Saddle points dimer method

The three initial points are different enough that the dimer searches converge to separate saddle points. In general the strategy for the Dimer method is to try many different initial configurations aroimd a minimum, in order to find the saddle points that lead out of that minimum basin. 

Figure 6 The calculation of the effectiveforce in the Dimer method. A pair of images, spaced apart by a small distance, on the order q/ 0.1A is rotated to minimize the energy. This gives the direction of the lowest frequency normal mode. The component of the force in the direction of the dimer is then inverted and the minimization of this effectiveforce leads to convergence to a saddle point. No reference is made to the final state.

Figure 7 Application of the dimer method to a two-dimensional test problem. Three different starting points are generated in the reactant region by taking extrema along a high temperature dynamical trajectory. From each one of these, the dimer isjirst translated only in the direction of the lowest mode, but once the dimer is out of the convex region a full optimization of the effective force is carried oat at each step (thus the kink in two of the paths). Each one of the three starting p>oints leads to a different saddle point in this case.

Figure 9 Thefrequency at which the various saddle points for the surface island transitions (illustrated in figure 8) are found with the Dimer method. The lowest saddle points are found with the highestjrequency. Also shown are the number of iterations required to go from the intial state to the saddle point to within a force tolerance of0.001 eV/AFor the more practical 0.01 eV/A tolerance, the average number offeree evaluations was a little under 300. The error bars show the standard deviation.

LSKMC) method [81], the search for saddle points in the vicinity of a given local minimum by the dimer method was used [82], For the found new local minima, the rate constants of transitions are calculated based on the TST... 

Baker J (1986) An algorithm for the location of transition states. J Comp Chem 7 385-395 Henkelman G, Jdnsson H (1999) A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. J Chem Phys 111 7010-7022 Hanggi P, Talkner P, Borkovec M (1990) Reaction-rate theory fifty years after Kramers. Rev Mod Phys 62 251-341... 

Henkelman G, J6nsson H (1999) A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. J Chem Phys 111 7010-7022... 

The transitional states (TS) were located with the dimer method (Henkehnan and Jonsson, 1999, 2001 Olsen et al., 2004). The most stable configurations of the reactant on the surface were determined by the standard DFT minimization. These configurations were used as the initial state, firom which the dimer method was used to find the lowest curvature mode and to chmb up the potential energy surface from minima to saddle points. A force tolerance of 0.03 eV/A was used in all the transition state searches. 

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