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.     

Finite size effects in the evaporation rate of3He clusters

We have computed the density of states and the evaporation rate of³He clusters, paying special attention to finite size effects which modify the³He level density parameter and chemical potential from their bulk values. Ready-to-use liquid-drop expansions of these quantities are given.     

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.     

IR dissociation of ammonia clusters

Dissociation spectra of NH₃ clusters have been recorded using a cw CO₂ laser. For the dimer two absorption bands have been found at 979 and 1004 cm⁻¹, which originate from the excitation of two non-equivalent NH₃ molecules. A tunneling motion is held responsible for the observed structure on one of these bands. The symmetry group of the NH₃ dimer is presented considering the tunneling motion solely. Heavier NH₃ clusters dissociate at frequencies between 1020 and 1100 cm⁻¹. The dissociation spectrum of the SiH₄-NH₃ complex shows one peak centered at 972.3 cm⁻¹.     

The role of dimers in evaporation of small argon clusters

Evaporation of small Lennard-Jones argon clusters has been studied using molecular dynamic simulations. An extensive library of clusters with 4, 5, 6, 11, and 21 atoms has been obtained from an earlier study. Analysis of the evaporation properties of the clusters indicate, that the fraction of dimer evaporations of all evaporation events increases with the total energy of the cluster. The fraction of evaporated dimers from clusters with a constant lifetime is independent of the cluster size for short-lived clusters and increases with cluster size for long-lived clusters. Only a few percent of the clusters which are long lived enough to participate in vapor-liquid nucleation decay by emitting dimers. The mean cluster lifetime as a function of total energy shows the same exponentially decreasing trend for monomer and dimer evaporation channels. The fraction of trimer evaporations is found to be vanishingly small.     

On ionisation induced unimolecular dissociation of sodium clusters

Fragmentation of sodium cluster ions (Na _x ⁺ ,x<42) was studied via photoionisation of neutral precursors. Expansions of metal vapor out of cylindrical and conical nozzles yielded supersonic beams with differing cluster compositions. Measurements of photoionisation efficiency curves in the 3–6 eV range for both types of expansion allow quantitative separation of direct ionisation and unimolecular dissociation contributions to specific ion signals. Data for Na ₈ ⁺ and Na ₇ ⁺ are analysed to yield lower limits on bond energies. Results obtained for larger clusters are also discussed.     

Gas-phase dissociation pathways of multiply charged peptide clusters

Numerous studies of cluster formation and dissociation have been conducted to determine properties of matter in the transition from the condensed phase to the gas phase using materials as diverse as atomic nuclei, noble gasses, metal clusters, and amino acids. Here, electrospray ionization is used to extend the study of cluster dissociation to peptides including leucine enkephalin with 7–19 monomer units and 2–5 protons, and somatostatin with 5 monomer units and 4 protons under conditions where its intramolecular disulfide bond is either oxidized or reduced. Evaporation of neutral monomers and charge separation by cluster fission are the competing dissociation pathways of both peptides. The dominant fission product for all leucine enkephalin clusters studied is a proton-bound dimer, presumably due to the high gas-phase stability of this species. The branching ratio of the fission and evaporation processes for leucine enkephalin clusters appears to be determined by the value of z²/n for the cluster where z is the charge and n the number of monomer units in the cluster. Clusters with low and high values of z²/n dissociate primarily by evaporation and cluster fission respectively, with a sharp transition between dissociation primarily by evaporation and primarily by fission measured at a z²/n value of 0.5. The dependence of the dissociation pathway of a cluster on z²/n is similar to the dissociation of atomic nuclei and multiply charged metal clusters indicating that leucine enkephalin peptide clusters exist in a state that is more disordered, and possibly fluid, rather than highly structured in the dissociative transition state. The branching ratio, but not the dissociation pathway of [somatostatin₅ + 4H]⁴⁺ is altered by the reduction of its internal disulfide bond indicating that monomer conformational flexibility plays a role in peptide cluster dissociation.     

Statistical modeling of sequential collision-induced dissociation thresholds

Thermochemistry determined from careful analysis of the energy dependence of cross sections for collision-induced dissociation (CID) reactions has primarily come from the primary dissociation channel. Higher order dissociations generally have thresholds measured to be higher than the thermodynamic limit because of the unknown internal and kinetic energy distributions of the primary products. A model that utilizes statistical theories for energy-dependent unimolecular decomposition to estimate these energy distributions is proposed in this paper. This permits a straightforward modeling of the cross sections for both primary and secondary dissociation channels. The model developed here is used to analyze data for K+(NH3)x, x=2-5, complexes, chosen because the thermochemistry previously determined by threshold CID studies agrees well with values from theory and equilibrium high pressure mass spectrometry. The model is found to reproduce the cross sections with high fidelity and the threshold values for secondary processes are found to be in excellent agreement with literature values. Furthermore, relative thresholds for higher order dissociation processes appear to provide accurate thermodynamic information as well.     

