Umbrella Sampling and Weighted Histogram Analysis

3 Umbrella Sampling and Weighted Histogram Analysis Umbrella Sampling (US) 

The US technique [45, 46] is often used to compute the potential of mean force (PMF), which is the free energy change along a chosen order parameter. US has been already discussed in Chap. 3, so here we remind the reader only of the main idea. 

Umbrella sampling is aimed at overcoming the sampling problem by modifying the potential function so that different favorable states separated by energetic barriers are sufficiently sampled. An artificial umbrella potential is introduced  

For the calculation of the free energy difference AA between two states 0 and 1, the umbrella sampling utilizes the biasing potential W to ensuring sampling of phase space important to both 0 and 1 (cf. Fig. 6.Id). Then, F in (6.80) is taken as 

In the simulations, the free energy parameters / are unknown. However they can be obtained by solving (6.82) and the following equation self-consistently  

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Fig. 5. Top a schematic representation of the threaded and unthreaded configurations are reported. For clarity the solvent molecules are omitted. Bottom the FES of the threading process reconstructed with umbrella sampling and weighted histogram analysis. After [59]...

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