waves (VASP, CASTEP, Quantum ESPRESSO), or wavelets (DFT ++) or hybrid
orbitals (L)APW (WIEN2k, elk, FLEUR, EXCITING) and (L)MTO (TB-LMTO,
RSPt), and the calculations are carried out in full crystalline potential or for various
approximate pseudopotentials. The results obtained by various methods are to a
large extent comparable; hence, their selection depends mainly on individual
preferences or the availability of a given program. It is worth noting, however, that
when attempting to analyze the impact of the level of complexity of a structural
fragment (cluster) on the spectrum, it is necessary to perform calculations for all
model structures using the same formalism and identical parameters and in this case
the choice of crystal orbital representation is limited in practice only to methods
using localized atomic orbitals (for a more detailed description of the aforementioned problems related to practical theoretical calculations, see Chap. 1 of this
monograph).
Regardless of the computational methods used, the basic problem in studies of
vibrational properties of zeolites is the selection of the framework fragment that will
be as representative as possible for the whole structure. Such representative models
should be complex enough to carry information not only about the short-range,
local order, but also generally about the whole framework, and on the other hand,
simple enough so that the estimated calculation time, with a given computing
power, was acceptable. Using the hierarchical structure of the discussed group of
aluminosilicates, it is usual to model and interpret their spectra on several levels of
approximation, providing complementary interpretive data.
10.4 Vibrational Spectra of Silicates
Single tetrahedra [TO 4 ] as well as proton-terminated oxygen bridges (which
undoubtedly constitute the simplest structural element of the tectosilicate frameworks [24, 25] belong to the oldest models used to interpret experimental vibrational
spectra of silicates (Fig. 10.2). However, the use of this type of models for calculations is a very poor approximation, due to the size of such systems being too small
and devoid of the interactions with the structural environment of real structures. For
this reason, there are no attempts in the literature to interpret the spectra of zeolites
based on the models of PBU or oxygen bridges. On the other hand, it should be noted
that such models were used to determine the position of bands and interpret the
associated vibrations in other groups of silicates [26]. For example, Tossell [27]
carried out calculations for a single silicon tetrahedron (unit H 4 SiO 4 ) using Hartree–
Fock method, while Kubicki and Sykes [28] for two connected tetrahedra (H 6 Si 2 O 7 )
system using DFT method, to determine the position of the vibration band m s
Si–O (being in the range of 730–710 cm
−1 and 755–709 cm
−1 , respectively)
depending on the adopted angle Si–O–Si. Guided by this type of information, it is
possible to indirectly analyze more complex systems (bearing in mind the discrepancy between the obtained results).
10 Vibrational Spectroscopy of Zeolites …
305
orbitals (L)APW (WIEN2k, elk, FLEUR, EXCITING) and (L)MTO (TB-LMTO,
RSPt), and the calculations are carried out in full crystalline potential or for various
approximate pseudopotentials. The results obtained by various methods are to a
large extent comparable; hence, their selection depends mainly on individual
preferences or the availability of a given program. It is worth noting, however, that
when attempting to analyze the impact of the level of complexity of a structural
fragment (cluster) on the spectrum, it is necessary to perform calculations for all
model structures using the same formalism and identical parameters and in this case
the choice of crystal orbital representation is limited in practice only to methods
using localized atomic orbitals (for a more detailed description of the aforementioned problems related to practical theoretical calculations, see Chap. 1 of this
monograph).
Regardless of the computational methods used, the basic problem in studies of
vibrational properties of zeolites is the selection of the framework fragment that will
be as representative as possible for the whole structure. Such representative models
should be complex enough to carry information not only about the short-range,
local order, but also generally about the whole framework, and on the other hand,
simple enough so that the estimated calculation time, with a given computing
power, was acceptable. Using the hierarchical structure of the discussed group of
aluminosilicates, it is usual to model and interpret their spectra on several levels of
approximation, providing complementary interpretive data.
10.4 Vibrational Spectra of Silicates
Single tetrahedra [TO 4 ] as well as proton-terminated oxygen bridges (which
undoubtedly constitute the simplest structural element of the tectosilicate frameworks [24, 25] belong to the oldest models used to interpret experimental vibrational
spectra of silicates (Fig. 10.2). However, the use of this type of models for calculations is a very poor approximation, due to the size of such systems being too small
and devoid of the interactions with the structural environment of real structures. For
this reason, there are no attempts in the literature to interpret the spectra of zeolites
based on the models of PBU or oxygen bridges. On the other hand, it should be noted
that such models were used to determine the position of bands and interpret the
associated vibrations in other groups of silicates [26]. For example, Tossell [27]
carried out calculations for a single silicon tetrahedron (unit H 4 SiO 4 ) using Hartree–
Fock method, while Kubicki and Sykes [28] for two connected tetrahedra (H 6 Si 2 O 7 )
system using DFT method, to determine the position of the vibration band m s
Si–O (being in the range of 730–710 cm
−1 and 755–709 cm
−1 , respectively)
depending on the adopted angle Si–O–Si. Guided by this type of information, it is
possible to indirectly analyze more complex systems (bearing in mind the discrepancy between the obtained results).
10 Vibrational Spectroscopy of Zeolites …
305