26
P. I. Ravikovitch
to predict the existence of a previously unknown expanded pore structure of ZIF4 [45]. In simulations, the new structure has been stabilized by favorable entropic
contributions to the free energy at high temperatures, while in experiments it has been
stabilized by enthalpic contributions due to strong adsorption of N 2 guest molecules
at low temperatures [45].
Here we focus on the calculations of the free energy changes associated with
the structural transitions in ZIF-7 and ZIF-4 materials using classical MD simulations. The approach includes calculations of the vibrational entropy and free energy
from the vibrational density of states (VDOS) using the quasi-harmonic approximation. The vibrational density of states is obtained directly from the classical MD
simulations.
2 Structural Transitions in Zeolitic Imidazolate
Frameworks
MD simulations were performed using the force field described in our previous publications [23, 45]. It has been adopted from the Amber-based force field developed by
Zhang et al. to simulate N 2 adsorption induced transition in ZIF-8 [31]. The major
modification was the use of the QEq charge equilibration scheme [46] for partial
atomic charges. With this modification, the force field predicts anisotropic mechanical properties of ZIF-8 in reasonable agreement with experimental measurements
[44, 45]. All parameters of the force field can be found in Refs. [23, 45].
In the temperature ramp method, we perform a series of short NpT simulations with an anisotropic barostat at progressively increasing temperatures. Higher
temperatures dramatically increase entropic contributions to the free energy (G =
H − T S), and may facilitate the crossing of free energy barriers, and transitions to entropically more favorable structures (if they exist). Such structures are
usually associated with a higher pore volume and symmetry [23, 45]. Likewise,
decreasing the temperature may facilitate transitions to dense structures, which are
favored entalpically. While this procedure does not guarantee that all possible polymorphs of the material will be observed in simulations, it has proved to be effective
for predicting the existence of high volume expanded structures.
MD simulations were performed using Forcite code from Materials Studio
(BIOVIA / Dassault). First, a ZIF structure was converted to P 1 symmetry, and energy
minimized to obtain a dense low energy structure at zero temperature. Starting with
the minimized structure, a series of short NpT simulations were performed at each
temperature, with the temperature first increasing to about 1000 K in 10 K intervals,
and then decreasing back to near zero. This temperature ramp procedure mimics the
experimental measurements of the high-temperature structural transition in ZIF-7
[23], and the low-temperature phase transition in ZIF-4 [24]. MD simulations were
performed with 0.2 fs time step, Nose–Hoover thermostat [47] with Q ratio 0.001,
and anisotropic Parrinello–Raman [48] barostat as implemented by Martyna et al.
P. I. Ravikovitch
to predict the existence of a previously unknown expanded pore structure of ZIF4 [45]. In simulations, the new structure has been stabilized by favorable entropic
contributions to the free energy at high temperatures, while in experiments it has been
stabilized by enthalpic contributions due to strong adsorption of N 2 guest molecules
at low temperatures [45].
Here we focus on the calculations of the free energy changes associated with
the structural transitions in ZIF-7 and ZIF-4 materials using classical MD simulations. The approach includes calculations of the vibrational entropy and free energy
from the vibrational density of states (VDOS) using the quasi-harmonic approximation. The vibrational density of states is obtained directly from the classical MD
simulations.
2 Structural Transitions in Zeolitic Imidazolate
Frameworks
MD simulations were performed using the force field described in our previous publications [23, 45]. It has been adopted from the Amber-based force field developed by
Zhang et al. to simulate N 2 adsorption induced transition in ZIF-8 [31]. The major
modification was the use of the QEq charge equilibration scheme [46] for partial
atomic charges. With this modification, the force field predicts anisotropic mechanical properties of ZIF-8 in reasonable agreement with experimental measurements
[44, 45]. All parameters of the force field can be found in Refs. [23, 45].
In the temperature ramp method, we perform a series of short NpT simulations with an anisotropic barostat at progressively increasing temperatures. Higher
temperatures dramatically increase entropic contributions to the free energy (G =
H − T S), and may facilitate the crossing of free energy barriers, and transitions to entropically more favorable structures (if they exist). Such structures are
usually associated with a higher pore volume and symmetry [23, 45]. Likewise,
decreasing the temperature may facilitate transitions to dense structures, which are
favored entalpically. While this procedure does not guarantee that all possible polymorphs of the material will be observed in simulations, it has proved to be effective
for predicting the existence of high volume expanded structures.
MD simulations were performed using Forcite code from Materials Studio
(BIOVIA / Dassault). First, a ZIF structure was converted to P 1 symmetry, and energy
minimized to obtain a dense low energy structure at zero temperature. Starting with
the minimized structure, a series of short NpT simulations were performed at each
temperature, with the temperature first increasing to about 1000 K in 10 K intervals,
and then decreasing back to near zero. This temperature ramp procedure mimics the
experimental measurements of the high-temperature structural transition in ZIF-7
[23], and the low-temperature phase transition in ZIF-4 [24]. MD simulations were
performed with 0.2 fs time step, Nose–Hoover thermostat [47] with Q ratio 0.001,
and anisotropic Parrinello–Raman [48] barostat as implemented by Martyna et al.