Monte Carlo simulations Metropolis

Miller, M.A. Amon, L.M. Reinhardt, W.P., Should one adjust the maximum step size in a Metropolis Monte Carlo simulation Chem. Phys. Lett. 2000, 331, 278-284... 

In Zeolite A. An extensive series of papers concerned with the sorption location and isotherms of Xe in zeolite A have been published (118-122). The locations of sorbates and their structures were investigated by using Metropolis Monte Carlo simulations of zeolite A models (118, 119). Initially, an idealized truncated cuboctahedron was used, with Si and Al atoms occupying vertices and O atoms occupying the midpoints of line segments (118). Subsequent calculations were based on the positions of atoms in... 

Since in a Metropolis Monte Carlo simulation one can generate paths only with a positive probability proportional to jwj, in order to compute expectation values of the type (5) one has to resort to a potentially problematic expression ... 

Figure 6 Energy vs. temperature calculated using graph invariant theoiy for a) the ice VII-Vlll, b) Ih-XI, c) Vl-Vl and d) V-XIII systems. Upward and downward triangles indicate results of Metropolis Monte Carlo simulations ascending and descending in tempemture. The dashed line in panel (a) indicates the transition point established by thermodynamic integration. The arrows indicate experimental transition temperatures (not well established for the IIl-lX system).

Electrical Polarizability of Polyelectrolytes by Metropolis Monte Carlo Simulation... 

Vanderbilt and Louie (Ref. 43) discuss the use of Gaussian kernels determined by Eq. (2.5) in the closely related situation of Metropolis Monte Carlo-simulated annealing. 

T. Weimar, B. Meyer, and T. Peters, / Biomol. NMR, 3, 399 (1993). Conformational Analysis of a-D-Fuc-(l-4)-p-D-GlcNAc-OMe. One-Dimensional Transient NOE Experiments and Metropolis Monte Carlo Simulations. 

By concatenating Monte Carlo transition probabilities according to Eq. (1.1), one obtains the probability of a particular stochastic path x. ) generated in a Metropolis Monte Carlo simulation. The time variable t describing the progress of this stochastic process is artificial. This Monte Carlo time can be approximately mapped to a physical timescale by comparing known dynamical properties such as transport coefficients [8,41]. 

A Metropolis Monte Carlo simulation starts with a collection of molecules in a known configuration. The simulation consists of a large number of steps, each of which is an attempt to introduce an acceptable change in the collection of molecules. This change is either accepted or rejected based on a simple set of rules that ensure consistency of the results with the desired ensemble. If a change is accepted, the new state is used to generate the next step of the simulation otherwise, the unmodified configuration is used. Translational and rotational moves in the canonical ensemble are described below, followed by... 

Metropolis Monte Carlo simulations of polyurethane, polyethylene, and betamethylstyrene-acrylonitrile copolymer... 

Addition of (16.105) and (16.106) gives the GB/SA expression for AG. The GB/SA expression is readily differentiated analytically, making it easy to use in molecular-mechanics energy minimizations (one finds the geometry that minimizes the sum of the MM steric energy and AG°oiv), and molecular-dynamics and Metropolis Monte Carlo simulations with inclusion of solvent effects. The GB/SA method is available in the MacroModel program (Section 16.6). 

Due to the lack of experimental data available, alternative methods for properly estimation are needed [3]. Such methods include modelling at both the macroscopic and microscopic scales. At the macroscopic scale, the development of theoretical EoS is needed for accurate prediction of properties and phase equilibria calculations. At the molecular level. Molecular Dynamics (MD) and Metropolis Monte Carlo simulations are used for the elucidation of microscopic structure and the prediction of thermodynamic and transport properties. Liu et al. [7] evaluated a series of force fields in their ability to predict properties of CO2-H2O systems and concluded that different force fields produce optimal results in different ranges of temperatures and pressures. 

Abstract. The interlamellar domain of semicrystalline polyethylene is studied by means of off-lattice Metropolis Monte Carlo simulations using a realistic united atom force field with inclusion of torsional contributions. Both structural as well as thermal and mechanical properties are discussed for systems with the 201 crystal plane parallel to the interface. In so doing, important data is obtained which is useful for modeling semicrystalline polyethylene in terms of multiphase models. Here, we review the main results published previously by us (P.J. in t Veld, M. Hiitter, G.C. Rutledge Macromolecules 39, 439 (2006) M. Hiitter, P.J. in t Veld, G.C. Rutledge Polymer (in press), (2006)]. 

To characterize the structure and to quantify the mechanical and thermal properties of the interlamellar, non-crystalline material. Metropolis Monte Carlo simulations have been performed [22-26] on systems kept in metastable equilibrium [27,28]. Here, we give a summary of our most recent results for a realistic model for polyethylene including torsion interactions. For more details the reader is referred to the original publications [29,30], Throughout the manuscript, we concentrate our attention on the 201 crystal surface, because it was found to be energetically favored in simulations [25] and predominant... 

Monte Carlo methods are perhaps the most frequently used in computational statistical mechanics. In particular, the Metropolis Monte Carlo technique has been used extensively in simulation of liquids. Monte Carlo methods are probabilistic, rather than deterministic, procedures atoms are moved more or less randomly during the course of the simulation. In a Metropolis Monte Carlo simulation of a molecular system, the following steps would be followed ... 

Figure 2. Schematic representation of a Metropolis Monte Carlo simulation. This scheme is suitable for most soft potentials, but constraints must be handled carefully (see footnote to text). N trial moves are attempted, with coordinate sampling carried out every N/N trial moves.

Metropolis Monte Carlo simulations coupled with well-tested potential functions have evolved into powerful methodology for modeling liquids over wide ranges of conditions. Agreement with available experimental thermodynamic and structural data is excellent. Moreover, the simulations provide a wealth of fascinating detail on intermolecular interactions, conformational equilibria, and structure that has done much to enhance the understanding of the liquid state. 

---