Catalytic Properties of Selected Transition Metal Oxides—Computational Studies
351
when distances r hkl from the centre of the polyhedron to the (hkl) surface with energy
of γ hkl are held by relationship: γ hkl /r hkl = const; ∀ hkl. The values of the surface
free energy are usually calculated via the well-established atomistic thermodynamic
modelling [73, 74].
2.3.5 Solvation Effects
The solid/liquid interfaces can be modelled via DFT augmented with solution effects
(DFTsol) [75, 76] or on the classical force-field level of theory. The solvation effects
are more abundantly implemented in the molecular codes (PCM and, more recently,
COSMO) than in the PBC programs [76]; the agreement between computational
results and the experimental data is very good, up to a few hundredths of eV in the
solvation energy.
Among the PBC codes, the VASPsol [76] extension to VASP belongs to the most
popular. Besides the energetics, the DFTsol extension of the DFT reproduces very
well the electrochemical properties [77] of the systems in thermodynamic equilibrium
with the liquid (e.g. the potential of zero charge, PZC).
3 Systems: Oxides
Out of the coordination environments for the TMs, definitely the oxide ligands are
the most common. Most of the industrial catalytic processes occurring on the surface
of transition metal oxide solids are the redox processes or the protic processes. In
the former, both TM cationic sites and the anionic oxide sites can act as the redox
centres, hence the number of elementary steps can be significant. Therefore, for the
detailed study thereof the simplified preliminary models can be used, like non-redox
metal oxide (e.g. alkaline earth oxides [78, 79]), where only oxide redox centres
exist. In both cases, the oxidiser atoms/molecules with surface ions atoms form the
reactive oxygen species (ROS) which are the by-products of the catalytic process.
3.1 Reducible and Non-reducible Oxides
Typically, the “reducible oxides”, RO, term concerns the oxides with relatively low
energy of O liberation [80], with band gaps <3 eV, and denotes the oxides of delectron metals: Ti, V, Fe, Co, Hf, Zr, Mn, W, Ni, and f -electron: Ce, Pr, and Sm.
The distinguishing between reducible and non-reducible oxides is, however, nonrigorous and is often dependent on the particular reaction, especially on the redox
potential of the reaction environment. For example, Paier et al. [81] reasonably define
the reducible oxides as those prone to reduction in the “catalytic” conditions, i.e. for
the O 2 partial pressure higher than ca. 10
−14 bar (ultra high vacuum lower limit) and
the temperatures up to ca. 1000
◦ C.
351
when distances r hkl from the centre of the polyhedron to the (hkl) surface with energy
of γ hkl are held by relationship: γ hkl /r hkl = const; ∀ hkl. The values of the surface
free energy are usually calculated via the well-established atomistic thermodynamic
modelling [73, 74].
2.3.5 Solvation Effects
The solid/liquid interfaces can be modelled via DFT augmented with solution effects
(DFTsol) [75, 76] or on the classical force-field level of theory. The solvation effects
are more abundantly implemented in the molecular codes (PCM and, more recently,
COSMO) than in the PBC programs [76]; the agreement between computational
results and the experimental data is very good, up to a few hundredths of eV in the
solvation energy.
Among the PBC codes, the VASPsol [76] extension to VASP belongs to the most
popular. Besides the energetics, the DFTsol extension of the DFT reproduces very
well the electrochemical properties [77] of the systems in thermodynamic equilibrium
with the liquid (e.g. the potential of zero charge, PZC).
3 Systems: Oxides
Out of the coordination environments for the TMs, definitely the oxide ligands are
the most common. Most of the industrial catalytic processes occurring on the surface
of transition metal oxide solids are the redox processes or the protic processes. In
the former, both TM cationic sites and the anionic oxide sites can act as the redox
centres, hence the number of elementary steps can be significant. Therefore, for the
detailed study thereof the simplified preliminary models can be used, like non-redox
metal oxide (e.g. alkaline earth oxides [78, 79]), where only oxide redox centres
exist. In both cases, the oxidiser atoms/molecules with surface ions atoms form the
reactive oxygen species (ROS) which are the by-products of the catalytic process.
3.1 Reducible and Non-reducible Oxides
Typically, the “reducible oxides”, RO, term concerns the oxides with relatively low
energy of O liberation [80], with band gaps <3 eV, and denotes the oxides of delectron metals: Ti, V, Fe, Co, Hf, Zr, Mn, W, Ni, and f -electron: Ce, Pr, and Sm.
The distinguishing between reducible and non-reducible oxides is, however, nonrigorous and is often dependent on the particular reaction, especially on the redox
potential of the reaction environment. For example, Paier et al. [81] reasonably define
the reducible oxides as those prone to reduction in the “catalytic” conditions, i.e. for
the O 2 partial pressure higher than ca. 10
−14 bar (ultra high vacuum lower limit) and
the temperatures up to ca. 1000
◦ C.