Truncated minimum energy path method for finding first order saddle points
https://doi.org/10.17586/22208054201785586595
Abstract
A method for finding a selected region of the minimum energy path between two local minima on an energy surface is presented. It can be used to find the highest saddle point and thereby estimate the activation energy for the corresponding transition when the shape of the path is known reasonably well and a good guess can be made of the approximate location of the saddle point. The computational effort is then reduced significantly as compared with a calculation of the full minimum energy path by focusing the images on the selected part of the path and making one of the images, the climbing image, converge rigorously on the saddle point. Unlike the commonly used implementation where a restraint is used to distribute the images along the path, the present implementation makes use of a constraint where the distance between images is controlled based on a predefined overall length of the path. A relatively even density of images on each side of the climbing image is maintained by allowing images to move from one side to the other. Applications to magnetic skyrmion annihilation and escape through boundary are used to illustrate the savings in computational effort as compared with full minimum energy path calculations.
Supporting agencies: This work was supported by the Government of the Russian Federation (grant 074U01) and by grant 161110330 of Russian Science Foundation.
About the Authors
I. S. Lobanov
ITMO University
Russian Federation
Russian Federation
Kronverkskiy, 49, St. Petersburg, 197101
M. N. Potkina
St. Petersburg State University; Science Institute and Faculty of Physical Sciences, University of Iceland
Russian Federation
Russian Federation
Kronverkskiy, 49, St. Petersburg, 197101
107 Reykjav´ık
H. H. J´onsson
Science Institute and Faculty of Physical Sciences, University of Iceland; Center for Nonlinear Studies
Iceland
Iceland
107 Reykjav´ık
Los Alamos, NM 87545
V. M. Uzdin
ITMO University; St. Petersburg State University
Russian Federation
Russian Federation
Kronverkskiy, 49, St. Petersburg, 197101
St. Petersburg, 198504
References
1. Mills G., J´onsson H., Schenter G.K. Reversible work based transition state theory: Application to H2 dissociative adsorption. Surf. Sci., 1995, 324, P. 305–337.
2. J´onsson H., Mills G., Jacobsen K.W., edited by Berne B.J., Ciccotti G., Coker D.F. Nudged elastic band method for finding minimum energy paths of transitions, in Classical and Quantum Dynamics in Condensed Phase Simulations. World Scientific, Singapore, 1998, P. 385–404.
3. Henkelman G., Arnaldsson A., J´onsson H. Theoretical calculations of CH4 and H2 associative desorption from Ni(111): Could subsurface hydrogen play an important role? J. Chem. Phys., 2006, 124, P. 044706(9).
4. Henkelman G., J´onsson H. A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. J. Chem. Phys., 1999, 111(15), P. 7010–7022.
5. Olsen R.A., Kroes G.J., Henkelman G., Arnaldsson A., J´onsson H. Comparison of methods for finding saddle points without knowledge of the final states. J. Chem. Phys., 2004, 121(20), P. 9776–9792.
6. Guti´errez M.P., Arg´aez C., J´onsson H. Improved minimum mode following method for finding first order saddle points. J. Chem. Theo. Comput., 2017, 13(1), P. 125–134.
7. Henkelman G., J´ohannesson G., J´onsson H. Methods for finding saddle points and minimum energy paths. in Theoretical Methods in Condensed Phase Chemistry, 2002, P. 269–302.
8. Henkelman G., Uberuaga B.P., J´onsson H. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys., 2000, 113(22), P. 9901–9904.
9. Maragakis P., Andreev S.A., Brumer Y., Reichman D.R., Kaxiras E. Adaptive nudged elastic band approach for transition state calculation. J. Chem. Phys. 2002, 117, P. 4651–4658.
10. Zhu T., Li J., Samanta A., Kim H.G., Suresh S. Interfacial plasticity governs strain rate sensitivity and ductility in nanostructured metals. PNAS, 2007, 104 (9), P. 3031–3036.
11. Einarsdo´ttir D.M., Arnaldsson A., O´ skarsson F. and Jo´nsson H. Path optimization with application to tunneling. Lecture Notes in Computer Science, 2012, 7134, P. 45–55.
12. Henkelman G., J´onsson H. Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J. Chem. Phys., 2000, 113(22), P. 9978–9985.
13. Weinan E., Weiqing R., VandenEijnden E. String method for the study of rare events. Phys. Rev. B, 2002, 66, P. 052301(4).
14. Ravishenker, et al. Reviews in Computational Chemistry, Volume 11, edited by Kenny B. Lipkowitz, Donald B. Boyd, John Wiley & Sons, Sep 22, 2009, chapter 6, P. 346–347.
15. Sheppard D., Terrell R., Henkelman G. Optimization methods for finding minimum energy paths. J. Chem. Phys., 2008, 128, P. 134106(10).
16. Bessarab P.F., Uzdin V.M. J´onsson H. Method for finding mechanism and activation energy of magnetic transitions, applied to skyrmion and antivortex annihilation. Comp. Phys. Commun., 2015, 196, P. 335–347.
17. Bessarab P.F. Comment on “Path to collapse for an isolated N´eel skyrmion”. Phys. Rev. B , 2017, 95(13), P. 136401(2).
18. Malottki S.V., Dup´e B., Bessarab P.F., Delin A., Heinze S. Enhanced skyrmion stability due to exchange frustration. Sci. Rep., 2017, 7, P. 12299(10).
Review
For citations:
Lobanov I.S., Potkina M.N., J´onsson H.H., Uzdin V.M. Truncated minimum energy path method for finding first order saddle points. Nanosystems: Physics, Chemistry, Mathematics. 2017;8(5):586–595. https://doi.org/10.17586/22208054201785586595
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