Metropolis Monte Carlo random number generators

The two major methods for the simulations are the Monte Carlo method (so named for its use of random number generation) and the molecular dynamics method. The Monte Carlo method, as applied to problems of chemistry, was first described by N. Metropolis and his co-workers at the Los Alamos... 

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 ... 

Well, we have a probability but what we need is a clear decision to be or not to be in state 2. This is where the Monte Carlo spirit comes in, see Fig. 7.12. By using a random number generator we draw a random number u from section [0,1] and... compare it with the number a. If m < a, then we accept the new conformation, otherwise conformation 2 is rejected (and we forget about it). The whole procedure is repeated over and over again drawing micro-modifications a new conformation comparison with the old one by the Metropolis criterion -> accepting (the new conformation becomes the current one) or rejecting (the old conformation remains the current one), etc. 

With the advent of fast computers, numerical simulations of liquid structure have become practical. There are two principal simulation methods, h Monte Carlo method and molecular dynamics. The Monte Carlo method is so named because it uses a random number generator, reminiscent of the six-sided random number generators (dice) used in gambling casinos, such as those in Monte Carlo. This method was pioneered by Metropolis. ... 

Because generalized Metropolis Monte Carlo methods are based on random sampling from probability distribution functions, it is necessary to use a high-quality random-number generator algorithm to obtain reliable results. A review of such methods is beyond the scope of this chapter, " but a few general considerations merit discussion. 

In the grand-canonical Monte Carlo method, the system volume, temperature, and chemical potential are kept fixed, while the number of particles is allowed to fluctuate.There exist three types of trial move (1) displacement of a particle, (2) insertion of a particle, and (3) removal of a particle. These trial moves are generated at random with equal probability. The acceptance probability of the Metropolis method can be used for the trial moves of type (1). For the two other types, the acceptance probabilities are different. Regarding zeolites, an adsorption isotherm can be calculated with the grand-canonical Monte Carlo method by running a series of simulations at varying chemical potentials. 

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