A dynamic lattice searching method with constructed core for optimization of large Lennard-Jones clusters

A variation of the previous dynamic lattice searching (DLS) method, named as DLS with constructed core (DLSc), was proposed for structural optimization of Lennard-Jones (LJ) clusters. In the new method, the starting random structure is generated with an icosahedron or a decahedron as a core. For a cluster with n shells, the atoms in the inner n - 2 shells are set as a fixed core, and the remaining atoms in the outer 2 shells are optimized by DLS. With applications of DLSc to optimization of LJ100-200 and LJ660-670, it was found that all the putative global minima can be obtained by using the DLSc method, and the method was proved to be high efficient compared with the previous DLS, because the searching space is reduced by the use of the fixed core. However, although DLSc is still an unbiased approach for smaller LJ clusters, it turned out to be biased for large ones. Further works are still needed to make it to be a more general method for cluster optimization problem.     

A dynamic lattice searching method with interior operation for unbiased optimization of large Lennard-Jones clusters

For improving the efficiency of dynamic lattice searching (DLS) method for unbiased optimization of large Lennard-Jones (LJ) clusters, a variant of the interior operation (IO) proposed by Takeuchi was combined with DLS. The method is named as DLS-IO. In the method, the IO moves outer atoms with higher energy toward the coordinates center, i.e., (0, 0, 0), of a cluster and a local minimization (LM) follows each IO. This makes the interior atoms more compact and the outer atoms more uniformly distributed with lower potential energy. Therefore, the starting structure for DLS operations is closer to the global optimum compared with the randomly generated structures. On the other hand, a method to identify the central atom is proposed for the central vacancy problem. Optimizations of LJ(500), LJ(561), LJ(660), LJ(665), and LJ(670) were investigated with the DLS-IO, and the structural transition during the optimization was analyzed. It was found that the method is efficient and unbiased for optimization of large LJ clusters, and it may be a promising approach to be universally used for structural optimizations.     

A dynamic lattice searching method for fast optimization of Lennard-Jones clusters

A highly efficient unbiased global optimization method called dynamic lattice searching (DLS) was proposed. The method starts with a randomly generated local minimum, and finds better solution by a circulation of construction and searching of the dynamic lattice (DL) until the better solution approaches the best solution. The DL is constructed adaptively based on the starting local minimum by searching the possible location sites for an added atom, and the DL searching is implemented by iteratively moving the atom located at the occupied lattice site with the highest energy to the vacant lattice site with the lowest energy. Because the DL can greatly reduce the searching space and the number of the time-consuming local minimization procedures, the proposed DLS method runs at a very high efficiency, especially for the clusters of larger size. The performance of the DLS is investigated in the optimization of Lennard-Jones (LJ) clusters up to 309 atoms, and the structure of the LJ(500) is also predicted. Furthermore, the idea of dynamic lattice can be easily adopted in the optimization of other molecular or atomic clusters. It may be a promising approach to be universally used for structural optimizations in the chemistry field.     

A conformational analysis method for understanding the energy landscapes of clusters.

A newly developed unbiased structural optimization method, named dynamic lattice searching (DLS), is proposed as an approach for conformational analysis of atomic/molecular clusters and used in understanding the energy landscape of large clusters. The structures of clusters are described in terms of the number of basic tetrahedron (BT) units they contain. We found that the hit numbers of different structural motifs in DLS runs is proportional to the number of BTs. A parameter T(max) is defined to limit the maximal number of atoms moved in a structural transition. Results show that T(max) is a key parameter for modulating the efficiency of the DLS method and has a great influence on the hit number of different motifs in DLS runs. Finally, the effect of potential range on the conformational distribution of the (Morse)(98) cluster is also discussed with different potential-range parameters.     

Geometry optimization and conformational analysis of (C60)N clusters using a dynamic lattice-searching method.

