Gravitational smoothing as a global optimization strategy

An optimization scheme for atomic cluster structures, based on exaggerating the importance of the gravitational force, is introduced. Results are presented for calculations on Lennard-Jones clusters of 13, 38, and 55 atoms, and the 13-atom Morse cluster.     

Composition-induced structural transitions in mixed Lennard-Jones clusters: global reparametrization and optimization

As extended benchmarks to global cluster structure optimization methods, we provide a first systematic point of entry into the world of strongly mixed rare gas clusters. A new set of generalized Lennard-Jones pair potentials is generated for this purpose, by fitting them to high-end ab initio reference data. Employing these potentials in our genetic algorithm-based global structure optimization framework, we examined various systems from binary to quinary mixtures of atom types. A central result from this study is that the famous fcc structure for 38 atoms can survive for certain binary mixtures but appears to be prone to collapsing into the dominating icosahedral structure, which we observed upon introduction of one single atom of a ternary type.     

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 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.     

Efficiency of tabu‐search‐based conformational search algorithms

Efficient conformational search or sampling approaches play an integral role in molecular modeling, leading to a strong demand for even faster and more reliable conformer search algorithms. This article compares the efficiency of a molecular dynamics method, a simulated annealing method, and the basin hopping (BH) approach (which are widely used in this field) with a previously suggested tabu‐search‐based approach called gradient only tabu search (GOTS). The study emphasizes the success of the GOTS procedure and, more importantly, shows that an approach which combines BH and GOTS outperforms the single methods in efficiency and speed. We also show that ring structures built by a hydrogen bond are useful as starting points for conformational search investigations of peptides and organic ligands with biological activities, especially in structures that contain multiple rings. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Gradient gravitational search: An efficient metaheuristic algorithm for global optimization

The adaptation of novel techniques developed in the field of computational chemistry to solve the concerned problems for large and flexible molecules is taking the center stage with regard to efficient algorithm, computational cost and accuracy. In this article, the gradient‐based gravitational search (GGS) algorithm, using analytical gradients for a fast minimization to the next local minimum has been reported. Its efficiency as metaheuristic approach has also been compared with Gradient Tabu Search and others like: Gravitational Search, Cuckoo Search, and Back Tracking Search algorithms for global optimization. Moreover, the GGS approach has also been applied to computational chemistry problems for finding the minimal value potential energy of two‐dimensional and three‐dimensional off‐lattice protein models. The simulation results reveal the relative stability and physical accuracy of protein models with efficient computational cost. © 2015 Wiley Periodicals, Inc.     

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.     

Single‐ended transition state finding with the growing string method

Reaction path finding and transition state (TS) searching are important tasks in computational chemistry. Methods that seek to optimize an evenly distributed set of structures to represent a chemical reaction path are known as double‐ended string methods. Such methods can be highly reliable because the endpoints of the string are fixed, which effectively lowers the dimensionality of the reaction path search. String methods, however, require that the reactant and product structures are known beforehand, which limits their ability for systematic exploration of reactive steps. In this article, a single‐ended growing string method (GSM) is introduced which allows for reaction path searches starting from a single structure. The method works by sequentially adding nodes along coordinates that drive bonds, angles, and/or torsions to a desired reactive outcome. After the string is grown and an approximate reaction path through the TS is found, string optimization commences and the exact TS is located along with the reaction path. Fast convergence of the string is achieved through use of internal coordinates and eigenvector optimization schemes combined with Hessian estimates. Comparison to the double‐ended GSM shows that single‐ended method can be even more computationally efficient than the already rapid double‐ended method. Examples, including transition metal reactivity and a systematic, automated search for unknown reactivity, demonstrate the efficacy of the new method. This automated reaction search is able to find 165 reaction paths from 333 searches for the reaction of NH₃BH₃ and (LiH)₄, all without guidance from user intuition. © 2015 Wiley Periodicals, Inc.     

