Landau fragmentation and deformation effects in dipoSe response of sodium clusters

Recent experimental data on the dipole plasmon in axial sodium clusters Na _N ⁺ with 11 ≤ N ≤ 57 are analyzed within a self-consistent separable random-phase approximation (SRPA) based on the deformed Konh-Sham functional. Good agreement with the data is achieved. The calculations show that, while in light clusters plasmon properties (gross structure and width) are determined mainly by deformation splitting, in medium clusters with N τ 50 the Landau fragmentation becomes decisive. Moreover, in medium clusters shape isomers come to play with contributions to the plasmon comparable with the ground state one. As a result, commonly used methods of the experimental analysis of cluster deformation become useless and correct treatment of cluster shape requires microscopic calculations.     

Influence of covalence and anion symmetry on the structure of small metal hydroxide clusters: Sodium versus silver hydroxide

An ab initio study of the Na_n(OH)_n, Na_n(OH)_n-1 ⁺, Ag_n(OH)_n, and Ag_n(OH)_n-1 ⁺ clusters with n up to four is presented. The results of this study show that, in accordance with experimental observations, the sodium hydroxide clusters are almost purely ionic, while the Ag-O bond exhibits a significant covalent character. The perturbation caused by the non-spherical OH^- group relatively to an atomic anion, as well as the influence on structures and energies of the covalent character of the metal-oxygen bond are determined. The appearance of metal-metal bonds in the silver hydroxide clusters is also discussed. Finally, the theoretical results obtained on the Na-OH clusters are compared to experimental results available on the dissociation of the Na_n(OH)_n-1 ⁺ clusters. Received 9 August 1999 and Received in final form 1st December 1999     

The influence of O and C doping on the ionization potentials of Li-clusters

The influence of doping of Li-clusters by electronegative O and C atoms on the ionization potentials was investigated. Experimentally, we report ionization potentials for bare Li_n clusters deduced from photoionization efficiency spectra. The values are compared with the results for Li_nO and Li_nC clusters. Observed differences are largely attributed to a quantum size effect caused by the segregated molecular part around the impurity, which changes the electron work function. Theoretically, the Fermi and exchange-correlation energies which enter the work function, are calculated in the frame of the augmented plane wave (APW) method by taking explicitly into account the presence of the molecular core. The other contribution to the work function, the moment of the double layer at the cluster surface, is computed by solving the corresponding Poisson's equation. Received 9 September 1999 and Received in final form 7 February 2000     

Combined experimental and theoretical study of small aluminum oxygen clusters

We report a combined experimental and computational investigation of small Al_nO_m species (n ≤20, m ≤ 12), produced in a laser vaporization cluster source. The oxygen content in the clusters was tuned by varying the oxygen concentration in the carrier gas. Ionization energies are bracketed using different ionizing photon energies in the energy range between 5.37 and 7.89 eV. Among the singly doped Al_nO species, Al₃O and Al₁₅O are found to have relatively low ionization energies, which can be related to the magic character of the corresponding cations. Peculiarly low ionization energies also are observed for specific oxygen rich species (m > 1), suggesting the formation of ionically bound subunits. The structures and ionization energies of singly doped Al_nO^0,+ (n = 1 - 7) clusters were determined using density functional theory (B3LYP/6-311+G(d)). Electronic supplementary material Supplementary Online Material     

Comparative study on the structure and properties of small C<Subscript>n</Subscript> and NaC<Subscript>n</Subscript> clusters

The structures, binding energies, and electronic properties of C_n and NaC_n (n=2–12) clusters have been systematically investigated using density functional theory (DFT). A number of previously undiscovered isomers of NaC_n clusters are reported, including fan-like, linear and three-dimensional structures. Moreover, NaC_n clusters with even n are found to be more stable than those with odd n, in contrast with the case of C_n clusters.     

