Catalytic Properties of Selected Transition Metal Oxides—Computational Studies
349
[46]. The parameterisation for given element is transferable, i.e. parameters set is
independent of the chemical environment of given atom.
2.3 Other Issues
2.3.1 Embedding Schemes
Embedding of the small, “active” system, described by high-accuracy, high-cost level
of theory in the large environment, treated with moderate-accuracy, computationally
cheap method is a concept frequently realised in practice. Typically, the high-level
method belongs to QC, e.g. DFT or post-Hartree–Fock method, while the environment (“host”) is described by the molecular mechanics (MM) based on the force-field,
or the semi-empirical method. Such arrangement is called the QM/MM scheme, or
the Integrated Molecular Orbital-Molecular Mechanics (IMOMM [47]) method. This
approach evolved also into high-level-QM/low-level-QM (IMOMO [48], Integrated
Molecular Orbital-Molecular Orbital method), or even into the generalised, multilayer ONIOM [49] (N -layered Integrated MO and MM) scheme. The introduction of
the potential calculated in the originally periodic molecular mechanics as the external
potential (through the hydrogen atom linkers) for the quantum-chemical calculations
is called QM-Pot [50].
2.3.2 Basis Sets
The most commonly used types of basis set in the solid-state calculations are the plane
waves (and augmented PW) and atom-centred analytical (Gaussian [51, 52], Slatertype [53, 54]), or numerical [55], basis sets (linear combination of atomic orbitals,
LCAO). In the planewave world, the localised orbitals (the Wannier functions [56,
57]), being the counterpart of localised molecular orbitals, are also regarded as a
useful canvas to describe the atomic properties and are often used in the interpretation
of the planewave calculation results.
To reduce the complexity, the pseudopotentials, or furthermore, to increase the
accuracy, the augmentation of the plane waves by the atom-centred wavefunctions
(WF), are often introduced. The replacement of rapidly oscillating wavefunctions by
the smooth pseudo wavefunctions (moreover, still preserving the way to calculate
all-electron properties; PAW [58]) allows for further reduction of the number of the
basis set.
For the sake of completeness, the real-space grid (generally orthorhombic) representation of the wavefunction ought to be mentioned, found in some computational
codes. For the PAW method, the grids of different density can be used [59]. The realspace grid approach removes the bottleneck of the PW approach—the interprocessor
communications in the fast Fourier transform (FFT) routines.
349
[46]. The parameterisation for given element is transferable, i.e. parameters set is
independent of the chemical environment of given atom.
2.3 Other Issues
2.3.1 Embedding Schemes
Embedding of the small, “active” system, described by high-accuracy, high-cost level
of theory in the large environment, treated with moderate-accuracy, computationally
cheap method is a concept frequently realised in practice. Typically, the high-level
method belongs to QC, e.g. DFT or post-Hartree–Fock method, while the environment (“host”) is described by the molecular mechanics (MM) based on the force-field,
or the semi-empirical method. Such arrangement is called the QM/MM scheme, or
the Integrated Molecular Orbital-Molecular Mechanics (IMOMM [47]) method. This
approach evolved also into high-level-QM/low-level-QM (IMOMO [48], Integrated
Molecular Orbital-Molecular Orbital method), or even into the generalised, multilayer ONIOM [49] (N -layered Integrated MO and MM) scheme. The introduction of
the potential calculated in the originally periodic molecular mechanics as the external
potential (through the hydrogen atom linkers) for the quantum-chemical calculations
is called QM-Pot [50].
2.3.2 Basis Sets
The most commonly used types of basis set in the solid-state calculations are the plane
waves (and augmented PW) and atom-centred analytical (Gaussian [51, 52], Slatertype [53, 54]), or numerical [55], basis sets (linear combination of atomic orbitals,
LCAO). In the planewave world, the localised orbitals (the Wannier functions [56,
57]), being the counterpart of localised molecular orbitals, are also regarded as a
useful canvas to describe the atomic properties and are often used in the interpretation
of the planewave calculation results.
To reduce the complexity, the pseudopotentials, or furthermore, to increase the
accuracy, the augmentation of the plane waves by the atom-centred wavefunctions
(WF), are often introduced. The replacement of rapidly oscillating wavefunctions by
the smooth pseudo wavefunctions (moreover, still preserving the way to calculate
all-electron properties; PAW [58]) allows for further reduction of the number of the
basis set.
For the sake of completeness, the real-space grid (generally orthorhombic) representation of the wavefunction ought to be mentioned, found in some computational
codes. For the PAW method, the grids of different density can be used [59]. The realspace grid approach removes the bottleneck of the PW approach—the interprocessor
communications in the fast Fourier transform (FFT) routines.