Free energy calculations convergence

An iterative procedure using WHAM31 35 was developed to improve sampling of the chemical space, and therefore to make free energy calculations converge more rapidly. The use of this method in conjunction with A-dynamics is described below.3 It s extension to MC/MD is straightforward. 

As we have already pointed out, the theoretical basis of free energy calculations were laid a long time ago [1,4,5], but, quite understandably, had to wait for sufficient computational capabilities to be applied to molecular systems of interest to the chemist, the physicist, and the biologist. In the meantime, these calculations were the domain of analytical theories. The most useful in practice were perturbation theories of dense liquids. In the Barker-Henderson theory [13], the reference state was chosen to be a hard-sphere fluid. The subsequent Weeks-Chandler-Andersen theory [14] differed from the Barker-Henderson approach by dividing the intermolecular potential such that its unperturbed and perturbed parts were associated with repulsive and attractive forces, respectively. This division yields slower variation of the perturbation term with intermolecular separation and, consequently, faster convergence of the perturbation series than the division employed by Barker and Henderson. 

To illustrate how stratification works in the context of free energy calculations, let us consider the transformation of state 0 into state 1 described by the parameter A. We further assume that these two states are separated by a high-energy barrier that corresponds to a value of A between Ao and Ai. Transitions between 0 and 1 are then rare and the free energy estimated from unstratified computer simulations would converge very slowly to its limiting value, irrespective of the initial conditions. If, however, the full range of A is partitioned into a number of smaller intervals, and... 

It has been mentioned that perhaps the greatest limitation to the precision of free energy calculations to date has been the often-inadequate sampling of a representative set of configurations of the system. Increases in computer power of course increase the radius of convergence of such calculations. Such increases come not only from the Moore s Law improvements in hardware, but also from algorithmic... 

Convergence properties of free energy calculations Alpha-cyclodextrin complexes as a case study. J. Am. Chem. Soc. 116 6293 (1994). 

Equations (16)-(24) are solved on a lattice in an iterative fashion until a convergence criterion (e.g., the difference between free energy calculations from the two successive iterations) is satisfied. 

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