A reversible minimum-to-minimum mapping method for the calculation of free-energy differences

Theodorou, DN

dc.contributor.author	Theodorou, DN	en
dc.date.accessioned	2014-03-01T01:23:30Z
dc.date.available	2014-03-01T01:23:30Z
dc.date.issued	2006	en
dc.identifier.issn	0021-9606	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16987
dc.subject.classification	Physics, Atomic, Molecular & Chemical	en
dc.subject.other	Bijective mapping	en
dc.subject.other	Free-energy differences	en
dc.subject.other	Minimum-to-minimum mapping	en
dc.subject.other	Probability densities	en
dc.subject.other	Algorithms	en
dc.subject.other	Molecular dynamics	en
dc.subject.other	Probability density function	en
dc.subject.other	Real time systems	en
dc.subject.other	Set theory	en
dc.subject.other	Free energy	en
dc.title	A reversible minimum-to-minimum mapping method for the calculation of free-energy differences	en
heal.type	journalArticle	en
heal.identifier.primary	10.1063/1.2138701	en
heal.identifier.secondary	http://dx.doi.org/10.1063/1.2138701	en
heal.identifier.secondary	034109	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	A general method is introduced for the calculation of the free-energy difference between two systems, 0 and 1, with configuration spaces Omega((0)), Omega((1)) of the same dimensionality. The method relies upon establishing a bijective mapping between disjoint subsets Gamma(i)((0)) of Omega((0)) and corresponding disjoint subsets Gamma(i)((1)) of Omega((1)), and averaging a function of the ratio of configurational integrals over Gamma(i)((0)) and Gamma(i)((1)) with respect to the probability densities of the two systems. The mapped subsets Gamma(i)((0)) and Gamma(i)((1)) need not span the entire configuration spaces Omega((0)) and Omega((1)). The method is applied for the calculation of the excess chemical potential mu(ex) in a Lennard-Jones (LJ) fluid. In this case, Omega((0)) is the configuration space of a (N-1) real molecule plus one ideal-gas molecule system, while Omega((1)) is the configuration space of a N real molecule system occupying the same volume. Gamma(i)((0)) and Gamma(i)((1)) are constructed from hyperspheres of the same radius centered at minimum-energy configurations of a set of "active" molecules lying within distance a from the ideal-gas molecule and the last real molecule, respectively. An algorithm is described for sampling Gamma(i)((0)) and Gamma(i)((1)) given a point in Omega((0)) or in Omega((1)). The algorithm encompasses three steps: "quenching" (minimization with respect to the active-molecule degrees of freedom), "mutation" (gradual conversion of the ideal-gas molecule into a real molecule, with simultaneous minimization of the energy with respect to the active-molecule degrees of freedom), and "excitation" (generation of points on a hypersphere centered at the active-molecule energy minimum). These steps are also carried out in reverse, as required by the bijective nature of the mapping. The mutation step, which establishes a reversible mapping between energy minima with respect to the active degrees of freedom of systems 0 and 1, ensures that excluded volume interactions emerging in the process of converting the ideal-gas molecule into a real molecule are relieved through appropriate rearrangement of the surrounding active molecules. Thus, the insertion problem plaguing traditional methods for the calculation of chemical potential at high densities is alleviated. Results are presented at two state points of the LJ system for a variety of radii a of the active domain. It is shown that the estimated values of mu(ex) are correct in all cases and subject to an order of magnitude lower statistical uncertainty than values based on the same number of Widom [J. Chem. Phys. 39, 2808 (1963)] insertions at high fluid densities. Optimal settings for the new algorithm are identified and distributions of the quantities involved in it [number of active molecules, energy at the sampled minima of systems 0 and 1, and free-energy differences between subsets Gamma(i)((0)) and Gamma(i)((1)) that are mapped onto each other] are explored.	en
heal.publisher	AMER INST PHYSICS	en
heal.journalName	Journal of Chemical Physics	en
dc.identifier.doi	10.1063/1.2138701	en
dc.identifier.isi	ISI:000234757400010	en
dc.identifier.volume	124	en
dc.identifier.issue	3	en