of a given structural isomer to dynamically adapt its structure so as to allow the
reaction to evolve on the most favorable free-energy path. Such fluxional propensity
is illustrated in Figures 17.7b and 17.7f where the more reactive two-layered Au 8
cluster is shown to undergo a large structural transformation upon adsorption of
molecular oxygen at the ‘‘periphery site’’; i.e., the approximate bi-capped octahedral geometry (Figure 17.7b) is transformed to a bi-capped trigonal prism (Figure
17.7f ). Note, that the structural fluxionality is essential for the reaction to occur,
since it was found that constraining the cluster to maintain its original geometry
(Figure 17.7b) prevents the adsorption and activation of O 2 .
2. Electronic Size Effects: Understanding the size-dependent electronic structure of
the Au n /MgO(F 5c ) model catalysts, which is fundamental for elucidation of their
atom-by-atom controlled reactivity, is facilitated by analysis of the spectra of the
local density of electronic states (LDOS) projected on the oxygen molecule and on
the metal cluster; a similar analysis is often employed in the context of the interaction of adsorbates with extended surfaces [67]. Figure 17.6a shows the LDOS
projected on the O 2 molecule which is adsorbed at the periphery site (Figure 17.5Bf ) of the more reactive isomer of the Au 8 /MgO(F 5c ) model catalyst. All the prominent peaks of the LDOS spectrum in Figure 17.6a can be unambiguously assigned
to orbitals of (free) molecular oxygen origins. In addition, these states overlap
with the entire d-band of the Au 8 cluster (shown in Figure 17.6b) in the range
À7 eV a E a E F , where E F is the Fermi energy. Bonding of the oxygen molecule to
the gold octamer involves mainly hybridization of the 5s, 1p k , and 1p ? oxygen
states with the gold d-band (Figure 17.6b). Most importantly, the full spin-manifold
of the antibonding 2p
à states of O 2 is located below E F , resulting in strong activation
of the O 2 molecule through occupation of the antibonding orbitals. This leads to
weakening of the OaO bond that is reflected in a significant increase in its length
(1.43 A ˚ in Figure 17.7f ) compared to that of the free molecule (1.25 A ˚ ). Accompanying the activation process is a change in the spin state of the molecule
from a triplet state in the gas phase to a peroxo-like adsorbed state with a zero net
spin.
A drastically different scenario is found for the interaction of O 2 with the smaller
gold cluster, Au 4 /MgO(F 5c ), where molecular oxygen adsorbs in an ‘‘on-top’’ configuration, with one of the oxygen atoms binding to a single gold atom (Figure
17.7g). This system exhibits rather weak binding of the molecule to the metal
cluster (0.18 eV), an almost unperturbed OaO bond length (1.28 A ˚ ), and a spinsplitting of the oxygen-projected LDOS spectrum (see Figure 17.6c). The weak
binding is attributed to the narrower d-band of the adsorbed Au 4 cluster compared
to that of Au 8 (see Figures 17.6b and 17.6d), with a consequent lack of overlap between the states at the bottom of the d-band of the gold cluster (Figure 17.6d) and
the molecular oxygen states with energies E < À5 eV. Moreover, the spin-down
antibonding 2p
à ? and 2p
Ã
k orbitals of the adsorbed oxygen molecule are now
located above E F (unlike the case of the larger cluster, compare Figures 17.6c
and 17.6a) which results in no activation of the molecule by the adsorbed Au 4
cluster.
3. Impurity-doping Effects: Finally, we address the possibility of enhancing the
17.3 Chemical Reactions and Catalytic Processes on Free and Supported Clusters 573
reaction to evolve on the most favorable free-energy path. Such fluxional propensity
is illustrated in Figures 17.7b and 17.7f where the more reactive two-layered Au 8
cluster is shown to undergo a large structural transformation upon adsorption of
molecular oxygen at the ‘‘periphery site’’; i.e., the approximate bi-capped octahedral geometry (Figure 17.7b) is transformed to a bi-capped trigonal prism (Figure
17.7f ). Note, that the structural fluxionality is essential for the reaction to occur,
since it was found that constraining the cluster to maintain its original geometry
(Figure 17.7b) prevents the adsorption and activation of O 2 .
2. Electronic Size Effects: Understanding the size-dependent electronic structure of
the Au n /MgO(F 5c ) model catalysts, which is fundamental for elucidation of their
atom-by-atom controlled reactivity, is facilitated by analysis of the spectra of the
local density of electronic states (LDOS) projected on the oxygen molecule and on
the metal cluster; a similar analysis is often employed in the context of the interaction of adsorbates with extended surfaces [67]. Figure 17.6a shows the LDOS
projected on the O 2 molecule which is adsorbed at the periphery site (Figure 17.5Bf ) of the more reactive isomer of the Au 8 /MgO(F 5c ) model catalyst. All the prominent peaks of the LDOS spectrum in Figure 17.6a can be unambiguously assigned
to orbitals of (free) molecular oxygen origins. In addition, these states overlap
with the entire d-band of the Au 8 cluster (shown in Figure 17.6b) in the range
À7 eV a E a E F , where E F is the Fermi energy. Bonding of the oxygen molecule to
the gold octamer involves mainly hybridization of the 5s, 1p k , and 1p ? oxygen
states with the gold d-band (Figure 17.6b). Most importantly, the full spin-manifold
of the antibonding 2p
à states of O 2 is located below E F , resulting in strong activation
of the O 2 molecule through occupation of the antibonding orbitals. This leads to
weakening of the OaO bond that is reflected in a significant increase in its length
(1.43 A ˚ in Figure 17.7f ) compared to that of the free molecule (1.25 A ˚ ). Accompanying the activation process is a change in the spin state of the molecule
from a triplet state in the gas phase to a peroxo-like adsorbed state with a zero net
spin.
A drastically different scenario is found for the interaction of O 2 with the smaller
gold cluster, Au 4 /MgO(F 5c ), where molecular oxygen adsorbs in an ‘‘on-top’’ configuration, with one of the oxygen atoms binding to a single gold atom (Figure
17.7g). This system exhibits rather weak binding of the molecule to the metal
cluster (0.18 eV), an almost unperturbed OaO bond length (1.28 A ˚ ), and a spinsplitting of the oxygen-projected LDOS spectrum (see Figure 17.6c). The weak
binding is attributed to the narrower d-band of the adsorbed Au 4 cluster compared
to that of Au 8 (see Figures 17.6b and 17.6d), with a consequent lack of overlap between the states at the bottom of the d-band of the gold cluster (Figure 17.6d) and
the molecular oxygen states with energies E < À5 eV. Moreover, the spin-down
antibonding 2p
à ? and 2p
Ã
k orbitals of the adsorbed oxygen molecule are now
located above E F (unlike the case of the larger cluster, compare Figures 17.6c
and 17.6a) which results in no activation of the molecule by the adsorbed Au 4
cluster.
3. Impurity-doping Effects: Finally, we address the possibility of enhancing the
17.3 Chemical Reactions and Catalytic Processes on Free and Supported Clusters 573