3He impurities on4He clusters

³He impurities on⁴He clusters form surface bound states analogous to the Andreev states on a planar liquid-gas interface. The energies and wave functions of such states are evaluated using the Feynman-Lekner variational theory as well as a density functional method, previously employed for the planar surface case. The two methods give similar results. The spectrum of the impurity states is studied as a function of the cluster dimension.     

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.     

Collective excitations of3He clusters

Collective excitations of³He clusters are studied by treating the cluster as a quantum liquid drop. We have used the Random-Phase Approximation sum rules technique within a Density Functional Formalism. Results forL=2 to 10 surface modes and theL=0 volume mode are presented.     

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.     

Particle size effects of clusters and crystallites

Size effects of pair distance, cohesive energy, surface stress, and compressibility have been calculated for shell-like structurated particles Y _N ofn complete shells (units Y: rare gases, molecules, ion pairs). The influence of surface definition on size effects has been discussed.     

Interpreting magic-number and evaporation effects in cluster size distributions

The Smoluchowski equations describe the coalescence of clusters to form larger clusters. If the kernels or rate constants in these equations are homogeneous, meaning thatK _{j, k} = ² K _jk (wherej andk are cluster sizes), it can be shown that the populationsn _k approachAk ^a e - ^bk for largek and large time, where the constantsa andb depend on the homogeneity parameter. Deviations of observed populations from this formula may be ascribed to magic-number and/or evaporation effects on the kernels. By integrating the Smoluchowski equations numerically for various choices of the kernels, we derive population distributions and show the effects of magic-number clusters and evaporation on the population distribution. Various methods are used to extract the value of, in order to determine the best way to extract the underlying value of from experimental data. Experimental populations for sodium metal clusters are then analyzed according to the same procedure, to extract the homogeneity parameter and explain the patterns in the population distribution.     

Dynamic and quantum size effects in molecular clusters

The evolution of thermodynamic, dynamic and quantum size effects in clusters is expected to contribute towards the merging between microscopic and macroscopic points of view in molecular, surface and bulk phenomena.     

Pressure and size effects in endohedrally confined hydrogen clusters

Density functional theory is used to carry out a systematic study of zero-temperature structural and energy properties of endohedrally confined hydrogen clusters as a function of pressure and the cluster size. At low pressures, the most stable structural forms of (H(2))(n) possess rotational symmetry that changes from C(4) through C(5) to C(6) as the cluster grows in size from n=8 through n=12 to n=15. The equilibrium configurational energy of the clusters increases with an increase of the pressure. The rate of this increase, however, as gauged on the per atom basis is different for different clusters sizes. As a consequence, the size dependencies of the configurational energies per atom at different fixed values of pressure are nonmonotonic functions. At high pressures, the molecular (H(2))(n) clusters gradually become atomic or dominantly atomic. The pressure-induced changes in the HOMO-LUMO gap of the clusters indicate a finite-size analog of the pressure-driven metallization of the bulk hydrogen. The ionization potentials of the clusters decrease with the increase of pressure on them.     

Finite element investigation of the ground states of the helium trimers 4He3 and 4He2–3He

A three‐dimensional finite element method is applied to the ground states of the symmetric and asymmetric atomic helium trimers ⁴He₃ and ⁴He₂–³He. Three different He–He interaction potentials of hard‐core nature were studied. Two extrapolation procedures based on the convergence properties of the finite element method are investigated. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Finite size effects in tightly meshed polymer networks

Molecular dynamics computer simulations on regular, tightly meshed model networks exhibit variations of the network density with system size. We show that these variations are due mainly to network elasticity. A theoretical expression derived on the basis of the self-consistent-field approach yields finite size scaling behavior in good accord with the simulation for a wide range of thermodynamic conditions.     

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.     

Spectroscopy of OCS-hydrogen clusters in He droplets

Clusters of para-hydrogen (pH2) and ortho-deuterium (oD2) have been assembled around an OCS chromophore molecule inside He droplets in a molecular beam and studied via IR diode laser depletion spectroscopy (nu approximately 2060 cm-1). The superfluid 4He droplets provide a gentle host ensuring a constant low temperature of either T = 0.38 K for 4He droplets or T = 0.15 K for both the pure 3He and mixed 4He-3He droplets. The spectra show well resolved rotational structure of the vibrational bands for each attached hydrogen molecule in the range n = 1-8. With only one (n = 1) attached pH2, HD or an oD2 molecule the best fit rotational constants were used to determine the structure of the complex, which was found to be in surprisingly good agreement with quantum chemical calculations for the free complex. With n = 5 and 6 the Q-branch disappears for the pH2 clusters but not for the oD2 clusters which is consistent with a donut model. The moments of inertia of the pH2 and the oD2 complexes are explained by a new model in which each of the 18 attached helium atoms in a shell surrounding the OCS molecule are assigned a mass of 0.55, while each attached H2 and D2 molecule has an effective mass of about 10 and 12 u, respectively.     

Finite system size effects in the interfacial dynamics of binary liquid films

We study the relaxation dynamics of capillary waves in the interface between two confined liquid layers by means of molecular dynamics simulations. We measure the autocorrelations of the interfacial Fourier modes and find that the finite thickness of the liquid layers leads to a marked increase of the relaxation times as compared to the case of fluid layers of infinite depth. The simulation results are in good agreement with a theoretical first-order perturbation derivation, which starts from the overdamped Stokes' equation. The theory also takes into account an interfacial friction, but the difference with no-slip interfacial conditions is small. When the walls are sheared, it is found that the relaxation times of modes perpendicular to the flow are unaffected. Modes along the flow direction are relatively unaffected as long as the equilibrium relaxation time is sufficiently short compared to the rate of deformation. We discuss the consequences for experiments on thin layers and on ultralow surface tension fluids, as well as computer simulations.     