An unbiased population-based search for the geometry optimization of Lennard-Jones clusters: 2 < or = N < or = 372

This article presents the results obtained using an unbiased Population Based Search (PBS) for optimizing Lennard-Jones clusters. PBS is able to repeatedly obtain all putative global minima, for Lennard-Jones clusters in the range 2 < or = N < or = 372, as reported in the Cambridge Cluster Database. The PBS algorithm incorporates and extends key techniques that have been developed in other Lennard-Jones optimization algorithms over the last decade. Of particular importance are the use of cut-and-paste operators, structure niching (using the cluster strain energy as a metric), two-phase local search, and a new operator, Directed Optimization, which extends the previous concept of directed mutation. In addition, PBS is able to operate in a parallel mode for optimizing larger clusters.     

Efficient pole‐search algorithm for dynamic polarizability: Toward alternative excited‐state calculation for large systems

This study presents an efficient algorithm to search for the poles of dynamic polarizability to obtain excited states of large systems with nonlocal excitation nature. The present algorithm adopts a homogeneous search with a constant frequency interval and a bisection search to achieve high accuracy. Furthermore, the subtraction process of the information about the detected poles from the total dynamic polarizability is used to extract the undetected pole contributions. Numerical assessments confirmed the accuracy and efficiency of the present algorithm in obtaining the excitation energies and oscillator strengths of all dipole‐allowed excited states. A combination of the present pole‐search algorithm and divide‐and‐conquer‐based dynamic polarizability calculations was found to be promising to treat nonlocal excitations of large systems. © 2016 Wiley Periodicals, Inc.     

Conformational search using a molecular dynamics–minimization procedure: Applications to clusters of coulombic charges,Lennard–Jones particles,and waters

A new conformational search method, molecular dynamics–minimization (MDM), is proposed, which combines a molecular dynamics sampling strategy with energy minimizations in the search for low-energy molecular structures. This new method is applied to the search for low energy configurations of clusters of coulombic charges on a unit sphere, Lennard–Jones clusters, and water clusters. The MDM method is shown to be efficient in finding the lowest energy configurations of these clusters. A closer comparison of MDM with alternative conformational search methods on Lennard–Jones clusters shows that, although MDM is not as efficient as the Monte Carlo–minimization method in locating the global energy minima, it is more efficient than the diffusion equation method and the method of minimization from randomly generated structures. Given the versatility of the molecular dynamics sampling strategy in comparison to Monte Carlo in treating molecular complexes or molecules in explicit solution, one anticipates that the MDM method could be profitably applied to conformational search problems where the number of degrees of freedom is much greater. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 60–70, 1998     

A graph‐based short‐cut to low‐energy structures

A new graph‐based move class for global optimization of cluster structures is presented. Its performance and efficiency is analyzed for water clusters (H₂O)_n, n = 24, 61. This analysis indicates superior basin exploitation capabilities of the new move class for large clusters, compared to traditional moves. © 2014 Wiley Periodicals, Inc.     

Optimization of bimetallic Cu–Au and Ag–Au clusters by using a modified adaptive immune optimization algorithm

A modified adaptive immune optimization algorithm (AIOA) is designed for optimization of Cu–Au and Ag–Au bimetallic clusters with Gupta potential. Compared with homoatom clusters, there are homotopic isomers in bimetallic cluster, so atom exchange operation is presented in the modified AIOA. The efficiency of the algorithm is tested by optimization of Cu_nAu_38‐n (0 ≤ n ≤ 38). Results show that all the structures with the putative global minimal energies are successfully located. In the optimization of Ag_nAu_55‐n (0 ≤ n ≤ 55) bimetallic clusters, all the structures with the reported minimal energies are obtained, and 36 structures with even lower potential energies are found. On the other hand, with the optimized structures of Cu_nAu_55‐n, it is shown that all 55‐atom Cu–Au bimetallic clusters are Mackay icosahedra except for Au₅₅, which is a face‐centered cubic (fcc)‐like structure; Cu₅₅, Cu₁₂Au₄₃, and Cu₁Au₅₄ have two‐shell Mackay icosahedral geometries with I_h point group symmetry. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009     

