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A constrained hybrid Monte‐Carlo algorithm and the problem of calculating the free energy in several variables
Author(s) -
Hartmann C.,
Schütte C.
Publication year - 2005
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200410218
Subject(s) - submanifold , monte carlo method , context (archaeology) , potential of mean force , energy (signal processing) , orthogonal coordinates , monte carlo algorithm , interpretation (philosophy) , statistical physics , mathematics , physics , geometry , molecular dynamics , computer science , mathematical analysis , statistics , paleontology , quantum mechanics , biology , programming language
We consider the problem of computing molecular free energy profiles along several orthogonal reaction coordinates by means of constrained simulations. The reaction coordinates define families of submanifolds, and the mean force along the reaction coordinates is the averaged force acting vertically to the submanifold. We give a rigorous justification for the calculation of the mean force along the constrained coordinates, and provide a concise geometrical interpretation of the different contributions to the mean force in terms of the extrinsic geometry of the submanifold. From this we are able derive a hybrid Monte‐Carlo‐based algorithm that can be used to compute expectation values from constrained simulations such as the mean force in the context of thermodynamic free energy statistics.