Biased Monte Carlo Simulations Research Articles

Halogen-Decorated Metal-Organic Frameworks for Efficient and Selective CO2 Capture, Separation, and Chemical Fixation with Epoxides under Mild Conditions.

In the present work, three novel halogen-appended cadmium(II) metal-organic frameworks [Cd2(L1)2(4,4'-Bipy)2]n·4n(DMF) (1), [Cd2(L2)2(4,4'-Bipy)2]n·3n(DMF) (2), and [Cd(L3)(4,4'-Bipy)]n·2n(DMF) (3) [where L1 = 5-{(4-bromobenzyl)amino}isophthalate; L2 = 5-{(4-chlorobenzyl)amino}isophthalate; L3 = 5-{(4-fluorobenzyl)amino}isophthalate; 4,4'-Bipy = 4,4'-bipyridine; and DMF = N,N'-dimethylformamide] have been synthesized under solvothermal conditions and characterized by various analytical techniques. The single-crystal X-ray diffraction analysis demonstrated that all the MOFs feature a similar type of three-dimensional structure having a binuclear [Cd2(COO)4(N)4] secondary building block unit. Moreover, MOFs 1 and 2 contain one-dimensional channels along the b-axis, whereas MOF 3 possesses a 1D channel along the a-axis. In these MOFs, the pores are decorated with multifunctional groups, i.e., halogen and amine. The gas adsorption analysis of these MOFs demonstrate that they display high uptake of CO2 (up to 5.34 mmol/g) over N2 and CH4. The isosteric heat of adsorption (Qst) value for CO2 at zero loadings is in the range of 18-26 kJ mol-1. In order to understand the mechanism behind the better adsorption of CO2 by our MOFs, we have also performed configurational bias Monte Carlo simulation studies, which confirm that the interaction between our MOFs and CO2 is stronger compared to those with N2 and CH4. Various noncovalent interactions, e.g., halogen (X)···O, Cd···O, and O···O, between CO2 and the halogen atom, the Cd(II) metal center, and the carboxylate group from the MOFs are observed, respectively, which may be a reason for the higher carbon dioxide adsorption. Ideal adsorbed solution theory (IAST) calculations of MOF 1 demonstrate that the obtained selectivity values for CO2/CH4 (50:50) and CO2/N2 (15:85) are ca. 28 and 193 at 273 K, respectively. However, upon increasing the temperature to 298 K, the selectivity value (S = 34) decreases significantly for the CO2/N2 mixture. We have also calculated the breakthrough analysis curves for all the MOFs using mixtures of CO2/CH4 (50:50) and CO2/N2 (50:50 and 15:85) at different entering gas velocities and observed larger retention times for CO2 in comparison with other gases, which also signifies the stronger interaction between our MOFs and CO2. Moreover, due to the presence of Lewis acidic metal centers, these MOFs act as heterogeneous catalysts for the CO2 fixation reactions with different epoxides in the presence of tetrabutyl ammonium bromide (TBAB), for conversion into industrially valuable cyclic carbonates. These MOFs exhibit a high conversion (96-99%) of epichlorohydrin (ECH) to the corresponding cyclic carbonate 4-(chloromethyl)-1,3-dioxolan-2-one after 12 h of reaction time at 1 bar of CO2 pressure, at 65 °C. The MOFs can be reused up to four cycles without compromising their structural integrity as well as without losing their activity significantly.

Hierarchical Computational Screening of Quantum Metal-Organic Framework Database to Identify Metal-Organic Frameworks for Volatile Organic-Compound Capture from Air.

