Electronic properties of divalent-metal clusters

The transition from van der Waals to metallic bonding expected to occur in divalent-metal clusters (e.g., Be _n , Mg _n , Hg _n ) as a function of cluster size is discussed. Theoretical results for several electronic properties reflecting this transition in Hg _n -clusters are briefly reviewed and compared with available experiments. The limitations of the present theory particularly concerning the role of correlations and van der Waals interactions are discussed and possible improvements are suggested.     

On the transition from localized to delocalized electronic states in divalent-metal clusters

The transition from van der Waals to covalent bonding, which is expected to occur in divalent-metal clusters with increasing cluster size, is discussed. We propose a model which takes into account, within the same electronic theory, the three main competing contributions, namely the kinetic energy of the electrons, the Coulomb interactions between electrons, and thes ?p intraatomic transitions responsible for van der Waals like bonding. The model is solved by taking into account electron correlations using a generalized Gutzwiller approximation (slave boson method). The occurrence of electron localization is studied as a function of the interaction parameters and cluster size.     

Time-resolved studies of neutral and ionized Nan clusters with femtosecond light pulses

The real-time dynamics of Na_n (n=3–21) cluster multiphoton ionization and fragmentation has been studied in beam experiments applying femtosecond pump-probe techniques in combination with ion and electron spectroscopy. Three dimensional wave packet motions in the trimer Na₃ ground state X and excited state B have been observed. We report the first study of cluster properties (energy, bandwidth and lifetime of intermediate resonancesNa _n ^* ) with femtosecond laser pulses. The observation of four absorption resonances for the cluster Na₈ with different energy widths and different decay patterns is more difficult to interpret by surface plasmon like resonances than by molecular structure and dynamics. Time-resolved fragmentation of cluster ions Na _n ⁺ indicates that direct photo-induced fragmentation processes are more important at short times than the statistical unimolecular decay.     

The momentum distribution in some electronic states of the neutral and singly ionized nitrogen molecule

Momentum densities for the N₂ molecule are investigated. Differences between the ground state and low-lying excited states as well as the effects of ionization are discussed. The densities are calculated by taking Fournier transforms of natural spin orbitals of wavefunctions calculated in a minimal basis with configuration interaction.     

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.     

A theoretical study of electronic and vibrational properties of neutral,cationic, and anionic B24 clusters

The equilibrium geometries, electronic and vibrational properties, and static polarizability of B₂₄, B, and B clusters are reported here. First‐principles calculations based on density functional theory predict the staggered double‐ring configuration to be the ground state for B₂₄, B, and B, in contrast to the quasi‐planar structure observed in small neutral and ionized B_n clusters with n ≤ 15. Furthermore, the (4 × B₆) tubular structure is found to be relatively stable in comparison to the 3D cage structure. The presence of delocalized π and multicentered σ bonds appears to be the cause of the stability of the double‐ring and tubular isomers. For the ground state of B₂₄, the lower and upper bound of the electron affinity is 2.67 and 2.81 eV, respectively, and the vertical ionization potential is 6.88 eV. Analysis of the frequency spectrum of the double‐ring and tubular isomers reveals the characteristic vibrational modes typically observed in carbon nanotubes. The corresponding IR spectrum also reflects the presence of some of these characteristic modes in the neutral and ionized B₂₄, suggesting that double‐ring and tubular structures can be considered as the building blocks of boron nanotubes. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Structural and electronic properties of compound metal clusters

The equilibrium geometries, relative stabilities, and vertical ionization potentials of compound clusters involving Li _n , Na, Mg, and Al atoms have been calculated using ab initio self-consistent field linear combination of atomic orbitals — molecular orbital (SCF-LCAO-MO) method. The exchange energies are calculated exactly using the unrestricted Hartree-Fock (UHF) method whereas the correlation correction is included within the framework of configuration interaction involving pair excitations of valence electrons. While the later correction has no significant effect on the equilibrium geometries of clusters, it is essential for the understanding of relative stabilities. Clusters with even numbers of electrons are found to be more stable than those with odd numbers of electrons regardless of their charge state and atomic composition. The equilibrium geometries of homo-nuclear clusters can be significantly altered by replacing one of its constituent atoms with a hetero-nuclear atom. The role of electronic structure on the geometries and stabilities of compound clusters is discussed.     

