8 Electronic Properties of Transition Metal-Benzene Sandwich Clusters
323
the multiple-decker sandwich clusters is quite metal-dependent, as depicted in
Fig. 8.6. Yasuike et al. [62] demonstrated that the sandwich formation is affected
not only by a thermodynamic but also by a kinetic factor, where the formation
process governs the reactivity rather than the thermodynamic stability of the reaction
products does. In particular, the spin multiplicity of the system has been proven
to be an important guideline in understanding the reactivity of transition metal
ions [63]. They carried out quantum chemical calculations to determine the most
preferable spin states for reactant and product clusters in the cluster growth process
of M n Bz n + 1 + M → M n + 1 Bz n + 1 (n = 1, 2), where M = Ti, V, and Cr.
According to the calculation results, both CrBz 2 and Cr 2 Bz 2 preferred a singlet
state, whereas the ground state of a Cr atom is septet [64]. This means that multiplestep nonadiabatic (i.e., spin-flip) transitions are needed for the growth from CrBz 2 to
Cr 2 Bz 2 as the overall reactant system (CrBz 2 + Cr) does not conserve its total spins
during the reaction. By contrast, the calculation results estimated the lowest-energy
state of V 2 Bz 2 to be either a singlet or triplet, which is close in energy to each other.
VBz 2 was determined to be a doublet while the ground state of a V atom is a quartet
[64]. Therefore, spin flipping is not required for the transition from VBz 2 + V to
the triplet-state V 2 Bz 2 . The reaction barrier arising from the spin conservation rule
explains the absence of Cr 2 Bz 2 and larger clusters, while the efficient production of
V n Bz n + 1 is likely due to spin conservation in the cluster growth process.
8.3 Electronic and Magnetic Properties of Transition
Metal-Benzene Sandwich Clusters
8.3.1 Physical Properties of Low-Dimensional Materials
It has been known that properties of materials which have low-dimensional (i.e.,
zero-, one-, and two-dimensional, hereafter 0D, 1D, and 2D, respectively) structures
are different from those of three-dimensional (3D) materials such as bulk materials
[65]. For instance, fullerenes, carbon nanotubes, and graphene (Fig. 8.10) are
regarded as typical low-dimensional materials that are distinguished from graphite.
There has been tremendous interest in extraordinary electron motion and resulting
unique electronic properties originating from the low dimensionality of these
materials. In fact, conductivity of carbon nanotubes has been a stimulating subject,
since it was shown that nanotubes with a certain chirality (i.e., degree of twist)
exhibit dramatically high conductivity [66–67]. It is understood that electron
transport in the nanotubes is an anisotropic phenomenon in which different periodic
boundary conditions are applied depending on the chirality [68]. Likewise, lowdimensional magnetism has gathered continuous attention since the discovery of
the first single-molecule magnet (SMM), which exhibited magnetic hysteresis of a
pure molecular origin [69]. Mn-containing SMMs have been studied for decades
because the high-spin (3d 5 4s 2 ) configuration of a Mn atom is advantageous
323
the multiple-decker sandwich clusters is quite metal-dependent, as depicted in
Fig. 8.6. Yasuike et al. [62] demonstrated that the sandwich formation is affected
not only by a thermodynamic but also by a kinetic factor, where the formation
process governs the reactivity rather than the thermodynamic stability of the reaction
products does. In particular, the spin multiplicity of the system has been proven
to be an important guideline in understanding the reactivity of transition metal
ions [63]. They carried out quantum chemical calculations to determine the most
preferable spin states for reactant and product clusters in the cluster growth process
of M n Bz n + 1 + M → M n + 1 Bz n + 1 (n = 1, 2), where M = Ti, V, and Cr.
According to the calculation results, both CrBz 2 and Cr 2 Bz 2 preferred a singlet
state, whereas the ground state of a Cr atom is septet [64]. This means that multiplestep nonadiabatic (i.e., spin-flip) transitions are needed for the growth from CrBz 2 to
Cr 2 Bz 2 as the overall reactant system (CrBz 2 + Cr) does not conserve its total spins
during the reaction. By contrast, the calculation results estimated the lowest-energy
state of V 2 Bz 2 to be either a singlet or triplet, which is close in energy to each other.
VBz 2 was determined to be a doublet while the ground state of a V atom is a quartet
[64]. Therefore, spin flipping is not required for the transition from VBz 2 + V to
the triplet-state V 2 Bz 2 . The reaction barrier arising from the spin conservation rule
explains the absence of Cr 2 Bz 2 and larger clusters, while the efficient production of
V n Bz n + 1 is likely due to spin conservation in the cluster growth process.
8.3 Electronic and Magnetic Properties of Transition
Metal-Benzene Sandwich Clusters
8.3.1 Physical Properties of Low-Dimensional Materials
It has been known that properties of materials which have low-dimensional (i.e.,
zero-, one-, and two-dimensional, hereafter 0D, 1D, and 2D, respectively) structures
are different from those of three-dimensional (3D) materials such as bulk materials
[65]. For instance, fullerenes, carbon nanotubes, and graphene (Fig. 8.10) are
regarded as typical low-dimensional materials that are distinguished from graphite.
There has been tremendous interest in extraordinary electron motion and resulting
unique electronic properties originating from the low dimensionality of these
materials. In fact, conductivity of carbon nanotubes has been a stimulating subject,
since it was shown that nanotubes with a certain chirality (i.e., degree of twist)
exhibit dramatically high conductivity [66–67]. It is understood that electron
transport in the nanotubes is an anisotropic phenomenon in which different periodic
boundary conditions are applied depending on the chirality [68]. Likewise, lowdimensional magnetism has gathered continuous attention since the discovery of
the first single-molecule magnet (SMM), which exhibited magnetic hysteresis of a
pure molecular origin [69]. Mn-containing SMMs have been studied for decades
because the high-spin (3d 5 4s 2 ) configuration of a Mn atom is advantageous