Relative Stability of Boron Planar Clusters in Diatomic Molecular Model

In the recently introduced phenomenological diatomic molecular model imagining the clusters as certain constructions of pair interatomic chemical bonds, there are estimated specific (per atom) binding energies of small all-boron planar clusters B_n, n = 1–15, in neutral single-anionic and single-cationic charge states. The theoretically obtained hierarchy of their relative stability/formation probability correlates not only with results of previous calculations, but also with available experimental mass-spectra of boron planar clusters generated in process of evaporation/ablation of boron-rich materials. Some overestimation in binding energies that are characteristic of the diatomic approach could be related to differences in approximations made during previous calculations, as well as measurement errors of these energies. According to the diatomic molecular model, equilibrium binding energies per B atom and B–B bond lengths are expected within ranges 0.37–6.26 eV and 1.58–1.65 Å, respectively.     

Electronic structure calculations of small Al n (n=2–8) clusters

The electronic states of small Al _n (n=2–8) clusters have been calculated with a relativistic ab-initio MO-LCAO Dirac-Fock-Slater method using numerical atomic DFS wave-functions. The excitation energies were obtained from a ground state calculation of neutral clusters, and in addition from negative clusters charged by half an electron in order to account for part of the relaxation. These energies are compared with experimental photo-electron spectra.     

Structure,stability, and vibrational properties of small silver cluster

The ground state geometries and binding energies of small silver clusters were found using Density Functional Theory (DFT) methods. We have compared various non local corrections for exchange and correlation energies, with or without treating explicitely all the electrons. The transferability of standard effective core potentials (ECP) is good, as far as their core size is small enough. From these results, and after comparison with ab initio CI one electron- ECP calculations, we have concluded to the ability of describing small silver clusters as one-electron systems. Thus, we have parametrized our distance-dependent tight- binding hamiltonian (DDTB), previously applied to alkali clusters. The geometries and energies provided by the model are very close to those found in ab initio calculations when available, that is, up to Ag₉. We have also computed the harmonic frequencies of small silver clusters.     

Shell effects in planar electron clusters

We investigate the electronic shell structure of planar metal clusters, having in mind clusters on insulating surfaces with an interface energy such that the cluster covers the surface in a monolayer. In this first survey we concentrate on the shell effects of such a planar electron cloud using the Ultimate Jellium Model where the structural effects of the positive background are completely eliminated. An axially symmetric electron cloud shows shell effects which are, however, somewhat smaller than those of fully free threedimensional clusters. The free variation of the shape for planar clusters on surfaces, leading to many triaxial clusters, diminishes the shell effects even further, leading to the existence of hybrid-deformed clusters and a lack of energetically favored “magic” clusters in an intermediate size range N ≈ 10.30. In contrary to the situation for free clusters the small shell energies have a minor effect on the energetics of the groundstate. As a consequence, electronic shell effects are only one ingredient amongst others to determine the kinetics of cluster growth on (insulating) substrates. With a bold rescaling assumption, we can relate axially symmetric planar clusters to the planar electron cloud in a neutral quantum dot, having the consequence that shell effects persist to play a role in these systems.     

Adsorbate binding energies for ammonia on cobalt and nickel clusters

Equilibrium reactions of ammonia with cobalt and nickel clusters are analyzed to determine cluster-adsorbate binding energies. The temperature dependence of reaction equilibrium constantsK _eq are measured and ?ΔH ⁰ values obtained from plots of lnK _eq vs 1/T. We find that binding energies generally decrease with increasing ammonia coverage, and that for a given number of NH₃ molecules binding energies increase with increasing cluster size. The pattern of binding energies is found to be consistent with proposed geometrical structures for Co₁₉ and for clusters in the 55-atom size range. Cluster-ammonia binding energies are generally somewhat higher than for bulk metal surfaces, an expected result considering the character of the cluster surface and the nature of the NH₃-metal interaction.     

