%0 Journal Article
%T A Variational Approach for Minimizing Lennard-Jones Energies
%A Carsten Peterson
%A Ola Sommelius
%A Bo S£¿derberg
%J Physics
%D 1995
%I arXiv
%R 10.1103/PhysRevE.53.1725
%X 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.
%U http://arxiv.org/abs/chem-ph/9502007v1