Algorithm based on the Thomson problem for determination of equilibrium structures of metal nanoclusters

A new algorithm for the determination of equilibrium structures suitable for metal nanoclusters is proposed. The algorithm performs a stochastic search of the minima associated with the nuclear potential energy function restricted to a sphere (similar to the Thomson problem), in order to guess configurations of the nuclear positions. Subsequently, the guessed configurations are further optimized driven by the total energy function using the conventional gradient descent method. This methodology is equivalent to using the valence shell electron pair repulsion model in guessing initial configurations in the traditional molecular quantum chemistry. The framework is illustrated in several clusters of increasing complexity: Cu₇, Cu₉, and Cu₁₁ as benchmark systems, and Cu₃₈ and Ni₉ as novel systems. New equilibrium structures for Cu₉, Cu₁₁, Cu₃₈, and Ni₉ are reported.