SC 98-04 Christof Schütte, Alexander Fischer, Wilhelm Huisinga, Peter Deuflhard: A Hybrid Monte Carlo Method for Essential Molecular Dynamics
Abstract: 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.
MSC: 47N55, 82B80, 60J05, 62M15, 65U0515A51, 15A18, 92E10