Metropolis method technique

The Monte Carlo (MC) simulation is performed using standard procedures [33] for the Metropolis sampling technique in the isothermal-isobaiic ensemble, where the number of molecules N, the pressure P and the temperature T are fixed. As usual, we used the periodic boundary conditions and image method in a cubic box of size L. In our simulation, we use one F embedded in 1000 molecules of water in normal conditions (T—29S K and P= 1 atm). The F and the water molecules interact by the Lennard-Jones plus Coulomb potential with three parameters for each interacting site i (e, o, - and qi). 

Dynamic Monte Carlo simulations were first used by Verdier and Stockmayer (5) for lattice polymers. An alternative dynamical Monte Carlo method has been developed by Ceperley, Kalos and Lebowitz (6) and applied to the study of single, three dimensional polymers. In addition to the dynamic Monte Carlo studies, molecular dynamics methods have been used. Ryckaert and Bellemans (7) and Weber (8) have studied liquid n-butane. Solvent effects have been probed by Bishop, Kalos and Frisch (9), Rapaport (10), and Rebertus, Berne and Chandler (11). Multichain systems have been simulated by Curro (12), De Vos and Bellemans (13), Wall et al (14), Okamoto (15), Kranbu ehl and Schardt (16), and Mandel (17). Curro s study was the only one without a lattice but no dynamic properties were calculated because the standard Metropolis method was employed. De Vos and Belleman, Okamoto, and Kranbuehl and Schardt studies included dynamics by using the technique of Verdier and Stockmayer. Wall et al and Mandel introduced a novel mechanism for speeding relaxation to equilibrium but no dynamical properties were studied. These investigations indicated that the chain contracted and the chain dynamic processes slowed down in the presence of other polymers. 

Our Monte Carlo (MC) simulation uses the Metropolis sampling technique and periodic boundary conditions with image method in a cubic box(21). The NVT ensemble is favored when our interest is in solvent effects as in this paper. A total of 344 molecules are included in the simulation with one solute molecule and 343 solvent molecules. The volume of the cube is determined by the density of the solvent and in all cases used here the temperature is T = 298K. The molecules are rigid in the equilibrium structure and the intermolecular interaction is the Lennard-Jones potential plus the Coulombic term... 

Monte Carlo technique Metropolis method) use random number from a given probability distribution to generate a sample population of the system from which one can calculate the properties of interest, a MC simulation usually consists of three typical steps ... 

The method of Monte Carlo simulation is often called the Metropolis method, since it was introduced by Metropolis and coworkers (64). Monte Carlo techniques in general provide data on equilibrium propaties only, wha-eas MD gives nonequilibrium properties, such as transport properties, as well as equilibrium properties. 

MC technique, also called Metropolis method, [24] is a stochastic method that uses random munbers to generate a sample population of the system from which one can calculate the properties of interest. A MC simulation usually consists of three typical steps. In the first step, the physical problem under investigation is translated into an analogous probabilistic or statistical model. In the second step, the probabilistic model is solved by a munerical stochastic sampling experiment. In the third step, the obtained data are analyzed by using statistical methods. MC provides only the information on equilibrium properties (e.g., free energy, phase equilibrium), different from MD whieh gives nonequilibrium as well as equilibrium properties. In a NVT ensemble with N atoms, one hypoth-... 

However, apart from lowest-energy and phase transition regions, the Metropolis method can be employed successfully, often in combination with reweighting techniques. 

Thus, the question is whether the combination of Metropolis data obtained in simulations at different temperatures can yield an improved estimate g E). This is indeed possible by means of the multiple-histogram reweighting method [86], sometimes also called weighted histogram analysis method (WHAM) [87]. Even though the general idea is simple, the actual implementation is not trivial. The reason is that conventional Monte Carlo simulation techniques such as the Metropolis method cannot yield absolute estimates for the partition sum Z T)= g E) i. e., estimates for the density of states at differ-... 

It is expected that in the limit of large n, (U will approach (U), that U will approach U, and that both E and Cy will converge to their correct values. But what are the uncertainties in the calculated values of E and Cy Because the Metropolis method is intrinsically based on the sampling of configurations from a probability distribution function, appropriate statistical error analysis methods can be applied. This fact alone is an improvement on most other numerical integration techniques, which typically lack such strict error bounds. 

Molecular dynamics (MD) and Monte Carlo (MC) simulation techniques have been used now for decades to characterize aqueous solutions. The most basic elements that underlie these techniques, such as numerical integration algorithms and the Metropolis method, are discussed thoroughly else-where, " so they are not included here. Our intention here is to survey methods used for determining the thermodynamic and structural quantities most closely tied to hydrophobicity. 

Monte Carlo search methods are stochastic techniques based on the use of random numbers and probability statistics to sample conformational space. The name Monte Carlo was originally coined by Metropolis and Ulam [4] during the Manhattan Project of World War II because of the similarity of this simulation technique to games of chance. Today a variety of Monte Carlo (MC) simulation methods are routinely used in diverse fields such as atmospheric studies, nuclear physics, traffic flow, and, of course, biochemistry and biophysics. In this section we focus on the application of the Monte Carlo method for... 

By far the most common methods of studying aqueous interfaces by simulations are the Metropolis Monte Carlo (MC) technique and the classical molecular dynamics (MD) techniques. They will not be described here in detail, because several excellent textbooks and proceedings volumes (e.g., [2-8]) on the subject are available. In brief, the stochastic MC technique generates microscopic configurations of the system in the canonical (NYT) ensemble the deterministic MD method solves Newton s equations of motion and generates a time-correlated sequence of configurations in the microcanonical (NVE) ensemble. Structural and thermodynamic properties are accessible by both methods the MD method provides additional information about the microscopic dynamics of the system. 

However, it is normally assumed that the conformers that bind to target sites will be those with a minimum potential energy. Since molecules may have large numbers of such metastable conformers a number of techniques, such as the Metropolis Monte Carlo method and comparative molecular field analysis (CoMFA), have been developed to determine the effect of conformational changes on the effectiveness of docking procedures. 

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