Comparison of line search minimization algorithms for exploring topography of multidimensional potential energy surfaces: Mg+Arn case

The most robust numerical algorithms for unconstrained optimization that involve a line search are tested in the problem of locating stable structures and transition states of atomic microclusters. Specifically, the popular quenching technique is compared with conjugate gradient and variable metric algorithms in the Mg⁺Ar_n clusters. It is found that the variable metric method BFGS combined with an approximate line minimization routine is the most efficient, and it shows global convergence properties. This technique is applied to find a few hundred stationary points of Mg⁺Ar₁₂ and to locate isomerization paths between the two most stable icosahedral structures found for Mg⁺Ar₁₂. The latter correspond to a solvated and a nonsolvated ion, respectively. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 :1011–1022, 1997