Determination of Reaction Pathways

One major problem of free energy methods is the need for extensive sampling of the phase space, which can lead to a prohibitively large computational effort for the QM part. The unavailability of complete sampling also limits the estimation of entropy differences, whereas free energy differences can be determined routinely today since extensive sampling of only the relevant part where the two states differ 

Umbrella sampling (US) is one of the most frequently used sampling methods to calculate the PMF. The original idea was first suggested by Torrie et al. [78, 500] 

Most QM/MM applications are devoted to biological questions. In this field QM/MM approaches are mandatory since the molecular nature of the enzymatic environment determines geometrical arrangements and the energetics of enzymatic processes. The use of continuum polarizable models is problematic since the dielectric constant, for example, is not well defined. For regions in the outer spheres 

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