Stability and structure of singly-charged argon clusters Ar n + ,n=3–27. A Monte-Carlo simulation

Monte-Carlo calculations have been performed for positively charged argon clusters in the temperature range between 10 K and 40 K using two different models (one with a dimer ion core, the other one with a trimer ion). The argon-argon interaction potential stems from empirical data, the ion-neutral atoms potential is determined by ab initio MRD-CI calculations. Special stability is found for clusters sizesn=13, 19, 23 and 25/26 atoms using the ‘trimeric core model’ and for those withn=14,n=17,n=20 using the ‘dimeric core model’. The geometrical structure of the clusters is given and the construction principles are discussed in light of the interactions among neutral argon atoms and the ion-neutral atoms interaction.     

Calculated electronic properties of medium sized sodium clusters: the inhomogeneous jellium model

Recently observed magic number data for Na _N clusters in the size range from 100 to 900 atoms cannot be fully explained by density functional calculations using a homogeneous, spherical positive charge background. However, a centrally compressed spherical background yields steps in the ionization potential at just those magic numbers observed experimentally.     

Structure of silver clusters with magic numbers of atoms by data of molecular dynamics

The behavior of silver clusters (cubic octahedron habit) with magic numbers of atoms N = 13, 55, 146, 309, 561, 923, 1415, and 2057 in the 0–1300 K temperature range is studied for the embeded atom model by the molecular dynamics method. The structural method for the analysis of the dynamics of local configurations of atoms based on the construction of angular characteristics of simplexes of the Delone partition of a cluster is proposed. Structural transitions of clusters with a cubic octahedron habit to the stable clusters with an icosahedron habit are revealed. Motions of atoms in clusters with an icosahedron habit are transformed into the stationary vibration mode. Middle positions of atoms in clusters tend to form shells with a regular structure. At N = 561, there are 15 such shells. The cluster with N = 561 at 650 K is characterized by a reduced density close to that of silver melt.     

Electronic properties of isolated GaNAsM clusters: photoionization-, photodissociation- and photoluminescence quantum yields

Photoionization quantum yields of Ga_NAs_M clusters with N + M = 85 ± 5 atoms in the spectral range of ω = 3.5–6.4 eV have been investigated by measuring their total photoabsorption and photoionization cross sections. It is found that the photoionization quantum yields of these clusters are strongly increased by about two orders of magnitude against the values of bulk GaAs. Photodissociation of the cluster provides another efficient channel whereas photoluminescence plays a minor role for the observed cluster size distributions with N + M typically between 30 and 130 atoms.     

Thermal behaviour of carbon clusters and small fullerenes

The structural and thermal properties of small carbon clusters (C _N , N = 13, 20, and 32) are investigated by constant energy Molecular Dynamics simulations over a wide range of temperatures, i.e., from T = 0K to above the melting point of graphitic carbon. The Tersoff interatomic potential [6] is used to mimic the covalent bond between the carbon atoms in the cluster. We find that small carbon clusters start to fragment or to evaporate atoms or C₂ or C₃ units before fully developing a liquidlike phase. As a consequence, some relevant isomers (such as rings, bowls, hollow cages) are thermally isolated from each other i.e., there are no thermally activated isomerization transitions between them. Possible implications of our results on the growth mechanism of fullerenes are discussed.     

Semiclassical variational calculation of liquid-drop model coefficients for metal clusters

We report on semiclassical density variational calculations for spherical alkali metal clusters in the jellium model. We derive liquid-drop model expansions for total energy, ionisation potential and electron affinity and test the coefficients numerically for clusters with up toN=10⁵ atoms. From the limitN→∞, we obtain excellent agreement with surface tensions and work functions evaluated for an infinite plane metal surface.     

