Silver-halogen cluster compounds Ag n X m (n≥2; 0≤m≤n;X=F,Br)

Nonstoichiometric silver-halogen cluster compounds Ag _n X _m (0≤m≤n;X=F, Br) are generated by cocondensation of Ag atoms and AgX species using a slightly modified gas aggregation technique. The AgX molecules are produced by partial decomposition of SF₆ and Br₂ respectively at the surface of the hot silver containing crucible, followed by the reaction of halogen atoms with silver, giving rise to the formation of AgX molecules. In a heterogeneous nucleation between these molecules and evaporated Ag atoms the afore mentioned cluster compounds are formed. The degree of halogenation can either be controlled by the adjustment of the silver evaporation rate, or even more easily by controlling the partial pressure of the halogenating agent. The mass spectra of singly charged halogenated clusters, which are generated by electron impact ionization, reflect the stability of ions. These mass spectra demonstrate that there is an alternation in the intensity pattern up to a relatively high degree of halogenation (m) for each of the investigated compound series Ag _n X _m ,n≤8. This behavior is similar to the well-known odd-even effect for pure metal clusters, allowing us to postulate the existence of a “metallic” core which governs the stability of the cluster ion (at least for not too high degree of halogenation).     

Compositions of the shells of nanoparticles with pentagonal symmetry

A method of calculation of the number of atoms in the structure of nanoforms with pentagonal symmetry (fullerenes, nanoparticles, clusters) depending on the arrangement of atoms on the symmetry elements of the I _h group has been developed. The formulas for calculation of the number of particles in all possible shells, including multilayer ones, are reported. The numbers of atoms in the shells of pentagonal symmetry are determined by four structurally invariant numbers and the “quantum number” of the order n of the group. The classification of all possible atomic shells S _{? + 60z} (z = 0, 1, ...) is presented, and the constructions of the basic shells S _? (? = 12, 20, 30, 50, 60) are given. For each basic shell, the sum rule is met: the sum of the coordination numbers of the elements of subshells is equal to 60. In clusters with magic numbers, basic shells are periodically repeated. In addition to the known shells of nanostructures, the formulas of new structures that are expected to be stable—B₂₀O₃₀, B₆₀O₉₀ (B₂O₃), and B₉₀O ₁₃₀ ¹⁰⁺ (borate)—are reported for the first time. The same is valid for similar compounds of Group III elements.     

Evaporation rates of hot sodium clusters

A scheme based in density functional theory with pseudopotentials is used to obtain the normal modes of vibration of Na _n clusters (4 ≤n ≤ 22). The monomer and dimer evaporation rates from thermally excited clusters are obtained in this harmonic approximation. The time evolution of the abundance spectra from an initial uniform mass distribution of hot clusters is studied and its influence in the experimentally observed spectra is discussed.     

Threshold photoionization behaviour of (Li2O)Lin clusters produced by a laser vaporization source

We report on the production of small and medium size lithium and lithium oxide clusters by a laser vaporization cluster source. The isotopomeric distribution of natural lithium allowed to identify Li_kO clusters as the most abundant components in the mass spectrum. Photoionization efficiency curves of Li_kO clusters with photon energies from 3.4 to 4.7 eV were measured for 8 ≤ k ≤ 27. Using linear extrapolation of the increase in photoionization efficiency with photon energy, ionization potentials were extracted. With the chemical bond of the O^2- anion to two Li atoms, leaving n = k-2 valence electrons in the (Li₂O)Li_n clusters, clear shell closure effects are present at n = 8 and n = 20.     

Compositions of nanoparticles of cubic symmetry

The formulas for calculation of the number of particles in structures of cubic symmetry O _h are reported. The numbers of atoms in the shells of cubic symmetry are determined by four structurally invariant numbers and the “quantum number” of the order n of the group. The classification of the shells of cubic symmetry is presented, and eight classes of shells are revealed. A key role in this classification is played by basic shells; in the case of close-packed spheres, these basic shells are repeated every six layers. The sum of all coordination numbers of all atoms of subshells is 24. The possibility of the existence of new fullerenes and nanoparticles of elemental boron and its oxides is considered.     