Predictions of geometrical structures and ionization potentials for small barium clusters Ba

The geometrical structure of ground state Ba_n clusters (n =2-14) has been predicted from various types of calculations including two ab initio approaches used for the smaller sizes namely HF+MP2( n =2-6), DFT (LSDA)( n =2-6, 9) and one model approach HF+pairwise dispersion used for all sizes investigated here. The lowest energy configurations as well as some isomers have been investigated. The sizes n =4, 7 and 13 are predicted to be the relatively more stable ones and they correspond to the three compact structures: the tetrahedron, the pentagonal bipyramid and the icosahedron. The growth behavior from Ba₇ to Ba₁₃ appears to be characterized by the addition of atoms around a pentagonal bipyramid leading to the icosahedral structure of Ba₁₃ which is consistent with the observed size-distribution of barium clusters. Values for vertical ionization potentials calculated for n =2-5 at the CI level are seen to be in quite good agreement with recent measures. Received: 14 May 1997 / Received in final form: 2 February 1998 / Accepted: 27 February 1998     

Systematic study of small BN clusters

We performed a systematic investigation of the small B_xN_y (x + y? 6) clusters using the ab initio Hartree-Fock scheme plus second-order perturbation theory. The nature of the potential energy surface extrema are analyzed through analytical total energy second derivatives. Ionization potentials, binding energies and the stability against some possible reaction mechanisms are calculated. Based on these results we propose that the growing process for these clusters is mainly due to the successive incorporation of BN molecules. A discussion of some mass spectrometry experimental results is also presented. Received 2 October 2000     

Tight-binding study of structural and electronic properties of silver clusters

Tight-binding model is developed to study the structural and electronic properties of silver clusters. The ground state structures of Ag clusters up to 21 atoms are optimized by molecular dynamics-based genetic algorithm. The results on small Ag_n clusters (n = 3-9) are comparable to ab initio calculations. The size dependence of electronic properties such as density of states, s-d band separation, HOMO-LUMO gap, and ionization potentials are discussed. Magic number behavior at Ag₂, Ag₈, Ag₁₄, Ag₁₈, Ag₂₀ is obtained, in agreement with the prediction of electronic ellipsoid shell model. We suggest that both the electronic and geometrical effect play significant role in the coinage metal clusters. Received 7 August 2000     

Fragmentation of neutral Cn clusters (n = 9): experimental and theoretical investigations

We report on experimental and theoretical efforts designed to understand the fragmentation of small carbon clusters. Experimentally, a new detection system for high velocity fragments has been recently developed allowing the fragmentation of high velocity clusters to be totally recorded [1]. Results for the branching ratios of deexcitation of C₅ and C₉ formed by electron capture in high velocity collisions are presented. Theoretically, the dissociation dynamics of C₅ has been investigated using a kinematical model based on the statistical theory of Weisskopf. In this model various structural quantities (geometries, dissociation energies, harmonic frequencies), are required for both the parent cluster and the fragments. They have been calculated within DFT and coupled-cluster formalisms for C_n up to n = 9. In all cases, a strong correlation between measured branching ratios and calculated dissociation energies is observed.     

Macroscopic-microscopic theory of semi-spheroidal atomic cluster

The macroscopic-microscopic method is adapted to atomic clusters deposited on a surface. Analytical relationships for the deformation-dependent liquid drop model (LDM) energies of oblate and prolate semi-spheroidal atomic clusters have been obtained. A superdeformed prolate semi-spheroid is the most stable semi-spheroidal shape within LDM. It is also the shape with maximum degeneracy of quantum states of the semi-spheroidal harmonic oscillator used to compute the shell and pairing corrections. The microscopic corrections as well as total deformation energy show parabolic valley and ridges of the potential energy surfaces in the plane (deformation, number of atoms). The ground state and isomeric state deformation of clusters of various sizes depends on the interplay between the minima of LDM and shell correction energies.     

EICO measurements of inner-core excited mixed rare-gas clusters

The spectra of deep inner-core excited mixed rare-gas clusters were recorded by using electron ion coincidence (EICO) and multi-hit momentum imaging (MHMI) techniques. The EICO spectra for Ar₉₉Kr₁ clusters reveal that singly charged ions are emitted from the inner-core excited clusters in addition to the multiple charged ions. The dependence of the EICO spectra on photon energy and cluster size suggests that the holes created through vacancy cascade on the krypton atoms are transferred to the surrounding atoms, and that the singly charged ions are the primary product of the krypton photoabsorption. Charge localization is suggested for the inner-core excited mixed rare-gas clusters from the analysis of the EICO peak width. The MHMI measurements give us direct evidence for the strong charge migration from X-ray absorbing atoms to surrounding atoms. The photon energy dependence of the PSD image for fragment ions suggests that the momentum of the fragment ions depends on the number of charges generated by the vacancy cascade.     

