Canonical and microcanonical Monte Carlo simulations of lattice-gas mixtures

We propose strict canonical and microcanonical Monte Carlo algorithms for an arbitrary lattice-gas binary mixture. We deduce formulas that allow us to obtain field quantities over the ensembles in which their conjugate extensive quantities are conserved. As an example, we have considered a lattice-gas mixture that is equivalent to the spin-1 Blume-Emery-Griffiths model [Phys. Rev. A 4, 1071 (1971)]. For a finite system and near a phase coexistence, the field as a function of its extensive conjugate shows a loop that disappears in the thermodynamic limit giving rise to the usual tie line. The first-order phase transition was determined by the use of three criteria.     

Monte Carlo simulations of oppositely charged macroions in solution

The structure and phase behavior of oppositely charged macroions in solution have been studied with Monte Carlo simulations using the primitive model where the macroions and small ions are described as charged hard spheres. Size and charge symmetric, size asymmetric, and charge asymmetric macroions at different electrostatic coupling strengths are considered, and the properties of the solutions have been examined using cluster size distribution functions, structure factors, and radial distribution functions. At increasing electrostatic coupling, the macroions form clusters and eventually the system displays a phase instability, in analogy to that of simple electrolyte solutions. The relation to the similar cluster formation and phase instability occurring in solutions containing oppositely charged polymers is also discussed.     

Monte Carlo structure simulations for aqueous 1,4-dioxane solutions

Monte Carlo simulations in the NpT ensembles have been performed for the structure exploration of aqueous 1,4-dioxane solutions. Three different systems with all-atom dioxane:TIP4P water molar compositions of 2:500 (code:D2), 8:465 (D8), and 17:425 (D17) modeled solutions of 0.22, 0.88, and 1.86 mol/dm3 concentrations, respectively, at T = 298 K and p = 1 atm. The calculated solution densities increase from 0.992 to 1.002 g/cm3 with increasing dioxane concentration and approach the experimentally determined densities within 1%. This close agreement was achieved by utilizing RESP charges fitted to the in-solution IEF-PCM/B3LYP/6-31G* electrostatic potential of dioxane taken in its chair conformation and recently developed C, H steric parameters for ethers for calculations with a 12-6-1 all-atom potential. Solution structure analyses pointed out that the dioxane molecules arrange in the solutions with favorable distances of 4-8 angstroms for the ring symmetry centers. Within this range not only pairs of rings but triangular triads and tetrads have also been observed with center-center distances <8 angstroms. For the D8 system, about 25% of the sampled configurations included such a triad. In the case of the D17 model, two simulations starting from different solution configuration predicted different degrees for the dioxane aggregation in aqueous solution. In the more aggregated structure 3-21 triads are consistently maintained and 1-2 tetrads are formed in 58% of the configurations. Each dioxane oxygen forms about one hydrogen bond, on average, to a water molecule in the 0.22-1.86 molar range. The most likely O(dioxane)...H(water) hydrogen bond distance is 1.75-1.80 angstroms compared to the optimal distance of 1.72 angstroms in the isolated dimer. The optimal dioxane-water interaction energy of -5.65 kcal/mol indicates a remarkable hydrogen-bond acceptor character for dioxane.     

Structure of the liquid-vapor interface of water-methanol mixtures as seen from Monte Carlo simulations

Monte Carlo simulation of the vapor-liquid interface of water-methanol mixtures of different compositions, ranging from pure water to pure methanol, have been performed on the canonical (N, V, T) ensemble at 298 K. The analysis of the systems simulated has revealed that the interface is characterized by a double layer structure: methanol is strongly adsorbed at the vapor side of the interface, whereas this adsorption layer is followed at its liquid side by a depletion layer of methanol of lower concentration than in the bulk liquid phase of the system. The dominant feature of the interface has been found to be the adsorption layer in systems of methanol mole fractions below 0.2, and the depletion layer in systems of methanol mole fractions between 0.25 and 0.5. The orientation of the molecules located at the depletion layer is found to be already uncorrelated with the interface, whereas the methanol molecules of the adsorption layer prefer to align perpendicular to the interface, pointing straight toward the vapor phase by their methyl group. Although both the preference of the molecular plane for a perpendicular alignment with the interface and the preference of the methyl group for pointing straight to the vapor phase are found to be rather weak, the preference of the methyl group for pointing as straight toward the vapor phase as possible within the constraint imposed by the orientation of the molecular plane is found to be fairly strong. One of the two preferred orientations of the interfacial water molecules present in the neat system is found to disappear in the presence of methanol, because methanol molecules aligned in their preferred orientation can replace these water molecules in the hydrogen-bonding pattern of the interface.     

