-row transition metals (Sc-Cu) play a special role in this, in the sense that
they are earth-abundant (allowing for sustainable, or green, catalysis) and in general
show a larger sensitivity to how the electrons are distributed over the d-orbitals than
the corresponding transition metals in higher rows of the periodic table. The possible
distributions of electrons over the d-orbitals obviously depend on the number of
electrons; which metal is involved; how many coordinating ligands are present;
and of which type. For instance, for a d
6 system, the six electrons can occupy the
three non-bonding orbitals, (xy)
2 (xz)
2 (yz)
2 , and hence lead to a low-spin state;
however, if the anti-bonding orbitals (x
2 -y
2 , z
2 ) are sufficiently low to overcome
the pairing energy by increased exchange interactions, the high-spin state
(xy)
2 (xz)
1
(yz)
1 (x
2 -y
2 )
1 (z
2 )
1 might be lower in energy. It is well established that
electrons, despite the electron-electron repulsion, have the tendency to pair up,
with an orbital being occupied by one spin-up and one spin-down electron. Nevertheless, for d-orbitals there exists a competition between this pairing energy and
exchange interactions; both are beneficial, but in high-spin states, there are more
electrons in parallel, leading to more exchange interactions (see Fig. 1).
In order to reach this larger number of exchange interactions in a high-spin state,
one has to place the electron in a higher-energy orbital. Therefore, depending on how
large is the separation between the d-orbitals, the balance between more exchange
and larger orbital separations could go either to low-, intermediate-, or high-spin
states. Because of the combination of these factors, it is difficult to predict a priori
which distribution is more favorable, and hence important insights are coming from
computational chemistry. However, it has been shown that spin states, as expected,
are difficult to treat properly, for both density functional approximations (DFAs) and
wavefunction theory in its many guises (vide infra) [1]. Furthermore, during a
chemical reaction, the transition-metal complex and substrate are able to switch
192
M. Swart
Oxidation chemistry · Spin states · Transition metals
Abbreviations
DFAs
Density functional approximations
DFT
Density functional theory
IPEA
Ionization potential, electron affinity
MECP Minimum energy crossing point
SCO
Spin cross-over
1 General Introduction
Chemistry can (or should) be defined as the discipline of transformation, where
molecules meet, interact, and then depart completely reshaped; these processes can
be enhanced or made more selective through the implication of (transition) metals.
The first-row transition metals (Sc-Cu) play a special role in this, in the sense that
they are earth-abundant (allowing for sustainable, or green, catalysis) and in general
show a larger sensitivity to how the electrons are distributed over the d-orbitals than
the corresponding transition metals in higher rows of the periodic table. The possible
distributions of electrons over the d-orbitals obviously depend on the number of
electrons; which metal is involved; how many coordinating ligands are present;
and of which type. For instance, for a d
6 system, the six electrons can occupy the
three non-bonding orbitals, (xy)
2 (xz)
2 (yz)
2 , and hence lead to a low-spin state;
however, if the anti-bonding orbitals (x
2 -y
2 , z
2 ) are sufficiently low to overcome
the pairing energy by increased exchange interactions, the high-spin state
(xy)
2 (xz)
1
(yz)
1 (x
2 -y
2 )
1 (z
2 )
1 might be lower in energy. It is well established that
electrons, despite the electron-electron repulsion, have the tendency to pair up,
with an orbital being occupied by one spin-up and one spin-down electron. Nevertheless, for d-orbitals there exists a competition between this pairing energy and
exchange interactions; both are beneficial, but in high-spin states, there are more
electrons in parallel, leading to more exchange interactions (see Fig. 1).
In order to reach this larger number of exchange interactions in a high-spin state,
one has to place the electron in a higher-energy orbital. Therefore, depending on how
large is the separation between the d-orbitals, the balance between more exchange
and larger orbital separations could go either to low-, intermediate-, or high-spin
states. Because of the combination of these factors, it is difficult to predict a priori
which distribution is more favorable, and hence important insights are coming from
computational chemistry. However, it has been shown that spin states, as expected,
are difficult to treat properly, for both density functional approximations (DFAs) and
wavefunction theory in its many guises (vide infra) [1]. Furthermore, during a
chemical reaction, the transition-metal complex and substrate are able to switch
192
M. Swart