Monte Carlo simulation of electron-ion recombination at high pressure

The Monte Carlo method is applied to the study of electron-ion recombination in CO₂, CH₄ and NH₃ over a wide range of pressures. Dissociative recombination is enhanced by energy transfer to the ambient gas molecules and the recombination rates peak at 11, 2 and 9 × 10⁵ CM³ s^?1, respectively. At very high pressures, the rate approaches the Langevin limit.     

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.     

Efficient combination of Wang-Landau and transition matrix Monte Carlo methods for protein simulations

An efficient combination of the Wang-Landau and transition matrix Monte Carlo methods for protein and peptide simulations is described. At the initial stage of simulation the algorithm behaves like the Wang-Landau algorithm, allowing to sample the entire interval of energies, and at the later stages, it behaves like transition matrix Monte Carlo method and has significantly lower statistical errors. This combination allows to achieve fast convergence to the correct values of density of states. We propose that the violation of TTT identities may serve as a qualitative criterion to check the convergence of density of states. The simulation process can be parallelized by cutting the entire interval of simulation into subintervals. The violation of ergodicity in this case is discussed. We test the algorithm on a set of peptides of different lengths and observe good statistical convergent properties for the density of states. We believe that the method is of general nature and can be used for simulations of other systems with either discrete or continuous energy spectrum.     

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.     

Microscopic solvation: spectroscopic results vs. Monte Carlo simulations

Van-der-Waals clusters of carbazole (representing the ‘solute’) with up to 40 nitrogen or methane solvent molecules were characterized using two-color resonant two-photon ionization spectroscopy. Features in these spectra (redshift, homogeneous and heterogeneous broadening, etc.) are interpreted as being caused by various static and dynamic effects of the solvent shell surrounding the aromatic substrate. For a better understanding of such effects, Monte Carlo simulations of the clusters were performed: Statics: Using a Monte Carlo simulated annealing minimization procedure, minimum energy structures (local, probably global) were found for the various cluster species. Using a simple empirical additivity rule, spectral shifts are rationalized from these structures.Dynamics: Starting from these minimum configurations, canonical ensemble simulations were carried out in a temperature range from 0 to 35 K. Severalorder-disorder transitions were identified including:

1. orientational isomerization or ‘melting’
2. surface isomerization or decoupling
3. rigid → fluxional transitions
4. full cluster ‘melting’

We present some of our experimental results on the systems carbazole · (N₂) _n and carbazole · (CH₄) _n together with the corresponding simulation data.     

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.     

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 segregation in Pt-Re catalyst nanoparticles

We have investigated the segregation of Pt atoms to the surfaces of Pt-Re nanoparticles using the Monte Carlo method and modified embedded-atom method potentials that we have developed for Pt-Re alloys. The Pt(75)Re(25) nanoparticles (containing from 586 to 4,033 atoms) are assumed to have disordered fcc configurations and cubo-octahedral shapes (terminated by [111] and [100] facets), while the Pt(50)Re(50) and Pt(25)Re(75) nanoparticles (containing from 587 to 4,061 atoms) are assumed to have disordered hcp configurations and truncated hexagonal bipyramidal shapes (terminated by [0001] and [1011] facets). We predict that due to the segregation process the equilibrium Pt-Re nanoparticles would achieve a core-shell structure, with a Pt-enriched shell surrounding a Pt-deficient core. For fcc cubo-octahedral Pt(75)Re(25) nanoparticles, the shells consist of almost 100 at. % of Pt atoms. Even in the shells of hcp truncated hexagonal bipyramidal Pt(50)Re(50) nanoparticles, the concentrations of Pt atoms exceed 85 at. % (35 at. % higher than the overall concentration of Pt atoms in these nanoparticles). Most prominently, all Pt atoms will segregate to the surfaces in the hcp truncated hexagonal bipyramidal Pt(25)Re(75) nanoparticles containing less than 1000 atoms. We also find that the Pt atoms segregate preferentially to the vertex sites, less to edge sites, and least to facet sites on the shell of Pt-Re nanoparticles.     