Hybrid Monte Carlo simulations of vertical electronic transitions in acetone in aqueous solution

A simulation of the absorption and the fluorescence of acetone in aqueous solution is reported. The model has an explicit solvent representation with an effective ab initio treatment of the solute. The model attempts to balance quantum chemistry, intermolecular interactions and statistical thermodynamics. It includes a non-electrostatic perturbation on the solute which models the solute–solvent exchange repulsion and the restriction put on the electronic structure of the solute by the antisymmetry to the solvent. The solvent shift to the absorption transition is found to be between 0.16 and 0.21 eV; the shift to the fluorescence transition is found to be between 0.02 and 0.05 eV. The simulation supports the conclusion that the first peak in the fluorescence spectrum of acetone is from a single molecule in equilibrium with the solvent, not from an excimer.     

Adsorption of binary mixtures on two-dimensional surfaces: theory and Monte Carlo simulations

The adsorption of binary mixtures on square lattices is studied by combining theoretical modeling and Monte Carlo (MC) simulations in grand canonical ensemble. The adsorption thermodynamics is analyzed through the total and partial isotherms. Two theoretical models have been used in the present study: (i) the first, which we called cluster approximation (CA), is based on exact calculations of configurations on finite cells. An efficient algorithm allows us to calculate the detailed structure of the configuration space for \(m = l \times l \) cells; and (ii) the second is a generalization of the classical quasi-chemical approximation (QCA) in which the adsorbate is a binary mixture of species \(a\) and \(b\) . Adsorbate–adsorbate lateral interactions are incorporated in the context of the two mentioned approximations. Results from CA and QCA are compared with MC simulations. Close agreement between simulated and theoretical data supports the validity of the theoretical models to describe the adsorption of mixed gases on two-dimensional surfaces.     

Fast protein structure prediction using Monte Carlo simulations with modal moves

Using normal modes to generate torsion space moves in Monte Carlo simulations of peptides and proteins is not a new idea; nevertheless, despite its power it has not received widespread application. We show that such a "Modal Monte Carlo" approach is an efficient tool for ab initio predictions of small-protein structures. We apply this method to the Trp cage, a 20-residue polypeptide designed to fold rapidly into a structure that includes tertiary contacts, despite its short length. We achieve a high-quality ab initio structure prediction in about 2 orders of magnitude less computation time than state of the art molecular dynamics techniques.     

Reactive Monte Carlo and grand-canonical Monte Carlo simulations of the propene metathesis reaction system

The influence of silicalite-1 pores on the reaction equilibria and the selectivity of the propene metathesis reaction system in the temperature range between 300 and 600 K and the pressure range from 0.5 to 7 bars has been investigated with molecular simulations. The reactive Monte Carlo (RxMC) technique was applied for bulk-phase simulations in the isobaric-isothermal ensemble and for two phase systems in the Gibbs ensemble. Additionally, Monte Carlo simulations in the grand-canonical ensemble (GCMC) have been carried out with and without using the RxMC technique. The various simulation procedures were combined with the configurational-bias Monte Carlo approach. It was found that the GCMC simulations are superior to the Gibbs ensemble simulations for reactions where the bulk-phase equilibrium can be calculated in advance and does not have to be simulated simultaneously with the molecules inside the pore. The confined environment can increase the conversion significantly. A large change in selectivity between the bulk phase and the pore phase is observed. Pressure and temperature have strong influences on both conversion and selectivity. At low pressure and temperature both conversion and selectivity have the highest values. The effect of confinement decreases as the temperature increases.     

