A robust and memory-efficient transition state search method for complex energy landscapes

Abstract

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. To resolve these challenges, we introduce a new double-ended method, the Binary-Image Transition State Search (BITSS). It uses just two states that converge to the transition state, resulting in a fast, flexible, and memory-efficient method. We also show that it is more robust compared to existing bracketing methods that use only two states. We demonstrate its versatility by applying BITSS to three very different classes of problems: Lennard-Jones clusters, shell buckling, and multiphase phase-field models.

Finding transition state and minimum energy path of bistable elastic continua through energy landscape explorations

“…To efficiently capture the saddle point, we adopt the binary image transition state search (BITSS) method that has recently been introduced by Avis, et al (Avis et al, 2022). They have also shown that BITSS is more reliable compared to other bracketing methods, where two images are manipulated until they converge to the saddle point.…”

“…(2.4) is relatively the same to guarantee a successful search. As a result, we keep updating the values of 𝑘𝑘 𝑒𝑒 and 𝑘𝑘 𝑑𝑑 every three calling of the BITSS energy 𝐸𝐸 𝐵𝐵𝐵𝐵𝑇𝑇𝑆𝑆𝑆𝑆 based on the following formula (Avis et al, 2022)…”

“…Song, et al (Song et al, n.d.) employed the conjugate peak refinement method to search for the transition path of multi-stable tensegrity structures. Avis, et al (Avis et al, 2022) developed a binary image transition state search (BITSS) algorithm to efficiently capture the saddle point of a buckling cylindrical shell based on the triangulated lattice model. This was initially used by Li, et al (Y. Li et al, 2021a) who integrated this BITSS method together with the string method into a discretized shell model to find the saddle point and MEP of a multi-stable ferromagnetic meso-structures.…”

100 Years of the Lennard-Jones Potential

“…The simplest harmonic transition state theory rates are found to agree to within an order of magnitude . LJ 7 2d has also been used to test methods based on reaction coordinates and dimensionality reduction ,, as well as new transition state optimization algorithms …”

“…409 LJ 7 2d has also been used to test methods based on reaction coordinates and dimensionality reduction 414,418,419 as well as new transition state optimization algorithms. 420 In contrast, calculating interconversion rates between the fcc and incomplete icosahedral morphologies in LJ 38 is significantly harder. The methodology that employs geometry optimization to construct a kinetic transition network 278,286−288 and then solves the corresponding master equation 421,422 for the dynamics produced quantitative analysis of the rates in 1999.…”