Quasiequilibrium multistate cellular automata.

In our effort to tackle the problem of letting nontrivial interactions, thermodynamic equilibrium, and full synchronicity coexist, and in the hope of reviving interest in cellular automata as promising tools for the quantitative, large-scale investigation of multiparticle systems, we built a fully synchronous cellular automaton rule for the simulation of occupancy-based lattice systems with multistate cells and neighboring interactions. The core of this rule, which constitutes an actual synchronous sampling scheme, is a negotiation stage; it produces cell occupancy distributions in very good agreement with their sequential Monte Carlo counterparts, and it satisfies a cellwise detailed balance principle thanks to the use of "mixed" intermediate states that allow for the computation of locally averaged acceptance probabilities. We took a square lattice (but the rule itself is not bound by dimensionality) as a basis for comparison with sequential Monte Carlo for showing that this synchronous rule leads to quasiequilibrium; the fulfillment of cellwise detailed balance is shown through results obtained for a small one-dimensional system, where the transition matrix could be computed exactly.

Scaling-Up Simulations of Diffusion in Microporous Materials.

We introduce and demonstrate the coarse-graining of static and dynamical properties of host-guest systems constituted by methane in two different microporous materials. The reference systems are mapped to occupancy-based pore-scale lattice models. Each coarse-grained model is equipped with an appropriate coarse-grained potential and a local dynamical operator, which represents the probability of interpore molecular jumps between different cages.

Molecular QCA embedding in microporous materials.

We propose an environment for information encoding and transmission via a nanoconfined molecular Quantum Dot Cellular Automata (QCA) wire, composed of a single row of head-to-tail interacting 2-dots molecular switches. While most of the research in the field refers to dots-bearing molecules bound on some type of surface, forming a bidimensional array of square cells capable of performing QCA typical functions, we propose here to embed the information bearing elements within the channels of a microporous matrix. In this way molecules would self-assemble in a row as a consequence of adsorption inside the pores of the material, forming an encased wire, with the crystalline environment giving stability and protection to the structure.

Local free energies for the coarse-graining of adsorption phenomena: The interacting pair approximation.

We investigate the coarse-graining of host-guest systems under the perspective of the local distribution of pore occupancies, along with the physical meaning and actual computability of the coarse-interaction terms. We show that the widely accepted approach, in which the contributions to the free energy given by the molecules located in two neighboring pores are estimated through Monte Carlo simulations where the two pores are kept separated from the rest of the system, leads to inaccurate results at high sorbate densities. In the coarse-graining strategy that we propose, which is based on the Bethe-Peierls approximation, density-independent interaction terms are instead computed according to local effective potentials that take into account the correlations between the pore pair and its surroundings by means of mean-field correction terms without the need for simulating the pore pair separately.

A network of discrete events for the representation and analysis of diffusion dynamics.

We developed a coarse-grained description of the phenomenology of diffusive processes, in terms of a space of discrete events and its representation as a network. Once a proper classification of the discrete events underlying the diffusive process is carried out, their transition matrix is calculated on the basis of molecular dynamics data. This matrix can be represented as a directed, weighted network where nodes represent discrete events, and the weight of edges is given by the probability that one follows the other.

Combining off-lattice Monte Carlo and cellular automata for the simulation of hard-sphere systems.

In the present work we show how the update rule of a diffusive cellular automaton with mutual exclusion can be exploited in off-lattice Monte Carlo simulations of hard spheres to obtain a synchronous Monte Carlo sampling that satisfies the detailed balance principle.

Thermodynamics of the one-dimensional parallel Kawasaki model: exact solution and mean-field approximations.

The adsorption isotherm for the recently proposed parallel Kawasaki (PK) lattice-gas model [Phys. Rev. E 88, 062144 (2013)] is calculated exactly in one dimension.

A coarse-grained method based on the analysis of short molecular dynamics trajectories for the simulation of non-Markovian dynamics of molecules adsorbed in microporous materials.

We developed a coarse-grained model suitable for the study of adsorbed molecules in microporous materials. A partition of the space available to the motion of adsorbed molecules was carried out, which allows to formulate the dynamics in terms of jumps between discrete regions. The probabilities of observing given pairs of successive jumps were calculated from Molecular Dynamics (MD) simulations, performed on small systems, and used to drive the motion of molecules in a lattice-gas model.

Conciliating synchronicity with spatial discretization, exclusion, interactions, and detailed balance.

The construction of a discrete stochastic system of interacting particles that evolves through a fully synchronous evolution rule while satisfying detailed balance is a highly demanding task. As a consequence, the presence of nontrivial interaction fields can make synchronicity and thermodynamic equilibrium look as two conflicting counterparts. We show that, with the proper prescriptions, the process of migration of particles in a lattice of mutually exclusive nodes can be simulated with a fully synchronous algorithm, which we call parallel Kawasaki dynamics (PKD), that incorporates site exclusion, local interactions, and detailed balance without the need of system partitioning schemes.

Synchronous equilibrium model for the diffusion of mutually exclusive particles in a heterogeneous lattice of adsorption sites.

Through straight synchronization and proper manipulation of a sequential Monte Carlo glass-forming rule introduced by Fröbose and Jäckle [J. Stat. Phys.

Chemical potential evaluation in NVT lattice-gas simulations.

