Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and Supercooled Liquids
By Jonathan P. K. Doye, David J. Wales. 2001
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The properties of higher-index saddle points have been invoked in recent theories of the dynamics of supercooled liquids. Here we examine in detail a mapping of configurations to saddle points using minimization of |∇E|2, which has been used in previous work to support these theories. The examples we consider are a two-dimensional model energy surface and binary Lennard-Jones liquids and solids. A shortcoming of the mapping is its failure to divide the potential energy surface into basins of attraction surrounding saddle points, because there are many minima of |∇E|2 that do not correspond to stationary points of the potential energy. In fact, most liquid configurations are mapped to such points for the system we consider. We therefore develop an alternative route to investigate higher-index saddle points and obtain near complete distributions of saddles for small Lennard-Jones clusters. The distribution of the number of stationary points as a function of the index is found to be Gaussian, and the average...
Subfields: Biomedical Engineering, Condensed Matter Physics, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/2d7a2357182561766bd9816fde7c23be2274c73a
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In Materials Chemistry
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- Modeling the mechanics of amorphous solids at different length scale and time scale (2011, background): “ minimizing the objective function 1 2 |∇V(R3N)|2 rather than the potential energy [6], although one has to be careful because the objective function has more minima than stationary points on the PEL [62]. The number of stationary points increases roughly as an exponential function of the number of ”