Density of states and evaporation rate of helium clusters

The density of states of⁴He clusters is calculated on the assumption that only surface vibrations are thermally excited. Results for mixed³He-⁴He and³He clusters are also given. The Weisskopf procedure is used to calculate the evaporation rates and the cooling laws of helium clusters at low temperatures.     

Proton dissociation and transfer in hydrated phosphoric acid clusters

The dynamics and mechanisms of proton dissociation and transfer in hydrated phosphoric acid (H₃PO₄) clusters under excess proton conditions were studied based on the concept of presolvation using the H₃PO₄–H₃O⁺–nH₂O complexes (n = 1–3) as the model systems and ab initio calculations and Born–Oppenheimer molecular dynamics (BOMD) simulations at the RIMP2/TZVP level as model calculations. The static results showed that the smallest, most stable intermediate complex for proton dissociation (n = 1) is formed in a low local‐dielectric constant environment (e.g., ε = 1), whereas proton transfer from the first to the second hydration shell is driven by fluctuations in the number of water molecules in a high local‐dielectric constant environment (e.g., ε = 78) through the Zundel complex in a linear H‐bond chain (n = 3). The two‐dimensional potential energy surfaces (2D‐PES) of the intermediate complex (n = 1) suggested three characteristic vibrational and ¹H NMR frequencies associated with a proton moving on the oscillatory shuttling and structural diffusion paths, which can be used to monitor the dynamics of proton dissociation in the H‐bond clusters. The BOMD simulations over the temperature range of 298–430 K validated the proposed proton dissociation and transfer mechanisms by showing that good agreement between the theoretical and experimental data can be achieved with the proposed rate‐determining processes. The theoretical results suggest the roles played by the polar solvent and iterate that insights into the dynamics and mechanisms of proton transfer in the protonated H‐bond clusters can be obtained from intermediate complexes provided that an appropriate presolvation model is selected and that all of the important rate‐determining processes are included in the model calculations. © 2015 Wiley Periodicals, Inc.     

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.     

Heterylimidazoles IV. Homolytic dissociation of hexaaryldimidazolyls and their heterocyclic analogs

The rate constants and activation energies for homolytic dissociation of 2,2-di[ ()-naphthyl]-, 2,2-diquinolinyl-, and 2,2-di(9-acridinyl)-4,4,5,5-tetraphenyldiimidazolyls in toluene in the presence of,-diphenyl--picrylhydrazine were determined. The degrees of dissociation of the diimidazolyls were found. The effect of substituents on the stability of imidazolyl radicals is discussed.See [1] for communication III.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1536–1539, November, 1974.     

Fractal growth of rotating DLA‐clusters

A theoretical model for fractal growth of DLA‐clusters in two‐ and three‐dimensional Euclidean space is proposed. This model allows to study some statistical properties of growing clusters in two different situations: in the static case (the cluster is fixed), and in the case when the growing structure has a nonzero rotation around its germ. By the direct computer simulation the growth of rotating clusters is investigated. The fractal dimension of such clusters as a function of the rotation velocity is found. It is shown that for small enough velocities the fractal dimension is growing, but then, with increasing rotation velocity, it tends to the unity.     

Nonadditive effects in metal clusters and chemisorption. Pseudopotential study of palladium clusters

The analysis of nonadditive effects in small palladium clusters via LCAO-MO-SCF calculations using the nonempirical pseudopotential model is presented. The results are tentatively correlated with previous studies on various metal clusters (Li, Be, Mg, etc.) for which a good knowledge of multibody terms has provided a valuable guide for understanding the cluster stabilities and their chemisorption capacity.     

Structures and relative stability of medium-sized silicon clusters. IV. Motif-based low-lying clusters Si21-Si30

