Metropolis sampling 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). 

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... 

We now illustrate the use of non-Metropolis sampling techniques to demonstrate how they can be used to enhance the efficiency of a simulation of a system containing chain molecules. 

As the appropriate Boltzmann weights are included in the Metropolis Monte Carlo sampling technique, the average value of the polarizability, or any other property calculated from the MC data, is given as a simple average over all the values calculated for each configuration. 

Another simulation approach often used that does not offer a simple deterministic time evolution of the system is the Metropolis Monte Carlo [MMC] method. Based on the Metropolis-Hasting algorithm [3, 4], MMC methods are weighted sampling techniques in which particles are randomly moved about to obtain a statistical ensemble of atoms with a particular probability distribution for some quantity. This is usually the energy but can also be other quantities such as experimental inputs that can be quickly calculated from an atomic... 

The Monte Carlo method, referred in this entry as Direct Monte Carlo (DMC), is a statistical sampling technique that has been originally developed by Stan Ulam, John von Neumann, Nick Metropolis (who actually suggested the name Monte Carlo (Metropolis 1987)), and their collaborators for solving the problem of neutron diffusion and other problems in mathematical physics (Metropolis and Ulam 1949). From a mathematical point of view, DMC allows to estimate the expected value of a quantity of interest. More specifically, suppose the goal is to evaluate [/i(x)], that is, an expectation of a function with respect to the PDF n x). 

Mass-polarization, 54 Mass-velocity correction, in relativistic methods, 209, 211 Matrix element, 55, 103 McLean-Chandler basis sets, 160 Mean field approximation, 64 Metal coordination compounds, force field, 36 Metropolis sampling, in Monte Carlo techniques, 376... 

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... 

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