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Trajectories of the bracketing methods on a hooked potential with a single saddle point. The equation for this potential is provided in appendix C 1. The minimum energy pathway is shown by the dashed line.
Source publication
Locating transition states is crucial for investigating transition mechanisms in wide-ranging phenomena, from atomistic to macroscale systems. Existing methods, however, can struggle in problems with a large number of degrees of freedom, on-the-fly adaptive remeshing and coarse-graining, and energy landscapes that are locally flat or discontinuous....
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Context 1
... the energy up to the transition state). Conversely in the DHS method, the energy of an image is minimised while the image separation is fixed (iteratively decreasing the separation and changing the frozen image up to the transition state). To illustrate how BITSS is superior compared to these methods, we consider the hooked 2d potential in fig. 2. For this potential the energies of the images ascend higher than that of the transition state and consequently both of these methods fail to converge to the saddle point regardless of the parameters that are used. The step and slide method fails in this situation because it always expects that the energy of the two states is below the ...
Context 2
... the particle cluster example system, the LennardJones potential is used for the interaction between each by cx cy -1 0 0 10 10 1 0 0 1 1 5 2 0 fig. ...
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... we test how the BITSS method performs when there are multiple transition states in the pathway between the two starting minima. For this we use a 2D potential, shown in fig. S2a, with a pathway that follows a chicane of two 135 • circular arcs. The energy ...
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... resulting in transition states A and B, with energies E A and E B . We then vary E B between 0 and E A , and the size of the distance reduction factor, f , to see if BITSS successfully converges to the higher transition state A. For each pair of parameters we perform 5 runs with slight variations in the starting positions, with the results in fig. S2b showing the points at which all 5 converge to ...
Citations
... Some methods are based on the principle of keeping the energies of the two nodes similar during the search. [5][6][7][8][9][10][11] We refer to these methods as same-energy methods. The same-energy principle helps avoid an early crossing of the barrier from one side, and the saddle point stays trapped between the two nodes throughout the search. ...
... The existing algorithms that are based on the same-energy principle [5][6][7][8][9] have not been widely used so far, and their efficiencies are difficult to assess because they either have not been tested for realistic chemical systems or the number of energy and force calculations has not been reported in the original papers. An exception is the elastic image pair method and its improved version 11 (i-EIP), which has been reported to have a very high efficiency needing only 45 energy and force evaluation on average to find saddle points of molecular reactions. ...
We present an algorithm to find first order saddle points on the potential energy surface (PES). The algorithm is formulated as a constrained optimization problem that involves two sets of atomic coordinates (images), a time-varying distance constraint and a constraint on the energy difference. Both images start in different valleys of the PES and are pulled toward each other by gradually reducing the distance. The search space is restricted to the pairs of configurations that share the same potential energy. By minimizing the energy while the distance shrinks, a minimum of the constrained search space is tracked. In simple cases, the two images are confined to their respective sides of the barrier until they finally converge near the saddle point. If one image accidentally crosses the barrier, the path is split at suitable locations and the algorithm is repeated recursively. The optimization is implemented as a combination of a quasi-Newton optimization and a linear constraint. The method was tested on a set of Lennard-Jones-38 cluster transitions and a set of 121 molecular reactions using density functional theory calculations. The efficiency in terms of energy and force evaluation is better than with competing methods as long as they do not switch to single-ended methods. The construction of a continuous search path with small steps and the ability to focus on arbitrary subsegments of the path provide an additional value in terms of robustness and flexibility.
... The transition states are central to describing reconfiguration mechanisms in chemistry, condensed matter physics and engineering [13]. The methods used for identifying the energy threshold between the states of compounds in the field of chemistry are well suited to provide a transformation strategy between the stable states of multistable tensegrity structures. ...
... Over the years, literature has given a number of mountain pass solutions, such as the nudged elastic band method [18,19], the dimer method [20], and conjugate peak refinement method [21]. Avis [13] distinguishes the Mountain Pass methods by the given information: whether a single stable state or multiple stable states are provided. The Conjugate Peak Refinement (CPR) method was first investigated to estimate the energy bound in chemical processes [22,23,21]; later it was expanded and used to study post-buckling of thin-walled shells in structural engineering [15]. ...
Multistable tensegrity structures are able to switch between equilibrium configurations and maintain these states with no additional energy input; as a result, they have found applications in reconfigurable robotics and deployable structures. However, the actuation strategy for multistable tensegrity structures to transform from one stable state to another remains unknown. In this work, we propose a method to identify a transition route between the known stable states of multistable tensegrity structures. The least-energy threshold and the transformation route formed by a series of deformed position point vectors are obtained. The method is based on the Conjugate Peak Refinement (CPR) method, which is one of the Mountain Pass Algorithms. To capture the fact that cable members could go slack during the transition route, a slack cable model is adapted into the CPR method so that the accurate energy state of the tensegrity structure is derived. The algorithms are successfully applied to examples of 3D multistable tensegrity structures from the literature. The work in this paper provides a minimum energy threshold between stable states, a measure of its shock sensitivity, and a reference actuation strategy to transform between the stable states of multistable tensegrity structures.