A newly developed unbiased global optimization method, named dynamic lattice searching (DLS), is used to locate putative global minima for all (C6O)N clusters with Girifalco potential up to N=150. A simple greedy strategy is adopted for the basic frame, so DLS has a very high convergence speed and may converge at various configurations. As most structures are packed by basic tetrahedra, some sequences are defined by both configurations and the size of the basic tetrahedra. A sequence-based conformational analysis is carried out with the defined sequences by counting the hit number over 10,000 independent DLS runs for all the cases up to N = 5. It was found that the hit rate of a sequence is related to the size of the basic tetrahedra. U.e of this method proved that the Leary tetrahedral sequence is dominant in a certain range of cluster sizes, although the sequence has no potential energy advantage. The calculation results are also consistent with those of annealing experiments at high temperature, both in magic numbers and height of the peaks in the mass spectrum.     

Evaluation of stochastic global optimization methods for modeling vapor–liquid equilibrium data

Parameter estimation for vapor–liquid equilibrium (VLE) data modeling plays an important role in design, optimization and control of separation units. This optimization problem is very challenging due to the high non-linearity of thermodynamic models. Recently, several stochastic optimization methods such as Differential Evolution with Tabu List (DETL) and Particle Swarm Optimization (PSO) have evolved as alternative and reliable strategies for solving global optimization problems including parameter estimation in thermodynamic models. However, these methods have not been applied and compared with respect to other stochastic strategies such as Simulated Annealing (SA), Differential Evolution (DE) and Genetic Algorithm (GA) in the context of parameter estimation for VLE data modeling. Therefore, in this study several stochastic optimization methods are applied to solve parameter estimation problems for VLE modeling using both the classical least squares and maximum likelihood approaches. Specifically, we have tested and compared the reliability and efficiency of SA, GA, DE, DETL and PSO for modeling several binary VLE data using local composition models. These methods were also tested on benchmark problems for global optimization. Our results show that the effectiveness of these stochastic methods varies significantly between the different tested problems and also depends on the stopping criterion especially for SA, GA and PSO. Overall, DE and DETL have better performance for solving the parameter estimation problems in VLE data modeling.     

Novel lattice-searching method for modeling the optimal strain-free close-packed isomers of clusters

Small icosahedral, decahedral, and fcc structures have been studied by unbiased global optimization methods or Wulff construction and Northby lattice methods. Strain-free close-packed structures are not much discussed because the structures are very difficult to optimize and there is no common strain-free close-packed lattice. We propose a new strategy to construct such a lattice containing all possible strain-free close-packed isomers, and by searching the lattice with an efficient method the optimal close-packed structures were modeled. Testing with the Morse potential at rho0=14.0 for cluster size 10相似文献   

Novel bare-bones particle swarm optimization and its performance for modeling vapor-liquid equilibrium data

Parameter estimation in models plays a significant role in developing mathematical models which are used for understanding and analyzing physical, chemical and biological systems. Parameter estimation problems for vapor-liquid equilibrium (VLE) data modeling are very challenging due to the high non-linearity of thermodynamic models. Recently, stochastic global optimizations and their applications to these problems have attracted greater interest. Of the many stochastic global optimization methods, Bare-bones particle swarm optimization (BBPSO) is attractive since it has no parameters to be tuned by the user. In this study, modifications are introduced to the original BBPSO using mutation and crossover operators of differential evolution algorithm to update certain particles in the population. The performance of the resulting algorithm is tested on 10 benchmark functions and applied to 16 VLE problems. The performance of the proposed BBPSO for VLE modeling is compared with that of other stochastic algorithms, namely, differential evolution (DE), DE with tabu list, genetic algorithm and simulated annealing in order to identify their relative strengths for VLE data modeling. The proposed BBPSO is shown to be better than or comparable to the other stochastic global optimization algorithms tested for parameter estimation in modeling VLE data.     

