Ariana Torres-Knoop

On the inner workings of Monte Carlo codes

We review state-of-the-art Monte Carlo (MC) techniques for computing fluid coexistence properties (Gibbs simulations) and adsorption simulations in nanoporous materials such as zeolites and metal–organic frameworks. Conventional MC is discussed and compared to advanced techniques such as reactive MC, configurational-bias Monte Carlo and continuous fractional MC. The latter technique overcomes the problem of low insertion probabilities in open systems. Other modern methods are (hyper-)parallel tempering, Wang–Landau sampling and nested sampling. Details on the techniques and acceptance rules as well as to what systems these techniques can be applied are provided. We highlight consistency tests to help validate and debug MC codes.

Determining In Situ Protein Conformation and Orientation from the Amide-I Sum-Frequency Generation Spectrum: Theory and Experiment

Vibrational sum-frequency generation (VSFG) spectra of the amide-I band of proteins can give detailed insight into biomolecular processes near membranes. However, interpreting these spectra in terms of the conformation and orientation of a protein can be difficult, especially in the case of complex proteins. Here we present a formalism to calculate the amide-I infrared (IR), Raman, and VSFG spectra based on the protein conformation and orientation distribution. Based on the protein conformation, we set up the amide-I exciton Hamiltonian for the backbone amide modes that generate the linear and nonlinear spectroscopic responses. In this Hamiltonian, we distinguish between nearest-neighbor and non-nearest-neighbor vibrational couplings. To determine nearest-neighbor couplings we use an ab initio 6-31G+(d) B3LYP-calculated map of the coupling as a function of the dihedral angles. The other couplings are estimated using the transition-dipole coupling model. The local-mode frequencies of hydrogen-bonded peptide bonds and of peptide bonds to proline residues are red-shifted. To obtain realistic hydrogen-bond shifts we perform a molecular dynamics simulation in which the protein is solvated by water. As a first application, we measure and calculate the amide-I IR, Raman, and VSFG spectra of cholera toxin B subunit docked to a model cell membrane. To deduce the orientation of the protein with respect to the membrane from the VSFG spectra, we compare the experimental and calculated spectral shapes of single-polarization results, rather than comparing the relative amplitudes of VSFG spectra recorded for different polarization conditions for infrared, visible, and sum-frequency light. We find that the intrinsic uncertainty in the interfacial refractive index--essential to determine the overall amplitude of the VSFG spectra--prohibits a meaningful comparison of the intensities of the different polarization combinations. In contrast, the spectral shape of most of the VSFG spectra is independent of the details of the interfacial refractive index and provides a reliable way of determining molecular interfacial orientation. Specifically, we find that the symmetry axis of the cholera toxin B subunit is oriented at an angle of 6° ± 17° relative to the surface normal of the lipid monolayer, in agreement with 5-fold binding between the toxins five subunits and the receptor lipids in the membrane.

A Comparison of Advanced Monte Carlo Methods for Open Systems: CFCMC vs CBMC.

Two state-of-the-art simulation methods for computing adsorption properties in porous materials like zeolites and metal-organic frameworks are compared: the configurational bias Monte Carlo (CBMC) method and the recently proposed continuous fractional component Monte Carlo (CFCMC) method. We show that CFCMC is a very significant improvement over CBMC, and we can recommend it as our preferred method of choice. It is faster, more reliable, and (in contrast to CBMC) provides insight on whether or not the results are properly equilibrated. We also show that it is possible to combine the methods in a new CB/CFCMC hybrid method and derive the acceptance rules. This method achieves even higher insertion acceptance ratios.

Entropic Separation of Styrene/Ethylbenzene Mixtures by Exploitation of Subtle Differences in Molecular Configurations in Ordered Crystalline Nanoporous Adsorbents

The separation of styrene/ethylbenzene mixture is of great importance in the petrochemical industry. Current technology uses distillation; this separation is difficult because of the small, 9 K, difference in the boiling points. An alternative separation method uses selective adsorption in nanoporous materials such as zeolites and metal-organic frameworks. Here we present a simulation screening study for the separation of styrene/ethylbenzene mixture by adsorptive means in nanoporous materials near pore saturation conditions. Under these conditions, different entropic mechanisms can dictate the separation process. Commensurate stacking has the best trade-off between selectivity and saturation capacity and offers a geometrical solution to the separation problem. MIL-47 has the right channel size and topology for styrene to exhibit commensurate stacking offering high capacity and selectivity for styrene over ethylbenzene. Out of all the screened structures, MIL-47 was found to be the best candidate for the separation of styrene/ethylbenzene mixture.

Exploiting Large-Pore Metal-Organic Frameworks for Separations through Entropic Molecular Mechanisms.

We review the molecular mechanisms behind adsorption and the separations of mixtures in metal-organic frameworks and zeolites. Separation mechanisms can be based on differences in the affinity of the adsorbate with the framework and on entropic effects. To develop next-generation adsorbents, the separation efficiency of the materials needs to be improved. The performance under industrially relevant conditions largely depends on two factors: 1) the separation selectivity and 2) the pore volume capacity of the material. Enthalpic mechanisms can lead to increased selectivities, but these are mostly restricted to the low loading regime, and hence these mechanisms are unable to make use of all of the large-pore volume that a metal-organic framework can provide. Industrial processes routinely operate in the pore saturation regime. In this Review, we focus on entropic molecular separation mechanisms that are effective under these conditions and, in particular, on a recent methodology to obtain high selectivities at high pore loading.

