Packing of protein structures in clusters with magic numbers

Recently we have proposed a model for folding proteins into packed’ clusters’. We have constructed a local homology measure for protein fold classes by projecting consecutively secondary structures onto a lattice. Taking into account hydrophobic forces we have found a mechanism for formation of clusters containing magic numbers of secondary structures and multipla of these clusters. A scheme for the relation between the sequence information and the native fold is given. We have performed a statistical analysis of available protein structures and found agreement with the predicted preferred abundances. In this paper we demonstrate that the results are robust to variations in the coordination number of the model.     

Carbon monoxide clusters: critical size and magic numbers

Fully resolved mass spectra of carbon monoxide clusters have been recorded in the size rangen≦320. Intensity anomalies in these spectra beyondn=135 are strikingly similar to those being observed in krypton and xenon spectra. Particularly pronounced intensity drops occur atn=147 and 309. For the first time, these data provide evidence for icosahedral structure in largemolecular cluster ions. Concerning doubly charged CO clusters, their lower size limit has been measured to ben _c =98.     

Phase changes in selected Lennard-Jones X13-nYn clusters

Detailed studies of the thermodynamic properties of selected binary Lennard-Jones clusters of the type X13-nYn (where n=1, 2, 3) are presented. The total energy, heat capacity, and first derivative of the heat capacity as a function of temperature are calculated by using the classical and path integral Monte Carlo methods combined with the parallel tempering technique. A modification in the phase change phenomena from the presence of impurity atoms and quantum effects is investigated.     

Molecular dynamics search for magic numbers for silver and copper clusters

Isothermal molecular dynamics is used to find the magic numbers corresponding to clusters of fcc transition metals: silver and copper. To that end, we use both our own computer program with a tight-binding potential and well-known LAMMPS software whose standard package is designed to model metal systems by the embedded atom method. Regardless of the choice between two relaxation techniques (lowtemperature relaxation at 1 K and the variant involving a gradual temperature decrease with subsequent relaxation at 1 K), magic number 13 is detected that corresponds to the first term of the Chini series. At the same time, other magic numbers are also found that belong and do not belong to this series.     

Evaporation of Lennard-Jones clusters

Extensive molecular dynamics simulations have been done to study the evaporation of a 13-atom Lennard-Jones cluster. The survival probability and the evaporative lifetime are calculated as a function of the cluster total energy from a classical trajectory analysis. The results are interpreted in terms of the RRK theory of unimolecular dissociation. The calculation of the binding energy of the evaporated species from the evaporation rate and the average kinetic energy release is discussed.     

Origin of the magic numbers of water clusters with an excess electron

Electron-bound water clusters [e(-)(H(2)O)(n)] show very strong peaks in mass spectra for n=2, 6, 7, and (11), which are called magic numbers. The origin of the magic numbers has been an enigma for the last two decades. Although the magic numbers have often been conjectured to arise from the intrinsic properties of electron-bound water clusters, we attributed them not to their intrinsic properties but to the particularly weak stability of the corresponding neutral water clusters (H(2)O)(n=2,6,7, and (11)). As the cluster size increases; this nonsmooth characteristic feature in stability of neutral water clusters is contrasted to the smooth increase in stability of e(-)-water clusters. As the magic number clusters have significant positive adiabatic electron affinities, their abundant distributions in atmosphere could play a significant role in atmospheric thermodynamics.     

Thermal decay of Lennard-Jones clusters

The decay mechanisms of argon clusters have been studied using Molecular Dynamics simulations and Lennard-Jones potentials. Heating up processes were applied to Ar₁₃ up to temperatures in the melting region. In this range of temperatures large fluctuations in the mean kinetic energy of the system are present and a sequential evaporation is observed. The thermal decay of these aggregates occurs in a time scale of nanoseconds.     

