Stochastic simulation Metropolis Monte Carlo method

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. 

Molecular Dynamics simulation is one of many methods to study the macroscopic behavior of systems by following the evolution at the molecular scale. One way of categorizing these methods is by the degree of determinism used in generating molecular positions [134], On the scale from the completely stochastic method of Metropolis Monte Carlo to the pure deterministic method of Molecular Dynamics, we find a multitude and increasingly diverse number of methods to name just a few examples Force-Biased Monte Carlo, Brownian Dynamics, General Langevin Dynamics [135], Dissipative Particle Dynamics [136,137], Colli-sional Dynamics [138] and Reduced Variable Molecular Dynamics [139]. 

Simulated annealing is a global, multivariate optimization technique based on the Metropolis Monte Carlo search algorithm. The method starts from an initial random state, and walks through the state space associated with the problem of interest by generating a series of small, stochastic steps. An objective function maps each state into a value in EH that measures its fitness. In the problem at hand, a state is a unique -membered subset of compounds from the n-membered set, its fitness is the diversity associated with that set, and the step is a small change in the composition of that set (usually of the order of 1-10% of the points comprising the set). While downhill transitions are always accepted, uphill transitions are accepted with a probability that is inversely proportional to... 

Monte Carlo (MC) simulations on the clay-water interface system have been studied by many researchers worldwide since the mid 1990s. The use of MC for clay-water simulation was popular because the stochastic Metropolis algorithm has been used successfully for many other liquid-state physical chemistry (63). This method has strong advantages in sampling conformational surface, and this advantageous technique has been used to find the clay-adsorbate-water equilibrium structure. 

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