Abstract
<p style='text-indent:20px;'>Searching saddle points on the potential energy surface is a challenging problem in the rare event. When there exist multiple saddle points, sampling different initial guesses are needed in local search methods in order to find distinct saddle points. In this paper, we present a novel global optimization-based dimer method (GOD) to efficiently search saddle points by coupling ant colony optimization (ACO) algorithm with optimization-based shrinking dimer (OSD) method. In particular, we apply OSD method as a local search algorithm for saddle points and construct a pheromone function in ACO to update the global population. By applying a two-dimensional example and a benchmark problem of seven-atom island on the (111) surface of an FCC crystal, we demonstrate that GOD shows a significant improvement in computational efficiency compared with OSD method. Our algorithm is the first try to apply the global optimization technique in searching saddle points and it offers a new framework to open up possibilities of adopting other global optimization methods.
Highlights
Saddle point search on the potential energy surface has attracted great attention over last two decades
We propose a novel global optimizationbased dimer method (GOD) algorithm for searching index-1 saddle points on the potential energy surface
This algorithm is a combination of modified ant colony optimization (ACO) algorithm with optimization-based shrinking dimer (OSD) method
Summary
Saddle point search on the potential energy surface has attracted great attention over last two decades. Abundant studies have focused on development of numerical methods of saddle point search If both initial and final states are available, path-finding methods are often used to compute the minimum energy path. To improve the computational efficiency, optimization algorithms are often applied to speed up the saddle point search [23, 24, 25]. When there exist multiple saddle points, sampling different initial guesses are needed in order to find distinct saddle points It remains unclear whether we can use global optimization algorithms to search unstable saddle points instead of stable minima on the potential energy surface. We develop a new global optimization-based dimer (GOD) method by combining modified ACO algorithm with OSD method to search the index-1 saddle points.
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