Designing New Materials Using Atomic Clusters

Designing principles for forming stable metallic clusters whose chemistry mimics different atoms of the periodic table are discussed. It is shown that while bulk Al is a metal, the chemistry of an Al₁₃ resembles that of a halogen atom, a CAl₁₂ resembles an inert atom, while a NAl₁₂ resembles an alkali atom. The feasibility of making new materials using clusters as the building blocks is discussed. An ionic solid made out of Al₁₃ (or BAl₁₂) and Cs is shown to be metastable and marked by a large gap at the Fermi energy even though bulk Al and Cs are metals.     

The Energy Landscape of Uranyl–Peroxide Species

Nanoscale uranyl peroxide clusters containing UO₂²⁺ groups bonded through peroxide bridges to form polynuclear molecular species (polyoxometalates) exist both in solution and in the solid state. There is an extensive family of clusters containing 28 uranium atoms (U₂₈ clusters), with an encapsulated anion in the center, for example, [UO₂(O₂)_3?x(OH)_x^4?], [Nb(O₂)₄^3?], or [Ta(O₂)₄^3?]. The negative charge of these clusters is balanced by alkali ions, both encapsulated, and located exterior to the cluster. The present study reports measurement of enthalpy of formation for two such U₂₈ compounds, one of which is uranyl centered and the other is peroxotantalate centered. The [(Ta(O₂)₄]‐centered U₂₈ capsule is energetically more stable than the [(UO₂)(O₂)₃]‐centered capsule. These data, along with our prior studies on other uranyl–peroxide solids, are used to explore the energy landscape and define thermochemical trends in alkali–uranyl–peroxide systems. It was suggested that the energetic role of charge‐balancing alkali ions and their electrostatic interactions with the negatively charged uranyl–peroxide species is the dominant factor in defining energetic stability. These experimental data were supported by DFT calculations, which agree that the [(Ta(O₂)₄]‐centered U₂₈ capsule is more stable than the uranyl‐centered capsule. Moreover, the relative stability is controlled by the interactions of the encapsulated alkalis with the encapsulated anion. Thus, the role of alkali‐anion interactions was shown to be important at all length scales of uranyl–peroxide species: in both comparing clusters to clusters; and clusters to monomers or extended solids.     

Density functional theory study of the adsorption of NO on CunX (n = 2–8; X = Cu,K) clusters

Density functional theory calculations are performed to analyze the structure and stability of Cu and Cu-K clusters with 3 to 9 atoms. The results indicate that the stability of the clusters decreases after doping with a K atom. With the increase of cluster size, the stability of the clusters shows odd-even alternation. Cu₈ and Cu₇K clusters exhibit the highest stability. Next, different adsorption sites are considered to investigate the geometry of Cu_nNO and Cu_n−1KNO clusters. By calculating the adsorption energy and the HOMO-LUMO energy gap, it is determined that both types of reactions are exothermic processes, indicating stable adsorption of NO. Notably, the Cu_nK clusters are more active (stronger adsorption) for NO than the Cu_n clusters. The most chemically active clusters among Cu_nNO and Cu_n−1KNO clusters are Cu₈NO and Cu₇KNO clusters. Finally, electron transfer and Mayer bond order analysis of Cu₈NO and Cu₇KNO clusters reveal that the N O bond order decreases due to electron transfer when Cu/Cu-K clusters adsorb NO. In this process, the N atom is the electron donor and the Cu atom is the electron acceptor. Fundamental insights obtained in this study can be useful in the design of Cu/Cu-K catalysts.     

ZnO and TiO2 clusters as catalyst in the addition and abstraction reaction of acrylic acid with the OH radical

The present work displays the theoretical analysis on the role of metal oxide clusters as an effective catalyst in the reaction between acrylic acid and OH radical, which has an energy barrier of 12.4 kcal/mol. The formation of metal oxide cluster such as ZnO and TiO₂ with varying size from monomer to hexamer is analyzed using cohesive energy, which increases with cluster size. Adsorption of acrylic acid on clusters reveals that dimer ZnO and tetramer TiO₂ are good adsorbed entities. The dimer ZnO and tetramer TiO₂ clusters have reduced the barrier height. However, from the thermodynamical analysis of H-abstraction and OH addition reaction, the dimer ZnO cluster is found to be a good catalyst than a tetramer TiO₂ cluster. The favorable H abstraction and OH addition reactions are feasible at the active methylene group (–CH). OH addition reactions dominate over the H abstraction reaction. Further, the presence of metal oxide clusters enhances the rate of the reaction between acrylic acid and OH radical. The kinetics of the favorable reaction with a dimer ZnO cluster has a rate constant of 7.80 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹, which is higher than the literature report (1.75 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹). Overall, ZnO and TiO₂ metal oxide clusters can be effectively utilized as catalyst.     

