Carsten Peterson, Ola Sommelius and Bo Söderberg A Variational Approach for Minimizing Lennard-Jones
Energies Physical Review E 53,
1725-1731 (1996)Abstract: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, 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.LU TP 94-04 |