DOI: 10.1063/1.1323224. Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points

Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points

10.1063/1.1323224

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

An improved way of estimating the local tangent in the nudged elastic band method for finding minimum energy paths is presented. In systems where the force along the minimum energy path is large compared to the restoring force perpendicular to the path and when many images of the system are included in the elastic band, kinks can develop and prevent the band from converging to the minimum energy path. We show how the kinks arise and present an improved way of estimating the local tangent which solves the problem. The task of finding an accurate energy and configuration for the saddle point is also discussed and examples given where a complementary method, the dimer method, is used to efficiently converge to the saddle point. Both methods only require the first derivative of the energy and can, therefore, easily be applied in plane wave based density-functional theory calculations. Examples are given from studies of the exchange diffusion mechanism in a Si crystal, Al addimer formation on the Al(100) surface, and dissociative adsorption of CH4 on an Ir(111) surface.

Bibliography

Henkelman, G., & JÃ³nsson, H. (2000). Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. The Journal of Chemical Physics, 113(22), 9978â9985.

Authors 2

Graeme Henkelman (first)
Hannes Jónsson (additional)

References 33 Referenced 8,133

10.1103/PhysRevLett.72.1124 / Phys. Rev. Lett. (1994)
10.1016/0039-6028(94)00731-4 / Surf. Sci. (1995)
{'key': '2024020623503678400_r3'}
10.1103/PhysRevLett.84.2441 / Phys. Rev. Lett. (2000)
{'key': '2024020623503678400_r5'}
10.1103/PhysRevLett.83.4345 / Phys. Rev. Lett. (1999)
10.1103/PhysRevB.59.16047 / Phys. Rev. B (1999)
10.1016/S0039-6028(99)01147-4 / Surf. Sci. (2000)
10.1016/0039-6028(94)90249-6 / Surf. Sci. (1994)
10.1016/0039-6028(94)00631-8 / Surf. Sci. (1995)
{'key': '2024020623503678400_r11'}
10.1103/PhysRevLett.77.5067 / Phys. Rev. Lett. (1996)
10.1103/PhysRevLett.79.3676 / Phys. Rev. Lett. (1997)
10.1016/0009-2614(87)80576-6 / Chem. Phys. Lett. (1987)
{'key': '2024020623503678400_r15', 'first-page': '167', 'volume': '24', 'year': '1990', 'journal-title': 'Int. J. Quantum Chem.'} / Int. J. Quantum Chem. (1990)
10.1063/1.458491 / J. Chem. Phys. (1990)
10.1063/1.463163 / J. Chem. Phys. (1992)
10.1063/1.480097 / J. Chem. Phys. (1999)
10.1063/1.1672194 / J. Chem. Phys. (1969)
10.1103/PhysRevLett.57.2287 / Phys. Rev. Lett. (1986)
10.1103/PhysRevB.39.5566 / Phys. Rev. B (1989)
{'key': '2024020623503678400_r21', 'first-page': '2384', 'volume': '82', 'year': '1987', 'journal-title': 'Mater. Res. Soc. Symp. Proc.'} / Mater. Res. Soc. Symp. Proc. (1987)
10.1103/PhysRev.136.B864 / Phys. Rev. (1964)
10.1103/PhysRev.140.A1133 / Phys. Rev. (1965)
10.1021/jp960669l / J. Phys. Chem. (1996)
10.1103/PhysRevB.47.558 / Phys. Rev. B (1993)
{'key': '2024020623503678400_r24a', 'first-page': '16', 'volume': '6', 'year': '1996', 'journal-title': 'Comput. Mater. Sci.'} / Comput. Mater. Sci. (1996)
10.1103/PhysRevB.54.11169 / Phys. Rev. B (1996)
{'key': '2024020623503678400_r25'}
10.1103/PhysRevB.41.7892 / Phys. Rev. B (1990)
10.1063/1.475306 / J. Chem. Phys. (1997)
{'key': '2024020623503678400_r28'}
{'key': '2024020623503678400_r29'}

Dates

Type	When
Created	23 years ago (July 26, 2002, 10:14 a.m.)
Deposited	1 year, 6 months ago (Feb. 6, 2024, 9:23 p.m.)
Indexed	18 minutes ago (Aug. 21, 2025, 6:32 a.m.)
Issued	24 years, 8 months ago (Dec. 8, 2000)
Published	24 years, 8 months ago (Dec. 8, 2000)
Published Print	24 years, 8 months ago (Dec. 8, 2000)

Funders 0

None

BibTeX

@article{Henkelman_2000, title={Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points}, volume={113}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1323224}, DOI={10.1063/1.1323224}, number={22}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Henkelman, Graeme and Jónsson, Hannes}, year={2000}, month=dec, pages={9978–9985} }

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