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.     

Density functional study of the structural,electronic, and magnetic properties of neutral and charged rhodium clusters up to tetramer

Model core potential computations were performed for Rh₂, Rh₃, and Rh₄ clusters and their respective cations and anions using the linear combination of Gaussian‐type orbital, nonlocal spin density method. The optimized geometries, electronic and magnetic structures, binding and fragmentation energies, adiabatic ionization potentials, and electron affinities were determined. Results show that the ionization potentials, electron affinities, binding energies, and magnetic moments decrease with the cluster size. For Rh₂ and Rh₃ the most stable structures exhibit ferromagnetic properties, while Rh₄ in its ground state is found to be paramagnetic. The structures of minimum energy for the charged species often differs from the corresponding neutral one. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Calculation of the properties of small boron and aluminum clusters

CNDO calculations were carried out for B _n and Al _n clusters, n=2–7, 12, and 13. The energetically most stable cluster structures were determined for each n. The results show that the stability of the more compact structures increases in going from boron to aluminum. We conclude that the CNDO model used is suitable for discerning the difference in the structure formation of boron and aluminum, which is manifest, in particular, in the formation of crystalline modifications by boron based on an icosahedral structural element, while crystalline aluminum has an FCC lattice.Institute of Theoretical and Applied Mechanics, Siberian Branch, Academy of Sciences of the USSR. Translated from Zhurnal Strukturnoi Khimii, Vol. 30, No. 5, pp. 48–54, September–October, 1989.     

Structural and electronic properties of neutral and ionic Ga(n)On clusters with n = 4-7

We report the results of a theoretical study of neutral, anionic, and cationic Ga(n)On clusters (n = 4-7), focusing on their ground-state configurations, stability, and electronic properties. The structural motif of these small gallium oxide clusters appears to be a rhombus or a hexagonal ring with alternate gallium and oxygen atoms. With the increase in the cluster size from Ga4O4 to Ga7O7, the ground-state configurations show a transition from planar to quasi-planar to three-dimensional structure that maximizes the number of ionic metal-oxygen bonds in the cluster. The ionization-induced distortions in the ground state of the respective neutral clusters are small. However, the nature of the LUMO orbital of the neutral isomers is found to be a key factor in determining the ordering of the low-lying isomers of the corresponding anionic clusters. A sequential addition of a GaO unit to the GaO monomer initially increases the binding energy, though values of the ionization potential and the electron affinity do not show any systematic variation in these clusters.     

Structural and electronic properties of hydrated MgO nanotube clusters

Hydrated MgO nanotube clusters are constructed and studied by the density functional theory at the B3LYP/6-31G(d) level. A strong exothermicity chemisorption reactivity of MgO nanotube clusters with water, which releases 137.5–171.8 kJ/mol. The averaged charge of Mg ions is steady, and presents a stronger ionic bonding. Mg ions are more sensitive to the coordination number. For the reaction of water onto clusters, electronic properties of hydrated clusters have remarkable change compared with anhydrous clusters.     

Probing the structural and electronic properties of small vanadium monoxide clusters

The structural evolution and bonding of a series of early transition-metal oxide clusters, V(n)O(q) (n = 3-9, q = 0,-1), have been investigated with the aid of previous photoelectron spectroscopy (PES) and theoretical calculations. For each vanadium monoxide cluster, many low-lying isomers are generated using the Saunders "Kick" global minimum stochastic search method. Theoretical electron detachment energies (both vertical and adiabatic) were compared with the experimental measurements to verify the ground states of the vanadium monoxide clusters obtained from the DFT calculations. The results demonstrate that the combination of photoelectron spectroscopy experiments and DFT calculation is not only powerful for obtaining the electronic and atomic structures of size-selected clusters, but also valuable in resolving structurally and energetically close isomers. The second difference energies and adsorption energies as a function of the cluster size exhibit a pronounced even-odd alternation phenomenon. The adsorption energies of one O atom on the anionic (6.64 → 8.16 eV) and neutral (6.41 → 8.13 eV) host vanadium clusters are shown to be surprisingly high, suggesting strong capabilities to activate O by structural defects in vanadium oxides.     

