Free energy sample problem

If X and Y do not overlap in phase space then the value of the free energy differei calculated using Equation (11.6) will not be very accurate, because we will not adequat sample the phase space of Y when simulating X. This problem arises when the enei difference between the two states is much larger than k T . y - x 3> kgT. How tl can we obtain accurate estimates of the free energy difference under such circumstanc Consider what happens if we introduce a state that is intermediate between X and with a Hamiltonian and a free energy A(l) ... 

This chapter reviewed some of our group s contributions to the development and application of QM/MM methods specifically as applied to enzymatic reactions, including the use of sequential MD/QM methods, the use of effective fragment potentials for reaction mechanisms, the development of the new QM/MM interface in Amber, as well as the implementation and optimization of the SCC-DFTB method in the Amber program. This last implementation allows the application of advanced MD and sampling techniques available in Amber to QM/MM problems, as exemplified by the potential and free energy surface surfaces for the reaction catalyzed by the Tripanosoma cruzi enzyme /ram-sialidasc shown here. 

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... 

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