Water‐Stable Homochiral Cluster Organic Frameworks Built by Two Kinds of Large Tetrahedral Cluster Units

Compared with metal organic frameworks (MOFs), the proton conductivity of cluster organic frameworks has been less studied. Herein, two supertetrahedral cluster organic frameworks (SCOFs) have been made that show two‐fold interpenetrated networks built by trivalent lanthanide tetrahedral clusters and monovalent cuprous T₃‐supertetrahedral clusters. The structure analysis, second harmonic generation signals, and solid‐state circular dichroism spectroscopy consistently reveal the chirality of these SCOFs. Remarkably, the water‐stable SCOFs show a high proton conductivity value of 1.4×10^?3 S cm^?1 at 80 °C and 95 % RH (relative humidity).     

Ab initio molecular orbital theory study of GaAs clusters: The geometry

We have studied the structure and geometry of neutral and charged atomic clusters consisting of Ga and As atoms via ab initio Hartree–Fock (HF) and second‐order Møller–Plesset methods. The Ga_mAs_n cluster with m≠n composition prefers a nontetrahedral geometry in the charge neutral (q=0) state. These clusters tend to be stable in tetrahedral geometry when appropriately charged. The Ga_mAs_n cluster with m=n composition (1:1 ratio of Ga to As atoms) tends to be stable in a tetrahedral geometry in the charge neutral (q=0) state. With increasing size of the cluster, the geometry of Ga_nAs_n cluster approaches the zinc‐belende‐type crystalline structure. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 563–573, 2000     

The possibilities for glassy clusters: (KCl)32

The (KCl)₃₂ cluster is used as a model system to study the possibilities for clusters to exhibit amorphous or glassy solid forms. The problem has two aspects: first, whether the potential surface of the cluster supports a myriad of locally stable, disordered structures, the ensemble of which would constitute the glassy state, and second, whether an ensemble of amorphous clusters can be prepared under laboratory conditions. Molecular dynamics studies give an emphaticyes to the first issue, and an equally emphaticno to the second, for cooling rates up to 10¹² K/s, a thousand-fold faster than the fastest rates yet reported. However, if the long-range Coulomb interaction of the ions is replaced by a shielded Coulomb (Debye or Yukawa) potential, the secondary minima are sufficiently stabilized and the saddles, sufficiently high, that disordered equilibrium structures can be reached by cooling at fast, but still conceivably attainable rates. The implication is that while alkali halide clusters probably cannot form glasses, binary clusters with shorter-range forces, such as those of II–VI and III–V compounds, probably can form glasses. The highly disordered structures of (KCl)₃₂ are perhaps the most disordered forms yet seen for solid matter.     

Atomic structure and collective excitations of medium size NanKm clusters

Density functional theory is used to study the atomic and electronic structure of Na_nK_m clusters with up to seventy atoms. The simplifying approximation has been made of replacing the external potential of the ionic background by its spherical average about the cluster centre in the iterative process of solving the Kohn-Sham equations for each geometry tested. The search for the equilibrium geometry is performed by employing steepest descent and simulated annealing techniques. We have found segregation of K to the surface and when the cluster is large enough, a neat stratification of K and Na shells. Those effects (segregation and stratification) do not perturb the electronic magic numbers well known for pure alkali metal clusters. Our results for the atomic structure are rather similar to those reported earlier for Na_nCs_n clusters. We have also studied in a selected case, Na₂₀Cs₂₀, the dependence of the collective electronic excitation spectrum on the segregation and other geometric characteristics of the cluster.     

Density functional study of AgnPd and AgnPdH clusters

Small Ag_nPd (n = 5) clusters and their hydrides Ag_nPdH (n = 5) have been studied by density functional theory calculations. For bare clusters, the structures in which the Pd atom has a maximum number of neighboring Ag atoms tend to be energetically favorable. Hydrogen prefers binding to Ag? Pd bridge site of Ag_nPd clusters except for Ag₅Pd. The binding energy has a strong odd–even oscillation. The electron transfers are from Ag atoms to Pd in bare clusters and are from metal clusters to H in cluster hydrides. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

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     

Pyridine adsorption on small Nin‐cluster (n = 2,3,4): A study of geometry and electronic structure