PDECO: Parallel differential evolution for clusters optimization

The optimization of the atomic and molecular clusters with a large number of atoms is a very challenging topic. This article proposes a parallel differential evolution (DE) optimization scheme for large‐scale clusters. It combines a modified DE algorithm with improved genetic operators and a parallel strategy with a migration operator to address the problems of numerous local optima and large computational demanding. Results of Lennard–Jones (LJ) clusters and Gupta‐potential Co clusters show the performance of the algorithm surpasses those in previous researches in terms of successful rate, convergent speed, and global searching ability. The overall performance for large or challenging LJ clusters is enhanced significantly. The average number of local minimizations per hit of the global minima for Co clusters is only about 3–4% of that in previous methods. Some global optima for Co are also updated. We then apply the algorithm to optimize the Pt clusters with Gupta potential from the size 3 to 130 and analyze their electronic properties by density functional theory calculation. The clusters with 13, 38, 54, 75, 108, and 125 atoms are extremely stable and can be taken as the magic numbers for Pt systems. It is interesting that the more stable structures, especially magic‐number ones, tend to have a larger energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital. It is also found that the clusters are gradually close to the metal bulk from the size N > 80 and Pt₃₈ is expected to be more active than Pt₇₅ in catalytic reaction. © 2013 Wiley Periodicals, Inc.     

Size‐guided multi‐seed heuristic method for geometry optimization of clusters: Application to benzene clusters

Since searching for the global minimum on the potential energy surface of a cluster is very difficult, many geometry optimization methods have been proposed, in which initial geometries are randomly generated and subsequently improved with different algorithms. In this study, a size‐guided multi‐seed heuristic method is developed and applied to benzene clusters. It produces initial configurations of the cluster with n molecules from the lowest‐energy configurations of the cluster with n − 1 molecules (seeds). The initial geometries are further optimized with the geometrical perturbations previously used for molecular clusters. These steps are repeated until the size n satisfies a predefined one. The method locates putative global minima of benzene clusters with up to 65 molecules. The performance of the method is discussed using the computational cost, rates to locate the global minima, and energies of initial geometries. © 2018 Wiley Periodicals, Inc.     

Geometry optimization of atomic clusters using a heuristic method with dynamic lattice searching

In this paper, a global optimization method is presented to determine the global-minimum structures of atomic clusters, where several already existing techniques are combined, such as the dynamic lattice searching method and two-phase local minimization method. The present method is applied to some selected large-sized Lennard-Jones (LJ) clusters and silver clusters described by the Gupta potential in the size range N = 13-140 and 300. Comparison with the results reported in the literature shows that the method is highly efficient and a lot of new global minima missed in previous papers are found for the silver clusters. The method may be a promising tool for the theoretical determination of ground-state structure of atomic clusters. Additionally, the stabilities of silver clusters are also analyzed and it is found that in the size range N = 13-140 there exist 12 particularly stable clusters.     

An adaptive immune optimization algorithm for energy minimization problems

Based on the immune theory of biology, a novel evolutionary algorithm, adaptive immune optimization algorithm (AIOA), is proposed. In AIOA, density regulation and immune selection is adopted to control the individual diversity and the convergence adaptively. By an application of the algorithm to the optimization of test functions, it is shown that the algorithm is a highly efficient optimization method compared with other stochastic optimization methods. The algorithm was also applied to the optimization of Lennard-Jones clusters, and the results show that the method can find the optimal structure of N相似文献   

Predicting structural models for silicon clusters

This article introduces an efficient method to generate structural models for medium-sized silicon clusters. Geometrical information obtained from previous investigations of small clusters is initially sorted and then introduced into our predictor algorithm in order to generate structural models for large clusters. The method predicts geometries whose binding energies are close (95%) to the corresponding value for the ground-state with very low computational cost. These predictions can be used as a very good initial guess for any global optimization algorithm. As a test case, information from clusters up to 14 atoms was used to predict good models for silicon clusters up to 20 atoms. We believe that the new algorithm may enhance the performance of most optimization methods whenever some previous information is available.     