Parallel Markov chain Monte Carlo simulations

With strict detailed balance, parallel Monte Carlo simulation through domain decomposition cannot be validated with conventional Markov chain theory, which describes an intrinsically serial stochastic process. In this work, the parallel version of Markov chain theory and its role in accelerating Monte Carlo simulations via cluster computing is explored. It is shown that sequential updating is the key to improving efficiency in parallel simulations through domain decomposition. A parallel scheme is proposed to reduce interprocessor communication or synchronization, which slows down parallel simulation with increasing number of processors. Parallel simulation results for the two-dimensional lattice gas model show substantial reduction of simulation time for systems of moderate and large size.     

Monte Carlo simulations of squalane in the Gibbs ensemble

We investigate the liquid–vapour coexistence curve of 2,6,10,15,19,23-hexamethyltetracosane (squalane) near the critical point with a new Lennard–Jones parameter set and compare our results to existing simulation data as well as to recent experimental vapour pressure data. Comparison of the liquid–vapour coexistence curve to previous simulation data reveals that this new force field, which includes tail corrections to the truncation of the non-bonded interactions increases the liquid density. We determine the critical temperature to 829 K and 825 K (with roughly 1% error) for two different system sizes, 72 and 108 molecules, and the critical density to 0.211 g/cm³ and 0.228 g/cm³, respectively. We extrapolate experimental vapour pressure data by use of Antoine's law to the temperature range covered by simulation and yield good agreement between simulation and experiment. We note that the vapour pressure in simulation is essentially governed by the ideal vapour pressure.     

Molecular dynamics and Monte Carlo simulations for the structure of the aqueous trimethylammonium chloride solution in the 0.2-1 molar range

Molecular dynamics and Monte Carlo simulations have been performed for characterizing the structure of the 0.2 and 1 molar aqueous trimethylammonium chloride solutions. Atomic charges were derived through the CHELPG and RESP fits to the molecular electrostatic potentials calculated for the cation in water at the IEF-PCM/B3LYP level using the 6-31G* and 6-311++G** basis sets. Maxima and minima of the calculated radial distribution functions were not sensitive to the four atomic charge sets. Simulated solution structures suggest non-negligible solute-solute interactions and remarkable inhomogeneity at both concentrations. This means that equilibrium ratios, derived for conformers/tautomers by means of ab initio calculations with the IEF-PCM continuum dielectric solvent model, should be corrected for free energy changes following solute association when compared to experimental data obtained for the 0.1-1 molar aqueous solutions.     

On the acceptance ratio in Monte Carlo computer simulations

The functional form of acceptance probabilities in Monte Carlo algorithms bears a resemblance to the distance functions which are specifically defined to be bracketed by the unit interval. This observation led us to seek the average distance between any two points on the unit interval and this by analogy resulted in a suggestion of an upper and a lower bound of 1/2 and 1/3, respectively, for the acceptance ratio or the average acceptance probability in Monte Carlo computer simulations.     

Monte Carlo simulations of low background detectors

An implementation of the Electron Gamma Shower 4 code (EGS4) has been developed to allow convenient simulation of typical gamma ray measurement systems. Coincidence gamma rays, beta spectra, and angular correlations have been added to adequately simulate a complete nuclear decay and provide corrections to experimentally determined detector efficiencies. This code has been used to strip certain low-background spectra for the purpose of extremely low-level assay. Monte Carlo calculations of this sort can be extremely successful since low background detectors are usually free of significant contributions from poorly localized radiation sources, such as cosmic muons, secondary cosmic neutrons, and radioactive construction or shielding materials. Previously, validation of this code has been obtained from a series of comparisons between measurements and blind calculations. An example of the application of this code to an exceedingly low background spectrum stripping will be presented.Pacific Northwest Laboratory is operated by Battelle Memorial Institute for the US Department of Energy under Contract DE-AC06-76RLO 1830.     

