Energetic ion bombardment of Ag surfaces by C<Stack><Subscript>60</Subscript><Superscript>+</Superscript></Stack> and Ga<Superscript>+</Superscript> projectiles

The ion bombardment-induced release of particles from a metal surface is investigated using energetic fullerene cluster ions as projectiles. The total sputter yield as well as partial yields of neutral and charged monomers and clusters leaving the surface are measured and compared with corresponding data obtained with atomic projectile ions of similar impact kinetic energy. It is found that all yields are enhanced by about one order of magnitude under bombardment with the C60+ cluster projectiles compared with Ga+ ions. In contrast, the electronic excitation processes determining the secondary ion formation probability are unaffected. The kinetic energy spectra of sputtered particles exhibit characteristic differences which reflect the largely different nature of the sputtering process for both types of projectiles. In particular, it is found that under C60+ impact (1) the energy spectrum of sputtered atoms peaks at significantly lower kinetic energies than for Ga+ bombardment and (2) the velocity spectra of monomers and dimers are virtually identical, a finding which is in pronounced contrast to all published data obtained for atomic projectiles. The experimental findings are in reasonable agreement with recent molecular dynamics simulations.     

Investigation of the formation of M 2 + -molecular ions in sputtering processes

The formation process of M₂⁺ molecular ions sputtered from elementary target materials is investigated. In a previous article it was shown that these molecules can be used to quantitate major elements [1]. The quantitation method was based on the assumption that the M₂⁺ molecular ions are formed by the atomic combination of independently sputtered M and M ⁺ particles above the surface. In this paper this assumption will be investigated using a Monte Carlo model to simulate the formation mechanism. The model is used to calculate the velocity distribution of the M₂⁺ dimers sputtered from three different elementary target materials (Fe, Ge, and Ni). The results are compared with experimental data. Good agreement exists between theory and experiment that supports the Monte Carlo model and hence also the assumed formation mechanism.     

钯团簇形成和增长机理的Monte Carlo研究

利用Monte Carlo（MC）方法和Lennard-Jones加Axilord-Teller （LJ＋AT）势能函数,研究了气相中钯团簇的形成过程和增长机理.发现具有二十面体结构的Pd13团簇可以在气相中自发形成,较大的团簇通过在Pd13二十面体结构的表面添加原子组成四面体的方式形成.通过分析团簇结构和能量之间的关系,发现除了Pd13和Pd55以外,Pd19和Pd39团簇也具有五次对称性,都是比较稳定的结构.     

Connection between the virial equation of state and physical clusters in a low density vapor

We carry out Monte Carlo simulations of physical Lennard-Jones and water clusters and show that the number of physical clusters in vapor is directly related to the virial equation of state. This relation holds at temperatures clearly below the critical temperatures, in other words, as long as the cluster-cluster interactions can be neglected--a typical assumption used in theories of nucleation. Above a certain threshold cluster size depending on temperature and interaction potential, the change in cluster work of formation can be calculated analytically with the recently proposed scaling law. The breakdown of the scaling law below the threshold sizes is accurately modeled with the low order virial coefficients. Our results indicate that high order virial coefficients can be analytically calculated from the lower order coefficients when the scaling law for cluster work of formation is valid. The scaling law also allows the calculation of the surface tension and equilibrium vapor density with computationally efficient simulations of physical clusters. Our calculated values are in good agreement with those obtained with other methods. We also present our results for the curvature dependent surface tension of water clusters.     

Monte Carlo simulations of critical cluster sizes and nucleation rates of water

We have calculated the critical cluster sizes and homogeneous nucleation rates of water at temperatures and vapor densities corresponding to experiments by Wolk and Strey [J. Phys. Chem B 105, 11683 (2001)]. The calculations have been done with an expanded version of a Monte Carlo method originally developed by Vehkamaki and Ford [J. Chem. Phys. 112, 4193 (2000)]. Their method calculates the statistical growth and decay probabilities of molecular clusters. We have derived a connection between these probabilities and kinetic condensation and evaporation rates, and introduce a new way for the calculation of the work of formation of clusters. Three different interaction potential models of water have been used in the simulations. These include the unpolarizable SPC/E [J. Phys. Chem. 91, 6269 (1987)] and TIP4P [J. Chem. Phys. 79, 926 (1983)] models and a polarizable model by Guillot and Guissani [J. Chem. Phys. 114, 6720 (2001)]. We show that TIP4P produces critical cluster sizes and a temperature and vapor density dependence for the nucleation rate that agree well with the experimental data, although the magnitude of nucleation rate is constantly overestimated by a factor of 2 x 10(4). Guissani and Guillot's model is somewhat less successful, but both the TIP4P and Guillot and Guissani models are able to reproduce a much better experimental temperature dependency of the nucleation rate than the classical nucleation theory. Using SPC/E results in dramatically too small critical clusters and high nucleation rates. The water models give different average binding energies for clusters. We show that stronger binding between cluster molecules suppresses the decay probability of a cluster, while the growth probability is not affected. This explains the differences in results from different water models.     