Structure and analysis of atomic vibrations in clusters of Cu n (n ≤ 20)

The binding energy, equilibrium geometry, and vibration frequencies of free clusters Cu _n (2 ≤ n ≤ 20) are calculated using the potentials of interatomic interactions found using the tight-binding approximation. The nonmonotonic dependence of the clusters’ minimum vibration frequency on their sizes and the extreme values for the number of atoms in a cluster n = 4, 6, 13, and 19 is demonstrated. It is noted that this result agrees with the theoretical and experimental data on stable structures of small and medium metallic clusters.     

Electronic and atomic structure of Na,Mg, Al and Pb clusters

Density functional theory is used to study the electronic and atomic structure of small clusters of Na, Mg, Al and Pb. We study the quantityE _N?1–E _N , which has relevance to the processes of cluster growth and evaporation (E _N is the total energy of the cluster withN atoms). By comparing the results of the jellium model with those of a more realistic model (although still simple) we are able to appreciate “structural” effects beyond the “electronic-shell effects” which form the essence of the predictions of the jellium model. The calculations predict formation of atomic shells and appreciable reconstruction as the cluster grows.     

Carbon monoxide clusters: critical size and magic numbers

Fully resolved mass spectra of carbon monoxide clusters have been recorded in the size rangen≦320. Intensity anomalies in these spectra beyondn=135 are strikingly similar to those being observed in krypton and xenon spectra. Particularly pronounced intensity drops occur atn=147 and 309. For the first time, these data provide evidence for icosahedral structure in largemolecular cluster ions. Concerning doubly charged CO clusters, their lower size limit has been measured to ben _c =98.     

Electronic structure and stability of charged beryllium clusters

Electronic structure studies on neutral, singly and doubly ionized Be _n clusters (n≤5) have been carried out in order to investigate the stability and observability of charged clusters. Our studies employ wave function expansion in terms of gaussian type orbitals and have been carried out within local spin density formalism. It is shown that although small doubly ionized clusters are unstable, they are protected from fragmentation by energy barriers. We illustrate this explicitly for trimers by presenting a Born-Oppenheimer surface of Be₃, Be ₃ ⁺ and Be ₃ ⁺⁺ . It is argued that depending on their geometries, the observable doubly charged clusters can be generated through a one or two photons ionization. We also present results on the distribution of “hole charge” in doubly ionized clusters and show that a small cluster exhibits metallic like behaviour in regard to distribution of missing electronic charge.     

Shell effects in singly and multiply charged silver and gold clusters

The mass spectra of silver- and gold-clusters, generated by a gas aggregation technique and ionized by electron impact, reveal anomalies in the relative abundance of both singly and multiply charged clusters. Concentration maxima for singly charged species Ag _n ⁺ and Au _n ⁺ (n=3, 9, 19, (21), 35) are in agreement with experimental data of Katakuse and the predictions from the electronic shell model. The observed anomalies in the abundance spectra of doubly charged silver and gold clusters as well as triply charged silver cluster ions are explained in terms of electronic shell closing.     

Structure and stability of (A1N)n clusters

AIN and AI₂N₂ have been observed in the record of time-of-flight mass-spectra as positive ions. Associating with density functional theory(DFT) B3LYP method with 6-31G* basis set, we have carried out the optimizing calculations of the geometry, electronic state and vibrational frequency for (AIN)_n (n = 1—15) clusters, moreover, discussed the character of the chemical bond and thermodynamical stability and explained the experimental mass spectra. The results show that there do not exist AI-AI and N-N bonds and only exists Al-N bond in the ground state structures of (AIN)_n clusters; and the “magical number” regularity of (AIN)_n is those whose atom number is 4, 8, 12, 16, 20, etc, all of which are times of four.     

