The Configurational Bias Monte Carlo Method

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 

Let us now consider how the configurational bias Monte Carlo method would deal with this problem. Again, the first site (S) is chosen at random. We next consider where to place the second unit. The sites adjacent to S are examined to see which are free. In this case, only two of the four sites are free. One of these free sites is chosen at random. Note that the conventional Monte Carlo procedure selected from all four adjoining sites at random, irrespective of whether it is occupied or not. A Rosenbluth weight for the move is then calculated. The Rosenbluth weight for each step i is given by  

If a segment has a zero Rosenbluth weight then growth of the chain is terminated. However, such chains must stiU be included in the averaging used to determine the excess chemical potential. 

So far, we have only considered a fixed number of neighbouring sites for each segment. The method can be extended to cover fuUy flexible chains, where the set of possible neighbouring positions is infinite [De Pablo et cd. 1992, 1993]. When growing each segment, a subset containing k random directions is chosen. These trial directions need not be uniformly distributed in space. For each of these orientations the energy vr(i) is calculated and so is the Boltzmann factor. An orientation is then chosen with probability  

The Rosenbluth algorithm can also be used as the basis for a more efficient way to perform Monte Carlo sampling for fully flexible chain molecules [Siepmann and Frenkel 1992], which, as we have seen, is difficult to do as bond rotations often give rise to high energy overlaps with the rest of the system. 

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Applications of the Configurational Bias Monte Carlo Method... 

The configurational-bias Monte Carlo method (CB-MC) (112) was developed to overcome these sorts of problems. Instead of a random insertion into the zeolite host, the guest molecule is grown atom by atom within the host in a way that avoids unfavorable overlap with the zeolite atoms. 

The configurational bias Monte Carlo method involves three types of move. Two of these are translational or rotational moves of the entire molecule, which are performed in the conventional way. The third type of move is a conformational change. A chain is selected at random and one of the segments within it is also randomly chosen. That part of the chain that lies above or below the segment (chosen with equal probability) is discarded and an... 

Panagiotopoulos and coworkers [51] use the same parameters as Larson for the study of phase behavior, but with two different simulation methodologies. The first technique is the Gibbs ensemble method, in which each bulk phase is simulated in a separate cell and molecules are interchanged and volumes adjusted between the two for equilibration of the system [52]. The second is a standard canonical ensemble simulation, like Larson s, but employs the configurational bias Monte Carlo method. The configurational bias Monte Carlo method is much more efficient than the ones based on reptation and other local moves but is not useful if any dynamic information is sought from the simulations. 

Af/ads is the heat of adsorption from the gas phase, which takes into account the dispersion interaction of hexene with the oxygen atoms in the wall of the zeolite pores. This energy depends both on the size of the reactant (hexene in this case) and the size o .the pores in the zeolite (Figure 8a and 8b) and is estimated with the configurational-bias Monte Carlo method (CB-MC). - The CB-MC method differs from conventional Monte Carlo (see Monte Carlo Simulations for Polymers) in so far as.ti guest species is grown atom by atom inside the host rather than inserted as a complete molecule. ... 

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