Two-dimensional Monte Carlo simulations of a polydisperse colloidal dispersion composed of ferromagnetic particles for the case of no external magnetic field

We have investigated the aggregation phenomena in a polydisperse colloidal dispersion composed of ferromagnetic particles by means of the cluster-moving Monte Carlo method. The results have been compared with those for a monodisperse system. The internal structures of aggregates have been analyzed in terms of the radial distribution function in order to clarify the quantitative differences in the internal structures of clusters. In addition, the cluster size distribution and angular distribution function have been investigated. The results obtained in the present study are summarized as follows. In a monodisperse system, open necklacelike clusters are formed and they extend with increasing strength of the magnetic particle-particle interaction. In a polydisperse system with a small standard deviation in the particle size distribution, sigma=0.2, larger necklacelike clusters are formed and some looplike clusters can also be observed. In a polydisperse system with a larger standard deviation, sigma=0.35, clumplike clusters are formed for a weak magnetic particle-particle interaction. For a stronger magnetic interaction, larger size clusters that exhibit a complicated network structure are formed. These complicated cluster formations found in a polydisperse system are mainly due to the effect of the presence of larger particles.     

A study of nucleic acid base-stacking by the Monte Carlo method: Extended cluster approach

The adenine-thymine (AT), adenine-uracil (AU) and guanine-cytosine (GC) base associates in clusters containing 400 water molecules were studied using a newly implemented Metropolis Monte Carlo algorithm based on the extended cluster approach. Starting from the hydrogen-bonded Watson-Crick geometries, all three base pairs are transformed into more favorable stacked configurations during the simulation. The obtained results show, for the first time, the transition from planar base pairs to stacked base associates in the Monte Carlo framework. Analysis of the interaction energies shows that, in the water cluster, the stacked dimers are energetically preferable compared to the corresponding Watson-Crick base pairs. This is due to the larger base-water interaction in the stacked structures. The water-water interaction is one of the main factors promoting the formation of stacked dimers, and the obtained data confirm the crucial role of the water-water interactions in base stacking.     

The molecular approach to heterogeneous nucleation

A molecular approach to heterogeneous nucleation has been developed. The expressions for the equilibrium cluster distribution, the reversible work of the cluster formation, and the nucleation rate have been derived. Two separate statements for the work of formation were formulated. If the equilibrium cluster distribution is normalized on the monomer concentration near the substrate surface, the reversible work of formation is expressed by DeltaG(het) (I) = (F(n) (het)-F(n) (hom))-(F(1) (het)-F(1) (hom)) + DeltaG(hom) where F(n) (het) and F(n) (hom) are the Helmholtz free energies of a cluster interacting with a substrate and a cluster not interacting with the substrate, respectively. If the equilibrium cluster distribution is normalized on the monomer concentration far from the substrate surface, the work of cluster formation is given by DeltaG(het) (II) = (F(n) (het)-F(n) (hom)) + DeltaG(hom). The former expression corresponds to the approach of the classical heterogeneous nucleation theory. The cluster partition function appears to be dependent on the location of a virtual plane, which separates the volume, where the interaction of the clusters with the substrate is effective from the one where interaction is negligible. Our Monte Carlo simulations have shown that the dependence is rather weak and thus the location of the plane is not very important. According to the simulations the variation of the plane position in the range from 20 to 50 Angstroms does not lead to a considerable change of the heterogeneous nucleation rate.     

Can we understand the different coordinations and structures of closed‐shell metal cation‐water clusters?

