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.     

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.     

Parallel random tunneling algorithm for structural optimization of Lennard-Jones clusters up to N=330

A random tunneling algorithm (RTA) is derived from the terminal repeller unconstrained subenergy tunneling (TRUST) algorithm, and the parallelization of the RTA is implemented with an island parallel paradigm. Combined with the techniques of angular moving, the parallel random tunneling algorithm (PRTA) is applied to the optimization of Lennard-Jones (LJ) atomic clusters, and all the global minima of LJ clusters with size up to 200 are successfully located. For the optimization of larger cluster, a PRTA with an improved seeding technique is developed and successfully applied to the optimization of LJ151-LJ309. Furthermore, the optimized structures of LJ309-330 with the PRTA, which have not been studied before, are also provided.     

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...     

A reversible minimum-to-minimum mapping method for the calculation of free-energy differences

A general method is introduced for the calculation of the free-energy difference between two systems, 0 and 1, with configuration spaces omega(0), omega(1) of the same dimensionality. The method relies upon establishing a objective mapping between disjoint subsets gamma(i)(0) of omega(0) and corresponding disjoint subsets gamma(i)(1) of omega(1), and averaging a function of the ratio of configurational integrals over gamma(i)(0) and gamma(i)(1) with respect to the probability densities of the two systems. The mapped subsets gamma(i)(0) and gamma(i)(1) need not span the entire configuration spaces omega(0) and omega(1). The method is applied for the calculation of the excess chemical potential mu(ex) in a Lennard-Jones (LJ) fluid. In this case, omega(0) is the configuration space of a (N-1) real molecule plus one ideal-gas molecule system, while omega(1) is the configuration space of a N real molecule system occupying the same volume. Gamma(i)(0) and gamma(i)(1) are constructed from hyperspheres of the same radius centered at minimum-energy configurations of a set of "active" molecules lying within distance a from the ideal-gas molecule and the last real molecule, respectively. An algorithm is described for sampling gamma(i)(0) and gamma(i)(1) given a point in omega(0) or in omega(1). The algorithm encompasses three steps: "quenching" (minimization with respect to the active-molecule degrees of freedom), "mutation" (gradual conversion of the ideal-gas molecule into a real molecule, with simultaneous minimization of the energy with respect to the active-molecule degrees of freedom), and "excitation" (generation of points on a hypersphere centered at the active-molecule energy minimum). These steps are also carried out in reverse, as required by the bijective nature of the mapping. The mutation step, which establishes a reversible mapping between energy minima with respect to the active degrees of freedom of systems 0 and 1, ensures that excluded volume interactions emerging in the process of converting the ideal-gas molecule into a real molecule are relieved through appropriate rearrangement of the surrounding active molecules. Thus, the insertion problem plaguing traditional methods for the calculation of chemical potential at high densities is alleviated. Results are presented at two state points of the LJ system for a variety of radii a of the active domain. It is shown that the estimated values of mu(ex) are correct in all cases and subject to an order of magnitude lower statistical uncertainty than values based on the same number of Widom [J. Chem. Phys. 39, 2808 (1963)] insertions at high fluid densities. Optimal settings for the new algorithm are identified and distributions of the quantities involved in it [number of active molecules, energy at the sampled minima of systems 0 and 1, and free-energy differences between subsets gamma(i)(0) and gamma(i)(1) that are mapped onto each other] are explored.     

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.     

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 new hybrid algorithm for finding the lowest minima of potential surfaces: approach and application to peptides

A new algorithm is presented for finding the global minimum, and other low-lying minima, of a potential energy surface (PES) of biological molecules. The algorithm synergetically combines three well-known global optimization methods: the diffusion equation method (DEM), which involves smoothing the PES; a simulated annealing (SA) algorithm; and evolutionary programming (EP), whose population-oriented approach allows for a parallel search over different regions of the PES. Tests on five peptides having between 6 and 9 residues show that the code implementing the new combined algorithm is efficient and is found to outperform the constituent methods, DEM and SA. Results of the algorithm, in the gas phase and with the GBSA implicit solvent model, are compared with crystallographic data for the test peptides; good accord is found in all cases. Also, for all but one of the examples, our hybrid algorithm finds a minimum deeper than those obtained by a very extensive scan. TINKERs implementation of the OPLS-AA force field is employed for the structure prediction. The results show that the new algorithm is a powerful structure predictor, when a reliable potential function is available. Our implementation of the algorithm is time-efficient, and requires only modest computational resources. Work is underway on applications of the new algorithm to structural prediction of proteins and other biological macro-molecules.     

