Umbrella sampling definition

In both solvents, the variational transition state (associated with the free energy maximum) corresponds, within the numerical errors, to the dividing surface located at rc = 0. It has to be underlined that this fact is not a previous hypothesis (which would rather correspond to the Conventional Transition State Theory), but it arises, in this particular case, from the Umbrella Sampling calculations. However, there is no information about which is the location of the actual transition state structure in solution. Anyway, the definition of this saddle point has no relevance at all, because the Monte Carlo simulation provides directly the free energy barrier, the determination of the transition state structure requiring additional work and being unnecessary and unuseful. 

It would be hard to write a definitive account of the development of extended sampling methods we will not attempt to do so. The seminal ideas are probably correctly attributed to Torrie and Valleau [22], who coined the terminology umbrella sampling. The huge literature of subsequent advances and rediscoveries may be rationalized a little by dividing it into two, according to how the macrostates to be weighted are defined. 

Umbrella sampling has been found to be especially useful in simulations where the changes are of a local character, such as in the calculation of the potential of mean force (PMF) along a reaction coordinate. The general definition of the PMF, W(x, x ) (see Chapter 5 of Ref. 80), is... 

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