Examining Saddle Point Searches in the Context of Off-Lattice Kinetic Monte Carlo (Communications in Computational Physics, 2021)
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 toTransition State Theory, in which the rate of rare transitions from one energy minimum to a neighboring minimum scales exponentially with an energy barrier on thepotential energy surface. This requires locating the index-1 saddle point, commonlyreferred to as a transition state, that separates two neighboring energy minima. Inmodeling 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 thepotential energy surface, exhaustively searching the landscape for these saddle pointsis 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 ofsaddle points found as a function of successful searches. We seek to understand thisbehavior by modeling the distribution of successful searches and sampling this distribution to create a stochastic process that mimics this behavior. Finally, we will discussan improvement to a rejection scheme for OLKMC where we terminate searches thatappear to be failing early in the search process.
Keywords: Off-lattice kinetic Monte Carlo; energy landscape; saddle point search; dimer method; Lennard-Jones clusters.