Blueshift and intramolecular tunneling of NH3 umbrella mode in 4He n clusters

We present diffusion Monte Carlo calculations of the ground and first excited vibrational states of NH(3) (4)He(n) for n< or =40. We use the potential energy surface developed by one of us [M. P. Hodges and R. J. Wheatley, J. Chem. Phys. 114, 8836 (2001)], which includes the umbrella mode coordinate of NH(3). Using quantum Monte Carlo calculations of excited states, we show that this potential is able to reproduce qualitatively the experimentally observed effects of the helium environment, namely, a blueshift of the umbrella mode frequency and a reduction of the tunneling splittings in ground and first excited vibrational states of the molecule. These basic features are found to result regardless of whether dynamical approximations or exact calculations are employed.     

A chemical bond theory of quantum size effects of semiconductor clusters

Size dependence effects in semiconductor clusters have been a subject of extensive studies for the last two decades. However, it is still difficult to employ the existing theoretical models to give reliable results of energies for clusters in the whole nanometer region. Here we offer a new theoretical method for the quantum size effects based on the idea that the energy gap shift of the cluster arises from the sum of the surface effect shift and quantum effect shift parts. We express the effects through algebraic relations rather than through variational solutions of the wave equation, without the use of any special adjustable parameter. Results reveal for the first time that the shape of the energy gap shift curve is dominated by the surface energy shift. Our method can also predict quantitatively the size dependence of dielectric constant. The new theoretical findings in the ultrasmall (<1 nm) anatase TiO(2) and the silicon clusters cannot be explained using previous theories.     

Atomic and molecular impurities in4He clusters

Recoil-ion charge distributions produced in single collisions of 8 MeV/u Kr¹³⁺ and Kr³²⁺ projectiles with Xe atoms have been measured using time-of-flight spectroscopy. The post-collision charge states of the projectile ions were determined by magnetic dispersion onto a position sensitive microchannel plate detector. The recoil-ion distributions for ionization accompanied by electron loss from Kr¹³⁺ projectiles were bell-shaped with averages that ranged from 7.4 for 1-electron loss to 13.9 for 5-electron loss. The recoil-ion distributions for ionization accompanied by electron capture to Kr³²⁺ projectiles were also bell-shaped, but had much higher average charges that ranged from 20.4 for 1-electron capture to 28.5 for 4-electron capture. The large difference in the average charges produced in the two types of collisions is mainly attributable to charge magnification by Auger decay. A simple model quantitatively explains the variation of the capture-ionization charge distribution width and average charge as a function of the number of captured electrons.     

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.     

Nonempirical statistical theory for atomic evaporation from nonrigid clusters: applications to the absolute rate constant and kinetic energy release

A high energy atomic cluster undergoing frequent structural isomerization behaves like a liquid droplet, from which atoms or molecules can be emitted. Even after evaporation, the daughter cluster may still keep changing its structure. We study the dynamics of such an evaporation process of atomic evaporation. To do so, we develop a statistical rate theory for dissociation of highly nonrigid molecules and propose a simple method to calculate the absolute value of classical phase-space volume for a potential function that has many locally stable basins. The statistical prediction of the final distribution of the released kinetic energy is also developed. A direct application of the Rice-Ramsperger-Kassed-Marcus (RRKM) theory to this kind of multichannel chemical reaction is prohibitively difficult, unless further modeling and/or assumptions are made. We carry out a completely nonempirical statistical calculation for these dynamical quantities, in that nothing empirical is introduced like remodeling (or reparametrization) of artificial potential energy functions or recalibration of the phase-space volume referring to other "empirical" values such as those estimated with the molecular dynamics method. The so-called dividing surface is determined variationally, at which the flux is calculated in a consistent manner with the estimate of the phase-space volume in the initial state. Also, for the correct treatment of a highly nonrigid cluster, the phase-space volume and flux are estimated without the separation of vibrational and rotational motions. Both the microcanonical reaction rate and the final kinetic energy distribution thus obtained have quite accurately reproduced the corresponding quantities given by molecular dynamics calculations. This establishes the validity of the statistical arguments, which in turn brings about the deeper physical insight about the evaporation dynamics.     

Modeling of HeN+ clusters. II. Calculation of He3+ vibrational spectrum

We have computed the vibrational spectrum of the helium ionized trimer He(3)(+) using three different potential energy surfaces [D. T. Chang and G. L. Gellene, J. Chem. Phys. 119, 4694 (2003); E. Scifoni et al., ibid. 125, 164304 (2006); I. Paidarova et al., Chem. Phys. 342, 64 (2007)]. Differences in the details of these potential energy surfaces induce discrepancies between bound state energies of the order of 0.01 eV. The effects of the geometric phase induced by the conical intersection between the ground electronic potential energy surface and the first excited one are studied by computing vibrational spectra with and without this phase. The six lowest vibrational bound states are negligibly affected by the geometric phase. Indeed, they correspond to wavefunctions localized in the vicinity of the linear symmetric configurations and can be assigned well defined vibrational quantum numbers. On the other hand, higher excited states are delocalized, cannot be assigned definite vibrational quantum numbers, and the geometric phase shifts their energies by approximately 0.005 eV.