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.
- Benderskii VA, Makarov DE, Wight CA (1994) Chemical dynamics at low temperatures. Adv Chem Phys 88:1Google Scholar
- Bessarab PF, Uzdin VM, Jónsson H (2013) Potential energy surfaces and rates of spin transitions. Zeitschrift für Physikalische Chemie 227:1543Google Scholar
- Bitzek E, Koskinen P, G’́ahler F, Moseler M, Gumbasch P (2006) Structural relaxation made simple. Phys Rev Lett 97(17):170201Google Scholar
- Hele TJH, Althorpe SC (2013) Derivation of a true (t → 0+) quantum transition-state theory. I. Uniqueness and equivalence to ring-polymer molecular dynamics transition-state-theory. J Chem Phys 138:084108Google Scholar
- Henkelman G, Jónsson H (2000) Improved tangent estimate in the NEB method for finding minimum energy paths and saddle points. J Chem Phys 113(22):9978–9985 [Note: There is a typographical error in the Appendix, 2Vi+1 − Vi should be − 2(Vi+1 − Vi)]Google Scholar
- Henkelman G, Jóhannesson G, Jónsson H (2000b) Theoretical methods in condensed phase chemistry, methods for finding saddle points and minimum energy paths. In: Schwartz SD (ed) Progress in theoretical chemistry and physics. Kluwer Academic Publishers, Dordrecht, pp 269–302Google Scholar
- Keck JC (1967) Variational theory of reaction rates. J Chem Phys 13:85Google Scholar
- Peters B (2017) Reaction rate theory and rare events. Elsevier Science & Technology, AmsterdamGoogle Scholar
- Trygubenko SA, Wales DJ (2004) A doubly nudged elastic band method for finding transition states. J Chem Theory Comput 120(5):2082–2094Google Scholar