A Hybrid Monte Carlo Method for Essential Molecular Dynamics

Please always quote using this URN: urn:nbn:de:0297-zib-3474
  • Recently, a novel concept for the computation of essential features of Hamiltonian systems (such as those arising in molecular dynamics) has been proposed. The realization of that concept was based on subdivision techniques applied to the Frobenius--Perron operator for the dynamical system. The present paper suggests an alternative but related concept based on statistical mechanics, which allows to attack realistic molecular systems. In a first step, the frequency of conformational changes is characterized in statistical terms leading to the definition of some Markov operator $T$ that describes the corresponding transition probabilities within the canonical ensemble. In a second step, a discretization of $T$ via hybrid Monte Carlo techniques (based on short term subtrajectories only) is shown to lead to a stochastic matrix $P$. With these theoretical preparations, an identification algorithm for conformations is applicable (to be presented elsewhere). Numerical results for the n-pentane molecule are given and interpreted.

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Metadaten
Author:Christof Schütte, Alexander Fischer, Wilhelm Huisinga, Peter Deuflhard
Document Type:ZIB-Report
MSC-Classification:15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A18 Eigenvalues, singular values, and eigenvectors
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J05 Discrete-time Markov processes on general state spaces
62-XX STATISTICS / 62Mxx Inference from stochastic processes / 62M15 Spectral analysis
82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Bxx Equilibrium statistical mechanics / 82B80 Numerical methods (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80]
92-XX BIOLOGY AND OTHER NATURAL SCIENCES / 92Exx Chemistry (For biochemistry, see 92C40) / 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
Date of first Publication:1998/01/21
Series (Serial Number):ZIB-Report (SC-98-04)
Published in:A compl. rev. vers. appeared under the title: " A Direct Approach to Conformational Dynamics Based on Hybrid Monte Carlo" in: J. Comput. Phys. 151 (1999) 146-168