|
The Bennett acceptance ratio method (sometimes abbreviated to BAR) is an algorithm for estimating the difference in free energy between two systems (usually the systems will be simulated on the computer). It was suggested by Charles H. Bennett in 1976.〔 ==Preliminaries== Take a system in a certain super state. By performing a Metropolis Monte Carlo walk it is possible to sample the landscape of states that the system moves between, using the equation : where Δ''U'' = ''U''(State''y'') − ''U''(State''x'') is the difference in potential energy, β = 1/''kT'' (''T'' is the temperature in Kelvin while ''k'' is the Boltzmann constant), and is the Metropolis function. The resulting states are then sampled according to the Boltzmann distribution of the super state at temperature ''T''. Alternatively, if the system is dynamically simulated in the canonical ensemble (also called the ''NVT'' ensemble), the resulting states along the simulated trajectory are likewise distributed. Averaging along the trajectory (in either formulation) is denoted by angle brackets . Suppose that two super states of interest, A and B, are given. We assume that they have a common configuration space, i.e., they share all of their micro states, but the energies associated to these (and hence the probabilities) differ because of a change in some parameter (such as the strength of a certain interaction). The basic question to be addressed is, then, how can the Helmholtz free energy change (Δ''F'' = ''F''B − ''F''A) on moving between the two super states be calculated from sampling in both ensembles? Note that the kinetic energy part in the free energy is equal between states so can be ignored. Note also that the Gibbs free energy corresponds to the ''NpT'' ensemble. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bennett acceptance ratio」の詳細全文を読む スポンサード リンク
|