Global Optimization For Molecular Clusters Using A New Smoothing Approach

Strategies involving smoothing of the objective function have been used to help solve difficult global optimization problems arising in molecular chemistry. This paper proposes a new smoothing approach and examines some basic issues in smoothing for molecular configuration problems. We first propose a new, simple algebraic way of smoothing the Lennard-Jones energy function, which is an important component of the energy in many molecular models. This simple smoothing technique is shown to have close similarities to previously-proposed, spatial averaging smoothing techniques. We also present some experimental studies of the behavior of local and global minimizers under smoothing of the potential energy in Lennard-Jones problems. An examination of minimizer trajectories from these smoothed problems shows significant limitations in the use of smoothing to directly solve global optimization problems.