Abstract
A method is presented for optimizing paths on high dimensional surfaces, i.e. scalar functions of many variables. The method involves optimizing simultaneously the end points and several intermediate points along the path and thus lends itself well to parallel computing. This is an extension of the nudged elastic band method (NEB) which is frequently used to find minimum energy paths on energy surfaces of atomic scale systems, often with several thousand variables. The method is illustrated using 2-dimensional systems and various choices of the object function, in particular (1) path length, (2) iso-contour and (3) quantum mechanical tunneling rate. The use of the tunneling paths to estimate tunneling rates within the instanton approximation is also sketched and illustrated with an application to associative desorption of hydrogen molecule from a copper surface, a system involving several hundred degrees of freedom.
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References
Jónsson, H., Mills, G., Jacobsen, K.W.: Classical and Quantum Dynamics in Condensed Phase Simulations. In: Berne, B.J., Ciccotti, G., Coker, D.F. (eds.), ch. 16, p. 385. World Scientific (1998)
Razavy, M.: Quantum Theory of Tunneling. World Scientific Publishing (2003)
Wigner, E.: Trans. Faraday Soc. 34, 29 (1938); Eyring, H.: J. Chem. Phys. 3, 107 (1935)
Vineyard, G.H.: J. Phys. Chem. Solids 3, 121 (1957)
Henkelman, G., Jónsson, H.: J. Chem. Phys. 113, 9978 (2000)
Henkelman, G., Uberuaga, B., Jónsson, H.: J. Chem. Phys. 113, 9901 (2000)
Rasmussen, T., Jacobsen, K.W., Leffers, T., Pedersen, O.B., Srinivasan, S.G., Jónsson, H.: Physical Review Letters 79, 3676 (1997)
Sheppard, D., Terrell, R., Henkelman, G.: J. Chem. Phys. 128, 134106 (2008)
Wilson, E.B., Decius, J.C., Cross, P.C.: Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra. Dover (1980)
Callan, C.G., Coleman, S.: Phys. Rev. D 16, 1762 (1977)
Miller, W.H.: J. Phys. Chem. 62, 1899 (1975)
Messina, M., Schenter, G., Garrett, B.C.: J. Chem. Phys. 103, 3430 (1995)
Skodje, R.T., Truhlar, D.G.: J. Chem. Phys. 77, 5955 (1982)
Mills, G., Schenter, G.K., Makarov, D., Jónsson, H.: Chem. Phys. Lett 278, 91 (1997); RAW Quantum Transition State Theory. In: Berne, B.J., et al. (eds.) Classical and Quantum Dynamics in Condensed Phase Simulations, page 405. World Scientific (1998)
Henkelman, G., Jónsson, H.: J. Chem. Phys. 111, 7010 (1999)
Kaestner, J., Sherwood, P.: J. Chem. Phys. 128, 014106 (2008)
Arnaldsson, A.: Ph.D. thesis, University of Washington, Seattle, WA, USA (2007)
Andersson, S., Nyman, G., Arnaldsson, A., Manthe, U., Jónsson, H.: J. Phys. Chem. A 113, 4468 (2009)
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Einarsdóttir, D.M., Arnaldsson, A., Óskarsson, F., Jónsson, H. (2012). Path Optimization with Application to Tunneling. In: Jónasson, K. (eds) Applied Parallel and Scientific Computing. PARA 2010. Lecture Notes in Computer Science, vol 7134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28145-7_5
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DOI: https://doi.org/10.1007/978-3-642-28145-7_5
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