Ultrafast photodissociation of Kn=3...9 clusters

By means of femtosecond pump and probe technique we investigated the temporal evolution of the photodissociation of excited potassium clusters (3 ≤ n ≤ 9). For three different excitation energies E = 1.47 eV, 2.00 eV, and 2.94 eV we were able to measure the transient multiphoton ionization spectra. In the frame of a simple energy level model the photodissociation process could be analyzed. Fragmentation time constants are estimated to be cluster size- and energydependent in the range of 200 fs up to 10 ps. The results are compared with data received from similar experiments on Nan clusters.     

Ionic structure and global deformation of axially symmetric simple metal clusters

The ground-state structure and shape parameters of neutral and singly charged simple metal clusters with up to 40 valence electrons have been calculated within the cylindrically averaged pesudopotential scheme (CAPS). Na and Ba have been chosen as typical monovalent and divalent metals. The obtained structures agree very well with the results of more elaborate methods. A simple growth pattern for the most stable ionic geometries is deduced. The ionic and electronic multipole moments from CAPS are very similar to those of the structure averaged jellium model (SAJM) and of the plasma model. The surface energies derived from the CAPS results agree with experimental values.     

Doubly charged sodium clusters: plasmon response and photoproduction

The optical response of doubly charged sodium clusters Na _n+2 ⁺⁺ was measured for n = 20, 40, and 58 valence electrons, for which the jellium model predicts spherical clusters. A new experimental scheme was developed which allows to separate doubly charged clusters of even mass from the singly charged with half the mass. The optical spectra are dominated by a plasmon-like resonance which is blue shifted and narrower than that of the singly charged clusters. The smallest doubly charged cluster observed was Na ₉ ⁺⁺ . The photo ionization cross section for singly charged clusters was found to be typically 2.6·10^-19cm² per Na atom for photon energies of around 6 eV, which is a factor of 400 smaller than the maximum in the plasmon absorption in the region of hω=2.6 eV.     

Photoionisation studies of homogeneous argon and krypton clusters using TPEPICO

The photoionisation threshold region of homogeneous Argon and Krypton clusters Ar _n and Kr _n forn up to 24 formed in a free jet expansion has been studied in detail, using the threshold photoelectron photoion coincidence (TPEPICO) time of flight technique. Measurements performed at a variety of different expansion conditions (nozzle temperature and stagnation pressure) demonstrate that fragmentation of larger clusters contributes substantially to the shape of the TPEPICO spectra even for the smallest clusters and at all photon energies higher than about 200 meV to 400 meV above the ionisation threshold. The determination of ionisation potentials for these cluster ions is discussed and careful estimates are given and compared with recent theoretical values.     

On the structure and stability of Ar n and Ar n + clusters at finite temperature

For Ar_2–29 and Ar _2–29 ⁺ clusters at 20 K in the polarization model presented here the electrodynamical dipole-dipole many-body problem is solved selfconsistently with the Monte-Carlo method (MC) at 20 K, i.e. the instantaneous dipole-dipole interaction is solved to infinite perturbation order and in cluster expansion to the order of the cluster size. The long range many-body dipole-dipole interaction is coupled to exchange interaction by a modified effective dipole polarizability. This model will be compared to the dimer model and classical MC simulation of Ar _n . The resulting different magic numbers in the binding energies are discussed in this connection with different experimental techniques of cluster ionization. By the mean square cluster diameter a shape parameter is introduced and it is found that with this parameter structural form transition in cluster growth can be resolved, and surprisingly do not correlate with the magic numbers.     

Electron detachment and fragmentation in collisions between 50 keV C n − (1 ≤ n ≤ 86) clusters and H2

The destruction cross section for 50 keV negative carbon clusters C _n ^? (1 ≤ n ≤ 88) in collisions with n ₂ is reported. The dominant destruction channel is believed to be electron detachment. The measured cross section values are compared with theoretical values based on a simple geometrical model of the carbon cluster, and structural information is obtained. Fragment spectra of both positive and negative clusters are also recorded and fragmentation patterns are discussed in relation to fragmentation energies and ionization potentials.     

