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W. Piskorz and F. Zasada
simplified, qualitative, manner, described through the crystal field theory [3] or the
ligand field theory [4] as well. Indeed, the present chapter is devoted to the extended
systems, particularly to the challenges of the application of computational methods
to the description of such systems. Such approach is particularly useful in qualitative and intuition-aimed description of the d-electron metal oxides (transition metal
oxides, TMO) like titania, zirconia, or spinels, to name just a few. The f -electron
systems (rare earths, RE) are most abundantly represented by ceria.
The coordination environment of the surface atoms is among the three pivotal
aspects in understanding the chemistry of the metal oxides surface as pointed out by
Barteau [5], the other being the redox properties of the oxide and the oxidation state
of the surface.
The local coordination environment can be used for study of the redox or protic
properties in heterogeneous catalytic processes. Focusing on the importance of the
coordination environment can also lead to the description of the charge transfer
processes (polaron theory) in such oxides.
In this chapter, the successes and challenges of the computational studies on
selected oxides, ceria, titania, zirconia, zeolites, d-electron spinels, and vanadia, are
reviewed to give the reader the general insight as for the applicability of certain levels
of theory and the possible quantities that can be calculated.
2 Methods
2.1 The DFT and Other Quantum-Chemical Methods
Due to the size of the models in the heterogeneous processes, the computational
methods of choice belong to the large DFT [6, 7] family. They comprise both computationally cheaper local density approximation, LDA [7, 8] or generalised gradient
approximation, GGA [9, 10], levels of theory or, more demanding, hybrid functionals, i.e. those with admixture of the Hartree–Fock exchange term in the functional,
e.g. the widely found B3LYP functional [11] (“classical” in organic chemistry) or,
more physically grounded, modern hybrid functionals like PBE0, HSE06.
The LDA functionals, despite their functional dependence only on the electron
density and stemming from the homogeneous electron gas model, surprisingly well
describe chemical systems due to the partial cancellation of exchange and Coulombic
correlation effects [12], and the reasonable reproduction of the spherical average of
the exchange–correlation hole [13] (even though the approximate and exact holes
differ qualitatively). For detailed discussion of the exchange and correlation approximation in the LDA approximations for the atomic systems, see, e.g., the monograph
[14].
In the Hartree–Fock method, which can be regarded as a special case of the DFT—
with exact exchange term but with complete neglect of Coulombic correlation—the
self-interaction energy is cancelled out by the exchange term. The uncompensated
W. Piskorz and F. Zasada
simplified, qualitative, manner, described through the crystal field theory [3] or the
ligand field theory [4] as well. Indeed, the present chapter is devoted to the extended
systems, particularly to the challenges of the application of computational methods
to the description of such systems. Such approach is particularly useful in qualitative and intuition-aimed description of the d-electron metal oxides (transition metal
oxides, TMO) like titania, zirconia, or spinels, to name just a few. The f -electron
systems (rare earths, RE) are most abundantly represented by ceria.
The coordination environment of the surface atoms is among the three pivotal
aspects in understanding the chemistry of the metal oxides surface as pointed out by
Barteau [5], the other being the redox properties of the oxide and the oxidation state
of the surface.
The local coordination environment can be used for study of the redox or protic
properties in heterogeneous catalytic processes. Focusing on the importance of the
coordination environment can also lead to the description of the charge transfer
processes (polaron theory) in such oxides.
In this chapter, the successes and challenges of the computational studies on
selected oxides, ceria, titania, zirconia, zeolites, d-electron spinels, and vanadia, are
reviewed to give the reader the general insight as for the applicability of certain levels
of theory and the possible quantities that can be calculated.
2 Methods
2.1 The DFT and Other Quantum-Chemical Methods
Due to the size of the models in the heterogeneous processes, the computational
methods of choice belong to the large DFT [6, 7] family. They comprise both computationally cheaper local density approximation, LDA [7, 8] or generalised gradient
approximation, GGA [9, 10], levels of theory or, more demanding, hybrid functionals, i.e. those with admixture of the Hartree–Fock exchange term in the functional,
e.g. the widely found B3LYP functional [11] (“classical” in organic chemistry) or,
more physically grounded, modern hybrid functionals like PBE0, HSE06.
The LDA functionals, despite their functional dependence only on the electron
density and stemming from the homogeneous electron gas model, surprisingly well
describe chemical systems due to the partial cancellation of exchange and Coulombic
correlation effects [12], and the reasonable reproduction of the spherical average of
the exchange–correlation hole [13] (even though the approximate and exact holes
differ qualitatively). For detailed discussion of the exchange and correlation approximation in the LDA approximations for the atomic systems, see, e.g., the monograph
[14].
In the Hartree–Fock method, which can be regarded as a special case of the DFT—
with exact exchange term but with complete neglect of Coulombic correlation—the
self-interaction energy is cancelled out by the exchange term. The uncompensated