Pivot method for global optimization: A study of structures and phase changes in water clusters

In this thesis, we have carried out a study of water clusters. The research work has been developed in two stages. In the first stage, we have investigated the properties of water clusters at zero temperature by means of global optimization. The clusters were modeled by using two well known pairwise potentials having distinct characteristics. One is the Matsuoka-Clementi-Yoshimine potential (MCY) that is an ab initio fitted function based on a rigid-molecule model, the other is the Sillinger-Rahman potential (SR) which is an empirical function based on a flexible-molecule model. The algorithm used for the global optimization of the clusters was the pivot method, which was developed in our group. The results have shown that, under certain conditions, the pivot method may yield optimized structures which are related to one another in such a way that they seem to form structural families. The structures in a family can be thought of as formed from the aggregation of single units. The particular types of structures we have found are quasi-one dimensional tubes built from stacking cyclic units such as tetramers, pentamers, and hexamers. The binding energies of these tubes form sequences that span smooth curves with clear asymptotic behavior; therefore, we have also studied the sequences applying the Bulirsch-Stoer (BST) algorithm to accelerate convergence. In the second stage of the research work, we have studied the thermodynamic properties of a typical water cluster at finite temperatures. The selected cluster was the water octamer which exhibits a definite solid-liquid phase change. The water octamer also has several low lying energy cubic structures with large energetic barriers that cause ergodicity breaking in regular Monte Carlo simulations. For that reason we have simulated the octamer using paralell tempering Monte Carlo combined with the multihistogram method. This has permited us to calculate the heat capacity from very low temperatures up to T = 230 K. We have found the melting temperature to be 178.5 K. In addition, we have been able to estimate at 12 K the onset temperature of a solid-solid phase change between the two lowest energy lying isomers