Structural fluctuation and atom-permutation in transition-metal clusters

The atomic structure and thermodynamic properties of transition-metal clusters containingN atoms are investigated forN=6 and 7 using the method of molecular dynamics, where Gupta's potential taking into account many-body interaction is employed. The caloric curve (total energy — temperature curve) and the structural fluctuations are studied. The “fluctuating state” is found forN=6 in the region of the temperature near below the melting point, where clusters undergo structural transition from one isomer to others without making any topological change. The fluctuating state differs from the coexistence state in that the former involves no atomic diffusion, and goes to a structural phase transition of the bulk whenN is increased. On the other hand, the motion of atom-permutation is found in the low-temperature region of the liquid state, being induced by the cooperative motion of two atoms. It is discussed that such a motion easily occurs along the surface and may be considered to be one of the characteristics of small clusters. The fluctuating state is discussed in relation to the structural fluctuation of gold clusters observed experimentally.     

Optical spectra of sodium microclusters

Photoabsorption spectra have been measured for free neutral sodium clusters containing fromN=3 to 40 atoms. In the size range ofN≈3 to 5, a transition occurs from molecule-like absorption to collective excitations of the valence electrons. ForN≈6 to 12, the data are well described by an ellipsoidal shell model. In open-shell clusters, the multiple surface plasma resonances expected for spheroidal or ellipsoidal shapes are observed. The experimental resonance positions provide a sensitive measurement of the cluster distortions. ForN?13, the per atom strength of these collective resonances is reduced; this may be due to peak fragmentation caused by interaction between the surface plasmon and nearby single-electron resonances. In three distinct wavelength regions, one of which corresponds to the position of the Na atom “D-lines”, additional absorption is seen in the spectra of all investigated clusters.     

The influence of shells,electron thermodynamics,and evaporation on the abundance spectra of large sodium metal clusters

Measurements of the mass abundance spectra of sodium clusters containing up to 600 atoms are presented. The clusters are produced in a seeded supersonic expansion of Ar or Kr gas, and the spectra are obtained by a time-of-flight technique. The sawtooth features in the spectra are interpreted as evidence of a regular spherical shell structure with magic numbers,N ₀, scaling approximately with the cube root of the number of sodium atoms. Altogether twelve shell closings are observed,N ₀=2, 8, 20, 40, 58, 92, 138, 196, 260, 344, 440 and 558. There is also a pronounced odd-even staggering all the way up toN=70. The experimentally observed intensity changes for the clusters around the magic numbers are discussed in terms of the electronic free energy,F(N), calculated at finite temperature, and the second differences of the free energy Δ₂ F(N)=F(N?1)?2F(N)+F(N+1). The processes behind the non-uniform abundance distributions, and the thermodynamics of finite electron systems with non-uniform level spacings are discussed on this basis.     

Thermal electronic properties of alkali clusters

We apply the finite-temperature Kohn-Sham method to alkali metal clusters, using the spherical jellium model and treating the valence electrons as a canonical system in the heat bath of the ions. We study the shell effects in the total free energyF(N) and the entropyS(N) for neutral clusters containingN atoms. Their strongest temperature dependence is due to the finite ground-state valueS ₀>0 of the electronic entropy for non-magic clusters. It leads to a decreasing amplitude and an increasing smear-out of the saw-tooth structure in the first difference Δ₁ F(N)=F(N?1)?F(N) with increasing temperatureT and cluster sizeN.     

Triaxial shapes of sodium clusters

A modified Nilsson-Clemenger model is combined with Strutinsky's shell correction method. For spherical clusters, the model potential is fitted to the single-particle spectra obtained from selfconsistent Kohn-Sham calculations. The deformation energy surfaces of sodium clusters with sizes of up toN=270 atoms are calculated for a combination of triaxial, quadrupole and hexadecapole deformations. The ground state shapes and energies are determined by simultaneous minimization with respect to the three shape parameters. A significant fraction of the clusters is predicted to be triaxial. The deviations from the axial shape do not generate any systematic odd-even staggering of the binding energies.     

