accounts on the quantum-mechanics background [27, 28], molecular fragments as
building blocks [29], or electron pushing [30] fall outside this chapter, but can be
found in textbooks.
A change in spin state occurs often in enzymes, with the cytochrome P450s as
most relevant example [31]: in the resting state of P450cam, the active site is filled by
water leading to a low-spin hexa-coordinate Fe(III); upon substrate binding, the axial
water is removed, leading to a high-spin square-pyramidal Fe(III); the first electron
reduction leads to a high-spin Fe(II), which is followed by dioxygen binding to form
a Fe(III)-superoxo, electron reduction to form the Fe(III)-peroxo, and protonation to
form the Fe(III)-hydroperoxo [32, 33]. Afterward, protonation to generate Compound I (an Fe(IV)-oxo coupled to a porphyrin radical) [34], involving two-state
reactivity [2], leads to product formation. The spin-flips involved in these steps are
ubiquitous in transition-metal chemistry and can be studied computationally
through, e.g., minimum energy crossing points (MECPs) and/or spin-orbit coupling
(vide infra).
A special case for the spin-state switching is formed by spin-crossover (SCO)
compounds, which under an external influence (temperature, light, pressure) switch
from one spin state to another. In most cases, this results from the cooperative
behavior of an ensemble of transition-metal compounds, although also isolated
compounds can show SCO behavior. The design of new SCO materials is widely
studied, with some recent successes [35] but also pitfalls (such as erratic behavior of
counterions [36]). The field of SCO compounds is too broad to be reviewed here, but
the reader is referred to recent reviews [36–39].
2.1.1 MECP
The minimum energy crossing point (MECP) is that point in space where the energy
surfaces of two spin states cross (see Fig. 3); the MECP is similar to conical
intersections [40–43], with similar strategies for structure determination. Instead of
normal geometry optimizations where the curvature of the Hessian (second derivative of energy w.r.t. atomic coordinates) should be all positive, or transition-state
searches where one normal coordinate should be maximized and all others minimized, in the case of MECP, the mathematical formulation is a bit more complex
because (1) it involves two energy surfaces and (2) there is the constrained search
such that the energy of surface A matches the energy of surface B; at the same time,
all other coordinates should be minimized. Harvey and co-workers [44] were among
the first to provide a computer program to handle this, based on ideas by Bearpark
and co-workers [45], which has since then been incorporated into many quantum
chemistry packages [46–49]. Based on many reports in the literature [50, 51], it
was observed that the energy needed to reach the MECP is of the order of
5–10 kcal mol
À1 , which is usually lower than the barriers for the chemical
reactions. Hence, usually one can assume that the spin-state crossing through
the MECP is sufficiently fast in comparison to the chemical reaction and will not
hinder the reaction mechanism.
Dealing with Spin States in Computational Organometallic Catalysis
195
building blocks [29], or electron pushing [30] fall outside this chapter, but can be
found in textbooks.
A change in spin state occurs often in enzymes, with the cytochrome P450s as
most relevant example [31]: in the resting state of P450cam, the active site is filled by
water leading to a low-spin hexa-coordinate Fe(III); upon substrate binding, the axial
water is removed, leading to a high-spin square-pyramidal Fe(III); the first electron
reduction leads to a high-spin Fe(II), which is followed by dioxygen binding to form
a Fe(III)-superoxo, electron reduction to form the Fe(III)-peroxo, and protonation to
form the Fe(III)-hydroperoxo [32, 33]. Afterward, protonation to generate Compound I (an Fe(IV)-oxo coupled to a porphyrin radical) [34], involving two-state
reactivity [2], leads to product formation. The spin-flips involved in these steps are
ubiquitous in transition-metal chemistry and can be studied computationally
through, e.g., minimum energy crossing points (MECPs) and/or spin-orbit coupling
(vide infra).
A special case for the spin-state switching is formed by spin-crossover (SCO)
compounds, which under an external influence (temperature, light, pressure) switch
from one spin state to another. In most cases, this results from the cooperative
behavior of an ensemble of transition-metal compounds, although also isolated
compounds can show SCO behavior. The design of new SCO materials is widely
studied, with some recent successes [35] but also pitfalls (such as erratic behavior of
counterions [36]). The field of SCO compounds is too broad to be reviewed here, but
the reader is referred to recent reviews [36–39].
2.1.1 MECP
The minimum energy crossing point (MECP) is that point in space where the energy
surfaces of two spin states cross (see Fig. 3); the MECP is similar to conical
intersections [40–43], with similar strategies for structure determination. Instead of
normal geometry optimizations where the curvature of the Hessian (second derivative of energy w.r.t. atomic coordinates) should be all positive, or transition-state
searches where one normal coordinate should be maximized and all others minimized, in the case of MECP, the mathematical formulation is a bit more complex
because (1) it involves two energy surfaces and (2) there is the constrained search
such that the energy of surface A matches the energy of surface B; at the same time,
all other coordinates should be minimized. Harvey and co-workers [44] were among
the first to provide a computer program to handle this, based on ideas by Bearpark
and co-workers [45], which has since then been incorporated into many quantum
chemistry packages [46–49]. Based on many reports in the literature [50, 51], it
was observed that the energy needed to reach the MECP is of the order of
5–10 kcal mol
À1 , which is usually lower than the barriers for the chemical
reactions. Hence, usually one can assume that the spin-state crossing through
the MECP is sufficiently fast in comparison to the chemical reaction and will not
hinder the reaction mechanism.
Dealing with Spin States in Computational Organometallic Catalysis
195