Rosenbluth weight

Having generated a trial conformation it must be decided whether to accept it or not. To d this a random number is generated in the range 0-1 and compared with the ratio of tf Rosenbluth weights for the trial conformation (W trial) and the old conformation (W/oid The new chain is then accepted using the following criterion ... 

The number of trial sites at any given step, km, can be chosen freely (k = 1 corresponds to an unbiased insertion) and should thus be optimized to improve efficiency [38]. For chain molecules with intramolecular potentials (e.g., bond bending and dihedral potentials), it is more convenient to divide the energy into a bonded part and a nonbonded part. The bonded part can then be used to efficiently bias the selection of trial positions and only the nonbonded part is used for the selection of trial sites and the calculation of the Rosenbluth weights [34,35,37]. Using an isolated chain with intramolecular interactions as the reference state, the excess chemical potential can now be obtained from... 

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. 

One chain can then be accepted based on its Rosenbluth weight. This strategy of multiple chain growth has been tried on a scalar machine, and has been shown to improve sampling efficiency within configuration bias MC [37]. It should also translate to parallel machines because a reasonable amount of computational time is required to generate a chain (or multiple chains) on each processor, relative to the inter-processor communication required at the end of chain regrowth. 

Generate a set of k orientations 0 = oi, 02, , ot about the new center of mass for the forward move. Calculate the orientation dependent potential energy C/"(/) for each orientation in O. Note that henceforth, superscripts F and R will be used to denote corresponding quantities for the forward and reverse moves respectively. Evaluate the so-called Rosenbluth weight for the new position as follows... 

After all the sites have been grown calculate the Rosenbluth weight of the chain as follows ... 

Normalize the Rosenbluth weight by dividing by where k is the number of trial positions proposed. 

The modified Rosenbluth weight and Random Walk weight for the chain are constructed as follows ... 

Generate a trial conformation using the Rosenbluth scheme to grow the entire molecule, or part thereof, and compute its Rosenbluth weight W(n). 

To compute the Rosenbluth weight for the remainder of the chain, we determine the energy of monomer i at its actual position, and also the energy it would have had it been placed in any of the other k — sites neighboring the actual position of monomer / — 1 (see Figure 1). These energies are used to calculate... 

The external energy of the first monomer is calculated. This energy involves only the external interactions. The Rosenbluth weight of this first monomer is given by... 

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