Chirality, defects, and disorder in gold clusters

Theoretical and experimental information on the shape and morphology of bare and passivated gold clusters is fundamental to predict and understand their electronic, optical, and other physical and chemical properties. An effective theoretical approach to determine the lowest-energy configuration (global minimum) and the structures of low energy isomers (local minima) of clusters is to combine genetic algorithms and many-body potentials (to perform global structural optimizations), and first-principles density functional theory (to confirm the stability and energy ordering of the local minima). The main trend emerging from structural optimizations of bare Au clusters in the size range of 12-212 atoms indicates that many topologically interesting low-symmetry, disordered structures exist with energy near or below the lowest-energy ordered isomer. For example, chiral structures have been obtained as the lowest-energy isomers of bare Au₂₈ and Au₅₅ clusters, whereas in the size-range of 75-212 atoms, defective Marks decahedral structures are nearly degenerate in energy with the ordered symmetrical isomers. For methylthiol-passivated gold nanoclusters [Au₂₈(SCH₃)₁₆ and Au₃₈(SCH₃)₂₄], density functional structural relaxations have shown that the ligands are not only playing the role of passivating molecules, but their effect is strong enough to distort the metal cluster structure. In this work, a theoretical approach to characterize and quantify chirality in clusters, based on the Hausdorff chirality measure, is described. After calculating the index of chirality in bare and passivated gold clusters, it is found that the thiol monolayer induces or increases the degree of chirality of the metallic core. We also report simulated high-resolution transmission electron microscopy (HRTEM) images which show that defects in decahedral gold nanoclusters, with size between 1-2 nm, can be detected using currently available experimental HRTEM techniques.     

Homogeneous and heterogeneous clustering in the accretion regime

Condensation of nano-droplets in a supersaturating vapor decomposes in two steps: the formation of a nucleation center, also called critical nuclei or nucleation seed, and the growth sequence, by accretion of further atoms on the nucleation center. These two steps have been investigated separately through the clustering of homogeneous particles Na_n and heterogeneous particles Na_nX in a helium buffer gas (X = (Na₂O)₂ or (NaOH)₂). The growth sequence is analyzed with preformed molecules X injected in a supersaturating sodium vapor and driving production of Na_nX clusters. Cluster distribution mean sizes are controlled by sodium concentration and by the condensation cell effective length. The signal intensities observed for homogeneous and heterogeneous clusters are proportional to the homogeneous and heterogeneous nucleation center numbers respectively. We can measure the efficiency for the homogeneous nucleation center production versus sodium concentration. This process is the onset of the condensation phase transition.     

Infrared ion dip and ultraviolet spectroscopy of 4-phenyl imidazole, its tautomer, 5-phenyl imidazole, and its multiply hydrated clusters

Mass-resolved resonant two photon ionisation (R2PI) and infrared ion dip spectra have been recorded for 4-phenylimidazole (4PI) and its singly and multiply hydrated clusters 4PI(H₂O)_{n = 0 - 4}, under supersonic expansion conditions. In the case of 4PI(H₂O)_0,1, it has also been possible to record infrared spectra in both the ground (S₀) and excited (S₁) states. Combining the experimental data with the results of ab initio calculations has led to the structural assignment of each cluster. In each case, the water molecules bind primarily to the NH site of the imidazole ring. Clusters with n≥ 2 incorporate linear water chains, in which the proton donating terminus bridges either to the π-electron system (n = 2) or to the >N: atom site (n = 3, 4) on the imidazole ring. Despite the creation of a “water wire”, connecting the donor and acceptor sites of imidazole, there is no evidence of proton transfer in either the ground or excited state. Received 20 December 2001 Published online 13 September 2002     

Experimental evidence for molecular ultrafast dissociation in O<Subscript>2</Subscript> clusters

Resonant Auger spectra of O₂ clusters excited at the O1s edge are reported. After excitation to the repulsive 1s^-13σ^* state, the resulting resonant Auger spectrum displays features that remain constant in kinetic energy as the photon energy is detuned. The shift between known atomic fragment features and these features is consistent with that observed for atoms and clusters in singly charged states in direct photoemission. These findings are strong evidence for the existence of molecular ultrafast dissociation processes within the clusters or on their surface.     

