Global optimization for molecular conformation problems

A primal-relaxed dual global optimization algorithm is presented along with an extensive review for finding the global minimum energy configurations of microclusters composed by particles interacting with any type of two-body central forces. First, the original nonconvex expression for the total potential energy is transformed to the difference of two convex functions (DC transformation) via an eigenvalue analysis performed for each pair potential that constitutes the total potential energy function. Then, a decomposition strategy based on the GOP algorithm [1-4] is designed to provide tight upper and lower bounds on the global minimum through the solutions of a sequence of relaxed dual subproblems. A number of theoretical results are included which expedite the computational effort by exploiting the special mathematical structure of the problem. The proposed approach attains ε-convergence to the global minimum in a finite number of iterations. Based on this procedure global optimum solutions are generated for small Lennard-Jones and Morse (a=3) microclusters n≤7. For larger clusters (8≤N≤24 for Lennard-Jones and 8≤N≤30 for Morse), tight lower and upper bounds on the global solution are provided which serve as excellent initial points for local optimization approaches.