Acceptance ratio method

Fenwick, M. K. Escobedo, F. A., On the use of Bennett s acceptance ratio method in multi-canonical-type simulations, J. Chem. Phys. 2004,120, 3066-3074... 

It would be valuable if one could proceed with a reliable free energy calculation without having to be too concerned about the important phase space and entropy of the systems of interest, and to analyze the perturbation distribution functions. The OS technique [35, 43, 44, 54] has been developed for this purpose. Since this is developed from Bennett s acceptance ratio method, this will also be reviewed in this section. That is, we focus on the situation in which the two systems of interest (or intermediates in between) have partial overlap in their important phase space regions. The partial overlap relationship should represent the situation found in a wide range of real problems. 

Equation (6.58) becomes identical to that of the Bennett method (also referred to as the acceptance ratio method), i.e. 

Since we do not know the value of C in advance, the optimal C and thus the free energy difference A A can be solved in practice by iterating self-consistently (6.65) and (6.66) or (6.67). A convenient way to do so is to record all the perturbation data during the simulation, then compute C and AA in a postsimulation analysis. This method is also referred to as Bennett s method or the acceptance ratio method. 

Other variations on these basic free energy methods have been published, although for various reasons they have not yet been widely adopted. These methods include MD/MC methods,38 the acceptance ratio method,39, 40 the weighted histogram method,41 the particle insertion method,42 43 and the energy distribution method.39 The reader is referred to the original publications for additional discussion of these approaches. 

D. M. Ferguson, On the use of acceptance ratio methods in free energy calculations, J. 

Following Bennett, Crooks proposed the generalized acceptance ratio (GAR) method to combine the forward and reverse NEW calculations to minimize the statistical error of the relative free energy [56]... 

W = AG. Of course, this relation can be tested only in the region of work values along the work axis where both distributions (forward and reverse) overlap. An overlap between the forward and reverse distributions is hardly observed if the molecules are pulled too fast or if the number of pulls is too small. In such cases, other statistical methods (Rennet s acceptance ratio or maximum likelihood methods. Section IV.B.3) can be applied to get reliable estimates of AG. The validity of the CFT has been tested in the case of the RNA hairpin CD4 previously mentioned and the three-way junction RNA molecule as well. Figure 9c,d and Fig. 10c show results for these two molecules. 

The ratio method provides an estimate of AS1 2.9 million. This can be regarded as reasonably accurate ( 30%) considering the original plant cost data is 7 years old. The factorial method has produced a surprisingly similar result. This is probably due to the fact that the plant is not particularly large, and the possibility of estimation cost inaccuracies is reduced. The estimate of AS1 3.5 million determined by the factorial cost technique should therefore also be regarded as an acceptably accurate value. 

When calculating financial ratios at the end of each quarter, keep in mind seasonal factors that may distort the ratio. Firms use different, accepted accounting methods to prepare their balance sheet and income statement. Therefore, it is imperative to understand how the values used in calculating the ratios were obtained. 

A Metropolis method with umbrella sampling was employed [74,98-102]. For transition between states i and j, the acceptance ratio for moves is Fy = exp(—(Ej — Ei)/ksT), where ) is the energy of configuration i, kB is the Boltzmann constant, and T is the absolute temperature. The energy of conformation i is obtained by summing the Coulombic interactions over all charged species in a cell or its adjacent image cell [74, 101]. If h is the number of ion pairs that are deleted or inserted, then the acceptance ratio for insertions is... 

CG residues and three atomistic, and so on. In addition, they also increased the temperature of each replica, such that while the fully atomistic model was simulated at 298 K, the fully CG model was simulated at 700 K. However, despite the small size of the system, the small difference between the CG and atomistic models (OPLSUA Vi. OPLSAA) and the use of incremental coarsening, the acceptance ratio of the swap moves was still very low, running between 2.5% and 5.8%. Applications of this method to larger systems, or using a greater difference between the atomistic and CG models therefore looks problematic. 

The reference intensity ratio method is based on the experimentally established intensity ratio between the strongest Bragg peaks in the examined phase and in a standard reference material. The most typical reference material is corundum, and the corresponding peak is (113). The reference intensity ratio k) is quoted for a 50 50 (wt. %) mixture of the material with corundum, and it is known as the corundum number . The latter is commonly accepted and listed for many compounds in the ICDD s Powder Diffraction File. Even though this method is simple and relatively quick, careful account and/or experimental minimization of preferred orientation effects are necessary to obtain reliable quantitative results. 

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