The design and discovery of novel porous materials that can efficiently capture volatile organic compounds (VOCs) from air are critical to address one of the most important challenges of our world, air pollution. In this work, we studied a recently introduced metal-organic framework (MOF) database, namely, quantum MOF (QMOF) database, to unlock the potential of both experimentally synthesized and hypothetically generated structures for adsorption-based n-butane (C4H10) capture from air. Configurational Bias Monte Carlo (CBMC) simulations were used to study the adsorption of a quaternary gas mixture of N2, O2, Ar, and C4H10 in QMOFs for two different processes, pressure swing adsorption (PSA) and vacuum-swing adsorption (VSA). Several adsorbent performance evaluation metrics, such as C4H10 selectivity, working capacity, the adsorbent performance score, and percent regenerability, were used to identify the best adsorbent candidates, which were then further studied by molecular simulations for C4H10 capture from a more realistic seven-component air mixture consisting of N2, O2, Ar, C4H10, C3H8, C3H6, and C2H6. Results showed that the top five QMOFs have C4H10 selectivities between 6.3 × 103 and 9 × 103 (3.8 × 103 and 5 × 103) at 1 bar (10 bar). Detailed analysis of the structure-performance relations showed that low/mediocre porosity (0.4-0.6) and narrow pore sizes (6-9 Å) of QMOFs lead to high C4H10 selectivities. Radial distribution function analyses of the top materials revealed that C4H10 molecules tend to confine close to the organic parts of MOFs. Our results provided the first information in the literature about the VOC capture potential of a large variety and number of MOFs, which will be useful to direct the experimental efforts to the most promising adsorbent materials for C4H10 capture from air.

Physics-separating artificial neural networks for predicting initial stages of Al sputtering and thin film deposition in Ar plasma discharges

Simulations of Al thin film sputter depositions rely on accurate plasma and surface interaction models. Establishing the latter commonly requires a higher level of abstraction and means to dismiss the fundamental atomic fidelity. Previous works on sputtering processes addressed this issue by establishing machine learning surrogate models, which include a basic surface state (i.e. stoichiometry) as static input. In this work, an evolving surface state and defect structure are introduced to jointly describe sputtering and growth with physics-separating artificial neural networks. The data describing the plasma–surface interactions (PSIs) stem from hybrid reactive molecular dynamics/time-stamped force bias Monte Carlo simulations of Al neutrals and Ar+ ions impinging onto Al(001) surfaces. It is demonstrated that the fundamental processes are comprehensively described by taking the surface state as well as defect structure into account. Hence, a machine learning PSI surrogate model is established that resolves the inherent kinetics with high physical fidelity. The resulting model is not restricted to input from modeling and simulation, but may similarly be applied to experimental input data.

Understanding the structural properties of zeolites for isobutane alkylation based on adsorption/diffusion behaviors

Although zeolites are well-accepted as environmentally friendly catalysts for the isobutane alkylation, the structure-performance relationship between C4 reactants (isobutane and butene) and zeolites is less reported. Herein, the adsorption and diffusion behaviors of C4 reactants on zeolites with different topologies were investigated using configuration bias Monte Carlo (CBMC) and molecular dynamics (MD) simulations under experimental conditions in 348 K and 2.5 MPa. It is revealed that surface area, largest cavity diameter, and pore limiting diameter are the most relevant structural parameters for zeolites to determine the adsorption and diffusion of C4 reactants. In addition, the dimensions of the zeolitic channels can also affect the selectivity of isobutane to butene and the diffusion of C4 reactants, thereby affecting the process of isobutane alkylation reaction. This work can provide a good reference for the design of novel zeolites for isobutane alkylation.

Rare-event properties in a classical stochastic model describing the evolution of random unitary circuits.

We investigate the statistics of selected rare events in a (1+1)-dimensional (classical) stochastic growth model which describes the evolution of (quantum) random unitary circuits. In such classical formulation, particles are created and/or annihilated at each step of the evolution process, according to rules which generally favor a growing cluster size. We apply a large-deviation approach based on biased Monte Carlo simulations, with suitable adaptations, to evaluate (a) the probability of ending up with a single particle at a specified final time t_{f} and (b) the probability of having particles outside the light cone, defined by a "butterfly velocity" v_{B}, at t_{f}. Morphological features of single-particle final configurations are discussed, in connection with whether the location of such particle is inside or outside the light cone; we find that joint occurrence of both events of types (a) and (b) drives significant changes to such features, signaling a second-order phase transition.