We present a model potential for studying M(q+)(H(2)O)(n=1,9) clusters where M stands for either Na(+), Cs(+), Ca(2+), Ba(2+), or La(3+). The potential energy surfaces (PES) are explored by the Monte Carlo growth method. The results for the most significant equilibrium structures of the PES as well as for energetics are favorably compared to the best ab initio calculations found in the literature and to experimental results. Most of these complexes have a different coordination number in cluster compared to experimental results in solution or solid phase. An interpretation of the coordination number in clusters is given. In order to well describe the transition between the first hydration sphere and the second one we show that an autocoherent treatment of the electric field is necessary to correctly deal with polarization effects. We also explore the influence of the cation properties (charge, size, and polarizability) on both structures and coordination number in clusters, as well as the meaning of the second hydration sphere. Such an approach shows that the leading term in the interaction energy for a molecule in the second hydration sphere is an electrostatic attraction to the cation and not a hydrogen bond with the water molecules in the first hydration sphere.     

Monte Carlo computer simulations and electron microscopy of colloidal cluster formation via emulsion droplet evaporation

We consider a theoretical model for a binary mixture of colloidal particles and spherical emulsion droplets. The hard sphere colloids interact via additional short-ranged attraction and long-ranged repulsion. The droplet-colloid interaction is an attractive well at the droplet surface, which induces the Pickering effect. The droplet-droplet interaction is a hard-core interaction. The droplets shrink in time, which models the evaporation of the dispersed (oil) phase, and we use Monte Carlo simulations for the dynamics. In the experiments, polystyrene particles were assembled using toluene droplets as templates. The arrangement of the particles on the surface of the droplets was analyzed with cryogenic field emission scanning electron microscopy. Before evaporation of the oil, the particle distribution on the droplet surface was found to be disordered in experiments, and the simulations reproduce this effect. After complete evaporation, ordered colloidal clusters are formed that are stable against thermal fluctuations. Both in the simulations and with field emission scanning electron microscopy, we find stable packings that range from doublets, triplets, and tetrahedra to complex polyhedra of colloids. The simulated cluster structures and size distribution agree well with the experimental results. We also simulate hierarchical assembly in a mixture of tetrahedral clusters and droplets, and find supercluster structures with morphologies that are more complex than those of clusters of single particles.     

Monte Carlo Simulation of the Assembly of bis‐Biotinylated DNA and Streptavidin

We present Monte Carlo simulations of the self‐assembly of bivalent bis‐biotinylated DNA molecules with the tetravalent biotin‐binding protein streptavidin (STV). By fitting the STV binding probabilities for the four possible valencies, the modelling correctly reproduces the dependencies of various network parameters experimentally observed in an earlier study. The combined results from the experimental and theoretical studies suggest that the binding probability for divalent STV formation is about 50 times larger than for the formation of trivalent and about 200 times larger than for tetravalent STV. In accordance with the experimental results, the modelling also indicates that the mixture of an equimolar ratio of DNA and STV leads to a maximum in size of the oligomeric DNA–STV clusters formed. Furthermore, we found a percolation transition in which the DNA cluster size increases rapidly with increasing DNA concentration resulting in the formation of a single supercluster at elevated concentrations. This behaviour coincides with the occurrence of an immobile band previously observed in electrophoretic experiments, indicating the formation of extremely large DNA–STV aggregate networks.     

Investigations of cluster ions formed between cesium cations and benzoic, salicylic and phthalic acids by electrospray mass spectrometry and density-functional theory calculations. Toward a modeling of the interaction of Cs+ with humic substances

A concerted theoretical (density-functional theory) and experimental electrospray mass spectrometry study was conducted on the formation of cesium cation adducts with small molecules taken as models of specific interactions sites in humic substances. Electrospray experiments with phenol, benzoic acid, salicylic acid, and phthalic acid, in methanolic solution containing cesium nitrate, were performed using a quadrupole ion trap. The formation of positively charged mixed clusters, [Cs(CsNO3)(n)(CsA1)(m)(Cs2A2)(p)]+ (A1 = benzoate, salicylate, and hydrogenophthalate, A2 = phthalate), was observed. Calculations of structures and bonding energetics of Cs+ in simple adducts formed with NO3-, CsNO3, A-, AH, and CsA are reported. The observation of variable cluster stoichiometry (n, m and p values) was interpreted in terms of more or less favorable interaction energies between Cs+ and the neutral species constituting the clusters. Phenol did not form clusters in significant abundances, despite a strong calculated interaction between Cs+ and cesium phenolate. This was attributed to its weak acid dissociation in the electrospray solution.     

