Global optimization analysis of water clusters (H2O)n (11⩽n⩽13) through a genetic evolutionary approach

Abstract

The structures and stabilities of water clusters (H2O)n with 11⩽n⩽13 are determined by a genetic algorithm approach with two new evolutionary operators—namely annihilator and history operators. These studies show that the modified genetic algorithm provides an efficient procedure for calculating global minima with an especial attention to molecular water clusters. The actual results are in quantitative agreement with previous calculations using the basin hopping Monte Carlo method.

The thermodynamic and ground state properties of the TIP4P water octamer

“…͑2͒, we use the trapezoid rule with N = k m + 1 points, and we evaluate the Hessian metric tensor and the potential at the end point of every interval u j = j / N. The end point choice yields a constant curvature for the quantum Jacobian that we can simply ignore. 18 Additionally, we can ignore the difference between the Jacobian obtained from the manifold and the Jacobian obtained in R 9n , with infinitely stiff springs replacing the holonomic constraints, 115 since their ratio is a constant. 70 To implement the Metropolis algorithm, we move the center of mass or the orientation of a randomly selected molecule, and we translate one path variable for each coordinate moved, e.g.,…”

Growth analysis of sodium-potassium alloy clusters from 7 to 55 atoms through a genetic algorithm approach

“…The evolutionary procedure starts all over again and the whole cycle is iterated until no better solution is encountered after a predetermined number of cycles. This approach has shown to yield improved results for systems of water clusters and metallic nanoalloys of gold and copper [28,29].…”

“…As the clusters grow, the number of local minima on the associated potential energy surface drastically increases, and seeking for the global one becomes much more laborious. In order to thoroughly explore the potential energy surface generated by the empirical potential just described, two different operators were added to the standard GA procedure, the history (HO) and the annihilator (AO) operators [28,29]. Within this approach, for a given cluster size and composition, an initial population of a chosen fixed number of trial solutions is randomly generated (by randomly generating the coordinates of each atom within a given interval).…”

“…We approach such task employing a genetic algorithm that, besides the standard evolutionary procedure, makes use of two different operators, the history and the annihilator operators [28].…”

Island models for cluster geometry optimization: how design options impact effectiveness and diversity

“…Floating point representation was first introduced in CGO by Zeiri [85] and soon became a widely preferred alternative [17,20,33,40,58], mostly because it allows non-discrete continuous positioning of particles. Advantages include increased precision and the ability to apply genetic operators that take into account properties of cluster geometry in a more convenient way and without the need of converting genes to atomic coordinates.…”