Throwing jellium at gallium--a systematic superatom analysis of metalloid gallium clusters

Motivated by recent developments in the field of so-called "superatom complexes", as well as by the challenge posed to theory in understanding the many polymorphs of gallium, we analyse the electronic structure of several previously synthesised ligand-protected gallium clusters and their model derivatives using density functional theory. The calculated electron charge densities within the respective gallium cores are shown to be consistent with the jellium superatom model, exhibiting well-defined global spherical shells and wide HOMO-LUMO gaps--indicating enhanced chemical stability. It is demonstrated that the HOMO-LUMO gaps are widened due to the presence of covalent gallium-ligand bonds and a closed electron shell (i.e. electron "magic" number). The tendency of retaining a filled electron shell is shown to be particularly apparent in two closely-related clusters, with one derived from the other simply via substituting a doubly negative charge by a single protective moiety containing a lone electron pair. This analysis verifies that spherical electron shells can influence the chemical stability of ligand-protected gallium clusters, and also demonstrates the significant stabilising effects of metal-ligand interactions-something that is poorly accounted for in the current superatom model.     

Metalloid aluminum and gallium clusters: element modifications on the molecular scale?

As members of the same group in the periodic table, the industrially significant elements aluminum and gallium exhibit strong similarities in the majority of their compounds. In contrast there are significant differences in the structures of the two elemental forms: Aluminum forms a typical closest-packed metallic structure whereas gallium demonstrates a diversity of molecular bonding principles in its seven structural modifications. It can therefore be expected that differences between Al and Ga compounds will arise when, as for the elemental forms, many metal-metal bonds are formed. To synthesize such cluster compounds, we have developed the following synthesis procedure: Starting from gaseous monohalides at around 1000 degrees C, metastable solutions are generated from which the elements ultimately precipitate by means of a disproportionation reaction at room temperature. On the way to the elemental forms, molecular Al and Ga cluster compounds can be obtained by selection of suitable ligands (protecting groups), in which a core of Al or Ga atoms are protected from the formation of the solid element by a ligand shell. Since the arrangement of atoms in such clusters corresponds to that in the elements, we have designated these clusters as metalloid or elementoid. In accordance with the Greek word [see text] (ideal, prototype), the atomic arrangement in metalloid clusters represents the prototypic or ideal atomic arrangement in the elements at the molecular level. The largest clusters of this type contain 77 Al or 84 Ga atoms and have diameters of up to two nanometers. They hold the world record with respect to the naked metal-atom core for structurally characterized metalloid clusters.     

A second metalloid Ga18 cluster and its topological similarity to the high-pressure Ga-II modification

The topology of many modifications of elemental gallium is reflected in the large variety of metalloid Ga clusters that have been isolated as intermediates on the way from the metastable molecular GaX species (X=Cl, Br, I) by means of disproportionation to the bulk metal. Herein, we report the synthesis and characterization of the first metalloid cluster anion [Ga(18)(PtBu(2))(10)](3-) with the singular core topology that resembles the gallium high-pressure modification Ga-II. The stabilization of the cluster anion through ion-pair contacts with a chainlike "Li(4)Br(2) backbone" is discussed. Furthermore, the compound is discussed in context of the other metalloid clusters Ga(18)R(8) and Ga(22)R(8) (R=SitBu(3)) and their structural relation to the elemental modifications Ga-III and beta-Ga, respectively.     

Metalloid Al- and Ga-clusters: a novel dimension in organometallic chemistry linking the molecular and the solid-state areas?

Formation and fragmentation of metal-metal bonds on the way between stable metal compounds in which the metal atoms are oxidised (e.g. isolated species in solution or metal salts in bulk) and the bulk metal are the fundamental steps to understand this process in which formation and chemical behaviour of metalloid Al and Ga clusters as intermediates are essential. Many examples of metalloid Al and Ga clusters show that their formation reflects a high degree of complexity like that of the simple seeming formation of the bulk metal itself: starting from metastable Al(i) and Ga(i) solutions containing small molecular entities, metalloid clusters grow during many self-organization steps including aggregation as well as irreversible redox cascades. This novel class of clusters seems to open a new dimension in chemistry between the molecular and the solid-state area, because, for the first time, it is shown that under well selected conditions definite molecular species, i.e. metalloid clusters, grow via the formation of additional metal-metal bonds and that the solid metal represents the final step.     

