Heuristic Optimization Of The Binary-morse Cluster

The main purpose of the optimization of atomic and molecular clusters is to optimize the geometry. The cluster will present the different physical and chemical properties according to the different locations of the atoms or molecules. And these properties also change along with the number of different atoms and molecules in the cluster. Therefore, it is of great importance to optimize and solve the stable configuration of the clusters in the area of cluster research.Many methods are applied to describe the cluster in cluster theory research. Usually the empirical potential energy model was adopted to describe the interactions between atoms or molecules. The construction of potential model refers to a group of analytical expressions with parameters to describe the interaction between atoms. We usually aim to figure out the corresponding minimum value of the energy function to obtain the global optimal configuration of clusters. However, the spatial configurations of clusters increase rapidly with the growth of cluster size. And it has been proved to be NP-hard problem. And for the NP-hard problem, previous studies have shown that it is not likely to exist an accurate algorithm within polynomial time. Therefore, the focus of our research is to design an efficient heuristic algorithm to solve the optimization problem of cluster configuration.Morse cluster potential is a simple pair potential, with only one parameter. And this parameter determines the width of the potential well. It can be used to construct models of various atomic materials. It can also be used as an algorithm of global optimization to evaluate some very strict testing systems. Binary Morse cluster and Single Morse clusters have a different place is that the former consists of two types of atoms. So the configuration of Binary Morse cluster is more diverse than the Single Morse cluster. And the difficulty of Binary Morse cluster theoretical research is relatively much higher.For Single Morse cluster, we use dynamic lattice algorithm. The main procedure of this algorithm is to initialize a cluster pattern, and then use the quasi Newton algorithm converges rapidly to obtain a local optimal result, and then use the traditional dynamic lattice search algorithm to jump out of the local value of looking for a lower energy configuration. In the final stage of the algorithm, we make some improvement on the dynamic lattice algorithm. We add the algorithm of operation on the surface, which is a more sophisticated global disturbance based on dynamic lattice algorithm. The experimental data show that the surface operation algorithm based on dynamic lattice algorithm can often be useful to get a reduced cluster potential energy, and get a better configuration. After calculation, the results of the algorithm to calculate the coefficients in the material for 3, atomic number is 5-80 and 147 of the cluster potential value can quickly reach Cambridge database records above the minimum value. This proves that the global optimal configuration of the algorithm of Morse cluster is highly efficient and stable.Binary Morse cluster is constituted by two kinds of different atom. Due to the presence of isomers in a binary cluster, the structural optimization problem is related to the continuous optimization and discrete optimization. Continuous optimization of the objective is to find the optimal configuration of the cluster, while discrete optimization is to find the best distribution position of the two kinds of atom on the basis of continuous optimization. For Binary Morse cluster characteristics, we increased an exchange algorithm based on the Single Morse clusters optimization algorithm. The exchange algorithm means that, we make two kinds of atoms in a number of high energy atomic position exchanged based on the optimal configuration of the cluster. The experimental data show that, in the use of the exchange algorithm, clusters tend to further reduce the potential. And it can always find a better configuration. We use the improved algorithm of dynamic lattice plus exchange algorithm to get the optimal configuration of the cluster, of which the coefficient of atoms are 5 and 7 respectively,and the total atom number is 38. There was no record of the lowest energy presented on the academic literature about the Binary Morse clusters demestic or abroad by now.