Path integral ground state study of finite-size systems: application to small (parahydrogen)N (N=2-20) clusters

We use the path integral ground state method to study the energetic and structural properties of small para-H2 clusters of sizes ranging from 2 to 20 molecules. A fourth order formula is used to approximate the short imaginary-time propagator and two interaction potentials are considered. Our results are compared to those of exact basis set calculations and other quantum Monte Carlo methods when available. We find that for all cluster sizes considered, our results show a lower ground state energy than literature values obtained by diffusion Monte Carlo and variational Monte Carlo. For the dimer and trimer, ground state energies are in good agreement with exact results obtained using the discrete variable representation. Structural properties are found to be insensitive to the choice of interaction potential. We explore the use of Pekeris coordinates to analyze the importance of linear arrangement in trimers and for trimers within clusters of larger size.     

Two-dimensional Monte Carlo simulations of a colloidal dispersion composed of rod-like ferromagnetic particles in the absence of an applied magnetic field

Influences of the magnetic interaction between particles and the aspect ratio of particles on aggregate structures in a colloidal dispersion composed of rod-like ferromagnetic particles were investigated by means of the cluster-moving Monte Carlo method. The internal structures of the aggregates obtained in simulations were analyzed in terms of the number density distribution of the clusters and radial distribution functions. The results show that as the magnetic interaction between particles increases, many small clusters such as anti-parallel particle pairs, raft-like clusters, and small loop-like clusters are formed; these gather to form larger aggregates. In the case of a relatively strong magnetic interaction between particles, solid-like rectangular clusters are formed when the aspect ratio is approximately 2, since the suitable distance between magnetic charges enables particles to form a fundamental structure of two normal anti-parallel particle pairs. As the aspect ratio increases beyond 2, many more stable raft-like clusters are formed, since the increase in distance between magnetic charges makes the two normal anti-parallel particle pair structures unstable. For a significantly larger aspect ratio, large network microstructures are produced by the formation of many chain-like and loop-like structures.     

Protein-polyelectrolyte cluster formation and redissolution: a Monte Carlo study

Aqueous solutions of proteins and oppositely charged polyelectrolytes were studied at different polyelectrolyte chain length, ionic strength, and protein-protein interaction potential as a function of the polyelectrolyte concentration. One of the protein models used represented lysozyme in aqueous environment. The model systems were solved by Monte Carlo simulations, and their properties were analyzed in terms of radial distribution functions, structure factors, and cluster composition probabilities. In the system with the strongest electrostatic protein-polyelectrolyte interaction the largest clusters were formed near or at equivalent amount of net protein charge and polyelectrolyte charge, whereas in excess of polyelectrolyte a redissolution appeared. Shorter polyelectrolyte chains and increased ionic strength lead to weaker cluster formation. An inclusion of nonelectrostatic protein-protein attraction promoted the protein-polyelectrolyte cluster formation.     

Clusterization of water molecules on crystalline β-AgI surface. Computer experiment

The free energy and the work of formation of the clusters of water molecules from the vapor on the ideal continuous crystalline surface of silver iodide at 260 and 300 K are calculated with the Monte Carlo method for a bicanonical statistical ensemble. Long-range electrostatic and polarization interactions with the surface are calculated with the two-dimensional Ewald method. It is shown that the adsorption of water molecules is accompanied by their intense clusterization. At negative Celsius temperatures, hydrogen-bonded molecules form the chains on the crystal surface. The closure of chains into rings begins with the clusters containing five molecules. As cluster sizes increase, the competition between five-and six-membered cycles is ended in favor of six-membered cycles. The substrate field stimulates the formation of six-membered cycles. Entropic effects strongly level the influence of clusterization on the probability of adsorption. Within the size interval 1 < N < 15, there are two clusterization barriers whose heights are negligible and equal to about 2k _B T. The presence of a substrate lowers the vapor pressure of clusterization by more than an order of magnitude.     

