Temperatures of rotating clusters

The effect of the spatial anisotropy in the distribution of components of particle momenta of the rotating Ar₃ cluster is studied at a given total energy and different values of the total angular momentum. The Schwarzschild formula applied to describe this distribution gives three parameters which can serve as a measure of the internal temperatures of the cluster. A new definition of the energy of the overall non-rigid rotation based on the Schwarzschild distribution is proposed.     

Statistical evaporation of rotating clusters. III. Molecular clusters

Unimolecular evaporation of weakly bound clusters made of rigid molecules is considered from the points of view of statistical theories and molecular dynamics simulations. We explicitly work out expressions for the kinetic energy released and product angular momentum distributions within the sphere+sphere and sphere+linear rigid body assumptions of phase space theory (PST). Various approximations are investigated, including the shape of the interaction potential between the two fragments and the anharmonicity of the vibrational density of states. The comparison between phase space theory and simulation for nitrogen and methane clusters shows a quantitative agreement, thereby suggesting that PST is accurate in predicting statistical observables in a wide range of systems under various physical conditions.     

Superfluid effects in rotating helium clusters

We study the response of Bose⁴He clusters to an external field corresponding to a rotation with frequency ω. An explicit form for the normal (nonsuperfluid) fraction of the system as a function of the temperatureT and of the mass numberN of the cluster is obtained under the assumption that only surface modes are thermally excited. The critical behaviour of⁴He clusters at high rotational frequencies is also investigated.     

Fractal structure of three-dimensional Witten—Sander clusters

Five large (25 000 particle) three-dimensional Witten—Sander clusters have been generated, and geometric relationships characterizing this structure have been examined. The quantities measured include the dependence of the radius of gyration. (r²)^{$\text{1}\text{2}$}, and (r⁴)^{$\text{1}\text{4}$} on cluster size N, the mass M(r) contained within a distance r from the center mass, the dependence of the areas of projections of the clusters onto a plane of cluster size N, the density—density correlation function and the distribution of particles (occupied lattice sites) in cubes of side λ as a function of λ. Although uncertainties are quite large, our results are consistent with the concept hat the geometric scaling properties of three-dimensional Witten—Sander clusters can be described in terms of a single effective dimensionality D with a value of = 2.45. Additional results are also presented for two-dimensional Witten—Sander clusters which indicate a single effective dimensionality with a value of = 5/3.     

Effective magnetization of rotating free ferromagnetic metal clusters

The deflection of free magnetic metal clusters in a Stern-Gerlach magnetic field is studied. In particular we investigate magnetic resonance effects resulting from lattice anisotropy and cluster rotation. In analogy to small suspended particles in an oscillating magnetic field the anisotropy field fixed to the rotating atomic lattice of the cluster acts on the cluster magnetization like an rf field in NMR experiments. In our calculation we have used the Bloch equations and assumed different anisotropy field symmetries (uniaxial, cubic). A minimum in the magnetization as a function of the Stern-Gerlach field and also of the cluster size, as observed recently, is obtained under certain conditions. However, such a resonance behavior occurs only if the distribution of the rotation frequency _rot is relatively narrow, while a broad distribution of _rot yields an almost superparamagnetic behavior. In addition, the strength of the anisotropy field and the relaxation time are important variables which determine the magnetic behavior of the clusters.     

Size‐guided multi‐seed heuristic method for geometry optimization of clusters: Application to benzene clusters

Since searching for the global minimum on the potential energy surface of a cluster is very difficult, many geometry optimization methods have been proposed, in which initial geometries are randomly generated and subsequently improved with different algorithms. In this study, a size‐guided multi‐seed heuristic method is developed and applied to benzene clusters. It produces initial configurations of the cluster with n molecules from the lowest‐energy configurations of the cluster with n − 1 molecules (seeds). The initial geometries are further optimized with the geometrical perturbations previously used for molecular clusters. These steps are repeated until the size n satisfies a predefined one. The method locates putative global minima of benzene clusters with up to 65 molecules. The performance of the method is discussed using the computational cost, rates to locate the global minima, and energies of initial geometries. © 2018 Wiley Periodicals, Inc.     

