J. Phys. Chem. A,
Web Release Date: April 7,
Diffusion Equation and Distance Scaling Methods of Global Optimization: Applications to Crystal Structure Prediction
Received: July 24, 1997 In Final Form: December 19, 1997 Abstract: Two methods of global minimization, the diffusion equation method and the
distance scaling method, are applied to predict the crystal structures of the
hexasulfur and benzene molecules. No knowledge about the systems other than the
geometry of the molecules and the pairwise potentials is assumed; i.e., no
assumptions are made about the space groups, cell dimensions, or number of
molecules in the unit cell. Both methods are based on smoothing transformations
of the original potential energy surface, which remove all insignificant local
minima; the surviving minima are traced back to the original potential energy
surface during the so-called reversing procedure, in which the transformations
are gradually removed. The crystal structures, known from experiment, were
predicted correctly. To verify the power of the methods, the problem of global
minimization of the potential energy of crystals of both molecules 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 benzene), and the search for
the global minimum was repeated; the method again located the global minimum for
each molecule. Additionally, local minimizations starting from the lowest-energy
structures were carried out with a pressure term included, leading to the
observed high-pressure structure of benzene.