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...     

Global optimization of Lennard-Jones clusters by a parallel fast annealing evolutionary algorithm

A parallel fast annealing evolutionary algorithm (PFAEA) was presented and applied to optimize Lennard-Jones (LJ) clusters. All the lowest known minima up to LJ(116) with both icosahedral and nonicosahedral structure, including the truncated octahedron of LJ(38), central fcc tetrahedron of LJ(98), the Marks' decahedron of LJ(75)(-)(77), and LJ(102)(-)(104), were located successfully by the unbiased algorithm. PFAEA is a parallel version of fast annealing evolutionary algorithm (FAEA) that combines the aspect of population in genetic algorithm and annealing algorithm with a very fast annealing schedule. A master-slave paradigm is used to parallelize FAEA to improve the efficiency. The performance of PFAEA is studied, and the scaling of execution time with the cluster size is approximately cubic, which is important for larger scale energy minimization systems.     

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.     

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.     

Clever and efficient method for searching optimal geometries of lennard-jones clusters

An unbiased algorithm for determining global minima of Lennard-Jones (LJ) clusters is proposed in the present study. In the algorithm, a global minimum is searched by using two operators: one modifies a cluster configuration by moving atoms to the most stable positions on the surface of a cluster and the other gives a perturbation on a cluster configuration by moving atoms near the center of mass of a cluster. The moved atoms are selected by employing contribution of the atoms to the potential energy of a cluster. It was possible to find new global minima for LJ506, LJ521, LJ536, LJ537, LJ538, and LJ541 together with putative global minima of LJ clusters of 10-561 atoms reported in the literature. This indicates that the present method is clever and efficient for cluster geometry optimization.     

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 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.     

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.     

All-exchanges parallel tempering

An alternative exchange strategy for parallel tempering simulations is introduced. Instead of attempting to swap configurations between two randomly chosen but adjacent replicas, the acceptance probabilities of all possible swap moves are calculated a priori. One specific swap move is then selected according to its probability and enforced. The efficiency of the method is illustrated first on the case of two Lennard-Jones (LJ) clusters containing 13 and 31 atoms, respectively. The convergence of the caloric curve is seen to be at least twice as fast as in conventional parallel tempering simulations, especially for the difficult case of LJ31. Further evidence for an improved efficiency is reported on the ergodic measure introduced by Mountain and Thirumalai [J. Phys. Chem. 93, 6975 (1989)], calculated here for LJ13 close to the melting point. Finally, tests on two simple spin systems indicate that the method should be particularly useful when a limited number of replicas are available.     

Geometry optimizations of benzene clusters using a modified genetic algorithm

A modified genetic algorithm with real-number coding, non-uniform mutation and arithmetical crossover operators was described in this paper. A local minimization was used to improve the final solution obtained by the genetic algorithm. Using the exp-6-1 interatomic energy function, the modified genetic algorithm with local minimization (MGALM) was applied to the geometry optimization problem of small benzene clusters (C6H6)N(N = 2-7) to obtain the global minimum energy structures. MGALM is simple but the structures optimized are comparable to the published results obtained by parallel genetic algorithms.     

Global minimum structure searches via particle swarm optimization

Novel implementation of the evolutionary approach known as particle swarm optimization (PSO) capable of finding the global minimum of the potential energy surface of atomic assemblies is reported. This is the first time the PSO technique has been used to perform global optimization of minimum structure search for chemical systems. Significant improvements have been introduced to the original PSO algorithm to increase its efficiency and reliability and adapt it to chemical systems. The developed software has successfully found the lowest-energy structures of the LJ(26) Lennard-Jones cluster, anionic silicon hydride Si(2)H(5) (-), and triply hydrated hydroxide ion OH(-) (H(2)O)(3). It requires relatively small population sizes and demonstrates fast convergence. Efficiency of PSO has been compared with simulated annealing, and the gradient embedded genetic algorithm.     

Structural transition from icosahedra to decahedra of large Lennard-Jones clusters

The lowest icosahedral and decahedral energies of LJ1001-1610 clusters are obtained using a greedy search method (GSM) based on lattice construction. By comparing the lowest energies of icosahedral and decahedral clusters with the same atoms, the structural transition of LJ clusters is studied. Results show that the critical size from icosahedra to decahedra is located at N = 1034. When the cluster size is larger than 1034, the optimal structures are decahedra except the LJ1367-1422 clusters near the magic number, 1402, of icosahedra. However, the energies of icosahedra near the next magic number, 2044, are higher than that of decahedra, which implies that decahedra will be the optimal structure when the cluster size is larger than 1422, even for those clusters near the magic numbers of icosahedra.     