Statistical evaporation of rotating clusters. IV. Alignment effects in the dissociation of nonspherical clusters

Unimolecular evaporation in rotating, nonspherical atomic clusters is investigated using phase space theory in its orbiting transition state version. The distributions of the total kinetic energy release epsilon(tr) and the rotational angular momentum J(r) are calculated for oblate top and prolate top main products with an arbitrary degree of deformation. The orientation of the angular momentum of the product cluster with respect to the cluster symmetry axis has also been obtained. This statistical approach is tested in the case of the small eight-atom Lennard-Jones cluster, for which comparison with extensive molecular dynamics simulations is presented. The role of the cluster shape has been systematically studied for larger, model clusters in the harmonic approximation for the vibrational densities of states. We find that the type of deformation (prolate versus oblate) plays little role on the distributions and averages of epsilon(tr) and J(r) except at low initial angular momentum. However, alignment effects between the product angular momentum and the symmetry axis are found to be significant, and maximum at some degree of oblateness. The effects of deformation on the rotational cooling and heating effects are also illustrated.     

Performance of density‐functional tight‐binding models in describing hydrogen‐bonded anionic‐water clusters

Density‐functional tight‐binding (DFTB) models are computationally efficient approximations to density‐functional theory that have been shown to predict reliable structural and energetic properties for various systems. In this work, the reliability and accuracy of the self‐consistent‐charge DFTB model and its recent extension(s) in predicting the structures, binding energies, charge distributions, and vibrational frequencies of small water clusters containing polyatomic anions of the Hofmeister series (carbonate, sulfate, hydrogen phosphate, acetate, nitrate, perchlorate, and thiocyanate) have been carefully and systematically evaluated on the basis of high‐level ab initio quantum‐chemistry [MP2/aug‐cc‐pVTZ and CCSD(T)/aug‐cc‐pVQZ] reference data. Comparison with available experimental data has also been made for further validation. The self‐consistent‐charge DFTB model, and even more so its recent extensions, are shown to properly account for the structural properties, energetics, intermolecular polarization, and spectral signature of hydrogen‐bonding in anionic water clusters at a fraction of the computational cost of ab initio quantum‐chemistry methods. This makes DFTB models candidates of choice for investigating much larger systems such as seeded water droplets, their structural properties, formation thermodynamics, and infrared spectra. © 2014 Wiley Periodicals, Inc.     

A model for thermal spin relaxation in rotating ferromagnetic clusters

A model for thermal spin relaxation in isolated ferromagnetic clusters is proposed and investigated theoretically by means of nonequilibrium thermodynamics. It is shown that thermal agitation mediates relaxation of the spin towards the total angular momentum vector of the cluster so that the clusters are magnetically polarized in the direction of their rotational axis. A relaxation mechanism via thermal moment of inertia fluctuations is proposed. The results are discussed for a Fe₁₂₅-cluster.     

The rotation‐vibration spectrum of diatomic molecules with the tietz‐hua rotating oscillator

The Tietz‐Hua (TH) potential is one of the very best analytical model potentials for the vibrational energy of diatomic molecules. By using the Nikiforov‐Uvarov method, we have obtained the exact analytical s‐wave solutions of the radial Schrödinger equation for the TH potential. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. Some numerical results for diatomic molecules are also presented. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Nanoscopic structure and function of polymer‐protected metal clusters

Colloidal dispersion of polymer‐protected metal clusters were prepared by heat treatment of macromolecule‐metal complexes, composed of water‐soluble polymer and noble metal ions. The mixtures of two kinds of noble metal ions can provide polymer‐protected bimetallic nanoclusters with a core/shell structure by the same procedure. In contrast, bimetallic clusters with the inverted core/shell structure are difficult to be prepared by the similar procedure. A sacrificial hydrogen strategy has been successfully proposed for the preparation of the inverted ones. When copper or nickel ions were used as one of the elements to prepare bimetallic clusters, rather random alloy structured nanoparticles were produced. The catalytic activity of these bimetallic clusters is, in general, higher than that of the corresponding monometallic ones.     

Self‐assembled supramolecular microgels: Fractal structure and aggregation mechanism

Multifunctional molecules were designed to produce microgels with specific structures. Both static light scattering and dynamic light scattering were employed to determine the fractal dimension of the microgels. The protein, avidin, was strongly bound to four biotin moieties. Biotin was attached covalently to specifically engineered peptide nucleic acid (PNA) oligomers. Three designed DNA oligomers self‐assembled to produce a trifunctional three‐way junction (TWJ) with single‐stranded ends that were complementary to the PNA sequence. The sizes of the supramolecular aggregates were characterized by dynamic light scattering. The fractal dimension was obtained from the angular dependence of the scattered intensity when the microgels were large enough. When the microgels were formed via cooling from a temperature above the melting point of the PNA–DNA helices, reversible structures with a fractal dimension of approximately 1.86 were formed, which is consistent with a cluster–cluster aggregation mechanism. When the microgels were formed by the slow addition of biotinylated PNA bound to the TWJ to a solution of avidin at room temperature, the observed fractal dimension approached 2.6, which is consistent with a point–cluster aggregation mechanism. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3037–3046, 2003     

A kinetic model of carbon clusters growth

A kinetic model of carbon cluster growth is suggested, including the processes of polycyclic clusters formation and their isomerization to fullerenes, discovered recently in experiments. The model is based on Smoluchowski equations, describing the rates of clusters formation in various possible reactions. The simulation results are in agreement with the experimental observations.     