Dynamic Monte Carlo simulations of anisotropic colloids

We put forward a simple procedure for extracting dynamical information from Monte Carlo simulations, by appropriate matching of the short-time diffusion tensor with its infinite-dilution limit counterpart, which is supposed to be known. This approach - discarding hydrodynamics interactions - first allows us to improve the efficiency of previous dynamic Monte Carlo algorithms for spherical Brownian particles. In the second step, we address the case of anisotropic colloids with orientational degrees of freedom. As an illustration, we present a detailed study of the dynamics of thin platelets, with emphasis on long-time diffusion and orientational correlations.     

The influence of side chains on the properties of simple model biopolymers: Monte Carlo simulations

A model for the simulation of proteins is introduced which is based on a new set of bond vectors and a new method for modeling the side chains of proteins. The drawbacks of united atoms models are summarized and the motivation for this new model is given. Some preliminary results are shown which shall demonstrate the suitability of the model proposed.     

A simple methodology for analyzing association effects on response functions via Monte Carlo simulations

A simple methodology was developed to analyze association effects on the thermodynamic response functions for a pure self-associated fluid via Monte Carlo simulations. The procedure essentially involves expressing the residual energy and volume of the fluid in terms of these properties for two hypothetical fluids consisting of monomers and associated molecules, respectively. This allows the thermodynamic response functions to be expressed in a perturbative form as a combination of the values for the property in the monomeric fluid and the contribution of association (the perturbative term). The proposed methodology was used to determine both contributions to the isobaric heat capacity and to the temperature and pressure derivatives of the volume for OPLS methanol along the 50 MPa isobar from 220 to 1500 K. Based on the results, both terms exert a substantial influence on the isobaric heat capacity; by contrast, the association term for the volumetric properties is negligible. These results are consistent with those of a previous work involving simulations with the same model under identical thermodynamic conditions but a different approach. They are also compared with others previously reported in context. Moreover, a comprehensive study of the different types of clusters present in the fluid was performed and the results were related to thermodynamic properties. A strong correlation between the heat capacity of the monomeric fluid and this structural analysis was found.     

Monte Carlo simulations of equilibrium solubilities and structure of water in n-alkanes and polyethylene

Gibbs ensemble Monte Carlo methods based on a force field that combines the simple point charge [Berendsen et al., in Intermolecular Forces, edited by Pullman (Reidel, Dordrecht, 1981), p. 331] and transferable potentials for phase equilibria [Martin and Siepmann, J. Phys. Chem. B 102, 2659 (1998)] models were used to study the equilibrium properties of binary systems consisting of water and n-alkanes with chain lengths from hexane to hexadecane. In addition, systems where extended linear alkane chains (up to 300 carbon units long) were used to represent amorphous polyethylene were simulated in the presence of water using a connectivity altering osmotic Gibbs ensemble. In these simulations the equilibrium between a liquid water phase and a polymer phase into which water was inserted was studied. The predicted solubilities, which were determined between 350 and 550 K, are in good agreement with experiment, where experimental results are available, and the density of water molecules in the hydrocarbons is approximately 63% as high as in saturated water vapor under the same conditions. At the lower temperatures most of the water exists as monomers; increasing the temperature leads to an increase in the density of water in the alkane phase and hence in the fraction of molecules that participate in clusters. Dimers are the most prevalent clusters in all hydrocarbons and at all temperatures studied, and the fraction of clusters of given size decrease with increasing cluster size. A large fraction of trimers, tetramers, and pentamers, which are the cluster sizes for which topologies have been studied, are cyclic at low temperatures, but at higher temperatures linear structures predominate. The same properties are observed for pure water vapor clusters in equilibrium with the liquid phase, showing that the cluster topologies are not significantly affected by the surrounding hydrocarbon.     

Monte Carlo simulations for the study of hemoglobin-fragment conformations

Monte Carlo simulations have been performed to study the conformations of the pentapeptide fragments of normal adult (Thr-Pro-Glu-Glu-Lys) and sickle-like anemia hemoglobin (Thr-Pro-Val-Glu-Lys). The results show that the energy optimized conformation of normal adult hemoglobin-fragment agrees with the X-ray experiment and the theoretically determined conformation of the sickle-like anemia hemoglobin-fragment is identical with the conformation of the normal adult hemoglobin-fragment.