4 Classical Simulation Methods and Theory
Molecular simulation encompasses a set of methods and techniques that, by using
models and force fields, allows to calculate a variety of properties. There are two
main methods that are commonly used in simulation: Molecular dynamics (MD) and
Monte Carlo (MC). Molecular dynamics is based on the integration of Newton’s
laws of motion, while Monte Carlo methods are based on statistical mechanics.
4.1 Monte Carlo
To compute the adsorption properties like heat of adsorption, Henry coefficient, or
adsorption isotherms, Monte Carlo methods are most commonly used. Essentially,
the particles of the system are randomly selected, and one Monte Carlo move (e.g.,
translation, rotation, insertion, deletion, etc.) is applied [108]. Moves are key feature
of the MC methods, and they are accepted or rejected based on an energy criterium.
Different ensembles are used depending on the desired calculation. For instance,
Henry coefficients are directly related to the excess free energy (or excess chemical
potential) of the adsorbed molecules. The heat of adsorption can be computed from
the energy of the system. Then, both quantities can be obtained from the total energy
of the system by means of the Widom test-particle method [109], having fixed the
number of molecules, the volume, and the temperature of the system (NVT ensemble). This technique can also be used to compute the pore volume, surface area, pore
size distribution, and helium void fraction of the structure. For this purpose, helium
atoms are employed as probes. The test particles are randomly placed inside the
zeolite; keeping track of the fraction that does not overlap with the structure, the
geometric pore volume can be computed.
4.1.1 Blocking
It is important to block non-accessible pores of the zeolite when calculating equilibrium adsorption properties using Monte Carlo simulations. This is essential to
avoid the spurious inclusion of inaccessible volumes and to prevent an
overestimation of the adsorption. A comparison between the blocked and the
non-blocked LTA and FAU zeolites is depicted in Fig. 4. As can be observed,
there are small cavities (red spheres) that are not connected to the zeolite framework,
and therefore they are not physically accessible to guest molecules. As these spots
are reachable by Monte Carlo moves, they have to be blocked to prevent that guest
molecules populate these additional sites. The first attempts of blocking
non-accessible pores in a zeolite were reported in 2004 [101]. Since then, this
methodology has been widely accepted and used. Gómez-Álvarez et al. [110]
made a pseudo-flexible approach to account for the instantaneous variations of
66
J. J. Gutiérrez-Sevillano and S. Calero
Molecular simulation encompasses a set of methods and techniques that, by using
models and force fields, allows to calculate a variety of properties. There are two
main methods that are commonly used in simulation: Molecular dynamics (MD) and
Monte Carlo (MC). Molecular dynamics is based on the integration of Newton’s
laws of motion, while Monte Carlo methods are based on statistical mechanics.
4.1 Monte Carlo
To compute the adsorption properties like heat of adsorption, Henry coefficient, or
adsorption isotherms, Monte Carlo methods are most commonly used. Essentially,
the particles of the system are randomly selected, and one Monte Carlo move (e.g.,
translation, rotation, insertion, deletion, etc.) is applied [108]. Moves are key feature
of the MC methods, and they are accepted or rejected based on an energy criterium.
Different ensembles are used depending on the desired calculation. For instance,
Henry coefficients are directly related to the excess free energy (or excess chemical
potential) of the adsorbed molecules. The heat of adsorption can be computed from
the energy of the system. Then, both quantities can be obtained from the total energy
of the system by means of the Widom test-particle method [109], having fixed the
number of molecules, the volume, and the temperature of the system (NVT ensemble). This technique can also be used to compute the pore volume, surface area, pore
size distribution, and helium void fraction of the structure. For this purpose, helium
atoms are employed as probes. The test particles are randomly placed inside the
zeolite; keeping track of the fraction that does not overlap with the structure, the
geometric pore volume can be computed.
4.1.1 Blocking
It is important to block non-accessible pores of the zeolite when calculating equilibrium adsorption properties using Monte Carlo simulations. This is essential to
avoid the spurious inclusion of inaccessible volumes and to prevent an
overestimation of the adsorption. A comparison between the blocked and the
non-blocked LTA and FAU zeolites is depicted in Fig. 4. As can be observed,
there are small cavities (red spheres) that are not connected to the zeolite framework,
and therefore they are not physically accessible to guest molecules. As these spots
are reachable by Monte Carlo moves, they have to be blocked to prevent that guest
molecules populate these additional sites. The first attempts of blocking
non-accessible pores in a zeolite were reported in 2004 [101]. Since then, this
methodology has been widely accepted and used. Gómez-Álvarez et al. [110]
made a pseudo-flexible approach to account for the instantaneous variations of
66
J. J. Gutiérrez-Sevillano and S. Calero