How Relevant are Free Energy Contributions

To understand better the difficulties connected with the partitioning of free energy into contributions, let us break down the potential energy into a sum of two terms, 

Ua and Ub. Assume further that the second-order perturbation theory applies. This means that Po(AU) can be represented as a bivariate Gaussian. Then, AA, from (2.30), is given by 

From (2.70), it follows that the free energy cannot be divided simply into two terms, associated with the interactions of type a and type b. There are also coupling terms, which would vanish only if fluctuations in AUa and AUb were uncorrelated. One might expect that such a decoupling could be accomplished by carrying out the transformations that involve interactions of type a and type 6 separately. In Sect. 2,8.4, we have already discussed such a case for electrostatic and van der Waals interactions in the context of single-topology alchemical transformations. Even then, however, correlations between these two types of interactions are not 

In addition, separation of the free energy into contributions depends on the path taken to transform the reference system into the target one. In other words, in contrast to AA, the contributions from the interactions of type a, type b and their coupling change if the transformation is performed along a different pathway. This is due to the fact that free energy is a state function of the system, but its contributions are not. 

Thermodynamic perturbation theory represents a powerful tool for evaluating free energy differences in complex molecular assemblies. Like any method, however, FEP has limitations of its own, and particular care should be taken not only when carrying out this type of statistical simulations, but also when interpreting their results. We summarize in a number of guidelines the important concepts and features of FEP calculations developed in this chapter  

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