Generation and characterization of low‐energy structures in atomic clusters

Factors relevant for controlling the structures determined in the local optimization of argon clusters are investigated. In particular, the role of volume and shape for the box where initial structures are generated is assessed. A thorough characterization of the optimization is also presented, based on a nearest‐neighbor analysis, in clusters ranging from 30 to 55 atoms. This includes the assessment of the degree of preservation of aspects of the initial randomly generated structure in the final optimized counterpart, and the correlation between optimized energy and the number of nearest neighbors and average departure from the diatomic reference distance. The usefulness of this analysis to explore the energy landscape of atomic clusters is also highlighted. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Imidazole‐initiated polymerizations of α‐amino acid N‐carboxyanhydrides – simultaneous chain‐growth and step‐growth polymerization

The N‐carboxyanhydrides (NCAs) of sarcosine (Sar), D ,L ‐leucine (D ,L ‐Leu), D ,L ‐phenylalanine (D ,L ‐Phe), and L ‐alanine (L ‐Ala) were polymerized in dioxane. Imidazole served as initiator and the NCA/initiator ratio was varied from 1/1 to 40/1. The isolated polypeptides were characterized by ¹H NMR spectroscopy, by MALDI‐TOF mass spectrometry, by viscosity measurements, and by SEC measurements in the case of poly(sarcosine). Cyclic oligopeptides were found in all reaction products and in the case of polySar, poly(D ,L ‐Leu), and poly(D ,L ‐Phe) the cycles were the main products. In the case of poly(L ‐Ala), rapid precipitation of β‐sheet lamellaes prevented efficient cyclizations and stabilized imidazolide endgroups. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5690–5698, 2005     

One‐Step Multicomponent Self‐Assembly of a First‐Generation Sierpiński Triangle: From Fractal Design to Chemical Reality

A novel terpyridine‐based architecture that mimics a first‐generation Sierpiński triangle has been synthesized by multicomponent assembly and features tpy? Cd^II? tpy connectivity (tpy=terpyridine). The key terpyridine ligands were synthesized by the Suzuki cross‐coupling reaction. Mixing two different terpyridine‐based ligands and Cd^II in a precise stoichiometric ratio (1:1:3) produced the desired fractal architecture in near‐quantitative yield. Characterization was accomplished by NMR spectroscopy, mass spectrometry, and transmission electron microscopy.     

NMR spin–spin coupling constants in hydrogen‐bonded glycine clusters

The influence of the hydrogen bond formation on the NMR spin–spin coupling constants (SSCC), including the Fermi contact (FC), the diamagnetic spin‐orbit, the paramagnetic spin‐orbit, and the spin dipole term, has been investigated systematically for the homogeneous glycine cluster, in gas phase, containing up to three monomers. The one‐bond and two‐bond SSCCs for several intramolecular (through covalent bond) and intermolecular (across the hydrogen‐bond) atomic pairs are calculated employing the density functional theory with B3LYP and KT3 functionals and different types of extended basis sets. The ab initio SOPPA(CCSD) is used as benchmark for the SSCCs of the glycine monomer. The hydrogen bonding is found to cause significant variations in the one‐bond SSCCs, mostly due to contribution from electronic interactions. However, the nature of variation depends on the type of oxygen atom (proton‐acceptor or proton‐donor) present in the interaction. Two‐bond intermolecular coupling constants vary more than the corresponding one‐bond constants when the size of the cluster increases. Among the four Ramsey terms that constitute the total SSCC, the FC term is the most dominant contributor followed by the paramagnetic spin‐orbit term in all one‐bond interaction.     

Many‐body energy decomposition analysis of cooperativity in hydrogen fluoride clusters

This article studies the cooperativity present in hydrogen fluoride clusters, (FH)_n, by means of a many‐body decomposition of the binding energy. With the aim of quantifying how the results depend on the calculation level, the partition was performed from dimer to hexamer at the RHF, MP2, and density functional (B3LYP) levels, and for the heptamer and octamer at the RHF and B3LYP levels, using a 6‐31++G(d, p) basis set in all cases. We obtain that, for a proper representation of the cooperative effects in hydrogen fluoride, at least the inclusion of the three‐body terms is fundamental. The contributions are found to be underestimated at the RHF level and overestimated at the B3LYP level, with respect to the MP2 results. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005