The electronic structure of Ge9[Si(SiMe3)3]3-: a superantiatom complex

We report on the electronic structure of Ge(9)[Si(SiMe(3))(3)](3)(-). Systematic density functional theory analysis of the electronic shell structure of the cluster and its derivatives reveals that the Ge(9)[Si(SiMe(3))(3)](3)(-) and its neutral counterpart have electronic shells that can be explained using the superatom model. The ligand-core interaction of these complexes is distinctly different from previously identified gold, gallium, and aluminium superatom complexes, indicating an electron-donating rather than electron-withdrawing ligand. We modify the electron-counting rule for this case and introduce a simple picture for superatom and superantiatom complexes. Discussions comparing shell models, Zintl clusters, the superhalogen Al(13) and superatom complexes to Ge(9)[Si(SiMe(3))(3)](3)(-) are presented.     

Density functional analysis of the structural evolution of Gan (n=30-55) clusters and its influence on the melting characteristics

Recent experimental results have reported surprising variations in the shapes of the heat capacity curves and melting temperatures of gallium clusters in the size range of 30-55 atoms [G. A. Breaux et al., J. Am. Chem. Soc. 126, 8628 (2004)]. In the present work, we have carried out an extensive density functional investigation on ten selected clusters in the above mentioned size range. In particular, we have analyzed the ground state geometry and the nature of bonding in these clusters using electron localization function. We demonstrate that the existence or otherwise of a large island of atoms bonded with similar strength (i.e., the local order) in the ground state geometry is responsible for the variation in the shape of the heat capacity curve. We attribute the observed higher melting temperatures of some of the clusters (viz., Ga45-Ga48) to the presence of a distinct core and strong covalent bonds between the core and surface atoms. The present work clearly demonstrates that it is possible to understand the general trends observed in the heat capacity curves across the entire series on the basis of the analysis of their ground state.     

Two metalloid Ga22 clusters containing a novel Ga22 core with an icosahedral Ga12 center

In addition to the two so far known types of metalloid Ga(22) clusters a new type is presented in two compounds containing the anions [Ga(22)Br[N(SiMe(3))(2)](10)Br(10)](3-) (1) and [Ga(22)Br(2)[N(SiMe(3))(2)](10)Br(10)](2-) (2). In both anions 10 Ga atoms of the icosahedral Ga(12) core are directly connected to further Ga atoms. The two remaining Ga atoms (top and bottom) of the Ga(12) icosahedron are bonded to one (1) and two Br atoms (2), respectively. The formation and structure of both compounds containing a slightly different average oxidation number of the Ga atoms is discussed and compared especially with regard to the Ga(84) cluster compound and similar metalloid Al(n) clusters. Finally, the consequences arising from the presence of two very similar but not identical Ga(22) cluster compounds are discussed and special consideration is given to the so far not understood physical properties (metallic conductivity and superconductivity) of the Ga(84) cluster compound.     

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.     

Evolution of the geometrical and electronic structures of Gan(n=2-26) clusters: a density-functional theory study

Density-functional theory with generalized gradient approximation for the exchange-correlation potential has been used to calculate the lowest-energy geometries and electronic structure of neutral gallium clusters containing up to 26 atoms. Harmonic vibrational frequency analysis is undertaken to assure that the lowest-energy geometries are real local minima. With increasing cluster size, we find that the gallium clusters tend to adopt compact structures. The structures comprise triangular units that connect each other with different dihedral angles. The lowest-energy structure can be obtained by capping an atom on the structure of smaller one. The capping site occurs at a site where interactions with more atoms are available. The binding energy evolves monotonically with size, but Ga(8), Ga(14), and Ga(20) exhibit particularly higher stability. Except Ga(2) and Ga(4), all even-numbered gallium clusters we studied are closed-shell singlet states with a substantial highest occupied and lowest unoccupied molecular orbitals gap. The odd-numbered clusters are open shell with a small gap. The size dependence of cluster's ionization potentials and electron affinities is discussed and compared with available experiment.     

