An effective Simulated Annealing-based Mathematical Optimization Algorithm for Minimizing the Lennard-Jones Potential

The Lennard-Jones (LJ) Potential Energy Problem is to construct the most stable form of N atoms of a molecule with the minimal LJ potential energy. This problem has a simple mathematical form Minimize f(x) =4 Sigma(i=1) Sigma(j=1,j<i) (1/tau(6)(ij) - 1/tau(3)(ij)) subject to x is an element of R-n. Where tau(ij) = (x(3i-2) - x(3j-2))(2) + (x(3i-1) - x(3j-1))(2) + (x(3i) - x(3j))(2), (x(3i-2), x(3i-1), x(3i)) is the coordinates ofatom, N >= 2. This paper is to minimize the L-J potential f(x) on R-n,where n = 3N. however it is a challenging and diffcult problem for many optimization methods when N is larger. This paper presents an effective mathematical optimization algorithm for minimizing the LJ Potential and a series of elegant optimal solutions of atoms up to 310 were got.