Communication: Newton homotopies for sampling stationary points of potential energy landscapes

Abstract

One of the most challenging and frequently arising problems in many areas of science is to find solutions of a system of multivariate nonlinear equations. There are several numerical methods that can find many (or all if the system is small enough) solutions but they each exhibit characteristic problems. Moreover, traditional methods can break down if the system contains singular solutions. Here, we propose an efficient implementation of Newton homotopies, which can sample a large number of the stationary points of complicated many-body potentials. We demonstrate how the procedure works by applying it to the nearest-neighbor ${\varphi }^4$ model and atomic clusters.

5 pages, 3 figures. Published in Communications of Journal of Chemical Physics

References in corpus (5)

• Some Further Results for the Stationary Points and Dynamics of Supercooled Liquids
• Phase transitions and configuration space topology
• Characterizing the network topology of the energy landscapes of atomic clusters
• Enumerating Gribov copies on the lattice
• Comment on ``Quasisaddles as relevant points of the potential energy surface in the dynamics of supercooled liquids'' [J. Chem. Phys. 116, 10297 (2002); cond-mat/0203301]

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