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.     

Monte Carlo simulations of XRF intensities in non-homogeneous matrices

In this paper a quantitative explanation is formulated for many discrepancies in the analysis of non-homogeneous materials. Metal alloys are the examples by excellence of such materials. Fe-Cr and Zn-Al alloys with a dispersed phase containing one of the elements only or both elements in a concentration different from the bulk, are simulated. Monte Carlo methods are used for generating the dispersions as well as for simulating the XRF processes.     

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 simulations of segregation in Pt-Ni catalyst nanoparticles

We have investigated the segregation of Pt atoms in the surfaces of Pt-Ni nanoparticles, using modified embedded atom method potentials and the Monte Carlo method. The nanoparticles are constructed with disordered fcc configurations at two fixed overall concentrations (50 at. % Pt and 75 at. % Pt). We use octahedral and cubo-octahedral nanoparticles terminated by {111} and {100} facets to examine the extent of the Pt segregation to the nanoparticle surfaces at T=600 K. The model particles contain between 586 and 4033 atoms (particle size ranging from 2.5 to 5 nm). Our results imply that a complete {100}-facet reconstruction could make the cubo-octahendral Pt-Ni nanoparticles most energetically favorable. We predict that at 600 K due to segregation the equilibrium cubo-octahedral Pt50Ni50 nanoparticles with fewer than 1289 atoms and Pt75Ni25 nanoparticles with fewer than 4033 atoms would achieve a surface-sandwich structure, in which the Pt atoms are enriched in the outermost and third atomic shells while the Ni atoms are enriched in the second atomic shell. We also find that, due to an order-disorder transition, the Pt50Ni50 cubo-octahedral nanoparticles containing more than 2406 atoms would form a core-shell structure with a Pt-enriched surface and a Pt-deficient homogenous core.     

Titration of hydrophobic polyelectrolytes using Monte Carlo simulations

The conformation and titration curves of weak (or annealed) hydrophobic polyelectrolytes have been examined using Monte Carlo simulations with screened Coulomb potentials in the grand canonical ensemble. The influence of the ionic concentration pH and presence of hydrophobic interactions has been systematically investigated. A large number of conformations such as extended, pearl-necklace, cigar-shape, and collapsed structures resulting from the subtle balance of short-range hydrophobic attractive interactions and long-range electrostatic repulsive interactions between the monomers have been observed. Titration curves were calculated by adjusting the pH-pK(0) values (pK(0) represents the intrinsic dissociation constant of an isolated monomer) and then calculating the ionization degree alpha of the polyelectrolyte. Important transitions related to cascades of conformational changes were observed in the titration curves, mainly at low ionic concentration and with the presence of strong hydrophobic interactions. We demonstrated that the presence of hydrophobic interactions plays an important role in the acid-base properties of a polyelectrolyte in promoting the formation of compact conformations and hence decreasing the polyelectrolyte degree of ionization for a given pH-pK(0) value.     

Efficient Monte Carlo trial moves for polypeptide simulations

A new move set for the Monte Carlo simulations of polypeptide chains is introduced. It consists of a rigid rotation along the (C(alpha)) ends of an arbitrary long segment of the backbone in such a way that the atoms outside this segment remain fixed. This fixed end move, or FEM, alters only the backbone dihedral angles phi and psi and the C(alpha) bond angles of the segment ends. Rotations are restricted to those who keep the alpha bond angles within their maximum natural range of approximately +/-10 degrees. The equations for the angular intervals (tau) of the allowed rigid rotations and the equations required for satisfying the detailed balance condition are presented in detail. One appealing property of the FEM is that the required number of calculations is minimal, as it is evident from the simplicity of the equations. In addition, the moving backbone atoms undergo considerable but limited displacements of up to 3 A. These properties, combined with the small number of backbone angles changed, lead to high acceptance rates for the new conformations and make the algorithm very efficient for sampling the conformational space. The FEMs, combined with pivot moves, are used in a test to fold a group of coarse-grained proteins with lengths of up to 200 residues.     