Theoretical Study of the Structure and Stability of Stepwise Hydrogenated Aluminum Clusters Al<Subscript>44</Subscript>H<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1−24)

The energies and structural and spectroscopic characteristics of a series of model stepwise hydrogenated aluminum clusters Al₄₄H _n (n = 1?24) obtained by successive introduction of hydrogen atoms into various surface positions of the Al₄₄ cluster have been calculated by the density functional theory method (B3LYP). According to these calculations, the [Al₃₉] surface layer of the cage retains a closed “nested doll” shape with a pentaatomic inner core [Al₅]. With increasing n, both the surface layer and the core tend to experience increasing asymmetric distortions. The surface is corrugated and undergoes significant axial and equatorial extensions and contractions, some of the Al?H two-center terminal bonds are transformed into threecenter hydrogen bridges, and some Al atoms are displaced from the surface layer to the outer sphere and are bound to the surface through hydrogen bridges. The inner core [Al₅] at n = 24 loses its bipyramidal shape and shifts to the surface layer so that one or two of its atoms are “built-in” into the concave regions of the surface layer. The calculated average energies of Al?H bonds are within the range ~55.5 ± 2.5 kcal/mol. The averaged energies of the Al₄₄H _n → Al₄₄H_n–2 + Н₂ dissociation reactions with elimination of a hydrogen molecule are on the order of a few kilocalories per mole and are evidence of small exothermicity (or isothermicity) of these reactions. For the Al₄₄H, Al₄₄H₂, and Al₄₄H₆ clusters as an example, the relative stabilities of isomers with terminal Al?H bonds in various nonequivalent positions of the [Al₃₉] surface layer are compared.     

Photoionization of small krypton clusters in the Kr 3d regime: evidence for site-specific photoemission

Kr 3d ionization energies of small, variable size krypton clusters are investigated by photoelectron spectroscopy, where the size regime of clusters with an average size N< or =30 is studied. Characteristic shifts in Kr 3d ionization energies to lower binding energies are found compared to the bare atom. These are also different from those of large krypton clusters. Moreover, we find evidence for photoionization of the krypton dimer. Its 3d ionization energy is barely shifted relative to the atomic value. Results from model calculations considering different isomers and cluster sizes as well as defect sites give evidence that the experimental results can be related to photoionization from different surface sites in variable size krypton clusters. This can be related to site-specific photoemission in small Kr clusters. The results are compared to size effects in Kr 3d near-edge features of variable size Kr clusters as well as recent results on Kr 3d photoionization of large Kr clusters.     

The elastic scattering on jellium clusters

The following calculations are based on the local density approximation potential (LDA) of W. Ekardt for the spherical jellium-background model (SJBM). Taking into account the smooth shape of the potential, the WKB approximation was used to calculate the energy and angular dependence of the electron scattering cross-sections fo rsmall Na clusters. The number of phase shifts needed to describe the scattering in the range of energies <4.5 eV increases with the size of cluster. The calculated elastic electron scattering cross-sections for the Na clusters, corresponding to the shell closings (8, 20, 40), are exhibiting a pronounced peak structure, correlated with resonance states. The computed peaks of the angular dependences of the cross-sections on energy are shifted to small angles with increasing the cluster size. The absence of fragmentation at these small electron energies presents a challenge for the experimentalists.     

Density functional study of structural and electronic properties of small bimetallic silver-nickel clusters

Theoretical study on the structure and electronic properties of small AgmNip (m + p < or = 6) clusters has been carried out in the framework of density functional theory. Structural features, cohesive energies, vertical ionization potentials, and charge transfers are evaluated for each Ag/Ni ratio. In all the AgmNip clusters, the nickel atoms are brought together, yielding a maximum of Ni-Ni bonds, and the silver atoms are located around a Ni core with a maximum of Ag-Ni bonds. The ionization potential and the highest occupied molecular orbital shape are directly related to the two- or three-dimensional character of the cluster's geometry. A very low electronic charge transfer from Ni to Ag is found, and the magnetic moment is located on Ni atoms but with a low spin polarization on silver in the Ni-rich clusters.     