A series of new ternary and quaternary compounds in the Li(I)-Ga(III)-Te(IV)-O system

Systematic explorations of new compounds in the Li(I)-Ga(III)-Te(IV)-O system led to two new isomeric ternary gallium tellurites, namely, α-Ga(2)(TeO(3))(3) and β-Ga(2)(TeO(3))(3), and two new quaternary lithium gallium tellurites, namely, HLi(2)Ga(3)(TeO(3))(6)(H(2)O)(6) and Li(9)Ga(13)Te(21)O(66). α-Ga(2)(TeO(3))(3) is a noncentrosymmetric structure (I4?3d) and displays a moderately strong second-harmonic-generation response that is comparable with that of KDP (KH(2)PO(4)). Its structure features a condensed three-dimensional (3D) network alternatively connected by GaO(4) tetrahedra and TeO(3) trigonal pyramids via corner sharing. β-Ga(2)(TeO(3))(3) is centrosymmetric (P6(3)/m) and features a 3D open framework composed of Ga(2)O(9) dimers bridged by TeO(3) groups with one-dimensional (1D) 12-MR channels along the c axis. Although both HLi(2)Ga(3)(TeO(3))(6)(H(2)O)(6) and Li(9)Ga(13)Te(21)O(66) crystallized in the same space group R3?, they belong to different structure types. The structure of HLi(2)Ga(3)(TeO(3))(6)(H(2)O)(6) can be viewed as the 1D tunnels of the 3D gallium tellurite being occupied by Li(+) and H(+) ions whereas the structure of Li(9)Ga(13)Te(21)O(66) is a complicated 3D framework composed of alternating gallium tellurite layers and GaO(6) octahedral layers with Li(+) cations being located at the cavities of the structure. Optical diffuse-reflectance spectrum measurements indicate that all four compounds are insulators and transparent in the range of 300-2500 nm.     

Structures and electronic properties of Al7x0,- and Al13 X1,2,12- clusters with X=F, Cl, and Br

The structures, binding energies, and electronic properties for Al7X, Al7X-, Al13X-, Al13X2-, and Al13X12- (X = F, Cl, Br) were studied at the B3LYP/6-311+G(2d,p) level. Among the systems studied, Al7 and Al13 clusters in Al7X and Al13X- reveal alkali-like and halogen-like superatom characters, respectively. Al7 can bind with one halogen atom to form a salt-like compound as Al7+delta-X-delta. Al13- can combine with one halogen atom to form a diatomic halogen anion Al13X-. However, when adding more halogens, the superatom structure would be destroyed, resulting in low-symmetry compounds with the center Al atom moving toward the cluster surface. The structures of Al13X1,2,12- (X = F, Cl, Br) are similar to those of X = I; however, their binding energies and electron structures are much different. In addition, the analyses of the calculated NBO charges show that Cl and Br have similar properties, but much different from F, when interacting with the Al clusters. The Al-Cl and Al-Br bonds have more covalent character in Al7X and Al13X2,12-, in contrast to the corresponding Al-F bond, which has prominent ionic character.     

Electronic structure, vibrational stability, and predicted infrared-Raman spectra of the As20, As @ Ni12, and As @ Ni12 @ As20 clusters

Recently an inorganic fullerine-like [As@Ni(12)@As(20)](3-) onion with near-perfect icosahedral symmetry in the crystalline phase was reported [M. J. Moses, J. C. Fettinger, and B. W. Eichhorn, Science 300, 778 (2003)]. This paper presents a detailed computational study in the framework of density functional theory on various aspects of this molecule. The electronic structure of the As@Ni(12)@As(20) is investigated in its neutral as well as -3 charged state together with its subunits As(20) and As@Ni(12) by the all electron linear combination of Gaussian-type orbitals method. The bonding is studied by examining the integrated charge within atomic sphere, the electron localization function, changes in the electron density distribution, and from vibrational modes. We find that strong covalent As-As bonds seen in isolated As(20) become weaker in the As@Ni(12)@As(20) and strong covalent As-Ni bonds are formed. The structural stability of all four clusters is examined by analyzing the energetics and by calculating the vibrational frequencies. Further, the infrared and Raman spectra is predicted for both the neutral and charged As@Ni(12)@As(20) clusters. Finally, the energy barrier for removal of a single arsenic atom is calculated for the neutral As@Ni(12)@As(20) cluster.     

Evidence of superatom electronic shells in ligand-stabilized aluminum clusters

Ligand-stabilized aluminum clusters are investigated by density functional theory calculations. Analysis of Kohn-Sham molecular orbitals and projected density of states uncovers an electronic shell structure that adheres to the superatom complex model for ligand-stabilized aluminum clusters. In this current study, we explain how the superatom complex electron-counting rule is influenced by the electron-withdrawing ligand and a dopant atom in the metallic core. The results may guide the prediction of new stable ligand-stabilized (superatom) complexes, regardless of core and electron-withdrawing ligand composition.     

