Free energy histogram methods

Kumar, S. Bouzida, D. Swendsen, R. H. Kollman, P. A. Rosenberg, J. M., The weighted histogram analysis method for free energy calculations on biomolecules. I. The method, J. Comput. Chem. 1992,13, 1011-1021... 

Troyer, M. Wessel, S. Alet, F., Flat histogram methods for quantum systems algorithms to overcome tunneling problems and calculate the free energy, Phys. Rev. Lett. 2003,12, 120201... 

These bounds are the nonequilibrium equivalents of the Gibbs-Bogoliubov bounds discussed in Chap. 2. Having the free energy now bounded from above and below already demonstrates the power of using both forward and backward transformations. Moreover, as was shown by Crooks [18, 19], the distribution of work values from forward and backward paths satisfies a relation that is central to histogram methods in free energy calculations... 

The next three chapters deal with the most widely used classes of methods free energy perturbation (FEP) [3], methods based on probability distributions and histograms, and thermodynamic integration (TI) [1, 2], These chapters represent a mix of traditional material that has already been well covered, as well as the description of new techniques that have been developed only recendy. The common thread followed here is that different methods share the same underlying principles. Chapter 5 is dedicated to a relatively new class of methods, based on calculating free energies from nonequilibrium dynamics. In Chap. 6, we discuss an important topic that has not received, so far, sufficient attention - the analysis of errors in free energy calculations, especially those based on perturbative and nonequilibrium approaches. 

Other variations on these basic free energy methods have been published, although for various reasons they have not yet been widely adopted. These methods include MD/MC methods,38 the acceptance ratio method,39, 40 the weighted histogram method,41 the particle insertion method,42 43 and the energy distribution method.39 The reader is referred to the original publications for additional discussion of these approaches. 

Multidimensional free-energy calculations using the weighted histogram analysis method, J. Comput. Chem. 16 1339 (1995). 

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