热处理对超疏水性含氟丙烯酸酯共聚物膜表面性能的影响

以微乳液聚合法和溶液聚合法制备丙烯酸全氟烷基乙基酯和甲基丙烯酸甲酯的共聚物, 以1,1,2-三氟三氯乙烷为溶剂, 采用溶剂挥发成膜法直接制备出超疏水膜, 并研究120 ℃热处理对超疏水膜表面性能的影响. 对于用乳液聚合方法制备的超疏水膜, 随着热处理时间的延长, 滚动角表现出先逐渐增大直至完全不能滚动, 然后重新回复到极小滚动角的特殊变化过程, 而静态接触角只是略微减小, 完全不同于热处理对平滑的含氟聚合物表面接触角的影响. 扫描电镜结果显示, 聚合物膜表面形貌对应出现从微/纳复合粗糙结构到微孔粗化并重新形成微/纳复合多层粗糙结构的变化.     

Structurally distinct active sites in the copper(II)-substituted aminopeptidases from Aeromonas proteolytica and Escherichia coli

The aminopeptidase from Aeromonas proteolytica (AAP) was titrated with copper, which bound sequentially at two distinct sites. Both the mono- and disubstituted forms of AAP exhibited catalytic hyperactivity relative to the native dizinc enzyme. Monosubstituted AAP exhibited an axial Cu(II) EPR spectrum with slight pH dependence: at pH 6.0 g(parallel) = 2.249, g( perpendicular ) = 2.055, and A(parallel)((63/65)Cu) = 1.77 x 10(-)(2) cm(-)(1), whereas at pH 9.65 g(parallel) = 2.245, g( perpendicular ) = 2.056, and A(parallel)((63/65)Cu) = 1.77 x 10(-)(2) cm(-)(1). These data indicate oxygen and nitrogen ligation of Cu. AAP further substituted with copper exhibited a complex signal with features around g approximately 2 and 4. The features at g approximately 4 were relatively weak in the B(0) perpendicular B(1) (perpendicular) mode EPR spectrum but were intense in the B(0) parallel B(1) (parallel) mode spectrum. The g approximately 2 region of the perpendicular mode spectrum exhibited two components, one corresponding to mononuclear Cu(II) with g(parallel) = 2.218, g( perpendicular ) = 2.023, and A(parallel)((63/65)Cu) = 1.55 x 10(-)(2) cm(-)(1) and likely due to adventitious binding of Cu(II) to a site distant from the active site. Excellent simulations were obtained for the second component of the spectrum assuming that two Cu(II) ions experience dipolar coupling corresponding to an inter-copper distance of 5 A with the two Cu(II) g(z)() directions parallel to each other and at an angle of approximately 17 degrees to the inter-copper vector (H = betaB.g(CuA).S(CuA) + betaB.g(CuB).S(CuB) + [S.A.I](CuA) + [S.A.I](CuB) + [S(CuA).J.S(CuB)]; g(parallel(CuA,CuB)) = 2.218, g( perpendicular )((CuA,CuB)) = 2.060; A(parallel(CuA,CuB))((63/65)Cu) = 1.59 x 10(-)(2) cm(-)(1), J(isotropic) = 50 cm(-)(1), r(Cu)(-)(Cu) = 4.93 A, and chi = 17 degrees ). The exchange coupling between the two copper ions was found to be ferromagnetic as the signals exhibited Curie law temperature dependence. The Cu-Cu distance of approximately 5 A indicated by EPR was significantly higher than the inter-zinc distance of 3.5 A in the native enzyme, and the dicopper species therefore represents a novel dinuclear site capable of catalysis of hydrolysis. In contrast to AAP, the related methionyl aminopeptidase from Escherichia coli (EcMetAP) was found to bind only one Cu(II) ion despite possessing a dinuclear binding site motif. A further difference was the marked pH dependence of the signal in EcMetAP, suggestive of a change in ligation. The structural motifs of these two Cu(II)-substituted aminopeptidases provide important insight into the observed catalytic activity.     

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.     

Simulated annealing and density functional theory calculations of structural and energetic properties of the ammonium chloride clusters (NH4Cl)n, (NH4+)(NH4Cl)n, and (Cl-)(NH4Cl)n, n = 1-13

