The geometric minimum action method for computing minimum energy paths

Journal of Chemical Physics

Volumn 128, Issue 6, 2008, Pages

  Vanden Eijnden, Eric ^a   Heymann, Matthias ^b  

^a NEW YORK UNIVERSITY   (United States)

^b DUKE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONAL ANALYSIS; VARIATIONAL TECHNIQUES;

GEOMETRIC MINIMUM ACTION METHOD; MINIMUM ENERGY PATH (MEP);

ALGORITHMS;

EID: 39449102156     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2833040     Document Type: Article

References (10)

1. H. Jónsson, G. Mills, and K. W. Jacobsen, in Classical and Quantum Dynamics in Condensed Phase Simulations, edited by, B. J. Berne, G. Ciccotti, and, D. F. Coker, (World Scientific, Singapore, 1998).
2. G. Henkelman and H. Jónsson, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1323224 113, 9978 (2000).
3. W. E, W. Ren, and E. Vanden-Eijnden, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66.052301 66, 052301 (2002).
4. W. E, W. Ren and E. Vanden-Eijnden, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2720838 126, 164103 (2007).
5. M. Heymann, Ph.D. thesis, New York University, 2007.
6. M. Heymann and E. Vanden-Eijnden, Commun. Pure Appl. Math. (in press). 0010-3640
7. R. Olender and R. Elber, J. Mol. Struct.: THEOCHEM 398-399, 63 (1997) 0166-1280; Proceeding of the WATOC Symposium.
8. This argument assumes that there is only one saddle point and no other critical point along the MEP joining x1 to x2, but it can be easily generalized to more complicated situations and the conclusion remains valid: The minimizers of Eq. are MEPs.
9. K. Müller, Angew. Chem. ANCEAD 0044-8249 10.1002/ange.19800920104 92, 1 (1980).
10. K. W. Morton and D. F. Mayers, Numerical Solution of Partial Differential Equations-An Introduction, 2nd ed. (Cambridge University Press, Cambridge, 2005).