A quasichemical approach for protein-cluster free energies in dilute solution

Reversible formation of protein oligomers or small clusters is a key step in processes such as protein polymerization, fibril formation, and protein phase separation from dilute solution. A straightforward, statistical mechanical approach to accurately calculate cluster free energies in solution is presented using a cell-based, quasichemical (QC) approximation for the partition function of proteins in an implicit solvent. The inputs to the model are the protein potential of mean force (PMF) and the corresponding subcell degeneracies up to relatively low particle densities. The approach is tested using simple two and three dimensional lattice models in which proteins interact with either isotropic or anisotropic nearest-neighbor attractions. Comparison with direct Monte Carlo simulation shows that cluster probabilities and free energies of oligomer formation (DeltaG(i) (0)) are quantitatively predicted by the QC approach for protein volume fractions approximately 10(-2) (weight/volume concentration approximately 10 g l(-1)) and below. For small clusters, DeltaG(i) (0) depends weakly on the strength of short-ranged attractive interactions for most experimentally relevant values of the normalized osmotic second virial coefficient (b(2) (*)). For larger clusters (i"2), there is a small but non-negligible b(2) (*) dependence. The results suggest that nonspecific, hydrophobic attractions may not significantly stabilize prenuclei in processes such as non-native aggregation. Biased Monte Carlo methods are shown to accurately provide subcell degeneracies that are intractable to obtain analytically or by direct enumeration, and so offer a means to generalize the approach to mixtures and proteins with more complex PMFs.     

Self-assembling of chain molecules in low dimensions: A Monte Carlo study

We studied the self-assembling of linear chain molecules in insoluble monolayers due to attractive interactions. We used lattice Monte Carlo simulations in a two-dimensional system. The molecules consist of segments occupying adjacent lattice sites. The head segments are confined to move along a line whereas the chain segments can arrange in a plane above the heads. Only one interaction parameter is applied. At high densities and small interaction energy the system shows percolation behavior. At moderate and small densities it can be characterized by a monotonous cluster size distribution. Self-assembling occurs at small densities for strong attractive interactions. The corresponding cluster size distributions indicate preferred cluster sizes which depend upon density and interaction strength. With increasing density the clusters grow. The internal cluster structure depends on the cluster size and the interaction parameter. The clusters tend to minimize their total energy. Molecules at cluster margins contribute less to the cluster energy and are mainly disordered. They cause that the cluster properties strongly depend on the cluster size. Large clusters only have minimum energy if the molecules in the cluster are in stretched-out conformation. With decreasing interaction strength the clusters get disordered thereby producing less energy-minimized domain boundaries.     

Nin(n=3～39)团簇结构，能量和稳定性的研究

The stable geometric structure and energy of Ni_n(n=3～39) clusters as a function of cluster size are studied by the Monte Carlo simulation. The interaction among atoms is calculated through Lennard-Jones plus Axilrod-Teller potentials. It is found that the clusters grow through adding atoms on one or more surfaces of Ni₇ or Ni₁₃ after the cluster size n is larger than 7. It is also found that there exists direct correlation between the stability and geometrical structures of clusters. Relatively, highly symmetry clusters are more stable. In addition, the nickel clusters with fcc-like structure such as Ni₃₃, Ni₃₆ and Ni₃₈ are more stable than their neighboring clusters.     

Quantum simulation of a hydrated noradrenaline analog with the torsional path integral method

An extended version of the torsional path integral Monte Carlo (TPIMC) method is presented and shown to be useful for studying the conformation of flexible molecules in solvated clusters. The new technique is applied to the hydrated clusters of the 2-amino-1-phenyl-ethanol (APE) molecule. APE + nH2O clusters with n = 0-4 are studied at 100 and 300 K using both classical and quantum simulations. Only at the lower temperature is the hydration number n found to impact the conformational distribution of the APE molecule. This is shown to be a result of the temperature-dependent balance between the internal energy and entropy contributions to the relative conformer free energies. Furthermore, at 100 K, large quantum effects are observed in the calculated conformer populations. A particularly large quantum shift of 30% of the total population is calculated for the APE + 2H2O cluster, which is explained in terms of the relative zero point energy of the lowest-energy hydrated structures for this cluster. Finally, qualitative agreement is found between the reported calculations and recent spectroscopy experiments on the hydrated clusters of APE, including an entropically driven preference for the formation of AG-type hydrated structures and the formation of a water "droplet" in the APE + 4H2O cluster.