Simulated annealing Monte Carlo conformer searches using the "mag-walking" algorithm are employed to locate the global minima of molecular clusters of ammonium chloride of the types (NH(4)Cl)(n), (NH(4)(+))(NH(4)Cl)(n), and (Cl(-))(NH(4)Cl)(n) with n = 1-13. The M06-2X density functional theory method is used to refine and predict the structures, energies, and thermodynamic properties of the neutral, cation, and anion clusters. For selected small clusters, the resulting structures are compared to those obtained from a variety of models and basis sets, including RI-MP2 and B3LYP calculations. M06-2X calculations predict enhanced stability of the (NH(4)(+))(NH(4)Cl)(n) clusters when n = 3, 6, 8, and 13. This prediction corresponds favorably to anomalies previously observed in thermospray mass spectroscopy experiments. The (NH(4)Cl)(n) clusters show alternations in stability between even and odd values of n. Clusters of the type (Cl(-))(NH(4)Cl)(n) display a magic number distribution different from that of the cation clusters, with enhanced stability predicted for n = 2, 6, and 11. None of the observed cluster structures resemble the room-temperature CsCl structure of NH(4)Cl(s), which is consistent with previous work. Numerous clusters have structures reminiscent of the higher-temperature, rock-salt phase of the solid ammonium halides.     

A comparison of heuristic search algorithms for molecular docking

This paper describes the implementation and comparison of four heuristic search algorithms (genetic algorithm, evolutionary programming, simulated annealing and tabu search) and a random search procedure for flexible molecular docking. To our knowledge, this is the first application of the tabu search algorithm in this area. The algorithms are compared using a recently described fast molecular recognition potential function and a diverse set of five protein–ligand systems. Statistical analysis of the results indicates that overall the genetic algorithm performs best in terms of the median energy of the solutions located. However, tabu search shows a better performance in terms of locating solutions close to the crystallographic ligand conformation. These results suggest that a hybrid search algorithm may give superior results to any of the algorithms alone.     

A doubly nudged elastic band method for finding transition states

A modification of the nudged elastic band (NEB) method is presented that enables stable optimizations to be run using both the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) quasi-Newton and slow-response quenched velocity Verlet minimizers. The performance of this new "doubly nudged" DNEB method is analyzed in conjunction with both minimizers and compared with previous NEB formulations. We find that the fastest DNEB approach (DNEB/L-BFGS) can be quicker by up to 2 orders of magnitude. Applications to permutational rearrangements of the seven-atom Lennard-Jones cluster (LJ7) and highly cooperative rearrangements of LJ38 and LJ75 are presented. We also outline an updated algorithm for constructing complicated multi-step pathways using successive DNEB runs.     

Comparison of double-ended transition state search methods

While a variety of double-ended transition state search methods have been developed, their relative performance in characterizing complex multistep pathways between structurally disparate molecular conformations remains unclear. Three such methods (doubly-nudged elastic band, a string method, and a growing string method) are compared for a series of benchmarks ranging from permutational isomerizations of the seven-atom Lennard-Jones cluster (LJ(7)) to highly cooperative LJ(38) and LJ(75) rearrangements, and the folding pathways of two peptides. A database of short paths between LJ(13) local minima is used to explore the effects of parameters and suggest reasonable default values. Each double-ended method was employed within the framework of a missing connection network flow algorithm to construct more complicated multistep pathways. We find that in our implementation none of the three methods definitively outperforms the others, and that their relative effectiveness is strongly system and parameter dependent.     

The role of pressure in rubber elasticity

We describe a series of molecular dynamics computations that reveal an intimate connection at the atomic scale between difference stress (which resists stretches) and pressure (which resists volume changes) in an idealized elastomer, in contrast to the classical theory of rubber elasticity. Our simulations idealize the elastomer as a "pearl necklace," in which the covalent bonds are stiff linear springs, while nonbonded atoms interact through a Lennard-Jones potential with energy epsilon(LJ) and radius sigma(LJ). We calculate the difference stress t(11)-(t(22)+t(33))/2 and mean stress (t(11)+t(22)+t(33))/3 induced by a constant volume extension in the x(1) direction, as a function of temperature T and reduced density rho(*)=Nsigma(IJ) (3)/nu. Here, N is the number of atoms in the simulation cell and nu is the cell volume. Results show that for rho(*)<1, the difference stress is purely entropic and is in good agreement with the classical affine network model of rubber elasticity, which neglects nonbonded interactions. However, data presented by van Krevelen [Properties of Polymers, 3rd ed. (Elsevier, Amsterdam, 1990), p. 79] indicate that rubber at standard conditions corresponds to rho(*)=1.2. For rho(*)>1, the system is entropic for kT/epsilon(LJ)>2, but at lower temperatures the difference stress contains an additional energy component, which increases as rho(*) increases and temperature decreases. Finally, the model exhibits a glass transition for rho(*)=1.2 and kT/epsilon(LJ) approximately 2. The atomic-scale processes responsible for generating stress are explored in detail. Simulations demonstrate that the repulsive portion of the Lennard-Jones potential provides a contribution sigma(nbr)>0 to the difference stress, the attractive portion provides sigma(nba) approximately 0, while the covalent bonds provide sigma(b)<0. In contrast, their respective contributions to the mean stress satisfy Pi(nbr)<0, Pi(nba)>0, and Pi(b)<0. Analytical calculations, together with simulations, demonstrate that mean and difference stresses are related by sigma(nbr)=-APi(nbr)P(2)(theta(b)), sigma(b)=BPi(b)P(2)(theta(b)), where P(2)(theta(b)) is a measure of the anisotropy of the orientation of the covalent bonds, and A and B are coefficients that depend weakly on rho(*) and temperature. For high values of rho(*), we find that [sigma(nbr)]>[sigma(b)], and in this regime our model predicts behavior that is in good agreement with experimental data of D.L. Quested et al. [J. Appl. Phys. 52, 5977 (1981)] for the influence of pressure on the difference stress induced by stretching solithane.     