Adsorption of pyridine on Ni_n‐clusters (with n = 2,3,4) is studied by quantum chemical calculations at B3LYP/LANL2DZ and B3LYP/6‐311G^** levels. First, Ni_n‐clusters are investigated for accessible structure and electronic states. The lowest electronic state with four unpaired electrons is predicted for Ni₄‐cluster based on geometry and electronic structure, showing that the cluster stability nicely depends on number of unpaired electrons. Correction for basis set superposition error of metal‐metal bond is appreciable and has increasing effect on cluster binding energy. Next, adsorption of pyridine in planar and vertical adsorption modes is investigated on rhombus Ni₄‐cluster. The vertical mode is found (at B3LYP/6‐311G^** level) as the most favorable adsorption mode. Adsorption energy (ΔE_ads) depends on cluster size; adsorption on Ni₄‐cluster is most favorable with ΔE_ads = ?207.33 kJ/mol. The natural bond orbital analysis reveals the charge transfer in adsorbate/metal‐cluster. Results of investigations for the Ni₂‐ and Ni₃‐cluster are also presented. © 2012 Wiley Periodicals, Inc.     

Electronic and magnetic properties of small RhnCa (n = 1–9) clusters: A DFT study

The equilibrium geometries, relative stabilities, electronic and magnetic properties of small Rh_nCa (n = 1–9) clusters have been investigated by DFT calculations. The obtained results show that the three‐dimensional geometries are adopted for the lowest‐energy Rh_nCa clusters, and the doped Ca atom prefers locating on the surface of the cluster. Based on the analysis of the second‐order difference of energies, fragmentation energies and the HOMO‐LUMO energy gaps, we identify that the Rh₄Ca, Rh₆Ca, and Rh₈Ca clusters are relatively more stable than their neighboring clusters, and the doping of Ca enhances the chemical reactivity of the pure Rh_n clusters, suggesting that the Rh_nCa clusters can be used as nanocatalysts in many catalytic reactions. The magnetic moment for these clusters is mostly localized on the Rh atoms, and the doping Ca atom has no effect on the total magnetic moment of Rh_nCa clusters. The partial density of states, VIP, VEA, and η of these clusters in their ground‐state structures were also calculated and discussed. © 2015 Wiley Periodicals, Inc.     

First Principles Study on Encapsulation of Alkali Metals into ZnO Nanocage

Encapsulation of alkali metals (Li, Na, K, and Rb) into Zn₁₂O₁₂ nanocage has been inves-tigated using density functional theory. Encapsulation of Li and Na atoms is found to be thermodynamically favorable at 298 K and 100 kPa, with negative Gibbs free energy change ΔG of about -130.12 and -68.43 kJ/mol, respectively. By increasing the size of encapsu-lated atom the process become less favorable so that in the cases of K and Rb encapsulations the ΔG values are positive. The results indicate that the LUMO, Fermi level, and specially HOMO of the cluster are shifted to higher energies so that the HOMO-LUMO gap of the cluster is significantly narrowed in all the cases. After encapsulation of the alkali metals the work function of cluster is decreased due to the shift of the Fermi level to higher energies. Therefore, the emitted electron current density from the Zn₁₂O₁₂ cluster will be increased.     

Theoretical study of silicon–sulfur clusters (SiS2)n− (n=1–6)

The possible geometrical structures and relative stability of silicon–sulfur clusters (SiS₂) (n=1–6) are explored by means of density functional theory (DFT) quantum chemical calculations. We also compare DFT with second‐order Møller–Plesset (MP2) and Hartree–Fock (HF) methods. The effects of polarization functions, diffuse functions, and electron correlation are included in MP2 and B3LYP quantum chemical calculations, and B3LYP is effective in larger cluster structure optimization, so we can conclude that the DFT approach is useful in establishing trends. The electronic structures and vibrational spectra of the most stable geometrical structures of (SiS₂)_n⁻ are analyzed by B3LYP. As a result, the regularity of the (SiS₂)_n⁻ cluster growing is obtained, and the calculation may predict the formation mechanism of the (SiS₂)_n⁻ cluster. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 280–290, 2001     

Photoionization,Structures, and Energetics of Na-Doped Formic Acid–Water Clusters

The influence of formic acid on water cluster aggregation has been investigated experimentally by mass spectrometry and tunable UV laser ionization applied to Na-doped clusters formed in the supersonic expansion of water vapors seeded with formic acid (FA) as well as theoretically using high level quantum chemistry methods. The mass spectra of Na−FA(H₂O)_n clusters show an enlarging of mass distribution toward heavier clusters with respect to the Na−(H₂O)_n clusters, suggesting similar mass distribution in neutral clusters and an influence of formic acid in water aggregation. Density functional theory and coupled-cluster type (DLPNO-CCSD(T)) calculations have been used to calculate structures and energetics of neutral and ionized Na−FA(H₂O)_n as well as neutral FA(H₂O)_n. Na-doped clusters are characterized by very stable geometries. The theoretical adiabatic ionization potential values match pretty well the measured appearance energies and the calculated first six electronic excited states show Rydberg-type characters, indicating possible autoionization contributions in the mass spectra. Finally, theoretical calculations on neutral FA(H₂O)_n clusters show the possibility of similarly stable structures in small clusters containing up to n=4–5 water molecules, where FA interacts significantly with waters. This suggests that FA can compete with water molecules in the starting stage of the aggregation process, by forming stable nucleation seed.     