The stability and structure of (N<Subscript>2</Subscript>)<Subscript>j</Subscript>(H<Subscript>2</Subscript>O)<Subscript>i</Subscript> and (Ar)<Subscript>j</Subscript>(H<Subscript>2</Subscript>O)<Subscript>i</Subscript> clusters

The stability and structure of water clusters absorbing nitrogen molecules or argon atoms was analyzed by molecular dynamics simulation at 233 K. The (?μ/?i)_{V, T} derivative of the chemical potential, a value characterizing the stability of a cluster with respect to its size, depends linearly on the number of molecules i. According to this criterion, the clusters under study become stable near i = 40. The average length of H-bonds increases monotonically in the growing cluster of pure water and exhibits oscillatory behavior if the growing cluster contains N₂ molecules or Ar atoms. The number of H-bonds per molecule oscillates between one and six as the cluster size changes. These oscillations are damped in pure water and sustained for clusters containing impurities, especially argon.     

A detailed investigation on the global minimum structures of mixed rare‐gas clusters: Geometry,energetics, and site occupancy

We performed a global minimum search of mixed rare‐gas clusters by applying an evolutionary algorithm (EA), which was recently proposed for binary atomic systems (Marques and Pereira, Chem. Phys. Lett. 2010, 485, 211). Before being applied to the potentials used in this work, the EA was further tested against results previously reported for the Ar_NXe_38?N clusters and several new putative global minima were discovered. We employed either simple Lennard‐Jones (LJ) potentials or more realistic functions to describe pair interactions in Ar_NKr_38?N, Ar_NXe_38?N, and Kr_NXe_38?N clusters. The long‐range tail of the pair‐potentials shows some influence on the energetic features and shape of the structure of clusters. In turn, core–shell type structures are mostly observed for global minima of the binary rare‐gas clusters, for both accurate and LJ potentials. However, the long‐range tail of the potential may have influence on the type of atoms that segregate on the surface or form the core of the cluster. While relevant differences for the preferential site occupancy occur between the two potentials for Ar_NKr_38?N (for N > 21), the type of atoms that segregate on the surface for Ar_NXe_38?N and Kr_NXe_38?N clusters is unaffected by the accuracy of the long‐range part of the interaction in almost all cases. Moreover, the global minimum search for model‐potentials in binary systems reveals that the surface‐site occupancy is mainly determined by the combination of two parameters: the size ratio of the two types of particles forming the cluster and the minimum‐energy ratio corresponding to the pair‐interactions between unlike atoms. © 2012 Wiley Periodicals, Inc.     

Energy exchanges following very low energy electron attachment to neat CS2 and CS2-containing clusters

We have studied electron transfer from state-selected Rydberg atoms to (CS₂) _N and CS₂(Ar) _N clusters and compared the results to Rydberg electron transfer to isolated CS₂ molecules. At large Rydberg principal quantum numbers (n>20), the influence of the positive ionic core becomes negligible and we are able to directly investigate the competition between electronic autodetachment of the anions and intracluster energy exchanges between the anions and their environment. We show that argon atoms are unable to achieve efficient internal energy exchanges in heterogeneous clusters as compared to the high efficiency of CS₂ molecules in homogeneous clusters.     

Connection between few-body systems and the bulk limit

To simplify the connection between few-body systems and the bulk limit, we propose a new variableX≡1?(1?N ^1/3)³=3N ^1/3?3N ^2/3+N ^?1 which roughly represents the fraction of surface of a spherical cluster ofN identical particles. Use of this variable is illustrated for clusters of alpha particles, nucleons, atoms and molecules, both in terms of extrapolation to a bulk limit and in terms of interpolation between a known bulk limit and clusters of moderateN, where 114 is “halfway” to the bulk.     