Aqueous Solution Chemistry of the Mo(3)PdS(4) Cube: Substitution Reactions and the Double to Single Cube Interconversion Induced by CO, Two Phosphines, Cl(-), Br(-), and NCS(-)

The kinetics of conversion of an edge-linked double cube, in this case [{Mo(3)PdS(4)(H(2)O)(9)}(2)](8+), to the corresponding single cube [Mo(3)(PdX)S(4)(H(2)O)(9)](4+), has been studied for the first time. Reaction is induced by six reagents X = CO, two water-soluble phosphines, Cl(-), Br(-), and NCS(-), which complex at the tetrahedral Pd. The first stage of reaction is fast and is accompanied by color changes, e.g. purple to dark blue in the case of Cl(-), assigned as double to single cube conversion. With X = CO and the two phosphines, when absorbance changes are intense enough for stopped-flow monitoring with reactants at Pd-SCN. On removal of e.g. Cl(-) by chromatography or addition of Ag(+), the double cube re-forms.     

Role of anions in the synthesis of cyclobutane derivatives via [2 + 2] cycloaddition reaction in the solid state and their isomerization in solution

trans-3-(4'-Pyridyl)acrylic acid (4-PA) is inert to photodimerization reaction both in solution and solid state. It is made photoreactive by forming salts with various acids. The anions of these salts play a key role in directing the packing of 4-PAH(+) in the solid state. The anions CF(3)CO(2)(-), Cl(-), ClO(4)(-), and BF(4)(-) direct the parallel alignments of 4-PAH(+) in head-to-tail (HT) fashion and lead to the formation of HT-photodimer. On the other hand, bivalent anion SO(4)(2-) directs parallel alignment of 4-PAH(+) in head-to-head (HH) fashion and lead to the formation of HH-photodimer. The details of the anion-controlled stereoselective syntheses of these two cyclobutane derivatives are presented. Interestingly, both cyclobutane compounds undergo isomerization from rctt-form to rctc-form in solution catalyzed by acid.     

Structure of complexes formed by dissolution of palladium diacetate in methanol and chloroform. In situ NMR study

The behavior of palladium diacetate cyclic trimer [Pd(OAc)(2)](3) (1) upon its dissolution in methanol and wet chloroform was studied by (1)H and (13)C NMR including 2D-HSQC and 2D-DOSY techniques. Upon dissolution, trimer 1 reacts with methanol and is completely transformed first into the methoxo complex Pd(3)(μ-OMe)(OAc)(5) (2), which already at -18 °C undergoes a slow exchange of second bridging acetate ligand between the same palladium atoms to form the symmetric dimethoxo complex Pd(3)(μ-OMe)(2)(OAc)(4), the maximum relative concentration of which reaches 20-30 mol % of initial loading trimer 1. Along with the dimethoxo complex, both soluble and insoluble polynuclear palladium clusters are gradually formed at -18 °C, and their total amount reaches up to 60% of the starting Pd(2+) loading. The increase of temperature to 27 °C results in the reduction of palladium(II) to Pd metal by methanol, which is oxidized and transformed into formaldehyde hemiacetal and methyl formate. Upon dissolution in wet chloroform, trimer 1 is reversibly hydrolyzed to the hydroxo complex Pd(3)(μ-OH)(OAc)(5) (10) in ratio 1/10 ≈ 3/1. The temperature decrease and addition of acetic acid shift the equilibrium in this system toward trimer 1, and addition of water shifts it in the opposite direction. Addition of methanol to the equilibrium mixture of 1 and 10 results in the fast exchange of bridging acetate in trimer 1 by the μ-OMe group. Substitution of the μ-OH ligand by μ-OMe in 10 occurs in parallel but more slowly. Complex 2 formed in both cases is more stable in chloroform than in methanol.     

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.