Is NaI soluble in water clusters?

clusters (solvents being , or ) have been studied by resonance enhanced two photons ionization, leading to the detection of clusters. When water is the solvent, large clusters up to n>50 can be observed, whereas for and no clusters larger than 10 could be evidenced. Because the first step in the ionization process is the excitation from the ground solvated () ion pair state to a covalent excited state, the differences in the cluster size distribution for different solvent may be interpreted as a difference in cluster structures leading to a difference in the charge separation in the ground state. Received: 30 September 1997 / Revised in final form: 30 October 1997 / Accepted: 30 October 1997     

New approaches to stored cluster ions

Ion traps are wall-less containers which allow the extended storage of selected species. During the storage various interaction steps may be repeatedly applied. To this end no further hardware has to be added - in contrast to beam experiments. In this progress report two examples of recent developments are presented: the experiments have been performed with metal clusters stored in a Penning (ion cyclotron resonance) trap. A new experimental scheme has been developed which allows precision measurements of the dissociation energies of polyatomic species. It has been triggered by investigations on the delayed photodissociation of stored metal clusters. However, the technique is also readily available for application to a broad variety of different species and it is not even restricted to trapping experiments. The second development is more closely connected with ion storage in Penning traps: by application of an electron bath singly charged anionic clusters can be converted into multiply charged species. Subsequently, they are charge selected and investigated with respect to their reaction upon excitation. In particular, preliminary results indicate that dianionic metal clusters emit two electrons upon photoexcitation whereas the singly charged species show dissociation.     

Molecular picture of excited states and fragmentation paths of the Na 5 F 4 cluster

The stability against fragmentation and possible relaxation of the lowest excited states of the Na₅F₄ cluster (representative of cubic non stoechiometric clusters with an excess sodium atom, also called sodium-tail) is investigated by means of one-electron pseudopotential calculations with particular reference to photoabsorption processes from the ground state. Whereas the equilibrium configuration of the ground state has C_3v symmetry, the doubly degenerate 1²E excited state is affected by a conical intersection and a Jahn-Teller effect associated with the rotation of the sodium tail around the C₃-axis. This yields a “Mexican hat" topology for the lowest sheet with three equivalent C_s minima. Alternatively the 2²A₁ state has a minimum retaining the C_3v symmetry. The dissociation paths of the cluster along the C₃-axis into respectively Na₄F_{4 +} Na and Na₄F_{3 +} NaF are also investigated. Among the former paths, the excited states are found adiabatically stable with respect to the products. However in the A₁ symmetry, fragmentation into NaF exhibits an interesting avoided crossing between configurations correlated respectively with Na₄F₃ ^{+ +} NaF^- and Na₄F_{3 +} NaF. Such interaction, similar to the well-known charge exchange processes in elementary molecules might induce non adiabatic predissociation of the 2²A₁ state. This mechanism is invoked to explain the differences between R2PI and depletion spectra, correlated with the dissociation or relaxation of the excited states. Received 24 March 2000 and Received in final form 11 July 2000     

Structure and dynamics of cationic van-der-Waals clusters

Ar_nHCl⁺ van-der-Waals clusters for n = 1–13 are investigated with the “minimal diatomics-in-molecules (DIM) model” using ab-initio input data obtained from multi-reference configuration-interaction calculations plus subsequent projection onto valence-bond wavefunctions. The results for the complexes with n = 1–3 are checked against ab-initio calculations at the coupled-cluster (CCSD) level with the same one-electron atomic basis set as for the input data generation (aug-cc-pVTZ from Dunning). In addition to the electronic ground state, the first excited state for the triatomic complex (n = 1) is also studied. The results from the DIM model are shown to be in fair agreement with those from advanced conventional ab-initio calculations, although there are differences in detail. The comparison justifies the extension of the DIM approach to n > 3. Systematic analysis of the local minima of the multi-dimensional potential-energy surfaces (PESs), carried out with the combined method described in part I (Monte-Carlo sampling plus subsequent steepest-descent optimization), reveals simple building-up regularities for the most stable structures (i.e. those corresponding to the global PES minimum) at each n: apart from always having a nearly linear (Ar–H–Cl)⁺ fragment as core, the aggregates show little or no symmetry. Secondary local minima are also determined and their structures interpreted. The PESs for the low-lying excited states reveal a much more complicated topography compared to the Ar_nH⁺ clusters allowing a variety of photo-processes. The energy level sequence of the first five excited electronic states and the stability of the clusters in these states is studied as a function of the cluster size n.