On the ion‐pair dissociation mechanisms in the small NaCl·(H2O)6 cluster: A perspective from reaction path search calculations

We performed reaction path search calculations for the NaCl·(H₂O)₆ cluster using the global reaction route mapping (GRRM) code to understand the atomic‐level mechanisms of the NaCl → Na⁺ + Cl⁻ ionic dissociation induced by water solvents. Low‐lying minima, transition states connecting two local minima and corresponding intrinsic reaction coordinates on the potential energy surface are explored. We found that the Na Cl distances at the transitions states for the dissociation pathways were distributed in a relatively wide range of 2.7–3.7 Å and that the Na Cl distance at the transition state did not correlate with the commonly used solvation coordinates. This suggests that the definition of the transition states with specific structures as well as good reaction coordinate is very difficult for the ionic dissociation process even in a small water cluster. © 2018 Wiley Periodicals, Inc.     

Blind docking method combining search of low‐resolution binding sites with ligand pose refinement by molecular dynamics‐based global optimization

This study describes the development of a new blind hierarchical docking method, bhDock, its implementation, and accuracy assessment. The bhDock method uses two‐step algorithm. First, a comprehensive set of low‐resolution binding sites is determined by analyzing entire protein surface and ranked by a simple score function. Second, ligand position is determined via a molecular dynamics‐based method of global optimization starting from a small set of high ranked low‐resolution binding sites. The refinement of the ligand binding pose starts from uniformly distributed multiple initial ligand orientations and uses simulated annealing molecular dynamics coupled with guided force‐field deformation of protein–ligand interactions to find the global minimum. Assessment of the bhDock method on the set of 37 protein–ligand complexes has shown the success rate of predictions of 78%, which is better than the rate reported for the most cited docking methods, such as AutoDock, DOCK, GOLD, and FlexX, on the same set of complexes. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Pentaatomic planar tetracoordinate silicon with 14 valence electrons: A large‐scale global search of (n + m = 4; q = 0, ±1, −2; X,Y = main group elements from H to Br)

Designing and characterizing the compounds with exotic structures and bonding that seemingly contrast the traditional chemical rules are a never‐ending goal. Although the silicon chemistry is dominated by the tetrahedral picture, many examples with the planar tetracoordinate‐Si skeletons have been discovered, among which simple species usually contain the 17/18 valence electrons. In this work, we report hitherto the most extensive structural search for the pentaatomic ptSi with 14 valence electrons, that is, (n + m = 4; q = 0, ±1, ?2; X, Y = main group elements from H to Br). For 129 studied systems, 50 systems have the ptSi structure as the local minimum. Promisingly, nine systems, that is, , HSiY₃ (Y = Al/Ga), Ca₃SiAl^?, Mg₄Si^2?, C₂LiSi, Si₃Y₂ (Y = Li/Na/K), each have the global minimum ptSi. The former six systems represent the first prediction. Interestingly, in HSiY₃ (Y = Al/Ga), the H‐atom is only bonded to the ptSi‐center via a localized 2c–2e σ bond. This sharply contradicts the known pentaatomic planar‐centered systems, in which the ligands are actively involved in the ligand–ligand bonding besides being bonded to the planar center. Therefore, we proposed here that to generalize the 14e‐ptSi, two strategies can be applied as (1) introducing the alkaline/alkaline‐earth elements and (2) breaking the peripheral bonding. In light of the very limited global ptSi examples, the presently designed six systems with 14e are expected to enrich the exotic ptSi chemistry and welcome future laboratory confirmation. © 2014 Wiley Periodicals, Inc.     

