Methods for Finding Saddle Points and Minimum Energy Paths

The problem of finding minimum energy paths and, in particular, saddle points on high dimensional potential energy surfaces is discussed. Several different methods are reviewed and their efficiency compared on a test problem involving conformational transitions in an island of adatoms on a crystal surface. The focus is entirely on methods that only require the potential energy and its first derivative with respect to the atom coordinates. Such methods can be applied, for example, in plane wave based Density Functional Theory calculations, and the computational effort typically scales well with system size. When the final state of the transition is known, both the initial and final coordinates of the atoms can be used as boundary conditions in the search. Methods of this type include the Nudged Elastic Band, Ridge, Conjugate Peak Refinement, Drag method and the method of Dewar, Healy and Stewart. When only the initial state is known, the problem is more challenging and the search for the saddle point represents also a search for the optimal transition mechanism. We discuss a recently proposed method that can be used in such cases, the Dimer method.

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