464
H. Hirao
The diversity of transition-metal complexes and the prominent role of computational chemistry in mechanistic studies can be seen, for example, in iron-containing
enzymes and their synthetic analogues in bioinorganic chemistry. In the case of
the cytochrome P450 enzymes (P450s), the central iron ion is coordinated by a
deprotonated protoporphyrin IX ligand in the equatorial sites and by a cysteinate
ligand in the proximal site [1, 2]. It is known that various intermediates are formed
in the catalytic cycle of P450s, in which the oxidation state of the iron can vary
between +2 and +4. The +4 state taken by the oxoiron(IV) porphyrin π-cation radical species called compound I (Cpd I) is of particular interest in the context of
catalysis, because Cpd I can effect difficult chemical transformations such as C–H
activation of alkane substrates via the rebound mechanism [3]. Other types of heme
enzymes also exist wherein an amino acid residue other than cysteinate is used as the
proximal ligand [4, 5]. Furthermore, there are a number of nonheme iron enzymes in
nature that use aspartate, glutamate, histidine, or other anionic groups as ligands [6,
7]. As in the case of heme enzymes, an oxoiron(IV) species is used for C–H activation in some cases [8], and other types of active species have also been identified [9,
10]. The intriguing but elusive nature of active species in heme and nonheme iron
enzymes has prompted chemists to prepare synthetic analogues of enzymatic active
species, and substantial progress has been made in this area [11–15]. Computational
chemistry has contributed significantly to understanding the reactivity patterns of
iron enzymes and synthetic analogues [16–24].
In this chapter, we discuss some of our recent attempts to study the structure and
catalytic properties of transition-metal-containing systems of different sizes, such
as homogeneous transition-metal complexes, metalloenzymes, and metal–organic
frameworks (MOFs). Kohn–Sham density-functional theory (DFT) is usually the
first choice for describing the quantum mechanical nature of these systems, yet we
also sometimes employ hybrid techniques such as quantum mechanics and quantum
mechanics (QM/QM’) and quantum mechanics and molecular mechanics (QM/MM)
to deal with large molecular systems. Application of these techniques to specific
chemical reactions often yields unexpected insights.
2 Computational Methods for Studying Catalysis
in Various Systems
The computational treatment of transition-metal-containing systems is challenging
in several respects. One of the major challenges pertains to high computational costs
of quantum mechanical calculations. Correlated ab initio molecular orbital (MO)
methods are usually too demanding for reaction pathway analyses of such systems.
As such, DFT in the Kohn–Sham formalism is often used for this purpose [25–38].
Many exchange–correlation functionals have been developed so far to approximate
the exchange–correlation energy in the Kohn–Sham DFT. Which functional performs
best for a given purpose has been (and will continue to be) a matter of intense debate,
H. Hirao
The diversity of transition-metal complexes and the prominent role of computational chemistry in mechanistic studies can be seen, for example, in iron-containing
enzymes and their synthetic analogues in bioinorganic chemistry. In the case of
the cytochrome P450 enzymes (P450s), the central iron ion is coordinated by a
deprotonated protoporphyrin IX ligand in the equatorial sites and by a cysteinate
ligand in the proximal site [1, 2]. It is known that various intermediates are formed
in the catalytic cycle of P450s, in which the oxidation state of the iron can vary
between +2 and +4. The +4 state taken by the oxoiron(IV) porphyrin π-cation radical species called compound I (Cpd I) is of particular interest in the context of
catalysis, because Cpd I can effect difficult chemical transformations such as C–H
activation of alkane substrates via the rebound mechanism [3]. Other types of heme
enzymes also exist wherein an amino acid residue other than cysteinate is used as the
proximal ligand [4, 5]. Furthermore, there are a number of nonheme iron enzymes in
nature that use aspartate, glutamate, histidine, or other anionic groups as ligands [6,
7]. As in the case of heme enzymes, an oxoiron(IV) species is used for C–H activation in some cases [8], and other types of active species have also been identified [9,
10]. The intriguing but elusive nature of active species in heme and nonheme iron
enzymes has prompted chemists to prepare synthetic analogues of enzymatic active
species, and substantial progress has been made in this area [11–15]. Computational
chemistry has contributed significantly to understanding the reactivity patterns of
iron enzymes and synthetic analogues [16–24].
In this chapter, we discuss some of our recent attempts to study the structure and
catalytic properties of transition-metal-containing systems of different sizes, such
as homogeneous transition-metal complexes, metalloenzymes, and metal–organic
frameworks (MOFs). Kohn–Sham density-functional theory (DFT) is usually the
first choice for describing the quantum mechanical nature of these systems, yet we
also sometimes employ hybrid techniques such as quantum mechanics and quantum
mechanics (QM/QM’) and quantum mechanics and molecular mechanics (QM/MM)
to deal with large molecular systems. Application of these techniques to specific
chemical reactions often yields unexpected insights.
2 Computational Methods for Studying Catalysis
in Various Systems
The computational treatment of transition-metal-containing systems is challenging
in several respects. One of the major challenges pertains to high computational costs
of quantum mechanical calculations. Correlated ab initio molecular orbital (MO)
methods are usually too demanding for reaction pathway analyses of such systems.
As such, DFT in the Kohn–Sham formalism is often used for this purpose [25–38].
Many exchange–correlation functionals have been developed so far to approximate
the exchange–correlation energy in the Kohn–Sham DFT. Which functional performs
best for a given purpose has been (and will continue to be) a matter of intense debate,