Exploring Potential Energy Surfaces with Saddle Point Searches
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The energy surface of an atomic scale representation of a material contains the essential information needed to determine the structure and time evolution of the system at a given temperature. Local minima on the surface represent (meta)stable states of the system, while first-order saddle points characterize the mechanisms of transitions between states. While many well-known methods make it relatively easy to find local minima, the identification of saddle points is more challenging. In this chapter, methods for finding saddle points are discussed as well as applications to materials simulations. Both doubly constrained search methods, where the final and the initial state minima are specified, and singly constrained search methods, where only the initial state is specified, are discussed. The focus is on a classical description of the atom coordinates, but saddle points corresponding to quantum mechanical tunneling are also mentioned. An extension to magnetic systems where the energy surface depends on the orientation of the magnetic vectors is sketched.
This work was supported in part by the Icelandic Research Fund (grant 185405-051) and by the Academy of Finland (grant 278260). V.Á. acknowledges support from a Doctoral Grant of the University of Iceland Research Fund.
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