A fast annealing evolutionary algorithm for global optimization

By combining the aspect of population in genetic algorithms (GAs) and the simulated annealing algorithm (SAA), a novel algorithm, called fast annealing evolutionary algorithm (FAEA), is proposed. The algorithm is similar to the annealing evolutionary algorithm (AEA), and a very fast annealing technique is adopted for the annealing procedure. By an application of the algorithm to the optimization of test functions and a comparison of the algorithm with other stochastic optimization methods, it is shown that the algorithm is a highly efficient optimization method. It was also applied in optimization of Lennard-Jones clusters and compared with other methods in this study. The results indicate that the algorithm is a good tool for the energy minimization problem.     

The elastic net algorithm and protein structure prediction

Predicting protein structures from their amino acid sequences is a problem of global optimization. Global optima (native structures) are often sought using stochastic sampling methods such as Monte Carlo or molecular dynamics, but these methods are slow. In contrast, there are fast deterministic methods that find near-optimal solutions of well-known global optimization problems such as the traveling salesman problem (TSP). But fast TSP strategies have yet to be applied to protein folding, because of fundamental differences in the two types of problems. Here, we show how protein folding can be framed in terms of the TSP, to which we apply a variation of the Durbin-Willshaw elastic net optimization strategy. We illustrate using a simple model of proteins with database-derived statistical potentials and predicted secondary structure restraints. This optimization strategy can be applied to many different models and potential functions, and can readily incorporate experimental restraint information. It is also fast; with the simple model used here, the method finds structures that are within 5-6 A all-Calpha-atom RMSD of the known native structures for 40-mers in about 8 s on a PC; 100-mers take about 20 s. The computer time tau scales as tau approximately n, where n is the number of amino acids. This method may prove to be useful for structure refinement and prediction.     

Lennard-Jones团簇最低能量构型的预测

针对Lennard-Jones(LJ)团簇的结构优化问题,在前人工作的基础上,提出了一个新的无偏优化算法,即DLS-TPIO(dynamic lattice searching method with two-phase local searchand interior operation)算法.对LJ2-650,LJ660,LJ665-680这666个实例进行了优化计算.为其中每个实例所找到的构型其势能均达到了剑桥团簇数据库中公布的最好记录.对LJ533与LJ536这两个算例,所达到的势能则优于先前的最好记录.在DLS-TPIO算法中,采用了内部操作,两阶段局部搜索方法以及动态格点搜索方法.在优化的前一阶段,内部操作将若干能量较高的表面原子移入团簇的内部,从而降低团簇的能量,并使其构型逐渐地变为有序.与此同时,两阶段局部搜索方法指导搜索进入更有希望的构型区域.这种做法显著地提高了算法的成功率.在优化的后一阶段,借用动态格点搜索方法对团簇表面原子的位置作进一步优化,以再一次降低团簇的能量.另外,为识别二十面体构型的中心原子,本文给出了一个简单的新方法.相比于文献中一些著名的无偏优化算法,DLS-TPIO算法具...     

Pharmacophore alignment search tool: influence of scoring systems on text-based similarity searching

The text-based similarity searching method Pharmacophore Alignment Search Tool is grounded on pairwise comparisons of potential pharmacophoric points between a query and screening compounds. The underlying scoring matrix is of critical importance for successful virtual screening and hit retrieval from large compound libraries. Here, we compare three conceptually different computational methods for systematic deduction of scoring matrices: assignment-based, alignment-based, and stochastic optimization. All three methods resulted in optimized pharmacophore scoring matrices with significantly superior retrospective performance in comparison with simplistic scoring schemes. Computer-generated similarity matrices of pharmacophoric features turned out to agree well with a manually constructed matrix. We introduce the concept of position-specific scoring to text-based similarity searching so that knowledge about specific ligand-receptor binding patterns can be included and demonstrate its benefit for hit retrieval. The approach was also used for automated pharmacophore elucidation in agonists of peroxisome proliferator activated receptor gamma, successfully identifying key interactions for receptor activation.     

