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

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 all 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 ϕ{sup 4} model and atomic clusters.
Authors:
 [1] ;  [2] ;  [3] ;  [1] ;  [4]
  1. Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, Indiana 46556 (United States)
  2. (United Kingdom)
  3. Department of Mathematics, Michigan State University, East Lansing, Michigan 48823 (United States)
  4. University Chemical Laboratory, The University of Cambridge, Cambridge CB2 1EW (United Kingdom)
Publication Date:
OSTI Identifier:
22308890
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 12; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ATOMIC CLUSTERS; MULTIVARIATE ANALYSIS; POTENTIAL ENERGY; POTENTIALS; SAMPLING; SOLUTIONS