Nose has derived a set of dynamical equations that can be shown to give canonically distributed positions and momenta provided the phase space average can be taken into the trajectory average, i.e., the system is ergodic [S. Nose, J. Chem. Phys. 81, 511 (1984), W. G. Hoover, Phys. Rev. A 31, 1695 (1985)]. Unfortunately, the Nose–Hoover dynamics is not ergodic for small or stiff systems. Here a modification of the dynamics is proposed which includes not a single thermostat variable but a chain of variables, Nose–Hoover chains. The ‘‘new’’ dynamics gives the canonical distribution where the simple formalism fails. In addition, the new method is easier to use than an extension [D. Kusnezov, A. Bulgac, and W. Bauer, Ann. Phys. 204, 155 (1990)] which also gives the canonical distribution for stiff cases.

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Nosé-Hoover chains : the canonical ensemble via continuous dynamics

5.1. Nanoalloys of Group 11 (Cu, Ag, Au) 865 5.1.1. Cu−Ag 866 5.1.2. Cu−Au 867 5.1.3. Ag−Au 870 5.1.4. Cu−Ag−Au 872 5.2. Nanoalloys of Group 10 (Ni, Pd, Pt) 872 5.2.1. Ni−Pd 872 * To whom correspondence should be addressed. Phone: +39010 3536214. Fax:+39010 311066. E-mail: ferrando@fisica.unige.it. † Universita di Genova. ‡ Argonne National Laboratory. § University of Birmingham. | As of October 1, 2007, Chemical Sciences and Engineering Division. Volume 108, Number 3

Nanoalloys: From Theory to Applications of Alloy Clusters and Nanoparticles

Core/Shell Nanoparticles: Classes, Properties, Synthesis Mechanisms, Characterization, and Applications

Metal species with different size (single atoms, nanoclusters, and nanoparticles) show different catalytic behavior for various heterogeneous catalytic reactions. It has been shown in the literature that many factors including the particle size, shape, chemical composition, metal–support interaction, and metal–reactant/solvent interaction can have significant influences on the catalytic properties of metal catalysts. The recent developments of well-controlled synthesis methodologies and advanced characterization tools allow one to correlate the relationships at the molecular level. In this Review, the electronic and geometric structures of single atoms, nanoclusters, and nanoparticles will be discussed. Furthermore, we will summarize the catalytic applications of single atoms, nanoclusters, and nanoparticles for different types of reactions, including CO oxidation, selective oxidation, selective hydrogenation, organic reactions, electrocatalytic, and photocatalytic reactions. We will compare the results o...

Metal Catalysts for Heterogeneous Catalysis: From Single Atoms to Nanoclusters and Nanoparticles.

The structural properties of free nanoclusters are reviewed. Special attention is paid to the interplay of energetic, thermodynamic, and kinetic factors in the explanation of cluster structures that are actually observed in experiments. The review starts with a brief summary of the experimental methods for the production of free nanoclusters and then considers theoretical and simulation issues, always discussed in close connection with the experimental results. The energetic properties are treated first, along with methods for modeling elementary constituent interactions and for global optimization on the cluster potential-energy surface. After that, a section on cluster thermodynamics follows. The discussion includes the analysis of solid-solid structural transitions and of melting, with its size dependence. The last section is devoted to the growth kinetics of free nanoclusters and treats the growth of isolated clusters and their coalescence. Several specific systems are analyzed.

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Structural properties of nanoclusters: Energetic, thermodynamic, and kinetic effects

Simulations by molecular dynamics of 13‐particle clusters of argon display distinct nonrigid, liquid‐like and near‐rigid, solid‐like ‘‘phases.’’ The simulations, conducted at constant total energy, display a low‐energy region in which only the solid‐like form appears, a high‐energy region in which only the liquid‐like form appears, and an intermediate band of energy—a ‘‘coexistence region’’— in which clusters exhibit both forms. The intervals of time spent in each phase in the two‐form coexistence region are long compared with the intervals required to establish equilibrium‐like properties distinctive of each form, such as mean square displacement and power spectrum, so that well‐defined phases can be said to exist. The fraction of time spent in each phase is a function of the energy. When a long simulation is separated into regions of solid‐like and liquid‐like behavior, the curve of the derived caloric equation of state is double valued in the two‐phase range of energy, forming two well‐defined, smooth branches. When, instead, the caloric curve is constructed from averages over all of a long run, its form is smooth and monotonic showing no trace of the ‘‘loop’’ that had been reported for earlier treatments with much shorter molecular dynamics runs, and which we could also reproduce with short runs.

Solid–liquid phase changes in simulated isoenergetic Ar13

Simulations by constant energy molecular dynamics have been performed for numerous clusters in the size range N=7–33. Detailed investigations have been conducted on the portions of the caloric curves in which the transition between rigid and nonrigid behavior occurs, to study the N dependence of the solid–liquid phase change. Clusters of several sizes display a coexistence of forms, each with a characteristic mean temperature, over a well‐defined energy range in the transition region, as had been observed for the Ar13 cluster. Within the coexistence region, the high temperature form is solid‐like and the low temperature form behaves in a liquid‐like fashion. The caloric curves of state for these clusters take on two‐valued forms when averages are calculated for each of the two ‘‘phases’’ separately; the two branches are smooth extensions of the curves from the single phase regions. Clusters of other sizes do not display this clear coexistence of phases, but appear to pass through a ‘‘slush‐like’’ state du...

Rare gas clusters: Solids, liquids, slush, and magic numbers

Phases and Phase Changes of Small Systems Physics of Clusters and Cluster Assemblies Structures, Vibrational Frequency Shifts and Photodissociation of ArnHF van der Waals Clusters Rearrangements of Water Dimer and Hexamer Fullerene Collisions Predicting the Properties of Semiconductor Clusters Structure, Reactivity and Dynamics of Atomic and Molecular Clusters .. Ultrafast Structural Response and Nonlinear Fragmentation Dynamics .. Electron Dynamics in Metal Clusters Accurate Phase Spase Theory and Molecular Dynamics Calculations of Aluminum Cluster Dissociation Electronic Structure of Bimetallic Clusters Based on Alkali Elements Alloy Clusters Quantum Mechanics of Hydrogen on Nickel and Palladium Clusters Metal-Cluster-Surface Interactions Experimental Studies of the Structures and Isomerization of Atomic Clusters Silver Clusters and Silver Cluster / Ammonia Complexes Laser-Femtochemistry of Small Clusters.

Julius Jellinek

Papers

Nanoalloys: From Theory to Applications of Alloy Clusters and Nanoparticles

Solid–liquid phase changes in simulated isoenergetic Ar13

Rare gas clusters: Solids, liquids, slush, and magic numbers

Nanoalloys: From Theory to Applications of Alloy Clusters and Nanoparticles

Theory of Atomic and Molecular Clusters: With a Glimpse at Experiments