Simulating the Reactions of CO2 in Aqueous Monoethanolamine Solution by Reaction Ensemble Monte Carlo Using the Continuous Fractional Component Method

Molecular simulations were used to compute the equilibrium concentrations of the different species in CO2/monoethanolamine solutions for different CO2 loadings. Simulations were performed in the Reaction Ensemble using the continuous fractional component Monte Carlo method at temperatures of 293, 333, and 353 K. The resulting computed equilibrium concentrations are in excellent agreement with experimental data. The effect of different reaction pathways was investigated. For a complete understanding of the equilibrium speciation, it is essential to take all elementary reactions into account because considering only the overall reaction of CO2 with MEA is insufficient. The effects of electrostatics and intermolecular van der Waals interactions were also studied, clearly showing that solvation of reactants and products is essential for the reaction. The Reaction Ensemble Monte Carlo using the continuous fractional component method opens the possibility of investigating the effects of the solvent on CO2 chemisorption by eliminating the need to study different reaction pathways and concentrate only on the thermodynamics of the system.

Direct Free Energy Calculation in the Continuous Fractional Component Gibbs Ensemble.

A new formulation of the Gibbs ensemble (GE) combined with the continuous fractional component Monte Carlo method is presented. In the proposed formulation, only a single fractional molecule per component is used instead of two in the original formulation by Shi and Maginn ( J. Comput. Chem. 2008 , 29 , 2520 - 2530 ). This has the following advantages: (1) one directly obtains chemical potentials, without using test particles. We show analytically that the expressions for the chemical potential are identical to those in the conventional Gibbs ensemble; (2) biasing is applied to each simulation box independently; (3) maximum allowed changes in the scaling parameter of intermolecular interactions can be chosen differently in each simulation box. Obtaining chemical potentials directly facilitates thermodynamic modeling using equations of state, and it can be used as an independent check to ensure that chemical equilibrium is achieved. As a proof of principle, our method is tested for Lennard-Jones (LJ) particles and the TIP3P-Ew water model. Results are compared with the conventional GE. Excellent agreement was found both for average densities and chemical potentials. In our new approach, the acceptance probability for molecule exchanges between the boxes is much higher (typically larger than 40% for LJ particles) than for the conventional GE (typically lower than 2% for LJ particles). It is also shown that the contribution of the fractional molecule should be disregarded when computing ensemble averages such as the average energy per molecule and the average densities. The algorithm can be easily extended to mixtures and molecules with intramolecular interactions.

Understanding DABCO Nanorotor Dynamics in Isostructural Metal-Organic Frameworks

Flexible framework dynamics present in the subset of metal-organic frameworks known as soft porous crystals give rise to interesting structural properties that are unique to this class of materials. In this work, we use experiments and molecular simulation to understand the highly dynamic nanorotor behavior of the 1,4-diazabicyclo[2.2.2]octane (DABCO) ligand in the pillared Zn-DMOF and Zn-DMOF-TM (TM = tetramethyl) structures. While DABCO is known to be displaced in the presence of water in the parent Zn-DMOF structure, the Zn-DMOF-TM variation is highly stable even after adsorbing significant amounts of water vapor. The dynamics of DABCO in the presence of water guest molecules is therefore also explored in the Zn-DMOF-TM structure via in situ NMR and IR experiments. This analysis shows that the rotational motion of the DABCO linkers is dependent on water content, but not a likely source of water instability because the dynamics are fast and largely unaffected by the presence of methyl functional groups.

Solubilities of CO 2 , CH 4 , C 2 H 6 , and SO 2 in ionic liquids and Selexol from Monte Carlo simulations

Monte Carlo simulations are used to calculate the solubility of natural gas components in ionic liquids (ILs) and Selexol, which is a mixture of poly(ethylene glycol) dimethyl ethers. The solubility of the pure gases carbon dioxide (CO2), methane (CH4), ethane (C2H6), and sulfur dioxide (SO2) in the ILs 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([Cnmim][Tf2N], n = 4, 6), 1-ethyl-3-methylimidazolium diethylphosphate ([emim][dep]), and Selexol (CH3O[CH2CH2O]nCH3, n = 4, 6) have been computed at 313.15 K and several pressures. The gas solubility trend observed in the experiments and simulations is: SO2 > CO2 > C2H6 > CH4. Overall, the Monte Carlo simulation results are in quantitative agreement with existing experimental data. Molecular simulation is an excellent tool to predict gas solubilities in solvents and may be used as a screening tool to navigate through the large number of theoretically possible ILs.

Computation of thermodynamic properties in the continuous fractional component Monte Carlo Gibbs ensemble

It is shown that ensemble averages computed in the Gibbs Ensemble with Continuous Fractional Component Monte Carlo (CFCMC GE) are different from those computed in the conventional Gibbs Ensemble (GE). However, it is possible to compute averages corresponding to the conventional GE while performing simulations in the CFCMC GE. In this way, one can benefit from the nice features of CFCMC GE (e.g. more efficient particle exchange) and at the same time compute the ensemble averages that correspond to the conventional GE. As a case study, the equilibrium pressure and densities of the systems of 256 and 512 LJ particles at different reduced temperatures () are computed in the conventional GE and CFCMC GE. The validity of the expressions derived for computation of the thermodynamic pressure and densities corresponding to the conventional GE and computed in the CFCMC GE is examined numerically. The thermodynamic pressure in the conventional GE and CFCMC GE typically differs by at most 4%. It is shown that a very good estimate of the average pressure and densities corresponding to the conventional GE can be obtained by performing simulation in CFCMC GE and ignoring the contributions of the fractional molecule. It is also shown that the fractional molecule does not have an influence on the structure of the liquid, even for very small system sizes (e.g. 40 particles). The approach used here to compute the equilibrium pressure and densities of the conventional GE using the CFCMC GE can be easily extended to other thermodynamic properties and other ensembles.