Monte Carlo configurationally biased

Table 1.1 Configurationally biased Monte Carlo simulations of the adsorption enthalpies of hydrocarbons for two zeolites.

Configurationally biased Monte Carlo techniques [63-65] have made it possible to compute adsorption isotherms for linear and branched hydrocarbons in the micropores of a siliceous zeolite framework. Apart from Monte Carlo techniques, docking techniques [69] have also been implemented in some available computer codes. Docking techniques are convenient techniques that determine, by simulated annealing and subsequent freezing techniques, local energy minima of adsorbed molecules based on Lennard-Jones-or Buckingham-type interaction potentials. 

The importance of the entropy of adsorption is illustrated by experimental and calculated adsorption free energies for hexane in the 12-ring one-dimensional channel mordenite (MOR) and 10-ring one-dimensional channel of ferrierite (TON). Table 4.4 compares the simulated values for the heats of adsorption from configurationally biased Monte Carlo calculations valid at low micropore filling. The corresponding adsorption equilibrium constants are also compared in Table 4.4. One notes the increase in the energy of adsorption for the narrow-pore zeolite. However, at the temperature of reaction, the equilibrium adsorption constant is also a factor 10 lower for the narrow-pore zeolite. 

C. Configurationally Biased Monte Carlo Simulation (CBMC)... 

Prepare the system After defining the geometry of the zeolite, the desired number of sorbate molecules (the loading) were placed within the silicalite using the configuration-biased Monte Carlo (CBMC) techniqne (Frenkel and Smit 1996 Smit et al. 2000). We used another open source software called TOWHEE (http //towhee.sourceforge.net) to prepare the initial state (Martin and Siepmann 1999). 

The essence of the configurational bias Monte Carlo method is that a growing molecule is preferentially directed (i.e. biased) towards acceptable structures The effects of these biases can then be removed by modifying the acceptance rules The configurational bias methods are based upon work published in 1955 by Rosenbluth and Rosenbluth... 

Sadanobu and Goddard (156) have used a Continuous Configuration Boltzmann Biased Monte Carlo calculation of the free energy of two independent imited atom Cioo chains from very dilute vapor up to about 70% of physical density. While these are longer chains than are typically attainable with CCB methods, the densities of the Sadanobu and Goddard systems are generally lower. 

There are basically two different computer simulation techniques known as molecular dynamics (MD) and Monte Carlo (MC) simulation. In MD molecular trajectories are computed by solving an equation of motion for equilibrium or nonequilibrium situations. Since the MD time scale is a physical one, this method permits investigations of time-dependent phenomena like, for example, transport processes [25,61-63]. In MC, on the other hand, trajectories are generated by a (biased) random walk in configuration space and, therefore, do not per se permit investigations of processes on a physical time scale (with the dynamics of spin lattices as an exception [64]). However, MC has the advantage that it can easily be applied to virtually all statistical-physical ensembles, which is of particular interest in the context of this chapter. On account of limitations of space and because excellent texts exist for the MD method [25,61-63,65], the present discussion will be restricted to the MC technique with particular emphasis on mixed stress-strain ensembles. 

This problem can be circumvented by biasing the "randomness" of step ii, introducing importance sampling. This causes the method to favor "good" configurations over bad. The most important approach to importance sampling is the Metropolis method (Monte Carlo is a city, but Metropolis is a person s name). Steps i and ii are the same as above, followed by ... 

The general idea of biased sampling is best explained by considering a simple example. Let us assume that we have developed a Monte Carlo scheme that allows us to generate trial configurations with a probability that depends on the potential energy of that configuration ... 

In summary. Metropolis Monte Carlo biases the generation of configurations toward those that make significant contributions to the integral... 

---