Two new cluster ions, Ga[GaH3]4(5-) with a neopentane structure in Rb8Ga5H15 and [GaH2]n(n-) with a polyethylene structure in Rb(n)(GaH2)n, represent a new class of compounds with direct Ga-Ga bonds mimicking common hydrocarbons

The first examples of a new class of gallium hydride clusters with direct Ga-Ga bonds and common hydrocarbon structures are reported. Neutron powder diffraction was used to find a Ga[GaH(3)](4)(5-) cluster ion with a neopentane structure in a novel cubic structure type of Rb(8)Ga(5)H(15). Another cluster ion with a polyethylene structure, [GaH(2)](n)(n-), was found in a second novel (RbGaH(2))(n) hydride. These hydrocarbon-like clusters in gallium hydride materials have significant implications for the discovery of hydrides for hydrogen storage as well as for interesting electronic properties.     

Experimental and theoretical characterization of aluminum-based binary superatoms of AL12X and their cluster salts

The geometric and electronic structures of aluminum binary clusters, AlnX (X = Si and P), have been investigated, using mass spectrometry, anion photoelectron spectroscopy, photoionization spectroscopy, and theoretical calculations. Both experimental and theoretical results show that Al12Si has a high ionization energy and low electron affinity and Al12P has a low ionization energy, both with the icosahedral structure having a central Si or P atom, revealing that Al12Si and Al12P exhibit rare-gas-like and alkali superatoms, respectively. Experiments confirmed the possibility that the change in the total number of valence electrons on substitution could produce ionically bound binary superatom complexes, the binary cluster salts Al12P+ F- and Al12B- Cs+.     

Ligand-field regulated superalkali behavior of the aluminum-based clusters with distinct shell occupancy

Protecting clusters from coalescing by ligands has been universally adopted in the chemical synthesis of atomically precise clusters. Apart from the stabilization role, the effect of ligands on the electronic properties of cluster cores in constructing superatoms, however, has not been well understood. In this letter, a comprehensive theoretical study about the effect of an organic ligand, methylated N-heterocyclic carbene (C₅N₂H₈), on the geometrical and electronic properties of the aluminum-based clusters XAl₁₂ (X = Al, C and P) featuring different valence electron shells was conducted by utilizing the density functional theory (DFT) calculations. It was observed that the ligand can dramatically alter the electronic properties of these aluminum-based clusters while maintaining their structural stability. More intriguingly, different from classical superatom design strategies, the proposed ligation strategy was evidenced to possess the capability of remarkably reducing the ionization potentials (IP) of these clusters forming the ligated superalkalis, which is regardless of their shell occupancy. The charge transfer complex formed during the ligation process, which regulates the electronic spectrum through the electrostatic Coulomb potential, was suggested to be responsible for such an IP drop. The ligation strategy highlighted here may provide promising opportunities in realizing the superatom synthesis in the liquid phase.     

On the shell structure and geometry of monovalent metal clusters

The Hückel model is used to study the electronic structure of monovalent metal clusters. In an fcc cluster the Hückel model gives an estimate to the electronic structure of a free electron cluster. It is shown that the surface faceting of the fcc cluster can destroy the electronic shell structure already when the cluster has about 100 electrons. In the Hückel model the icosahedral structure has smaller total energy than the fcc structures, from which the Wulff construction has the smallest energy already when the cluster has 600 atoms.     

A study of the phase Mg2Cu6Ga5, isotypic with Mg2Zn11. A route to an icosahedral quasicrystal approximant

The new title compound was synthesized by high-temperature means and its X-ray structure refined in the cubic space group Pm3macro, Z = 3, a = 8.278(1) A. The structure exhibits a 3-D framework made from a Ga(14) and Mg network within which large and small cavities are occupied by centered GaCu(12) icosahedral and Cu(6) octahedral clusters, respectively. The clusters are well bonded within the network. Electronic structure calculations show that a pseudogap exists just above the Fermi energy, and nearly all pairwise covalent interactions remain bonding over a range of energy above that point. Analysis suggests that the compound is hypoelectronic with a four-electron deficiency per unit cell, and such a derivative with Sc substituting for Mg is an appropriate quasicrystal approximant (Im3macro). Such characteristics seem to be key factors in the formation of icosahedral quasicrystals.