Calculation of the electronic properties of metal dimers

The low-energy excitation spectra of metal dimers are determined by solving exactly a realistic many-body Hamiltonian with inter- and intra-atomic Coulomb interactions. Our results for Cu₂ and Ag₂ are in very good agreement with the excitation energies derived from recent photodetachment experiments. The characteristics of the many-body excited states in these clusters are briefly discussed.     

Structure and energy of the positively ionized water clusters

Geometry optimization of small (H₂O)_n⁺ clusters (n ≤ 4) at the UHF/4–31 + + G^** level indicates that the cations consist of two fragments: the OH radical and the H_2n−1 O⁺_n−1 ion. The latter can be considered as a thermodynamically stable combination of a distorted H₃O⁺ ion and (n−2) H₂O molecules. The H bond between the fragments becomes weaker with increasing cluster size. Extrapolation of the adiabatic ionization potentials calculated for the (H₂O)_n oligomers (n ≤ 4) at the MP2 level to an infinite cluster size provides the value of approximately 8.7 eV, which can be presumably necessary for the ionization of liquid water in a vacuum. © 1997 John Wiley & Sons, Inc.     

Fission of ionized alkali metal clusters

We study the symmetric fragmentation of ionized alkali clusters within a liquid-drop type model. The interplay of surface and Coulomb interactions leads to a stability condition against small deformations which depends on the ratioZ ²/N. For systems which are stable against small-amplitude oscillations we consider the possibility of large-amplitude modes eventually leading to fission and give in terms of the same quantity an estimate of the potential barrier for this fission channel.     

Structures and properties of neutral gallium clusters: a theoretical investigation

A systematic and unbiased structure search based on a genetic algorithm in combination with density functional theory (DFT) procedures has been carried out to locate low-energy isomers of Ga(n) up to n = 25. For the smaller clusters up to n = 8 results are checked by coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)) employing a quadruple zeta type basis set. The CCSD(T) calculations confirm a (3)Π(u) ground state for the dimer. Ga(3) has a doublet ground state 0.2 eV below two quartet states, whereas two isoenergetic triplet states are predicted for Ga(4) with D(4h) and a rhombus structure (D(2h)). Three low-lying isomers with doublet electronic states are found for Ga(5): a W-structure (C(2v)), a planar envelope (C(s)) at 0.015 eV, and a non-planar envelope (C(1)) 0.086 eV above the ground state. A triplet state for a trigonal prism (D(3h)) and a singlet for an open prism (C(2v)) are computed with virtually identical energy for Ga(6). The global minimum for Ga(7) is a capped trigonal prism (C(s)) and that for Ga(8) a distorted cube in D(2h). DFT provides a fair agreement with CCSD(T), deviations in dissociation energies are up to 0.2 eV for n ≤ 8. The structures for Ga(n) are mostly irregular for n ≥ 9, those for Ga(12) to Ga(17) can be derived from the truncated decahedron with D(5h) symmetry though highly distorted by Jahn-Teller effects, for example. For Ga(18) to Ga(23) we find stacks of five- and six-membered rings as global minima, e.g., 5-1-5-1-6 for Ga(18). Ga(24) and Ga(25) consist of layers with packing sequence ABCBA similar to those found for clusters of aluminum. The most important feature of computed cohesive energies is a rapid increase with n: for Ga(25) it reaches 2.46 eV, the experimental bulk value is 2.84 eV. Particularly stable clusters for Ga(n) are seen for n = 7, 14, and 20.     

Theoretical studies of structural and electronic properties of AlnAsn clusters

We present theoretical results of size dependent structural, electronic, and optical properties of ligand‐free stoichiometric Al_nAs_n clusters of zinc‐blende modification. The investigation is done using a simplified parametrized linear combination of atomic orbital–density functional theory‐local density approximation–tight‐binding (LCAO–DFT–LDA–TB) method and consider clusters with n up to around 100. Initial structures have assumed as spherical parts of infinite zinc‐blende structure and then allowed to relax to the closest local‐energy‐minimum structure. We analyze the radial distributions of atoms, Mulliken populations, electronic energy levels (in particular, HOMO and LUMO), bandgap, and stability as a function of size and composition. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006