THF/H~2O二元团簇中“幻数”现象研究

利用分子束、同步辐射光源和飞行时间质谱研究了HF/H~2O二元团簇体系,观察到了一系列组成为(THF)~n·(H~2O)~mH^+(n=2～5,m=0～n-1)离子峰,其中(THF)~n(H~2O)~n~-~2H^+(n=2～5)离子峰强为“幻数”峰。运用从头算(abinitio)分子轨道法,在HF/3-21G基组水平上对(THF)~n(H~2O)~n~-~2H^+(n=2～4)团簇几何构型进行了优化,计算结果表明团簇离子(THF)~n(H~2O)~n~-~2H^+具有较大的稳定性,解释了实验中观察到的“幻数”现象。     

Structural rearrangements and magic numbers in reactions between pyridine-containing water clusters and ammonia

Molecular cluster ions H(+)(H(2)O)(n), H(+)(pyridine)(H(2)O)(n), H(+)(pyridine)(2)(H(2)O)(n), and H(+)(NH(3))(pyridine)(H(2)O)(n) (n = 16-27) and their reactions with ammonia have been studied experimentally using a quadrupole-time-of-flight mass spectrometer. Abundance spectra, evaporation spectra, and reaction branching ratios display magic numbers for H(+)(NH(3))(pyridine)(H(2)O)(n) and H(+)(NH(3))(pyridine)(2)(H(2)O)(n) at n = 18, 20, and 27. The reactions between H(+)(pyridine)(m)(H(2)O)(n) and ammonia all seem to involve intracluster proton transfer to ammonia, thus giving clusters of high stability as evident from the loss of several water molecules from the reacting cluster. The pattern of the observed magic numbers suggest that H(+)(NH(3))(pyridine)(H(2)O)(n) have structures consisting of a NH(4)(+)(H(2)O)(n) core with the pyridine molecule hydrogen-bonded to the surface of the core. This is consistent with the results of high-level ab initio calculations of small protonated pyridine/ammonia/water clusters.     

Structure of silver clusters with magic numbers of atoms by data of molecular dynamics

The behavior of silver clusters (cubic octahedron habit) with magic numbers of atoms N = 13, 55, 146, 309, 561, 923, 1415, and 2057 in the 0–1300 K temperature range is studied for the embeded atom model by the molecular dynamics method. The structural method for the analysis of the dynamics of local configurations of atoms based on the construction of angular characteristics of simplexes of the Delone partition of a cluster is proposed. Structural transitions of clusters with a cubic octahedron habit to the stable clusters with an icosahedron habit are revealed. Motions of atoms in clusters with an icosahedron habit are transformed into the stationary vibration mode. Middle positions of atoms in clusters tend to form shells with a regular structure. At N = 561, there are 15 such shells. The cluster with N = 561 at 650 K is characterized by a reduced density close to that of silver melt.     

A new proposal for the reason of magic numbers in alkali cation microhydration clusters

Alkali cation microhydration clusters M⁺(H₂O)_n, n≤24, M = Na, K, Cs, have been globally optimised, using a specialised version of genetic algorithms and the common TIP4P/OPLS model potential. The results constitute a first unbiased and systematic overview on structures of alkali cation microhydration clusters. Simple reasons for differing structural trends could be provided. Dodecahedral cages occur, but do not play as prominent a role as frequently believed. In particular, they do not seem to determine the occurrence of magic numbers. A structural pattern all magic number cluster structures do have in common is that only three and/or four-coordinated water molecules can be observed. Molecular dynamics simulations were run in the canonical ensemble, and free energy differences of dissociating clusters were obtained, with dodecahedral cages again showing no special feature. Structures containing only three and/or four-coordinated water molecules, however, are more stable than others thus arriving at a possible explanation for magic numbers.     

Melting of Lennard-Jones clusters in confined geometries

The melting of Lennard-Jones (argon) clusters of various size (N = 500 to 10000 atoms), confined in a rigid matrix, is studied by molecular dynamics simulations. For spherical clusters we show the existence of a cluster size below which the dependence of the melting temperature cannot be described by the classical Gibbs-Thompson equation. We also provide evidence of the formation of a quasi-liquid layer at the surface of mesoscopic clusters. A good agreement is found between the theoretical model due to Celestini et al. and the simulation results obtained in this work. The melting of an ellipsoidal cluster is also investigated. We observe, in agreement with recent experimental and theoretical work, that the thickness of the molten layer is larger in the region of higher local curvature.     

