Free energy perturbation theory

In the canonical partition function of (5.1), we have for simplicity ignored combinatorial prefactors. Free energy perturbation theory [12] relies on evaluating effectively the ratio of the partition functions to obtain the free energy difference between the initial and final states corresponding to coupling parameters A = 1 and 0 (see also Chap. 2),... 

Jarzynski s identity, (5.8), immediately leads to the second law in the form of (5.6) because of Jensen s inequality, (e x) > e. Moreover, in the limit of an infinitely fast transformation, r —> 0, we recover free energy perturbation theory. In that limit, the configurations will not relax during the transformation. The average in... 

Instead of estimating -/ 1 ln(exp(-/W(f)) directly using (5.44), one can use cumulant expansion approaches, as in regular free energy perturbation theory (see e.g., [20, 39] for combining cumulant expansions about the initial and final states). Unbiased estimators for cumulants can be used. Probably the most useful relations involve averages and variances of the work ... 

B. G. Rao and U. C. Singh, Hydrophobic hydration A free energy perturbation theory, J. 

Details and uses of these thermodynamic cycles using free energy perturbation theory can be found in Volume 1 of this series. 

Decide whether entropic effects are likely to be important (for example if charged species are released to the solvent) and, if so, decide on whether a quantum chemical approach (calculating the partition function within a harmonic-oscillator approximation) may be used or whether a molecular dynamics-based approach (e.g., free-energy perturbation theory) should be used to properly sample phase space. 

We conclude this section with some remarks on the RNA polymerase enzyme for which cluster calculations have been discussed in Sect. 2.2.2. Extensions of that work to include more of the protein and solvent environment through QM/MM calculations and free-energy perturbation theory are in progress, but they are not yet ready for publication. Instead, we will give a glimpse of some related work from the literature on DNA polymerases, which show many of the same essential features as their RNA counterparts. 

In the middle ground between the rigorous free energy perturbation theory methods and the nearly empirical 3D QSAR methods are a vast array of energy... 

---