41 research outputs found
A Variational Approach for Minimizing Lennard-Jones Energies
A variational method for computing conformational properties of molecules
with Lennard-Jones potentials for the monomer-monomer interactions is
presented. The approach is tailored to deal with angular degrees of freedom,
{\it rotors}, and consists in the iterative solution of a set of deterministic
equations with annealing in temperature. The singular short-distance behaviour
of the Lennard-Jones potential is adiabatically switched on in order to obtain
stable convergence. As testbeds for the approach two distinct ensembles of
molecules are used, characterized by a roughly dense-packed ore a more
elongated ground state. For the latter, problems are generated from natural
frequencies of occurrence of amino acids and phenomenologically determined
potential parameters; they seem to represent less disorder than was previously
assumed in synthetic protein studies. For the dense-packed problems in
particular, the variational algorithm clearly outperforms a gradient descent
method in terms of minimal energies. Although it cannot compete with a careful
simulating annealing algorithm, the variational approach requires only a tiny
fraction of the computer time. Issues and results when applying the method to
polyelectrolytes at a finite temperature are also briefly discussed.Comment: 14 pages, uuencoded compressed postscript fil