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+Arn
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