Structures and relative stability of four families of low-lying silicon clusters in the size range of Sin(n=21-30) are studied, wherein two families of the clusters show prolate structures while the third one shows near-spherical structures. The prolate clusters in the first family can be assembled by connecting two small-sized magic clusters Sin (n=6, 7, 9, or 10) via a fused-puckered-hexagonal-ring Si9 unit (a fragment of bulk diamond silicon), while those in the second family can be constructed on the basis of a structural motif consisting of a puckered-hexagonal-ring Si6 unit (also a fragment of bulk diamond silicon) and a small-sized magic cluster Sin (n=6, 7, 9, or 10). For Si21-Si29, the predicted lowest-energy clusters (except Si27) exhibit prolate structures. For clusters larger than Si25, the third family of near-spherical clusters becomes energetically competitive. These near-spherical clusters all exhibit endohedral cagedlike structures, and the cages are mostly homologue to the carbon-fullerene cages which consist of pentagons and hexagons exclusively. In addition, for Si26-Si30, we construct a new (fourth) family of low-lying clusters which have "Y-shaped" three-arm structures, where each arm is a small-sized magic cluster (Si6, Si7, or Si10). Density-functional calculation with the B3LYP functional shows that this new family of clusters is also energetically competitive, compared to the two prolate and one near-spherical low-lying families.     

Statistical theory of evaporation and condensation processes in liquid droplets

The process of evaporation of liquid droplets is described by the nonequilibrium statistical operator method. A microscopic expression for the evaporation coefficient is derived; it considers the influence of several factors (presence of ions, external fields, ultraviolet irradiation, etc.) on the evaporation process. Algorithms for determining the steady-state evaporation rate under various conditions are found. Original Russian Text ? V.V. Ryazanov, 2006, published in Kolloidnyi Zhurnal, 2006, Vol. 68, No. 2, pp. 243–254.     

A theoretical study of the effects of transition metal dopants on the adsorption and dissociation of hydrogen on nickel clusters

The structure, stability, adsorption, and dissociation of H₂ on nickel clusters doped with late transition metals were investigated using density functional theory with the BP86 functional. Molecular hydrogen physisorption occurred at a vertex atom with a low coordination number. Charge transfer between clusters and the H₂ molecule stabilized the physisorption. The chemisorption of H₂ occurred at the bridge sites, without any structural or spin change of the clusters. Among the pentamer clusters, Cd, Zn, and Au had the lowest chemisorption energies, while Ir and Pt had higher chemisorption energies for hydrogen. The computed reaction energies and activation barriers for the dissociation mechanism showed that dopants such as Rh, Pd, Pt, and Au have endothermic reaction energies and low activation barriers. This facilitates the reversible adsorption/dissociation of the H₂ molecule on these metal‐doped clusters. The dopant atoms play a major role in modulating the physisorption, chemisorption, and dissociation mechanism of H₂ on nickel clusters. © 2013 Wiley Periodicals, Inc.     

Statistical fragmentation of hot atomic metal clusters

Fragmentation processes of highly excited neutral and charged atomic metal clusters are studied in the framework of an equilibrium statistical model. In the particular case of hot (near and above melting) neutral and charged sodium clusters of 100 and 200 atoms, a microcanonical Metropolis sampling is used to compute mass (or charge) correlation functions as a function of the excitation energy. This method allows to take the strong anharmonicities in the internal phonon spectrum realistically into account which are linked to the internal structural changes like melting. It is found that, at high enough excitation energy, the system exhibits a phase transition. This phase transition is specific for fragmenting finite systems. From the shape of the caloric curve one sees that the two phases involved are connected by a van der Waals loop characterizing a first order phase transition. Here we observe an enhanced fission and multifragmentation into two or more charged clusters with more than 10 atoms each. Various fragment correlations are studied.     

Aggregation-induced chemical reactions: acid dissociation in growing water clusters

Understanding chemical reactivity at ultracold conditions, thus enabling molecular syntheses via interstellar and atmospheric processes, is a key issue in cryochemistry. In particular, acid dissociation and proton transfer reactions are ubiquitous in aqueous microsolvation environments. Here, the full dissociation of a HCl molecule upon stepwise solvation by a small number of water molecules at low temperatures, as relevant to helium nanodroplet isolation (HENDI) spectroscopy, is analyzed in mechanistic detail. It is found that upon successive aggregation of HCl with H(2)O molecules, a series of cyclic heteromolecular structures, up to and including HCl(H(2)O)(3), are initially obtained before a precursor state for dissociation, HCl(H(2)O)(3)···H(2)O, is observed upon addition of a fourth water molecule. The latter partially aggregated structure can be viewed as an "activated species", which readily leads to dissociation of HCl and to the formation of a solvent-shared ion pair, H(3)O(+)(H(2)O)(3)Cl(-). Overall, the process is mostly downhill in potential energy, and, in addition, small remaining barriers are overcome by using kinetic energy released as a result of forming hydrogen bonds due to aggregation. The associated barrier is not ruled by thermal equilibrium but is generated by athermal non-equilibrium dynamics. These "aggregation-induced chemical reactions" are expected to be of broad relevance to chemistry at ultralow temperature much beyond HENDI spectroscopy.