Photoelectron spectroscopy of jet-cooled aluminium cluster anions

Aluminium cluster anions (Al _n ^? ) are produced by laser vaporization without additional ionization and cooled by supersonic expansion. Photoelectrons from mass-identified anion bunches (n=2...25) are detached by laser light (hv=3.68 eV) and undergo energy analysis in a magnetic bottle-type time-of-flight spectrometer. The measurements provide information about the electronic excitation energies from ionic ground states to neutral states of the clusters. In contrast to bulk aluminium these cluster photoelectron spectra partially have well-resolved bands which originate from low-lying excited bands. For small clusters, especially the aluminium dimer and trimer, quantum-chemical calculations will be compared to the measurements. The electron affinity size dependence of larger clusters shows conclusive evidence for “shell” effects.     

General properties of the electronic structure of alkali metal clusters and Ia-IIa mixed clusters

The results of the systematic ab-initio CI investigation of neutral and charged Li _n , Na _n , BeLi _k and MgNa _k clusters are summarized and analyzed. The general characteristic features of the electronic structure are pointed out:a) The participation of the atomic orbitals, which are empty in Ia and IIa metal atoms, allows for a higher valency of these atoms in clusters.b) Jahn-Teller and pseudo-Jahn-Teller effects strongly influence the electronic and geometric structure of clusters.c) Deformations of cluster geometry can lead to biradicaloid structures with higher spin multiplicity in their ground states.d) The peculiarities of the electronic structures of clusters can be deduced from the presence of many “surface” atoms. The theoretical results agree with experimental data presently available and they are useful for interpretation of the experimental findings.     

Theoretical study of “sandwich” clusters of fused magnesium porphyrin oligomers with alkali metal atoms

The structural characteristics, energies, and spectroscopic properties of two-layer and multilayer “sandwich” clusters in which rings (layers) of fused porphyrin oligomers Mg₂P₂ and Mg₄P₄ (P = C₂₀H₁₂N₄) are separated by (Li) _n metal interlayers containing from 8 to 32 lithium atoms have been calculated by the density functional theory B3LYP method. The trends in the changes in these characteristics have been scrutinized as a function of the number of introduced Li atoms and the size and number of porphyrin layers. Calculations predict the high energetic stability and possibility of the existence of these sandwiches as paramagnetic clusters with mobile intercalated lithium ions. The latter, like intercalated graphite clusters, are expected to exhibit high electronic and ionic conductivity. The most favorable (with low or zero barriers) channels of migration of metal ions between the porphyrin layers are discussed.     

Statistics of aggregates

Aggregation phenomena of elementary particles into clusters has received considerable attention during the past few decades. We adopt here a stochastic approach for the modeling of these phenomena. More precisely, we formulate the problem in the following dynamical setup: given a population of n discernible atoms partitioned into p discernible (model 1) or indiscernible (model 2) groups, how does a new atom eventually connect to any of these p groups forming up a new partition of n+1 atoms into a certain amount of clusters? Nucleation is said to occur when the inserted atom does not connect (it nucleates), whereas aggregation takes place if it does (clusters coalesce). Depending on this local “logic” of pattern formation, the asymptotic structure of groups can be quite different, in the thermodynamic limit N→∞. These studies are the main purpose of this work. Understanding these aggregation phenomena requires first to derive the fragment size distributions (that is, the number P of fragments, or clusters, and the number n_m of size-m fragments with m fragments with constitutive atoms), as a function of the control parameter which is chosen here to be the average number of atoms 〈N〉. As 〈N〉 approaches infinity, we derive the study of these variables in the thermodynamic limit n → ∞. It is shown, making extensive use of combinatorics, that two regimes are to be distinguished: the one of weakly connected aggregates where nucleation dominates aggregation and the one of strongly connected aggregates where aggregation dominates nucleation. In the first (“diluted”) regime, the number of clusters P(n) always diverges as n → ∞, the asymptotic equivalent of which being under control in most cases. Large deviation results are shown to be available. Concerning N _m(n), distinct behaviours are observed in models 1 and 2. In the second (“condensed”) regime, the number of groups P(n) and size-m groups N _m(n) may converge in the thermodynamic limit, with a special role played by the geometric and Poisson distributions. The asymptotic variables become observable macroscopically. This work is therefore aimed toward a better understanding of the fundamentals involved in clusters' formation processes.     

