Equations (1) and (2) contain parameters (q, ε, σ) that need to be fixed for each
system. These parameters can be derived from ab initio calculations, fitted to
experimental results or developed by means of other methods. Based on this, a
force field can be defined as a set of functions and parameters to describe the
interactions between the elements of a system. There are a wide variety of force
fields [67] that can be applied to zeolites. Some examples are the universal force field
(UFF) [68], Discover (CFF) [69], MM2 [70], MM3 [71–73], MM4 [74], Dreiding
[75], SHARP [76], VALBON [77], AMBER [78], CHARMM [79], OPLS [80],
Tripos [81], ECEPP/2 [82], GROMOS [83], MMFF [84], BKS [85], and specific
force fields for morphology predictions [86] or for computing adsorption [87]. Usually, the ε and σ parameters of these force fields are parameterized to define the
interaction between atoms of the same type (atom A to atom A, atom B to atom B,
etc.). To obtain the parameters for the interaction between different atoms (atom A to
atom B), it is common to use mixing rules [88–94], the Lorentz-Berthelot rules [95]
being the most popular ones. Although most of these force fields have been
developed to be generic and transferable for any system (not only for zeolites),
they do not perform well for zeolite-gas systems. For this reason, several ad hoc
force fields have been developed that could be used with specific zeolites and gases
[25, 47, 49, 96–106].
During simulations, it is important to set a cut-off for the potentials. For shortranged potentials like the Lennard-Jones potential, the cut-off is usually chosen as
half of the shortest width of the unit cell. For long-range potentials (coulombic) this
construction is inadequate because of the need to include a prohibitively huge
number of interaction pairs. To overcome this problem, Ewald summations [107]
are used to compute the electrostatic interactions [67].
The extra framework cations of zeolites can have a significant impact on the
interactions of zeolite-guest molecules. For instance, Martín-Calvo et al. [97]
explored the mechanisms governing the CO 2 adsorption in zeolites with different
aluminum content and concentration and nature of extra framework cations. They
found that the accessible pore volume of the zeolite was affected by the amount and
strength of carbonate-like complexes formed upon carbon dioxide adsorption. Due
to the strong interaction of carbonate-like complexes in zeolites with a high number
of cations, previous force fields were not able to reproduce CO 2 adsorption within
the structures. Therefore, they developed a new set of charges to accurately reproduce the experimental adsorption in structures containing carbon dioxide-cation
complexes [97]. Their work shows the importance of having an accurate force
field to describe the motion of the cations. In another example, Perez-Carbajo
et al. [7] focused on the aluminosilicate zeolite MFI and established the link between
the nature of the cation, the region in which the cation is free to move, and the
diffusion of adsorbates. The differences observed between the molecules of CO 2 and
methane highlight the importance of using a proper force field to describe the
interactions between the framework atom and the guest molecules and between the
guest molecules and the extra framework cations.
Computational Approaches to Zeolite-Based Adsorption Processes
65
system. These parameters can be derived from ab initio calculations, fitted to
experimental results or developed by means of other methods. Based on this, a
force field can be defined as a set of functions and parameters to describe the
interactions between the elements of a system. There are a wide variety of force
fields [67] that can be applied to zeolites. Some examples are the universal force field
(UFF) [68], Discover (CFF) [69], MM2 [70], MM3 [71–73], MM4 [74], Dreiding
[75], SHARP [76], VALBON [77], AMBER [78], CHARMM [79], OPLS [80],
Tripos [81], ECEPP/2 [82], GROMOS [83], MMFF [84], BKS [85], and specific
force fields for morphology predictions [86] or for computing adsorption [87]. Usually, the ε and σ parameters of these force fields are parameterized to define the
interaction between atoms of the same type (atom A to atom A, atom B to atom B,
etc.). To obtain the parameters for the interaction between different atoms (atom A to
atom B), it is common to use mixing rules [88–94], the Lorentz-Berthelot rules [95]
being the most popular ones. Although most of these force fields have been
developed to be generic and transferable for any system (not only for zeolites),
they do not perform well for zeolite-gas systems. For this reason, several ad hoc
force fields have been developed that could be used with specific zeolites and gases
[25, 47, 49, 96–106].
During simulations, it is important to set a cut-off for the potentials. For shortranged potentials like the Lennard-Jones potential, the cut-off is usually chosen as
half of the shortest width of the unit cell. For long-range potentials (coulombic) this
construction is inadequate because of the need to include a prohibitively huge
number of interaction pairs. To overcome this problem, Ewald summations [107]
are used to compute the electrostatic interactions [67].
The extra framework cations of zeolites can have a significant impact on the
interactions of zeolite-guest molecules. For instance, Martín-Calvo et al. [97]
explored the mechanisms governing the CO 2 adsorption in zeolites with different
aluminum content and concentration and nature of extra framework cations. They
found that the accessible pore volume of the zeolite was affected by the amount and
strength of carbonate-like complexes formed upon carbon dioxide adsorption. Due
to the strong interaction of carbonate-like complexes in zeolites with a high number
of cations, previous force fields were not able to reproduce CO 2 adsorption within
the structures. Therefore, they developed a new set of charges to accurately reproduce the experimental adsorption in structures containing carbon dioxide-cation
complexes [97]. Their work shows the importance of having an accurate force
field to describe the motion of the cations. In another example, Perez-Carbajo
et al. [7] focused on the aluminosilicate zeolite MFI and established the link between
the nature of the cation, the region in which the cation is free to move, and the
diffusion of adsorbates. The differences observed between the molecules of CO 2 and
methane highlight the importance of using a proper force field to describe the
interactions between the framework atom and the guest molecules and between the
guest molecules and the extra framework cations.
Computational Approaches to Zeolite-Based Adsorption Processes
65