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Explicit factorization of external coordinates in constrained statistical mechanics models
Author(s) -
Echenique Pablo,
Calvo Iván
Publication year - 2006
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.20499
Subject(s) - curvilinear coordinates , log polar coordinates , monte carlo method , metric (unit) , tensor (intrinsic definition) , metric tensor , cartesian tensor , statistical physics , generalized coordinates , work (physics) , classical mechanics , physics , mathematics , geometry , mathematical analysis , tensor density , tensor field , quantum mechanics , statistics , operations management , economics , exact solutions in general relativity , geodesic
Abstract If a macromolecule is described by curvilinear coordinates or rigid constraints are imposed, the equilibrium probability density that must be sampled in Monte Carlo simulations includes the determinants of different mass‐metric tensors. In this work, the authors explicitly write the determinant of the mass‐metric tensor G and of the reduced mass‐metric tensor g , for any molecule, general internal coordinates and arbitrary constraints , as a product of two functions; one depending only on the external coordinates that describe the overall translation and rotation of the system, and the other only on the internal coordinates. This work extends previous results in the literature, proving with full generality that one may integrate out the external coordinates and perform Monte Carlo simulations in the internal conformational space of macromolecules. © 2006 Wiley Periodicals, Inc. J Comput Chem, 2006