A note on the application of the "Boltzmann simplex"-simulated annealing algorithm to global optimizations of argon and water clusters

Francis M. Torres, Eugene Agichtein, Leonid Grinberg, Guowei Yu, Robert Q. Topper^*

Department of Chemistry, The Cooper Union for the Advancement of Science and Art, Albert Nerken School of Engineering, 51 Astor Place, New York, NY 10003

Abstract

We report our application of a recently published simulated annealing algorithm which we call "Boltzmann simplex"-simulated annealing (BSSA) to global optimizations of argon and water clusters. The Lennard-Jones model of argon clusters serves as a challenging benchmark for global optimization methods, and we use it as a test case. We find that the BSSA method is most useful when followed by a local optimization via the Powell method. This is because the Powell method quenches to the equilibrium geometry more effectively than a downhill simplex, which is the zero-temperature limit of the BSSA algorithm. We also find that very slow annealing rates are required to achieve acceptable results. A study of small water clusters [(H₂O)_m, m=2-6] using a recently published flexible-monomer interaction potential yields ringlike structures, in good agreement with other theoretical and experimental studies, for m=2-5. A highly puckered ring structure is obtained for m=6.

^*Corresponding author. Email address: topper@cooper.edu.