32
and substrate atoms (or molecules) and the interactions between the particles
involved. If the interactions between the adsorbed species are repulsive, the resulting
overlayer often shows a homogeneous structure. On the contrary, if attractive forces
exist, there is a tendency to form islands or patches on the surface.
4.4 Density Functional Theory Calculations
in Electrocatalysis
A derivation of the density functional theory (DFT) method can be found in reference [13]. The DFT approach first computes electron density and then predicts system properties. Reliable exchange-correlation energies obtained by DFT method
are expressed by the electron density. In electrocatalysis, among many approximations, the standard generalized gradient approximation (GGA) functionals are used
widely because of their higher accuracy. Another major step in applying DFT calculations lies in constructing a surface model to properly interpret the experimental
findings or to formulate a rational design. In general, cluster and periodic slab models are applicable in resolving these problems.
The d-band theory of surface reactivity helped a rational approach to catalyst
design. Theoretical treatment of the atomic-level factors that determine catalytic
activity and selectivity became possible. The d-band theory for metal surfaces
regards the electronic states in the entire valence band of a metal surface responsible
for its reactivity [13]. For the transition and noble metals, the contribution from the
metal sp states is dominant but relatively constant. The coupling between an adsorbate and the metal d-states is mainly responsible for the variation in the interaction
energy on different metals. The key properties of the d-band are its energy-weighted
center (ε d ), the filling of the d-band, and the coupling matrix element.
An important feature of the theory is the prediction that the position of the d-band
center determines the binding energy of the adsorbate. Subsequent studies have
demonstrated a strong correlation between these two variables for a great number of
systems involving small atoms and molecules interacting with similar metal surfaces. In particular, the theory has proved very useful when applied to explaining
metal alloy reactivity and the strain, ligand, and ensemble effect. The identification
of ε d as a key factor in the reactivity of metal surfaces is significant until recently but
fell short in explaining, for example, the enhanced ORR activity of bulk Pt alloy
catalysts. Note that the d-band theory inherently assumes that surface reactivity is a
local property, which differs from another earlier perspective that bulk properties
determine catalytic properties. Following Sabatier’s principle stating that the interactions between the metal and the substrate should be “just right” (see Sect. 2.1), a
good ORR electrocatalyst may exhibit a moderate interaction with the adsorbates.
Previous DFT calculations demonstrated that compared to the bulk, the tensile
strain tends to shift ε d to a higher value, whereas compressive strain has the opposite
effect [13]. The position of the d-band depends both on the amount of strain and the
electron distribution between the monolayer and its substrates (ligand effect) [13].
4 Studies of Electrocatalytic Reactions
and substrate atoms (or molecules) and the interactions between the particles
involved. If the interactions between the adsorbed species are repulsive, the resulting
overlayer often shows a homogeneous structure. On the contrary, if attractive forces
exist, there is a tendency to form islands or patches on the surface.
4.4 Density Functional Theory Calculations
in Electrocatalysis
A derivation of the density functional theory (DFT) method can be found in reference [13]. The DFT approach first computes electron density and then predicts system properties. Reliable exchange-correlation energies obtained by DFT method
are expressed by the electron density. In electrocatalysis, among many approximations, the standard generalized gradient approximation (GGA) functionals are used
widely because of their higher accuracy. Another major step in applying DFT calculations lies in constructing a surface model to properly interpret the experimental
findings or to formulate a rational design. In general, cluster and periodic slab models are applicable in resolving these problems.
The d-band theory of surface reactivity helped a rational approach to catalyst
design. Theoretical treatment of the atomic-level factors that determine catalytic
activity and selectivity became possible. The d-band theory for metal surfaces
regards the electronic states in the entire valence band of a metal surface responsible
for its reactivity [13]. For the transition and noble metals, the contribution from the
metal sp states is dominant but relatively constant. The coupling between an adsorbate and the metal d-states is mainly responsible for the variation in the interaction
energy on different metals. The key properties of the d-band are its energy-weighted
center (ε d ), the filling of the d-band, and the coupling matrix element.
An important feature of the theory is the prediction that the position of the d-band
center determines the binding energy of the adsorbate. Subsequent studies have
demonstrated a strong correlation between these two variables for a great number of
systems involving small atoms and molecules interacting with similar metal surfaces. In particular, the theory has proved very useful when applied to explaining
metal alloy reactivity and the strain, ligand, and ensemble effect. The identification
of ε d as a key factor in the reactivity of metal surfaces is significant until recently but
fell short in explaining, for example, the enhanced ORR activity of bulk Pt alloy
catalysts. Note that the d-band theory inherently assumes that surface reactivity is a
local property, which differs from another earlier perspective that bulk properties
determine catalytic properties. Following Sabatier’s principle stating that the interactions between the metal and the substrate should be “just right” (see Sect. 2.1), a
good ORR electrocatalyst may exhibit a moderate interaction with the adsorbates.
Previous DFT calculations demonstrated that compared to the bulk, the tensile
strain tends to shift ε d to a higher value, whereas compressive strain has the opposite
effect [13]. The position of the d-band depends both on the amount of strain and the
electron distribution between the monolayer and its substrates (ligand effect) [13].
4 Studies of Electrocatalytic Reactions