The shape selectivity of zeolites in isobutane alkylation: An investigation using CBMC and MD simulations

The adsorption and diffusion behaviors of C8 isomers and C9 component as main products of the isobutane alkylation catalyzed by zeolites with different topologies were investigated using configurational bias Monte Carlo (CBMC) and MD simulations in this work. The adsorption capacity of zeolites at 353 K and 2.0 MPa relies on their pore volume with the order of FAU > BEA > LTL > MOR. The diffusion coefficient of C8 and C9 molecules increases with the decrease of loading and the increase of temperature, and the more compact molecules diffuse slower than the slimmer ones at low loadings while quicker at higher loadings. It was found that for zeolites, small adsorption heat of C8 isomers, or large molecular diffusion coefficient would correspond to a high selectivity of target alkylates. Particularly, BEA zeolite with large RPLD/LCD shows high reaction selectivity, rendering it a good candidate catalyst for C4 alkylation.

Partial Order–Disorder Transformation of Interpenetrated Porous Coordination Polymers

Controlling interpenetration and flexibility behaviors is intriguing and fundamental for porous coordination polymers. We report exceptional interpenetration behaviors involving controllable partia...

Efficient and Highly Selective CO2 Capture, Separation, and Chemical Conversion under Ambient Conditions by a Polar-Group-Appended Copper(II) Metal–Organic Framework

A polar sulfone-appended copper(II) metal-organic framework (MOF; 1) has been synthesized from the dual-ligand approach comprised of tetrakis(4-pyridyloxymethylene)methane and dibenzothiophene-5,5'-dioxide-3,7-dicarboxylic acid under solvothermal conditions. This has been studied by different techniques that included single-crystal X-ray diffractometry, based on which the presence of Lewis acidic open-metal sites as well as polar sulfone groups aligned on the pore walls is identified. MOF 1 displays a high uptake of CO2 over N2 and CH4 with an excellent selectivity (S = 883) for CO2/N2 (15:85) at 298 K under flue gas combustion conditions. Additionally, the presence of Lewis acidic metal centers facilitates an efficient size-selective catalytic performance at ambient conditions for the conversion of CO2 into industrially valuable cyclic carbonates. The experimental investigations for this functional solvent-free heterogeneous catalyst are also found to be in good correlation with the computational studies provided by configurational bias Monte Carlo simulation for both CO2 capture and its conversion.

Water/Alcohol Mixture Adsorption in Hydrophobic Materials: Enhanced Water Ingress Caused by Hydrogen Bonding.

Microporous crystalline porous materials such as zeolites, metal–organic frameworks, and zeolitic imidazolate frameworks (ZIFs) have potential use for separating water/alcohol mixtures in fixed bed adsorbers and membrane permeation devices. For recovery of alcohols present in dilute aqueous solutions, the adsorbent materials need to be hydrophobic in order to prevent the ingress of water. The primary objective of this article is to investigate the accuracy of ideal adsorbed solution theory (IAST) for prediction of water/alcohol mixture adsorption in hydrophobic adsorbents. For this purpose, configurational bias Monte Carlo (CBMC) simulations are used to determine the component loadings for adsorption equilibrium of water/methanol and water/ethanol mixtures in all-silica zeolites (CHA, DDR, and FAU) and ZIF-8. Due to the occurrence of strong hydrogen bonding between water and alcohol molecules and attendant clustering, IAST fails to provide quantitative estimates of the component loadings and the adsorption selectivity. For a range of operating conditions, the water loading in the adsorbed phase may exceed that of pure water by one to two orders of magnitude. Furthermore, the occurrence of water–alcohol clusters moderates size entropy effects that prevail under pore saturation conditions. For quantitative modeling of the CBMC, simulated data requires the application of real adsorbed solution theory by incorporation of activity coefficients, suitably parameterized by the Margules model for the excess Gibbs free energy of adsorption.

Multivariable extrapolation of grand canonical free energy landscapes.