Thermodynamic properties of van der Waals fluids from Monte Carlo simulations and perturbative Monte Carlo theory

Computer simulations have been performed for fluids with van der Waals potential, that is, hard spheres with attractive inverse power tails, to determine the equation of state and the excess energy. On the other hand, the first- and second-order perturbative contributions to the energy and the zero- and first-order perturbative contributions to the compressibility factor have been determined too from Monte Carlo simulations performed on the reference hard-sphere system. The aim was to test the reliability of this "exact" perturbation theory. It has been found that the results obtained from the Monte Carlo perturbation theory for these two thermodynamic properties agree well with the direct Monte Carlo simulations. Moreover, it has been found that results from the Barker-Henderson [J. Chem. Phys. 47, 2856 (1967)] perturbation theory are in good agreement with those from the exact perturbation theory.     

Water in nanopores. I. Coexistence curves from Gibbs ensemble Monte Carlo simulations

Coexistence curves of water in cylindrical and slitlike nanopores of different size and water-substrate interaction strength were simulated in the Gibbs ensemble. The two-phase coexistence regions cover a wide range of pore filling level and temperature, including ambient temperature. Five different kinds of two-phase coexistence are observed. A single liquid-vapor coexistence is observed in hydrophobic and moderately hydrophilic pores. Surface transitions split from the main liquid-vapor coexistence region, when the water-substrate interaction becomes comparable or stronger than the water-water pair interaction. In this case prewetting, one and two layering transitions were observed. The critical temperature of the first layering transition decreases with strengthening water-substrate interaction towards the critical temperature expected for two-dimensional systems and is not sensitive to the variation of pore size and shape. Liquid-vapor phase transition in a pore with a wall which is already covered with two water layers is most typical for hydrophilic pores. The critical temperature of this transition is very sensitive to the pore size, in contrast to the liquid-vapor critical temperature in hydrophobic pores. The observed rich phase behavior of water in pores evidences that the knowledge of coexistence curves is of crucial importance for the analysis of experimental results and a prerequiste of meaningful simulations.     

Grand canonical Monte Carlo simulations of water in protein environments

The grand canonical simulation algorithm is considered as a general methodology to sample the configuration of water molecules confined within protein environments. First, the probability distribution of the number of water molecules and their configuration in a region of interest for biochemical simulations, such as the active site of a protein, is derived by considering a finite subvolume in open equilibrium with a large system serving as a bulk reservoir. It is shown that the influence of the bulk reservoir can be represented as a many-body potential of mean force acting on the atoms located inside the subvolume. The grand canonical Monte Carlo (GCMC) algorithm, augmented by a number of technical advances to increase the acceptance of insertion attempts, is implemented, and tested for simple systems. In particular, the method is illustrated in the case of a pure water box with periodic boundary conditions. In addition, finite spherical systems of pure water and containing a dialanine peptide, are simulated with GCMC while the influence of the surrounding infinite bulk is incorporated using the generalized solvent boundary potential [W. Im, S. Berneche, and B. Roux, J. Chem. Phys. 114, 2924 (2001)]. As a last illustration of water confined in the interior of a protein, the hydration of the central cavity of the KcsA potassium channel is simulated.     

Kinetic Monte Carlo simulations of nucleation and growth in electrodeposition

Nucleation and growth during bulk electrodeposition is studied using kinetic Monte Carlo (KMC) simulations. Ion transport in solution is modeled using Brownian dynamics, and the kinetics of nucleation and growth are dependent on the probabilities of metal-on-substrate and metal-on-metal deposition. Using this approach, we make no assumptions about the nucleation rate, island density, or island distribution. The influence of the attachment probabilities and concentration on the time-dependent island density and current transients is reported. Various models have been assessed by recovering the nucleation rate and island density from the current-time transients.