Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-19T12:21:07.221Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimization-Based String Method for Finding Minimum Energy Path

Published online by Cambridge University Press:  03 June 2015

Amit Samanta  and
Weinan E
Amit Samanta*
Affiliation:
Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey, USA
Weinan E*
Affiliation:
Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey, USA Beijing International Center for Mathematical Research, Peking University, Beijing, China
*
Corresponding author.Email:[email protected]
Email:[email protected]
Get access

Abstract

We present an efficient algorithm for calculating the minimum energy path (MEP) and energy barriers between local minima on a multidimensional potential energy surface (PES). Such paths play a central role in the understanding of transition pathways between metastable states. Our method relies on the original formulation of the string method [Phys. Rev. B, 66,052301 (2002)], i.e. to evolve a smooth curve along a direction normal to the curve. The algorithm works by performing minimization steps on hyperplanes normal to the curve. Therefore the problem of finding MEP on the PES is remodeled as a set of constrained minimization problems. This provides the flexibility of using minimization algorithms faster than the steepest descent method used in the simplified string method [J. Chem. Phys., 126(16), 164103 (2007)]. At the same time, it provides a more direct analog of the finite temperature string method. The applicability of the algorithm is demonstrated using various examples.

Keywords

37C10Rare eventsstring methodminimum energy pathdislocation nucleation
Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 2 , August 2013 , pp. 265 - 275
Copyright
Copyright © Global Science Press Limited 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Dao, M., Lu, L., Asaro, R. J., De Hosson, J. T. M., and Ma, E., Acta Materialia 55, 4041 (2007).Google Scholar
[2]Asaro, R. J. and Suresh, S., Acta Mater. 53, 3369 (2005).Google Scholar
[3]E, W., Ren, W. Q., and Vanden-Eijnden, E., Journal of Physical Chemistry B 109, 6688 (2005).Google Scholar
[4]Vanden-Eijnden, E. and Venturoli, M., Journal of Chemical Physics 130, 194103 (2009).Google Scholar
[5] W. E and Zhou, X., Nonlinearity 24, 1831 (2011).Google Scholar
[6]Henkelman, G. and Jonsson, H., Journal of Chemical Physics 111, 7010 (1999).Google Scholar
[7]E, W., Ren, W. Q., and Vanden-Eijnden, E., Physical Review B 66, 052301 (2002).Google Scholar
[8]E, W., Ren, W. Q., and Vanden-Eijnden, E., Journal of Chemical Physics 126, 164103 (2007).Google Scholar
[9]Maragliano, L. and Vanden-Eijnden, E., Chemical Physics Letters 446, 182 (2007).Google Scholar
[10]Vanden-Eijnden, E., Journal of Computational Chemistry 30, 1737 (2009).Google Scholar
[11]Henkelman, G. and Jonsson, H., Journal of Chemical Physics 113, 9978 (2000).Google Scholar
[12]Henkelman, G., Uberuaga, B. P., and Jonsson, H., Journal of Chemical Physics 113, 9901 (2000).Google Scholar
[13]Sheppard, D., Terrell, R., and Henkelman, G., Journal of Chemical Physics 128, 134106 (2008).Google Scholar
[14]Peters, B., Heyden, A., Bell, A. T., and Chakraborty, A., Journal of Chemical Physics 120, 7877 (2004).Google Scholar
[15]Quapp, W., Journal of Chemical Physics 122, 174106 (2005).Google Scholar
[16]Quapp, W., Kraka, E., and Cremer, D., Journal of Physical Chemistry A 111, 11287 (2007).Google Scholar
[17]Ren, W., Ph.D. thesis, Courant Institute, New York University (2002).Google Scholar
[18]Czerminski, R. and Elber, R., Proceedings of The National Academyof Sciences of The United States of America 86, 6963 (1989).Google Scholar
[19]Choi, C. and Elber, R., Journal of Chemical Physics 94, 751 (1991).Google Scholar
[20]Bitzek, E., Koskinen, P., Gahler, F., Moseler, M., and Gumbsch, P., Physical Review Letters 97, 170201 (2006).Google Scholar
[21]Nocedal, J. and Wright, S. J., Numerical Optimization, vol. 2 (Springer Verlag, 2000).Google Scholar
[22]Mishin, Y., Mehl, M. J., Papaconstantopoulos, D. A., Voter, A. F., and Kress, J. D., Physical Review B 63, 224106 (2001).CrossRefGoogle Scholar
[23]Hemker, K. J. and Nix, W. D., Nature Materials 7, 97 (2008).CrossRefGoogle Scholar
[24]Yip, S., Nature 391, 532 (1998).Google Scholar
[25]Rabkin, E. and Srolovitz, D. J., Nano Lett. 7, 101 (2007).Google Scholar
[26]Hyde, B., Espinosa, H. D., and Farkas, D., JOM 57, 62 (2005).Google Scholar
[27]Shan, Z. W., Mishra, R. K., Asif, S. A. S., Warren, O. L., and Minor, A. M., Nature Materials 7, 115 (2008).Google Scholar
[28]Kelchner, C. L., Plimpton, S. J., and Hamilton, J. C., Physical Review B 58, 11085 (1998).Google Scholar
[29]Zhu, T., Li, J., Samanta, A., Leach, A., and Gall, K., Physical Review Letters 100, 025502 (2008).Google Scholar
[30]http://www.math.princeton.edu/string.Google Scholar