We derive an approach for extrapolating the free energy landscape of multicomponent systems in the grand canonical ensemble, obtained from flat-histogram Monte Carlo simulations, from one set of temperature and chemical potentials to another. This is accomplished by expanding the landscape in a Taylor series at each value of the order parameter which defines its macrostate phase space. The coefficients in each Taylor polynomial are known exactly from fluctuation formulas, which may be computed by measuring the appropriate moments of extensive variables that fluctuate in this ensemble. Here we derive the expressions necessary to define these coefficients up to arbitrary order. In principle, this enables a single flat-histogram simulation to provide complete thermodynamic information over a broad range of temperatures and chemical potentials. Using this, we also show how to combine a small number of simulations, each performed at different conditions, in a thermodynamically consistent fashion to accurately compute properties at arbitrary temperatures and chemical potentials. This method may significantly increase the computational efficiency of biased grand canonical Monte Carlo simulations, especially for multicomponent mixtures. Although approximate, this approach is amenable to high-throughput and data-intensive investigations where it is preferable to have a large quantity of reasonably accurate simulation data, rather than a smaller amount with a higher accuracy.

Modeling of Adsorption Thermodynamics of Linear and Branched Alkanes in the Aluminum Fumarate Metal Organic Framework

Aluminum fumarate is one of the most stable metal–organic frameworks (MOFs), showing good cycling performance in water adsorption and desorption. Because of its rather small pore size, this MOF shows shape selectivity in the adsorption of linear and branched alkanes. In this work, the interaction of a broad series of alkanes with this MOF was studied through molecular simulations. We expand the transferability of a periodic density functional theory (DFT)-derived force field previously reported by Kulkarni and Sholl to the case of alkane adsorption on this aluminum fumarate MOF. With this force field and using configurational bias Monte Carlo simulations (CBMC), low coverage adsorption enthalpies, adsorption entropies, and Henry’s adsorption constants were calculated. Experimental enthalpies of adsorption (−ΔH0) of C5–C8 n- and iso-alkanes are accurately reproduced by our calculations, e.g., within 5% relative error for n-alkanes. Interestingly, a compensation effect between adsorption enthalpy and adsorption entropy is found in the simulations, with a calculated slope almost identical to the experimental value. This indicates that the force field is very well capable of predicting tendencies with respect to the energetic interactions between the confined molecules and the MOF pore walls. Our calculations also predict separation between linear and branched alkanes with very good accuracy.

Structures of apolipoprotein A-I in high density lipoprotein generated by electron microscopy and biased simulations

BackgroundApolipoprotein A-I (apoA-I) in high-density lipoprotein (HDL) is a key protein for the transport of cholesterol from the vascular wall to the liver. The formation and structure of nascent HDL, composed of apoA-I and phospholipids, is critical to this process. MethodsThe HDL was assembled in vitro from apoA-I, cholesterol and 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) at a 1:4:50 molar ratio. The structure of HDL was investigated in vitreous samples, frozen at cryogenic temperatures, as well as in negatively stained samples by transmission electron microscopy. Low resolution electron density maps were next used as restraints in biased Monte Carlo simulations of apolipoprotein A-I dimers, with an initial structure derived from atomic resolution X-ray structures. ResultsTwo final apoA-I structure models for the full-length structure of apoA-I dimer in the lipid bound conformation were generated, showing a nearly circular, flat particle with an uneven particle thickness. ConclusionsThe generated structures provide evidence for the discoidal, antiparallel arrangement of apoA-I in nascent HDL, and propose two preferred conformations of the flexible N-termini. General significanceThe novel full-length structures of apoA-I dimers deepens the understanding to the structure-function relationship of nascent HDL with significance for the prevention of lipoprotein-related disease. The biased simulation method used in this study provides a powerful and convenient modelling tool with applicability for structural studies and modelling of other proteins and protein complexes.

Composition dependence of the glass forming ability in binary mixtures: The role of demixing entropy.

