DIFFUSION EQUATION AND DISTANCE SCALING METHODS OF GLOBAL OPTIMIZATION - APPLICATIONS TO CRYSTAL-STRUCTURE PREDICTION

Two methods of global minimization, the diffusion equation method and the distance scaling method, are applied to predict the crystal struct ures of the hexasulfur and benzene molecules. No knowledge about the s ystems other than the geometry of the molecules and the pairwise poten tials is assumed; i.e., no assumptions are made about the space groups , cell dimensions, or number of molecules in the unit cell. Both metho ds are based on smoothing transformations of the original potential en ergy surface, which remove all insignificant local minima; the survivi ng minima are traced back to the original potential energy surface dur ing the so-called reversing procedure, in which the transformations ar e gradually removed. The crystal structures, known from experiment, we re predicted correctly. To verify the power of the methods, the proble m of global minimization of the potential energy of crystals of both m olecules was intentionally increased considerably in complexity: viz., the numbers of molecules in the unit cell were doubled (from three to six in the case of hexasulfur and from four to eight in the case of b enzene), and the search for the global minimum was repeated; the metho d again located the global minimum for each molecule. Additionally, lo cal minimizations starting from the lowest-energy structures were carr ied out with a pressure term included, lending to the observed high-pr essure structure of benzene.