Nonadiabatic sudden increase of the cooperative kinetic effect at lattice energy stabilization—Microscopic mechanism of superconducting state transition: Model study of MgB2

The theory of the nonadiabatic electron–vibration interactions has been applied to the study of MgB₂ superconducting state transition. It has been shown that at nonadiabatic conditions in which the Born–Oppenheimer approximation is not valid and electronic motion is dependent not only on the nuclear coordinates but also on the nuclear momenta, the fermionic ground‐state energy of the studied system can be stabilized by nonadiabatic electron–phonon interactions at broken translation symmetry. Moreover, the new arising state is geometrically degenerate; i.e., there are an infinite number of different nuclear configurations with the same fermionic ground‐state energy. The model study of MgB₂ yields results that are in a good agreement with the experimental data. For distorted lattice, with 0.016 Å/atom of in‐plane out‐of‐phase B? B atoms displacements out of the equilibrium (E_2g phonon mode) when the nonadiabatic interactions are most effective, it has been calculated that the new arising state is 87 meV/unit cell more stable than the equilibrium–high symmetry clumped nuclear structure at the level of the Born–Oppenheimer approximation. The calculated T_c is 39.5 K. The resulting density of states exhibits two‐peak character, in full agreement with the tunneling spectra. The peaks are at ±4 meV, corresponding to the change of the π band density of states, and at ±7.6 meV, corresponding to the σ band. The superconducting state transition can be characterized as a nonadiabatic sudden increase of the cooperative kinetic effect at lattice energy stabilization (NASICKELES). © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Intramolecular screening effects in nondilute polymer solutions: An equation‐of‐state approach

In a previous article, we presented a simple modification of the traditional Flory–Huggins theory that took intramolecular screening effects (or same chain contacts) into account. In this article, we present a natural extension of that work, in which free‐volume effects are also explained with an equation‐of‐state model. The predictions of the interaction parameter, χ, for several polymer–solvent systems are presented, over the entire concentration range, in θ solvents and good solvents. A geometric mean assumption is applied to the calculation of an exchange energy interaction term. The predictions of χ are successful to various degrees when internal pressures are used, whereas the use of solubility parameters in most cases produces fairly good agreement with experimental results. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2911–2922, 2003     

Sensitization mechanisms from excited‐singlet state of pyrromethene dye to a radical‐generating reagent in a poly(methylmethacrylate) film

The sensitization mechanisms of a pyrromethene dye with a radical‐generating reagent, 3,5,3′,5′‐tetramethylpyrromethene‐BF₂ (BH) with 3,3′,4,4′‐tetrakis(t‐butyldioxycarbonyl)benzophenone (BP), in a poly‐ (methylmethacrylate) (PMMA) film were investigated by laser flash phoptolysis using a total reflection cell and single photon counting. From the laser flash photolysis, strong fluorescence was detected though no transient absorption was detected. The fluorescence intensity was significantly decreased with increasing concentration of BP, apparently exhibiting Perrin‐type static quenching at a quenching radius, R_f = 26 Å. From the examination of decay profile using single photon counting, logarithmic plots of fluorescence decay in a PMMA film afforded a nonlinear, convex reduction, corresponding to a streched exponential decay, while the logarithmic plots in acetonitrile showed a linear relationship. With increasing concentration of BH, the fluorescence maximum was shifted to red, and the intensity of fluorescence was significantly reduced. The red shift of fluorescence, the nonlinear fluorescence logarithmic decay and the large reduction in fluorescence indicate a dispersive photoexcited state and a relaxation of excitation energy hopping across an array of sites with Gaussian energy distribution. Moreover, after incorporating BP, the convex logarithmic plots became more steep, and the fluorescence maximum was also shifted to red, exhibiting a nonstatic quenching process competitive to the excitation energy hopping. Thus the sensitization of photoinitiator system containing BH and BP, whose contents were almost same as that in the commercial products, was due to a static quenching process from dispersive singlet excited BH to BP ground state, and the nonstatic quenching process competitive to the excitation energy hopping was minimal. Copyright © 1999 John Wiley & Sons, Ltd.