We present a comparative study of the glass forming ability of binary systems with varying composition, where the systems have similar global crystalline structure (CsCl+fcc). Biased Monte Carlo simulations using umbrella sampling technique show that the free energy cost to create a CsCl nucleus increases as the composition of the smaller particles is decreased. We find that systems with comparatively lower free energy cost to form CsCl nucleus exhibit more pronounced pre-crystalline demixing near the liquid/crystal interface. The structural frustration between the CsCl and fcc crystal demands this demixing. We show that closer to the equimolar mixture, the entropic penalty for demixing is lower and a glass forming system may crystallize when seeded with a nucleus. This entropic penalty as a function of composition shows a non-monotonic behaviour with a maximum at a composition similar to the well known Kob-Anderson (KA) model. Although the KA model shows the maximum entropic penalty and thus maximum frustration against CsCl formation, it also shows a strong tendency towards crystallization into fcc lattice of the larger "A" particles which can be explained from the study of the energetics. Thus for systems closer to the equimolar mixture although it is the requirement of demixing which provides their stability against crystallization, for KA model it is not demixing but slow dynamics and the presence of the "B" particles make it a good glass former. The locally favoured structure around "B" particles is quite similar to the CsCl structure and the incompatibility of CsCl and fcc hinders the fcc structure growth in the KA model. Although the glass forming binary systems studied here are quite similar, differing only in composition, we find that their glass forming ability cannot be attributed to a single phenomenon.

Combination of membrane separation and gas condensation for advanced natural gas conditioning

Membrane separation and gas condensation are combined to reveal an advanced method for the separation of alkanes. First, the applicability of MFI membranes for alkane separation is principally demonstrated by means of realistic adsorption isotherms computed by configurational biased Monte Carlo (CBM) simulations. Next, dew point curves of mixtures comprising different ratios of n-butane (C4) and methane (C1) were calculated according to the thermodynamic methods of Soave–Redlich–Kwong (SRK) and Peng Robinson (PR). From that, isothermal phase boundaries in dependence on the composition of the gas mixture were derived and process parameters under which condensation of the alkane mixture occurs were predetermined. Experimentally, the separation performance of MFI membranes was recorded during separation of n-butane from methane. It was found that liquefied n-butane in the feed and a further liquefaction in the permeate enhance the separation selectivity of MFI zeolite membranes under sweeping conditions tremendously. At the dew point of the feed mixture a sudden rise of the separation factor α is observed. At a temperature of 258K a mixture with χC4=0.5 can be separated with a separation factor αC4/C1=174 due to liquefaction. Experiments without sweeping show a similar behaviour. When forming a two phase mixture in the feed an increase in overall condensation efficiency ηC4 is detected in the permeate. At 258K and pfeed=2bar and ppermeate=1bar 29.6% liquefied n-butane was isolated in the permeate from a mixture comprising χC4=0.5.

Specific and Non-Specific Protein Association in Solution: Computation of Solvent Effects and Prediction of First-Encounter Modes for Efficient Configurational Bias Monte Carlo Simulations

Weak and ultraweak protein-protein association play a role in molecular recognition and can drive spontaneous self-assembly and aggregation. Such interactions are difficult to detect experimentally, and are a challenge to the force field and sampling technique. A method is proposed to identify low-population protein-protein binding modes in aqueous solution. The method is designed to identify preferential first-encounter complexes from which the final complex(es) at equilibrium evolve. A continuum model is used to represent the effects of the solvent, which accounts for short- and long-range effects of water exclusion and for liquid-structure forces at protein/liquid interfaces. These effects control the behavior of proteins in close proximity and are optimized on the basis of binding enthalpy data and simulations. An algorithm is described to construct a biasing function for self-adaptive configurational-bias Monte Carlo of a set of interacting proteins. The function allows mixing large and local changes in the spatial distribution of proteins, thereby enhancing sampling of relevant microstates. The method is applied to three binary systems. Generalization to multiprotein complexes is discussed.