The discrete nature of the partition function of a lattice-gas system can be exploited to build an efficient strategy for the evaluation of the chemical potential of a periodic lattice-gas with arbitrarily ranged interactions during a simulation in the canonical ensemble, with the need of no additional sampling as it were required instead by the Widom insertion/deletion approach. The present method is based on the main concepts of the small system grand ensemble [for details, see G. Soto-Campos, D.

A parallelizable block cellular automaton for the study of diffusion of binary mixtures containing CO2 in microporous materials.

We applied a method based on a block cellular automaton (BCA) algorithm to the study of diffusion of various binary mixtures adsorbed in a model microporous material, such as zeolite ZK4. Our aim was to test the capability of our model to cope with systems in which more than one species is present, using a set of parameters based on heuristic considerations from the molecular dynamics (MD) results present in the literature. A rigorous methodology for the assignment of suitable adsorption energies and diffusion activation barriers for our BCA has not been developed yet, nonetheless the results were quite interesting at this stage and we obtained a good qualitative agreement with MD data in the literature.

Speeding up simulation of diffusion in zeolites by a parallel synchronous kinetic Monte Carlo algorithm.

Understanding the behaviors of molecules in tight confinement is a challenging task. Standard simulation tools like kinetic Monte Carlo have proven to be very effective in the study of adsorption and diffusion phenomena in microporous materials, but they turn out to be very inefficient when simulation time and length scales are extended. In this paper we have explored the possibility of application of a discrete version of the synchronous parallel kinetic Monte Carlo algorithm introduced by Martínez et al.

Estimation of Partial Charges in Small Zeolite Imidazolate Frameworks from Density Functional Theory Calculations.

Zeolitic Imidazolate Frameworks (ZIFs) are the new frontier in the field of metal-organic materials. They incorporate the confining properties of the more traditional aluminosilicate zeolites together with the catalytic activity provided by transition metal ions and organic links. Computation of atomic point charges for these hybrid materials is important in the field of molecular simulations for substantial prediction of experimental results.

Atomistic simulation studies on the dynamics and thermodynamics of nonpolar molecules within the zeolite imidazolate framework-8.

Statistical-mechanics-based simulation studies at the atomistic level of argon (Ar), methane (CH(4)), and hydrogen (H(2)) sorbed in the zeolite imidazolate framework-8 (ZIF-8) are reported. ZIF-8 is a product of a special kind of chemical process, recently termed as reticular synthesis, which has generated a class of materials of critical importance as molecular binders. In this work, we explore the mechanisms that govern the sorption thermodynamics and kinetics of nonpolar sorbates possessing different sizes and strength of interactions with the metal-organic framework to understand the outstanding properties of this novel class of sorbents, as revealed by experiments published elsewhere.

From thermodynamic cell models to partitioning cellular automata for diffusion in zeolites. II. Static and dynamic properties.

In this second paper we exploit our thermodynamic partitioning cellular automaton (PCA) developed in Paper I [Pazzona et al., J. Chem.

From thermodynamic cell models to partitioning cellular automata for diffusion in zeolites. I. Structure of the algorithm.

In the study of adsorption of simple adsorbates in microporous materials like zeolites, thermodynamic models of small grand-canonical cells with very local interactions [e.g., see K.

Effective interactions in multisite cells for adsorption in microporous materials.

Local, discrete models of self-interacting multisite adsorption cells have been shown to be able to provide a coarse-grained representation of equilibrium properties of small molecules adsorbed in nanoporous materials at the mesoscopic scale. In the present work we show how the essential statistical properties of a host cell of structured sites with multiple adsorption energies and particle-particle interactions (that is the partition function, the average energy, and the average number of guests close to the windows connecting the cell to its surroundings) can be reproduced by a less-structured cell with two occupancy-dependent adsorption energy levels.

Introducing a cellular automaton as an empirical model to study static and dynamic properties of molecules adsorbed in zeolites.

A new lattice gas cellular automaton (LGCA) simulation approach to study static and dynamic properties of molecules adsorbed in zeolites is proposed. The motivation for the present work arises from the ongoing effort to develop efficient numerical tools where conventional approaches like molecular dynamics and Monte Carlo have been revealed as inefficient for a real extension of length and time scales in such inhomogeneous systems. Our LGCA is constituted by a constant number of interacting identical particles, distributed among a fixed number of identical cells arranged in a three-dimensional cubic network and performing a synchronous random walk at constant temperature.

Diffusion in tight confinement: a lattice-gas cellular automaton approach. II. Transport properties.

In this second paper the authors study the transport properties of the lattice-gas cellular automaton presented in Paper I [J. Chem. Phys.

Diffusion in tight confinement: a lattice-gas cellular automaton approach. I. Structural equilibrium properties.

The thermodynamic and transport properties of diffusing species in microporous materials are strongly influenced by their interactions with the confining framework, which provide the energy landscape for the transport process. The simple topology and the cellular nature of the alpha cages of a ZK4 zeolite suggest that it is appropriate to apply to the study of the problem of diffusion in tight confinement a time-space discrete model such as a lattice-gas cellular automaton (LGCA). In this paper we investigate the properties of an equilibrium LGCA constituted by a constant number of noninteracting identical particles, distributed among a fixed number of identical cells arranged in a three-dimensional cubic network and performing a synchronous random walk at constant temperature.