on the ion or cluster net charge sign). This allows performing successful calculations devoted to geometry optimization; however, in the analysis of the obtained
results, it is a must to take into account the influence of this additional neutralizing
charge (type of cations or anions, their position, valence, etc.) on the spatial conformation of the ion or cluster and hence its properties.
The most computationally complex are solids, both amorphous and crystalline
with translational symmetry. Crystalline solids, if they maintain stoichiometry, and all
Wyckoff’s positions are fully occupied, are not usually a challenge for modern programs (apart from the very long, sometimes prohibitive, calculations in the case of
structures with unit cells containing a very large number of atoms and hence sometimes computationally still unavailable for computer modeling). In the latter case, it is
necessary to apply structure simplifications (reduction of the size of the unit cell), so as
to maintain long-range structural properties with significantly shortened calculation
time. The example materials with a large number of atoms in the unit cell are zeolites
(see Chapter 10). The structure simplifications are necessary even for the most
structurally simple zeolites like zeolite A (LTA-type structure), whose unit cell is
shown in Fig. 1.2a—for the sake of clarity, the figure omits oxygen atoms and
non-tetrahedral, extra-framework cations (the latter constitute a separate computational problem because they partially occupy some of Wyckoff’s positions in unit cell
—more on this problem later in this section). The unit cell is composed of sodalite b
cages (Fig. 1.2c) connected to each other by D4R double four-membered rings
(Fig. 1.2b), forming a system of 8 a chambers (Fig. 1.2a). Thus, it is possible to
simplify this unit cell in such a way that the new and smaller unit cell consists of only
one sodalite chamber and eight single four-membered rings constituting the halves of
the respective double four-membered rings (Fig. 1.2d). In this way, significant simplification of the unit cell is achieved and the computational complexity for this
structure reduced. Unfortunately, this gain is related to the appearance of additional
Al–O–Al and Si–O–Si bonds in the model LTA structure, which are much less
probable in real structure (Löwenstein’s rule of aluminum avoidance, which in fact is
not always fulfilled [124]). However, it is an acceptable cost—as shown in [86], this
simplified model allows the calculation of LTA vibrational spectra of high accuracy,
thanks to which it was possible to investigate the influence of the type and amount of
selected non-tetrahedral cations on the structural properties and vibrational spectra of
zeolite A and to compare the results with experimental data obtained for synthesized
LTA subjected to sorption processes. This approach can be an effective way to significantly reduce computation time and is often the only (as in the described case of
LTA) possibility to model, within the framework of ab inito theories, the properties of
more complex structures using the currently available computing power of
supercomputers.
A separate problem to deal with often is the partial occupation of some of
Wyckoff’s position in unit cell and the presence of adsorbed molecules, like water,
carbon and nitrogen oxide or dioxide, methane. While the latter can in many cases
be omitted in calculations (which is often practiced), this cannot be done with the
atoms that partially occupy Wyckoff’s positions. This is a big challenge, because
the vast majority of quantum mechanical programs do not allow partial occupancy
34
A. Koleżyński
results, it is a must to take into account the influence of this additional neutralizing
charge (type of cations or anions, their position, valence, etc.) on the spatial conformation of the ion or cluster and hence its properties.
The most computationally complex are solids, both amorphous and crystalline
with translational symmetry. Crystalline solids, if they maintain stoichiometry, and all
Wyckoff’s positions are fully occupied, are not usually a challenge for modern programs (apart from the very long, sometimes prohibitive, calculations in the case of
structures with unit cells containing a very large number of atoms and hence sometimes computationally still unavailable for computer modeling). In the latter case, it is
necessary to apply structure simplifications (reduction of the size of the unit cell), so as
to maintain long-range structural properties with significantly shortened calculation
time. The example materials with a large number of atoms in the unit cell are zeolites
(see Chapter 10). The structure simplifications are necessary even for the most
structurally simple zeolites like zeolite A (LTA-type structure), whose unit cell is
shown in Fig. 1.2a—for the sake of clarity, the figure omits oxygen atoms and
non-tetrahedral, extra-framework cations (the latter constitute a separate computational problem because they partially occupy some of Wyckoff’s positions in unit cell
—more on this problem later in this section). The unit cell is composed of sodalite b
cages (Fig. 1.2c) connected to each other by D4R double four-membered rings
(Fig. 1.2b), forming a system of 8 a chambers (Fig. 1.2a). Thus, it is possible to
simplify this unit cell in such a way that the new and smaller unit cell consists of only
one sodalite chamber and eight single four-membered rings constituting the halves of
the respective double four-membered rings (Fig. 1.2d). In this way, significant simplification of the unit cell is achieved and the computational complexity for this
structure reduced. Unfortunately, this gain is related to the appearance of additional
Al–O–Al and Si–O–Si bonds in the model LTA structure, which are much less
probable in real structure (Löwenstein’s rule of aluminum avoidance, which in fact is
not always fulfilled [124]). However, it is an acceptable cost—as shown in [86], this
simplified model allows the calculation of LTA vibrational spectra of high accuracy,
thanks to which it was possible to investigate the influence of the type and amount of
selected non-tetrahedral cations on the structural properties and vibrational spectra of
zeolite A and to compare the results with experimental data obtained for synthesized
LTA subjected to sorption processes. This approach can be an effective way to significantly reduce computation time and is often the only (as in the described case of
LTA) possibility to model, within the framework of ab inito theories, the properties of
more complex structures using the currently available computing power of
supercomputers.
A separate problem to deal with often is the partial occupation of some of
Wyckoff’s position in unit cell and the presence of adsorbed molecules, like water,
carbon and nitrogen oxide or dioxide, methane. While the latter can in many cases
be omitted in calculations (which is often practiced), this cannot be done with the
atoms that partially occupy Wyckoff’s positions. This is a big challenge, because
the vast majority of quantum mechanical programs do not allow partial occupancy
34
A. Koleżyński