## ABSTRACT

Unlike thermodynamics integration (TI), where a difference in the free energy ΔF(a, b) is obtained by integrating along a path from state a to b, direct techniques enable one to calculate the absolute F_{a}
and F_{b}
, where ΔF(a, b) = F_{a}
− F_{b}
and the integration process is avoided. This is, in particular, useful for calculating ΔF (and ΔS) of two microstates (e.g., an α-helix and a hairpin) of a peptide or a loop in a protein, where the integration between them would be complicated. To this category, pertain all the methods discussed in Chapter 19 and in the present Chapter 18, where the most popular are “the harmonic approximation” (Gō & Scheraga) and “the quasi-harmonic approximation”(QH) of Karplus and Kushick. With QH, the probability density of a microstate is approximated by a multivariate Gaussian and the covariance matrix is obtained from a local MD sample. However, these methods are limited to a single microstate, which has a close to harmonic shape. A method related to the harmonic approximation is “the second generation mining minima” (M2) of Gilson’s group. With M2, low-energy minimized structures are initially identified, the free energies of the corresponding local potential wells are calculated using a method that considers both harmonic and anharmonic effects, and the contribution of the individual wells is then accumulated. Other methods discussed are “the mutual information expansion” (MIE) (Killian et al.), “the nearest neighbor technique” (Hnizdo et al.), the combined MIE-NN (Hnizdo et al.), and hybrid approaches (Hensen et al.).