Basin hopping method

Abstract. We present a quantum-classieal determination of stable isomers of Na Arii clusters with an electronically excited sodium atom in 3p P states. The excited states of Na perturbed by the argon atoms are obtained as the eigenfunctions of a single-electron operator describing the electron in the field of a Na Arn core, the Na and Ar atoms being substituted by pseudo-potentials. These pseudo-potentials include core-polarization operators to account for polarization and correlation of the inert part with the excited electron . The geometry optimization of the excited states is carried out via the basin-hopping method of Wales et al. The present study confirms the trend for small Na Arn clusters in 3p states to form planar structures, as proposed earlier by Tutein and Mayne within the framework of a first order perturbation theory on a "Diatomics in Molecules" type model. 

In order to determine the structures of total-energy minima we used the basin-hopping method. For the binary clusters the additional existence of so-called homotops increases the computational demands enormously. Homotops for, e.g., clusters are defined as clusters with the same size, composition and geometric arrangement, differing only in the way in which A and B-type atoms are arranged. Their number for the ApB cluster equals... 

In some studies we used instead the basin-hopping method (Li and Scheraga 1987 Wales and Doey 1997) to determine the structures of total-energy minima. This method is closely related to the Monte Carlo methods, but considers a transformed total-energy surface. Thus,... 

Figure 3. Energy vs. RMSB plot for the final energies of the twenty basin hopping simulations described in the text (diamonds). For comparison we also indicate the best energy result for the STUN method (circle) and for the thirty processor PT simulation (square).

An improved parallel evolutionary algorithm [84] and basin hopping combined with vibrational modes [50] are examples of successful approaches to the problem of global optimization of water clusters. However, these methods are not able to find the lowest energy geometry for systems with more than 30 water molecules. A detailed comparison of results for each cluster size can be found in our publication that describes an application of minima hopping to water clusters [41]. 

---