Ensemble acceptance ratio

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... 

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]. 

In order to have a reasonable acceptance ratio, however, the step size must be fairly can be deriyed from the simulation data, as shown in Table 16.1. Ensembles generated... 

As mentioned earlier, the limiting probabilities occur only in the ratio pjpm and the value of the denominator, Qc, is therefore not required. Hence, in the canonical ensemble, the acceptance of a trial move depends only on the Boltzmann factor of the energy difference, AU, between the states m and n. If the system looses energy, then the trial move is always accepted if the move goes uphill, that is, if the system gains energy, then we have to play a game of chance on exp(—fi AU) [6]. In practical terms, we have to calculate a random number, uniformly distributed in the interval [0,1]. If < exp(—p AU), then we accept the move, and reject otherwise. 

A technique that can be particularly useful for simulation of mixtures is the so-called semigrand ensemble of Kofke and Glandt [93]. A thorough review of this technique and its applications is given in the chapter by D. Kofke (this volume). In that ensemble, ratios of the chemical potential of each component and that of a reference component are specified, whereas the composition of the system is allowed to fluctuate. The equilibrium composition is attained by trial changes of the identity of each species, at constant number of particles (such changes are accepted according to the... 

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