Computer-aided study of oxygen absorption by water clusters. IR spectra of heteroclusters

Spectral characteristics of (H₂O)_n, (O₂)_m(H₂O)_n, and (O)_i(H₂O)_n cluster systems, where m≤2, i≤4, and 10 ≤ n ≤ 50, are studied with the molecular dynamics method using a flexible molecule model. The IR absorption spectra are changed substantially as a result of O₂ molecule dissociation, and in the presence of atomic oxygen in the clusters, the spectra are characterized by a deep minimum at 520 cm^?1. The absorption of oxygen causes a marked reduction in reflection coefficient R of monochromatic IR radiation. The number of peaks in the R(ω) spectra decreases to two in the case of molecular oxygen absorption and is no larger than four in the case of atomic oxygen absorption. The absorption of atomic oxygen by the clusters is also accompanied by a significant increase in the dissipation of energy accumulated by the clusters. This effect weakens when molecular oxygen is absorbed. An increase in atomic oxygen concentration in the clusters renders their radiation harder.     

Calculation of the electronic properties of neutral and ionized divalent-metal clusters

The electronic properties of neutral and ionized divalent-metal clusters have been studied using a microscopic theory, which takes into account the interplay between van der Waals (vdW) and covalent bonding in the neutral clusters, and the competition between hole delocalization and polarization energy in the ionized clusters. By calculating the ground-state energies of neutral and ionized Hg _n clusters, we determine the size dependence of the bond character and the ionization potentialI _p (n). For neutral Hg _n clusters we obtain a transition from van der Waals to covalent behaviour at the critical sizen _c ～10–20 atoms. Results forI _p (Hg _n ) withn≤20 are in good agreement with experiments, and suggest that small Hg _n ⁺ clusters can be viewed as consisting of a positive trimer core Hg ₃ ⁺ surrounded byn?3 polarized neutral atoms.     

Free sodium-water clusters: photoionisation studies in a pulsed molecular beam source

Neutral Na·(H₂O) _n clusters are studied by near-uv one-photon ionisation and time-of-flight mass spectroscopy. The clusters are formed in a “pickup source” by injection of a beam of Na atoms into the expansion zone of a pulsed nozzle beam of water vapour seeded into an argon carrier gas. The performance of this novel technique for studying cold aggregates of potentially reactive species is discussed in detail. The photoion efficiency (PIE) spectrum of the monomer near its ionisation threshold (4.379(2) eV) shows a rich structure. Vibrational frequencies of the ion can be deduced and some indication of molecular Rydberg states is seen. Ionisation potentials for larger clusters and the binding energies of the neutral clusters up ton=5 are reported.     

Cluster cations ejected from liquid metal ion source: alkali metals (Li,Na) and group IV elements (Si,Ge, Sn,Pb)

Cluster abundance of Li _n ⁺ (n≤19), Na _n ⁺ (n≤25), Si _n ^z+ (n≤8 forz=1, 3≤n≤7 forz=2), Ge _n ^z+ (n≤11 forz=1, 3≤n≤9 forz=2,n=4 forz=3), Sn _n ^z+ (n≤7 forz=1, 3≤n≤9 forz=2,n=4 forz=3) and Pb _n ^z+ (n≤6 forz=1, 5≤n≤7 forz=2) ejected from a liquid metal ion source has been investigated by mass spectrometry. The abundance spectra of alkali metal clusters showed distinct maxima and steps atn=3, 7, 9, 13 and 19 for Li, and atn=3, 5, 11, 13 and 19 for Na. Mass spectra of Si, Ge and Sn clusters were very similar each other, showing intensity drops aftern=4 and 6 (and alson=10 for Ge) for singly charged clusters. The magic numbers observed are discussed in terms of stability of charged clusters.     

Electron energy loss spectroscopy of van-der-Waals clusters

A method to measure electron energy loss spectra (EELS) of clusters with a high resolution (30 meV) has been developed and has been applied to some van der Waals clusters (Ar _n , Kr _n ). Structures have been found which relate to the excitation of atoms on the surface and inside the cluster. An influence of the cluster size on the spectra has been observed.