@Article{CiCP-30-749,
author = {Hicks , Jonathan and P. Schulze , Timothy},
title = {Examining Saddle Point Searches in the Context of Off-Lattice Kinetic Monte Carlo},
journal = {Communications in Computational Physics},
year = {2021},
volume = {30},
number = {3},
pages = {749--770},
abstract = {<p style="text-align: justify;">In calculating the time evolution of an atomic system on diffusive timescales,
off-lattice kinetic Monte Carlo (OLKMC) can sometimes be used to overcome the limitations of Molecular Dynamics. OLKMC relies on the harmonic approximation to
Transition State Theory, in which the rate of rare transitions from one energy minimum to a neighboring minimum scales exponentially with an energy barrier on the
potential energy surface. This requires locating the index-1 saddle point, commonly
referred to as a transition state, that separates two neighboring energy minima. In
modeling the evolution of an atomic system, it is desirable to find all the relevant transitions surrounding the current minimum. Due to the large number of minima on the
potential energy surface, exhaustively searching the landscape for these saddle points
is a challenging task. In examining the particular case of isolated Lennard-Jones clusters of around 50 particles, we observe very slow convergence of the total number of
saddle points found as a function of successful searches. We seek to understand this
behavior by modeling the distribution of successful searches and sampling this distribution to create a stochastic process that mimics this behavior. Finally, we will discuss
an improvement to a rejection scheme for OLKMC where we terminate searches that
appear to be failing early in the search process.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2020-0211},
url = {http://global-sci.org/intro/article_detail/cicp/19309.html}
}