Molecular Level Insights on the Liquid–Solid Transition of Large Organics by Biased Monte Carlo Simulations

The transition of computational ensembles of organic molecules from a liquid state to semi- or fully ordered solid phases, simulated by a biased Monte Carlo procedure driving the system via a forced increase of translational correlation, provide a vivid insight of molecular events accompanying the early stages of nucleation. The onset of anisotropy, conformational changes at the transition points, and the swapping of hydrogen bonds on the way to crystallization are portrayed in detail. Energy and density fluctuations are monitored and discussed in connection with molecular structure; complex flexible molecules meet a crystallization barrier in density decrease and destabilization of total configurational energy. The limitations of the procedure are amply discussed, as for optimization of force field and interpretation of the results of a biased, nonequilibrium simulation. Conclusions are given in a spectrum or reliability, from robust to tentative. In any case the procedure allows the tracing of continuous trajectories through phase space, in some cases leading to a correct reproduction of the experimental crystal structures. Force field, method, and computer programs, developed ex novo, are deposited for reproducibility.

Lattice model of correlated forces in granular solids near jamming

We have devised a lattice model to study force correlations in jamming granular solids in d=2 dimensions. We perform biased Monte Carlo simulations, favoring configurations with more bonds that bear no force, to "starve" the network of bonds and thereby control the distance from the isostatic point J. Increasingly long-ranged correlations are visible as point J is approached, not in the structure of the network of force-bearing bonds but in the spatial extent of perturbations of the force magnitudes consistent with a given starved network. The correlation length so defined diverges as the isostatic point is approached as a power law with an exponent of about ξ~δZ(-5). This divergence is much stronger than for the length scale of "soft modes" observed in jammed systems approaching point J from above.

On the Efficiency of Importance Sampling Techniques for Polarization-Mode Dispersion in Optical Fiber Transmission Systems

An adaptive variance reduction technique was recently proposed to efficiently study transmission errors induced by polarization-mode dispersion (PMD) in optical fiber transmission systems. The technique combines importance sampling (IS) and the cross entropy (CE) method to bias Monte Carlo simulations. Here we (i) present a detailed study to quantify the computational efficiency of this technique, (ii) introduce a novel variant of the hinge model for PMD in optical fiber communication systems, and (iii) use the IS-CE technique to compare the statistical properties of various hinge models. Specifically, we compare the statistics of PMD-induced transmission impairments due to the traditional hinge model (isotropic hinge output), the waveplate hinge model (anisotropic hinge output), and the novel variant of the waveplate hinge model introduced here. We use computationally efficient expressions to determine the probability density function of the differential group delay, and we couple these techniques with the outage map method to compute statistical probabilities of system outages, as quantified by the noncompliant capacity ratio.

Formation of single layer graphene on nickel under far-from-equilibrium high flux conditions

We investigate the theoretical possibility of single layer graphene formation on a nickel surface at different substrate temperatures under far-from-equilibrium high precursor flux conditions, employing state-of-the-art hybrid reactive molecular dynamics/uniform acceptance force bias Monte Carlo simulations. It is predicted that under these conditions, the formation of a single layer graphene-like film may proceed through a combined deposition-segregation mechanism on a nickel substrate, rather than by pure surface segregation as is typically observed for metals with high carbon solubility. At 900 K and above, nearly continuous graphene layers are obtained. These simulations suggest that single layer graphene deposition is theoretically possible on Ni under high flux conditions.

Numerical estimate for boiling points via Wang–Landau simulations

We show how molecular simulations, based on the Wang–Landau (WL) sampling method, can be used to determine the boiling points of a wide range of fluids. The simulations presented here rely on an efficient sampling of the isothermal–isobaric ensemble. This circumvents the difficult deletion/insertion of molecules in dense liquid phases, such as those encountered at the standard boiling point. Using a combination of the WL sampling and hybrid Monte Carlo simulations, we show how we can determine the standard boiling point of atomic fluids, such as liquid metals. We then apply WL configurational bias Monte Carlo simulations to determine the boiling points for a series of long n-alkane chains (icosane, tetracosane and triacontane). The results obtained in this work are in good agreement with the available experimental data and simulation results.