Between Localization and Delocalization: Ru(cod)2+ Units in the Zintl Clusters [Bi9{Ru(cod)}2]3− and [Tl2Bi6{Ru(cod)}]2−

Reactions of [K(crypt‐222)]₂(TlBi₃)⋅0.5 en ( 1 b ) with [Ru(cod)(H₂CC(Me)CH₂)₂] ( A ) in 1,2‐diaminoethane (en) led to the formation of two compounds with new bismuth‐rich cluster anions, [K(crypt‐222)]₃[Bi₉{Ru(cod)}₂]⋅1.5 en ( 2 ) and [K(crypt‐222)]₂[Tl₂Bi₆{Ru(cod)}]⋅2 tol ( 3 ), alongside the salt of a binary nido cluster, [K(crypt‐222)]₃(Tl₄Bi₅)⋅2 en ( 4 ). The anions in 2 and 3 are two further examples of rare heterometallic clusters containing Ru atoms. As one cod ligand is retained on each Ru atom in both clusters, the anions may be viewed as intermediates on the way towards larger, ligand‐free intermetalloid clusters. Quantum‐chemical studies provided insight into the bonding situation in these clusters. According to these studies, the anion of 2 features both electron‐precise and electron‐deficient parts. Electrospray ionization mass spectrometry analysis indicated that the clusters undergo stepwise fragmentation.     

Modulation of Benzene or Naphthalene Binding to Palladium Cluster Sites by the Backside‐Ligand Effect

The backside‐ligand modulation strategy to enhance the substrate binding property of Pd clusters is reported. The benzene or naphthalene binding ability of Pd₃ or Pd₄ clusters is enhanced significantly by the backside cyclooctatetraene ligand, leading to the formation of the first solution‐stable benzene‐ or naphthalene Pd clusters. The present results imply that the ligand design of the metal clusters, especially for the backside ligand of the metal cluster site, is crucial to acquire a desired reactivity of metal clusters.     

The Structural and Electronic Properties of Tin-Based Heteroatom Clusters Studied by the Density Functional Theory

The focus of this study is on compound clusters and, due to the existence of many phases with different structural properties, tin-based materials have been chosen as the reference case. The clusters considered below are of two types: in the first case the clusters have the skeleton of the pure tin clusters and are doped with oxygen and aluminum atoms with composition Sn _x Y _y with Y = Al, O, x = 1, 10 and y = 1, 2. In the second case the clusters have a rutile lattice with a columnar or a spherical shape and a size up to 80 atoms and are doped with a number of aluminum atoms up to 20. The calculations are based on the Density Functional Theory (DFT) and the results describe the cluster structure, its binding energy and the density of states (DOS). The general indication of the calculations is that the additive coordinates outside, rather than inside, the pristine skeleton with the formation of hybrid bonds with properties similar to the ones of the host atoms. Also conspicuous effects of hybridization are observed in the electronic structure and, due to these effects, the binding energy may decrease with respect to the one in the undoped clusters.     

Chemi-Inspired Silicon Allotropes—Experimentally Accessible Si9 Cages as Proposed Building Block for 1D Polymers, 2D Sheets,Single-Walled Nanotubes,and Nanoparticles

Numerous studies on silicon allotropes with three-dimensional networks or as materials of lower dimensionality have been carried out in the past. Herein, allotropes of silicon, which are based on structures of experimentally accessible [Si₉]⁴⁻ clusters known as stable anionic molecular species in neat solids and in solution, are predicted. Hypothetical oxidative coupling under the formation of covalent Si–Si bonds between the clusters leads to uncharged two-, one- and zero-dimensional silicon nanomaterials not suffering from dangling bonds. A large variety of structures are derived and investigated by quantum chemical calculations. Their relative energies are in the same range as experimentally known silicene, and some structures are even energetically more favorable than silicene. Significantly smaller relative energies are reached by the insertion of linkers in form of tetrahedrally connected Si atoms. A chessboard pattern built of Si₉ clusters bridged by tetrahedrally connected Si atoms represents a two-dimensional silicon species with remarkably lower relative energy in comparison with silicene. We discuss the structural and electronic properties of the predicted silicon materials and their building block nido-[Si₉]^4– based on density functional calculations. All considered structures are semiconductors. The band structures exclusively show bands of low dispersion, as is typical for covalent polymers.