Bennett acceptance ratio

Shirts, M. R. Pande, V. S., Comparison of efficiency and bias of free energies computed by exponential averaging. The Bennett acceptance ratio and thermodynamic integration, J. Chem. Phys. 2005,122, 144107... 

A superior estimator, generally called the Bennett acceptance ratio (BAR), was originally proposed by Bennett [27] and later rederived in alternate ways which illustrate important facets of its efficiency [24,28]. If makes use of expecfafions computed at both the initial and final states ... 

Finding the best estimate of the free energy difference between two canonical ensembles on the same configurational space, for which finite samples are available, is a nontrivial problem. Charles Bennett [11] addressed this problem by developing the acceptance ratio estimator, which corresponds to the minimum statistical... 

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. 

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]... 

A and B (and thus of the controlling Hamiltonian ) at a point in w -space, averaged over that space. In the numerator this switch is from S h to A and the average is with respect to the canonical distribution in ensemble B in the denominator the roles of A and B are reversed. This is Bennett s acceptance ratio formula [61]. 

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