Daniel Sheppard and Rye Terrell
This project is a comparison of different saddle point finding methods. All the methods we studied only need the force and energy of the system (and not the Hessian matrix of second derivative). Because of this, the methods scale well with system size, and can be used for relatively large systems using interaction potentialas expensive as density functional theory.
The Nudged Elastic Band (NEB) method is used to find reaction pathways when both the initial and final states are known. Using this code, the Minimum Energy Path (MEP) for any given chemical process may be calculated, however both the initial and final states must be known. The code works by linearly interpolating a set of images between the known initial and final states (as a "guess" at the MEP), and then minimizes the energy of this string of images. Each "image" corresponds to a specific geometry of the atoms on their way from the initial to the final state, a snapshot along the reaction path. Thus, once the enery of this string of images has been minimized, the true MEP is revealed.
More about the NEB method
The Dimer Method
The dimer method (or more generally a min-mode method) is used to find saddle points on a potential energy surface. It is complimentary to the nudged elastic band method because it does not require a final state. We have used the dimer method in two ways. The first is to evolve a configuration from an initial guess to a saddle point. The second application, which is much more challenging, is to find all low lying saddle points connecting the initial basin to adjacent basins. This problem is of particular interest in rate theory. If the transitions out of a basin are found, their individual rates can be evaluated, and the system can be evolved over long time scales using kinetic Monte Carlo. This involves randomly picking one of the transitions out of a Boltzmann distribution, and moving the system over that saddle point to an adjacent basin.
The NEB and Dimer in VASP
The dimer method has been incorperated into the DFT code VASP (Vienna Ab-initio Simulation Package). Our local collection of information, source and scripts is located here.
See the results of our testing on our benchmarking page.
D. Sheppard, R. Terrell, and G. Henkelman,
Optimization methods for finding minimum energy paths,
J. Chem. Phys. 128, 134106 (2008).
R. A. Olsen, G. J. Kroes, G. Henkelman, A. Arnaldsson, and H. Jónsson, Comparison of methods for finding saddle points without knowledge of the final states, J. Chem. Phys. 121, 9776-9792 (2004).
G. Henkelman, G. Jóhannesson, and H. Jónsson, Methods for Finding Saddle Points and Minimum Energy Paths, in Progress on Theoretical Chemistry and Physics, Ed. S. D. Schwartz, 269-300 (Kluwer Academic Publishers, 2000).
G. Henkelman, B.P. Uberuaga, and H. Jónsson, A climbing image nudged elastic band method for finding saddle points and minimum energy paths, J. Chem. Phys., 113, 9901 (2000).
G. Henkelman and H. Jónsson, Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points, J. Chem. Phys., 113, 9978 (2000).
Henkelman and H. Jónsson, A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives, J. Chem. Phys., 111, 7010 (1999).
H. Jónsson, G. Mills, K. W. Jacobsen, Nudged Elastic Band Method for Finding Minimum Energy Paths of Transitions, in Classical and Quantum Dynamics in Condensed Phase Simulations, Ed. B. J. Berne, G. Ciccotti and D. F. Coker, 385 (World Scientific, 1998).