Structural transitions and melting in LJ(74-78) Lennard-Jones clusters from adaptive exchange Monte Carlo simulations

Phase changes in Lennard-Jones (LJ) clusters containing between 74 and 78 atoms are investigated by means of exchange Monte Carlo simulations in the canonical ensemble. The replica temperatures are self-adapted to facilitate the convergence. Although the 74- and 78-atom clusters have icosahedral global minima, the clusters with 75-77 atoms have decahedral ground-state structures and they undergo a structural transition to icosahedral minima before melting. The structural transitions are characterized by quenching and by looking at the Q4 and Q6 orientational bond order parameters. The transition temperatures are estimated to be 0.114, 0.065, and 0.074 reduced units for LJ75, LJ76, and LJ77, respectively. These values, their ordering and the associated latent heats are compared with other estimates based on the harmonic superposition approach.     

Geometry optimization of bimetallic clusters using an efficient heuristic method

In this paper, an efficient heuristic algorithm for geometry optimization of bimetallic clusters is proposed. The algorithm is mainly composed of three ingredients: the monotonic basin-hopping method with guided perturbation (MBH-GP), surface optimization method, and iterated local search (ILS) method, where MBH-GP and surface optimization method are used to optimize the geometric structure of a cluster, and the ILS method is used to search the optimal homotop for a fixed geometric structure. The proposed method is applied to Cu(38-n)Au(n) (0 ≤ n ≤ 38), Ag(55-n)Au(n) (0 ≤ n ≤ 55), and Cu(55-n)Au(n) (0 ≤ n ≤ 55) clusters modeled by the many-body Gupta potential. Comparison with the results reported in the literature indicates that the present method is highly efficient and a number of new putative global minima missed in the previous papers are found. The present method should be a promising tool for the theoretical determination of ground-state structure of bimetallic clusters. Additionally, some key elements and properties of the present method are also analyzed.     

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.     

Combining genetic algorithm and simulated annealing: a molecular geometry optimization study

We introduce a new hybrid approach to determine the ground state geometry of molecular systems. Firstly, we compared the ability of genetic algorithm (GA) and simulated annealing (SA) to find the lowest energy geometry of silicon clusters with six and 10 atoms. This comparison showed that GA exhibits fast initial convergence, but its performance deteriorates as it approaches the desired global extreme. Interestingly, SA showed a complementary convergence pattern, in addition to high accuracy. Our new procedure combines selected features from GA and SA to achieve weak dependence on initial parameters, parallel search strategy, fast convergence and high accuracy. This hybrid algorithm outperforms GA and SA by one order of magnitude for small silicon clusters (Si₆ and Si₁₀). Next, we applied the hybrid method to study the geometry of a 20-atom silicon cluster. It was able to find an original geometry, apparently lower in energy than those previously described in literature. In principle, our procedure can be applied successfully to any molecular system.     

具有多体效应的胶体聚团的特征

考察了多体效应（用Ｓｔｕｔｔｏｎ－Ｃｈｅｎ势，ＳＣ）对胶体聚团的影响并与双体（ＬＪ）势下的结果作了比较。研究表明，ＳＣ和ＬＪ势下簇团的性质有其相似的一面，如：随着剪应力的增加，系统里颗粒的平均势能增加，而每个簇团的颗粒数减少；在较强的剪应力场里，簇团沿剪应力方向（Ｘ轴）被明显拉长且其主轴偏离Ｘ轴等。但它们间的差异也是明显的，在剪应力下ＳＣ系统内颗粒排列得更合理，从而使得平均位能比ＬＪ系统低约１－３     

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   

New method for parallel computation of Hessian matrix of conformational energy function in internal coordinates

A new algorithm for parallel calculation of the second derivatives (Hessian) of the conformational energy function of biomolecules in internal coordinates is proposed. The basic scheme of this algorithm is the division of the entire calculation of the Hessian matrix (called "task") into subtasks and the optimization of the assignment of processors to each subtask by considering both the load balancing and reduction of the communication cost. A genetic algorithm is used for this optimization considering the dependencies between subtasks. We applied this method to a glutaminyl transfer RNA (Gln-tRNA) molecule for which the scalability of our previously developed parallel algorithm was significantly decreased when the large number of processors was used. The speedup for the calculation was 32.6 times with 60 processors, which is considerably better than the speedup for our previously reported parallel algorithm. The elapsed time for the calculation of subtasks, data sending, and data receiving was analyzed, and the effect of the optimization using the genetic algorithm is discussed.