We present some new theoretical and computational results for the stationary points of bulk systems.First we demonstrate how the potential energy surface can be partitioned into catchment basins associated wtih every stationary point using a combination of Newtor-Raphson and eignvector-floolwing techniques.Numerical results are presented for a 256-atom supercell representation of a binary Lennard-Jones system.We then derive analytical formulae for the mumber of statonary points as a function of both system size and the Hessian index,using a framework based upon weakly interaction subsystems.This analysis revals a simple relation between the total number of stationary points,the number of local minima,and the number of transition states connected on average to each minimum.Finally we calculate two measures of localization for the displacement corresponding to Hessian eigenvectors in samples or stationary points obtained from te Newton-Raphson-based geometry optimization scheme.Systematic differences are found between the properties of eigenvectors corresponding to positive and enegative Hessian eigenvalues,and localized character is most pronounced for stationary points with low values of the Hessian index.
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