Synthesis and characterization of a tetraruthenium butterfly cluster containing a quadruply-bridging ligand derived from an N,N′-dipyrid-2-ylurea

The tetraruthenium cluster complex [Ru₄(μ₄-κ⁴-dmpu)(CO)₁₀], H₂dmpu = N,N′-bis(6-methylpyrid-2-yl)urea, has been prepared by treating [Ru₃(CO)₁₂] with H₂dmpu in toluene at reflux temperature. An X-ray diffraction study has determined that this cluster has a butterfly metallic skeleton hold up by a doubly-deprotonated N,N′-bis(6-methylpyrid-2-yl)urea ligand (dmpu). This ligand has the pyridine N atoms attached to the wing-tip Ru atoms and the amido N atoms spanning Ru-Ru wing-edges, in such a way that the cluster has C₂ symmetry. The donor atoms of doubly-deprotonated N,N′-dipyrid-2-ylureas seem to be appropriately arranged to hold butterfly tetranuclear clusters.     

The local electronic and magnetic properties of Fe impurity in Al clusters

The local magnetic property,d electronic structure and the charge transfer effect of Fe impurity in Al clusters have been studied by using a tight-binding model Hamiltonian in the unrestricted Hartree-Fock approximation, which includes intra-atomic and interatomic Coulomb interactions. We have obtained that local magnetic moment of Fe impurity in FeAl _N clusters decreases with increasing cluster size and convergences to zero (that of bulk given by Anderson) withN larger than 12, meanwhile, the local magnetic moment for smaller clusters depends on the clusters size and it is a monotonous descent function of cluster size. We have also found that the spin splitting of the localizedd states decreases as the cluster size increases, which mainly results from the interaction between the localized electrons of Fe atom and the delocalized electrons of Al atoms.     

Icosahedral structure of large charged argon clusters

Measurements of the mass distribution of large argon clusters formed about positive ions in a free jet expansion are reported. The results support an icosahedrally derived shell model of cluster structure through completion of the fourth shell (N = 309 atoms), but significant differences are found near the completion of the fifth shell (N = 561).     

Stability and structure of singly-charged xenon-argon clusters [Xe1Arn−1]+,n=3–27

Monte-Carlo calculations have been performed for positively charged xenon-argon clusters in the temperature range between 10K and 40K for cluster sizes up ton=27. The argon-argon interaction potential stems from empirical data, the Xe⁺-Ar potential is determined by ab initio MRD-CI calculations and a semi-empirical treatment of spin-orbit effects. Special stability is found for cluster sizesn=10, 13, 19 and less pronounced forn=23 and 25 fairly independent of the temperature. The geometrical structure of the clusters are given and the construction principle is discussed in light of the interactions among neutral argon atoms and the xenon ion — argon interaction. Comparison with measured mass spectra for mixed rare-gas clusters and [Xe_n]⁺ clusters is made and shows a consistent picture for the building principle.     

A density functional theory study of gold clusters supported on layered double hydroxides

The geometrical structure and electronic properties of a series of Au _N (N = 1–8) clusters supported on a Mg²⁺, Al³⁺-containing layered double hydroxides (MgAl–LDH) are investigated using density functional theory. The Au clusters are supported on two typical crystal faces of the LDH platelet, the basal {0001} and the lateral $ \{ 10\,\bar{1}\,0\} $ crystal face, respectively, corresponding to the top and edge site of monolayer MgAl–LDH lamella for the sake of simplicity. It is revealed that an increase in the charge transfer from the LDH lamella to the Au _N clusters at the edge site rather than clusters on the top surface, demonstrating a preferential adsorption for Au _N clusters at the edge of LDH lamella. Moreover, the calculated adsorption energy of the Au _N clusters on the LDH lamella increases with the cluster size, irrespective of the adsorption site. The investigation on the interaction between O₂ and Au _N clusters on the LDH lamella is further carried out for understanding the catalytic oxidation properties of the LDH-supported Au catalyst. The formation of reactive O₂ ^? species, a necessary prerequisite in catalytic oxidation of CO, by O₂ bridging two Au atoms of Au _N clusters indicates that the LDH-supported Au catalyst has the required characteristics of a chemically active gold catalyst in CO oxidation.