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 chem istry. 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. T his simple smoothing technique is shown to have close similarities to previ ously-proposed, spatial averaging smoothing techniques. We also present som e experimental studies of the behavior of local and global minimizers under smoothing of the potential energy in Lennard-Jones problems. An examinatio n of minimizer trajectories from these smoothed problems shows significant limitations in the use of smoothing to directly solve global optimization p roblems.