More on the melting of Lennard-Jones clusters

The melting of 13-atom clusters interacting via Lennard-Jones potentials has been revisited using molecular dynamics coupled to steepest descent quenches. A procedure was devised to account for the fraction of times the global and local minima of the potential energy surface are accessed during a long trajectory. This quantity presents a sigmoid shape. A phenomenological model of melting is given in terms of a correlated walk that maps the short time excursions among the global and local minima in configuration space. Comparison between the simulation results and the theoretical model shows that the melting transition is well described in terms of the temperature changes of the fraction of high energy minima accessed during the cluster trajectory. Cooperativity is clear from the S shape of this quantity, i.e., the access to a local minimum favours the access to other local minima.     

Excitation levels and magic numbers of small parahydrogen clusters (N<or=40)

The excitation energies of parahydrogen clusters have been systematically calculated by the diffusion Monte Carlo technique in steps of 1 molecule from 3 to 40 molecules. These clusters possess a very rich spectra, with angular momentum excitations arriving up to L=13 for the heavier ones. No regular pattern can be guessed in terms of the angular momenta and the size of the cluster. Clusters with N=13 and 36 are characterized by a peak in the chemical potential and a large energy gap of the first excited level, which indicate the magical character of these clusters. From the calculated excitation energies, the partition function has been obtained, thus allowing for an estimate of thermal effects. An enhanced production is predicted for cluster sizes of N=13, 31, and 36, which is in agreement with the experiment.     

Structure and dynamics of Lennard-Jones clusters with impurities

Molecular dynamics simulations and Lennard-Jones potentials have been used to study binary mixed clusters. The low temperature structures, impurity solvation and the melting and freezing transitions for different values of the relative atomic size and interaction energy have been studied forA ₁₃ B,A ₁₂ B,A ₅₅ B andA ₁₃ B ₁₃ clusters. ForA ₁₃ B large impurities do not solvate even for high interaction energy. ForA ₅₅ B larger impurities remain on the surface for low interaction energies but solvate as the energy of interaction increases. The presence of the impurity very strongly affects the solid-liquid transition. Icosahedral structures remain as the minimum energy configurations forA ₁₃ B ₁₃ clusters with atoms of the same size and different interaction energies. ForA ₁₃ B ₁₃ clusters with atoms of the same interaction energy and different size, smaller atoms go inside surrounded by the bigger surface atoms.     

Binding energy of large icosahedral and cuboctahedral Lennard-Jones clusters

It is widely believed that the lowest energy configurations for small rare gas clusters have icosahedral symmetry. This contrasts with the bulk crystal structures which have cuboctahedral fcc symmetry. It is of interest to understand the transition between this finite and bulk behavior. To model this transition in rare gas clusters we have undertaken optimization studies within the Lennard-Jones pair potential model. Using a combination of Monte Carlo and Partan Search optimization methods, the lowest energy relaxed structures of Lennard-Jones clusters having icosahedral and cuboctahedral symmetry were found. Studies were performed for complete shell clusters ranging in size from one shell having 13 atoms to 14 shells having 10,179 atoms. It was found that the icosahedral structures are lower in energy than the cuboctahedral structures for cluster sizes having 13 shells or fewer. Additional studies were performed using the more accurate Aziz-Chen [HFD-C] pair potential parameterized for argon. The conclusions appear to be relatively insensitive to the form of the potential.     

Some aspects of dynamic chaos in small Lennard-Jones clusters

For the purpose of studying stochastic phenomena in the clusters due to an instability of their trajectories in phase space, an evolution of ensembles of the clusters with the representative points initially located in small regions of phase space is investigated using the molecular dynamics method. A path of a cloud of the representative points through the subspace of phase space available for the clusters, and cloud growth in size and in volume are considered. Specific results are presented for Ar₄. A “cold” cluster (subjected to neither an isomerization nor an evaporation) is examined in details. A brief comparison with a “hot” cluster (both the phenomena are available) is given.     

Prediction of the lowest energy configuration for Lennard-Jones clusters

Based on the work of previous researchers, a new unbiased optimization algorithm—the dynamic lattice searching method with two-phase local search and interior operation (DLS-TPIO)—is proposed in this paper. This algorithm is applied to the optimization of Lennard-Jones (LJ) clusters with N=2–650, 660, and 665–680. For each case, the putative global minimum reported in the Cambridge Cluster Database (CCD) is successfully found. Furthermore, for LJ533 and LJ536, the potential energies obtained in this study a...     

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...     

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.