The relevance of boranes and metallaboranes to the structures of p-block element nanoparticles

Recent d-block element metallaborane chemistry, in which metal identity is varied with constant ancillary ligand, demonstrates how the rising energy of the d orbitals as one moves to earlier metals gives rise to non spherical cluster shapes that permit low formal cluster electron counts. In essence, the separation of frontier orbitals from “nonbonding” orbitals required by the isolobal analogy breaks down and the resulting mixing generates additional high-lying empty orbitals concurrently with shape change. A very similar mechanism explains recent p-block cluster chemistry albeit with variation in extent of external cluster ligation as the variable and separation of external lone pair orbitals from cluster bonding as the problem. Sensible, novel explanations of the shape/electron count relationships can be discovered for large group 13 clusters by recognizing the perturbation in cluster orbital energies when stabilization by ligand interactions is removed. These observations are pertinent to an understanding of large p-block clusters with internal atoms often referred to as nanoparticles.     

Au-doped carbon clusters AuC n with n = 1–11: a theoretical investigation

The hybrid HF/DFT method B3LYP has been employed to investigate the geometrical and electronic structures of AuC _n (n = 1–11) clusters. The properties such as geometrical parameters and electronic energies are determined for open-chain and cyclic species. Our results indicate that the open-chain structures with low spin states (doublet) are more stable than the cyclic ones for the small sizes clusters (n ≤ 9), as the cluster sizes increase (n = 10, 11), the cyclic species are more stable. The incremental binding energies show a smooth even–odd alternation phenomenon for open-chain species, n-even (n is the numbers of C atom in the clusters) species have the stronger stabilities relative to the adjacent odd-numbered ones. In addition, the most favorable dissociation channels are determined by calculating the fragmentation energies accompanying various possible pathways. The studied clusters incline to be dissociated to Au + C _n and AuC _n?3 + C₃ fragments.     

A density functional study for the isomers of anionic sulfur clusters Sn− (n=3–20)

The signals of anionic sulfur clusters are intense in the mass spectrum of sulfur clusters generated in direct laser vaporization. We have acquired numerous isomers of sulfur clusters by means of the B3LYP DFT method. According to total energies, the most stable S_n⁻ (n=3–13) isomers are predicted. The helical S_n (n=14–20) structures are also calculated. Most of the anionic clusters are with chain configurations; the ring clusters with threefold atom(s) are higher in total energy. The most stable forms of isomers, from S₉⁻ to S₁₃⁻, show helical configurations that are completely different from those of the corresponding neutral and cationic clusters.     

INDO calculations of small copper clusters and CO adsorbed on copper(100) surfaces

A new parameterization for copper at the INDO/CI level is presented. Results for excitation energies, ionization potentials, and electron detachment energies are presented for selected copper clusters with up to ten atoms. The parameterization gives improved results for calculations of spectroscopic properties for systems with significant copper–copper interactions, such as clusters and model surfaces. Results for the O1s shakeup of CO attached to Cu(100) model surfaces for the new parameters are compared with experiments and with results obtained using the standard parameters. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1221–1228, 2000     

Search for global-minimum geometries of medium-sized germanium clusters. II. Motif-based low-lying clusters Ge21-Ge29

We performed a constrained search for the geometries of low-lying neutral germanium clusters Ge(N) in the size range of 21 < or = N < or = 29. The basin-hopping global optimization method is employed for the search. The potential-energy surface is computed based on the plane-wave pseudopotential density functional theory. A new series of low-lying clusters is found on the basis of several generic structural motifs identified previously for silicon clusters [S. Yoo and X. C. Zeng, J. Chem. Phys. 124, 054304 (2006)] as well as for smaller-sized germanium clusters [S. Bulusu et al., J. Chem. Phys. 122, 164305 (2005)]. Among the generic motifs examined, we found that two motifs stand out in producing most low-lying clusters, namely, the six/nine motif, a puckered-hexagonal-ring Ge6 unit attached to a tricapped trigonal prism Ge9, and the six/ten motif, a puckered-hexagonal-ring Ge6 unit attached to a bicapped antiprism Ge10. The low-lying clusters obtained are all prolate in shape and their energies are appreciably lower than the near-spherical low-energy clusters. This result is consistent with the ion-mobility measurement in that medium-sized germanium clusters detected are all prolate in shape until the size N approximately 65.