一种四臂聚苯乙烯凝胶的激光光散射研究

采用原子转移自由基方法(ATRP)合成窄分布的末端基为巯基的四臂星型聚苯乙烯(4-PS-SH).巯基容易被空气中的氧气氧化生成二硫键,会引起四臂星型聚苯乙烯分子间交联.利用激光光散射研究了四臂聚苯乙烯在亚浓溶液中氧化交联生成大的胶束进而生成宏观化学凝胶的过程.静态激光光散射测量结果表明四臂聚苯乙烯亚浓溶液以及凝胶样品的时间平均散射光强不随测量位置的变化而涨落,说明此凝胶是结构均一的化学凝胶.动态光散射结果表明在四臂聚苯乙烯亚浓溶液氧化生成凝胶的过程中,动态强度-强度时间相关函数的慢运动衰减的贡献最初随着氧化时间的增加逐渐增强,当氧化反应进行到一定程度时慢运动的贡献又逐渐减弱,最终慢运动消失.生成的化学凝胶的相关函数与最初亚浓溶液的相关函数几乎重合.静态和动态激光光散射结果表明生成的四臂聚苯乙烯凝胶是结构均匀的化学凝胶.     

Structural variation of silver clusters from Ag13 to Ag160

The structures of silver clusters from Ag(121) to Ag(160) were optimized with a modified dynamic lattice searching (DLS) method, named as DLS with constructed core (DLSc). The interaction among silver atoms is modeled by the Gupta potential. Structural characteristic of silver clusters with the growth of cluster size is investigated with the newly optimized structures and our previous results from Ag(13) to Ag(120). A set of amorphous structures was obtained in the size range of 13-48, together with several ordered structures. The putative stable motif is an icosahedron from Ag(49) to Ag(61) and then changes to a decahedron in the size range of 62-160. Some of the results are consistent with experiments. Furthermore, it was also found that, for clusters with decahedral motif, the stable structure is a result of the competition among the different Marks decahedral motifs. On the other hand, different from the Lennard-Jones cluster, there are some silver clusters with the face-centered cubic (fcc) motif in the size range of 13-160. But the fcc motif can only be obtained for some specific sizes.     

Monte Carlo temperature basin paving with effective fragment potential: an efficient and fast method for finding low-energy structures of water clusters (H2O)20 and (H2O)25

Determining low-energy structures of large water clusters is a challenge for any optimization algorithm. In this work, we have developed a new Monte Carlo (MC)-based method, temperature basin paving (TBP), which is related to the well-known basin hopping method. In the TBP method, the Boltzmann weight factor used in MC methods is dynamically modified based on the history of the simulation. The states that are visited more are given a lower probability by increasing their temperatures and vice versa. This allows faster escapes from the states frequently visited in the simulation. We have used the TBP method to find a large number of low-energy minima of water clusters of size 20 and 25. We have found structures energetically same to the global minimum structures known for these two clusters. We have compared the efficiency of this method to the basin-hopping method and found that it can locate the minima faster. Statistical efficiency of the new method has been investigated by running a large number of trajectories. The new method can locate low-energy structures of both the clusters faster than some of the reported algorithms for water clusters and can switch between high energy and low-energy structures multiple times in a simulation illustrating its efficiency. The large number of minima obtained from the simulations is used to get both general and specific features of the minima. The distribution of minima for these two clusters based on the similarity of their oxygen frames shows that the (H(2)O)(20) can have different variety of structures, but for (H(2)O)(25), low-energy structures are mostly cagelike. Several (H(2)O)(25) structures are found with similar energy but with different cage architectures. Noncage structures of (H(2)O)(25) are also found but they are 6-7 kcal/mol higher in energy from the global minimum. The TBP method is likely to play an important role for exploring the complex energy landscape of large molecules.