Bonding and energetics in small clusters of gallium and arsenic

Density functional theory is used to study the electronic, geometric, and bonding properties of small Ga_n, As_m, and Ga_nAs_m clusters with up to eight atoms. New ground state structures for many of these clusters are reported. Electronic states, stabilities, and charges are also reported and discussed in terms of the bonding in the clusters. © 2003 Wiley Periodicals, Inc. Heteroatom Chem 14:189–196, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.10127     

Theoretical study on the interaction of neutral and charged Tin (n = 1–7) clusters with one oxygen molecule

The interactions between the neutral and charged (?2, ?1, +1, and +2) Ti_n (n = 1–7) clusters and one O₂ molecule were investigated by density functional theory. The calculated results show that the oxygen molecule is dissociative on the neutral Ti_n clusters. Geometrically, the two O atoms are distributed at the two sides across the neutral Ti_n cluster for n = 1–4 and the oxygen atom favors the three‐fold hollow site for n = 5, 6, and 7. The binding energy per atom (E_b) and energy gap (E_gap) show higher stability and lower chemical activity of the neutral Ti_nO₂ (n = 1–7) systems compared with the corresponding Ti_n clusters. The adsorption energies (E_ad) exhibit a continuously ascending tendency except for n = 4. The results of the addition of different charges (?2, ?1, +1, and +2) on the most stable neutral Ti_nO₂ (n = 1–7) systems indicate that their geometries are usually perturbed. The stabilities of the neutral Ti_nO₂ systems are enhanced by adding one negative charge. The strongest interaction of the charged Ti_n clusters (?2, ?1, +1, and +2) with O₂ molecule is found at charge +2. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Comprehensive understanding of size‐, shape‐, and composition‐dependent polarizabilities of SimCn (m,n = 1–4) clusters

We performed a comprehensive study of the size‐, shape‐, and composition‐dependent polarizabilities of Si_mC_n (m, n = 1–4) clusters on the basis of the density‐functional‐based coupled perturbed Hartree–Fock calculations. We found better correlations between the polarizabilities and both the binding energies (E_b) and change in charge distribution (Δq) than the energy gaps. The α values exhibit overall decreasing and increasing trends with increases in the E_b and Δq values, respectively. For isomers with the same E_b values and different polarizabilities, Δq can well explain the difference in polarizabilities. The π‐electron delocalization effect is the best factor for understanding the shape‐dependence. For a given m/n value, the linear clusters have an obviously larger polarizability than both the prolate and compact clusters, irrespective of the cluster size. We fit a quantitative expression [α = A ? (A ? B) × exp(?k(m/n))] to describe the composition‐dependent polarizabilities. © 2012 Wiley Periodicals, Inc.     

Stability,Infrared Spectra and Electronic Structures of (ZrO2)n(n=3-6)Clusters:DFT Study

The stability, infrared spectra and electronic structures of (ZrO₂)_n (n=3–6) clusters have been investigated by using density‐functional theory (DFT) at B3LYP/6‐31G* level. The lowest‐energy structures have been recognized by considering a number of structural isomers for each cluster size. It is found that the lowest‐energy (ZrO₂)₅ cluster is the most stable among the (ZrO₂)_n (n=3–6) clusters. The vibration spectra of Zr? O stretching motion from terminal oxygen atom locate between 900 and 1000 cm^?1, and the vibrational band of Zr? O? Zr? O four member ring is obtained at 600–700 cm^?1, which are in good agreement with the experimental results. Mulliken populations and NBO charges of (ZrO₂)_n clusters indicate that the charge transfers occur between 4d orbital of Zr atoms and 2p orbital of O atoms. HOMO‐LUMO gaps illustrate that chemical stabilities of the lowest‐energy (ZrO₂)_n (n=3–6) clusters display an even‐odd alternating pattern with increasing cluster size.     

Adsorption of Propene on Neutral Gold Clusters in the Gas Phase

The adsorption of propene on neutral gold clusters is investigated in a collision cell under a few collision conditions. The adsorption reaction is studied by pressure‐dependent kinetic measurements and delayed unimolecular dissociation of the excited Au_n?propene complexes. The cluster size (n=9–25) and temperature (T=90–300 K) dependence of the propene adsorption is analyzed. Strong size dependences of the absorption reaction are observed; a larger propene adsorption probability was found for gold clusters composed of an even number of atoms. Propene binding energies are estimated by comparison of the temperature‐dependent unimolecular dissociation rates with rates obtained by using statistical RRKM modeling. The Au_n–propene binding energies decrease non‐monotonously with cluster size and are in the range of 1.2–0.85 eV for n=9–25. Finally, the bonding of C₃H₆ on Au_n is qualitatively described and similarities with the absorption of CO molecules on gold clusters are discussed.     

Observable Structures of Small Neutral and Anionic Gold Clusters

Since gold clusters have mostly been studied theoretically by using DFT calculations, more accurate studies are of importance. Thus, small neutral and anionic gold clusters (Au_n and Au_n^?, n=4–7) were investigated by means of coupled cluster with singles, doubles, and perturbative triple excitations [CCSD(T)] calculations with large basis sets, and some differences between DFT and CCSD(T) results are discussed. Interesting isomeric structures that have dangling atoms were obtained. Structures having dangling atoms appear to be stable up to n=4 for neutral gold clusters and up to n=7 for anionic clusters. The relative stabilities and electronic properties of some isomers and major structures are discussed on the basis of the CCSD(T) calculations. This accurate structure prediction of small gold clusters corresponding to experimental photoelectron spectral peaks is valuable in the field of atom‐scale materials science including nanocatalysts.     

Hydrogen‐Atom Abstraction from Methane by Stoichiometric Vanadium–Silicon Heteronuclear Oxide Cluster Cations

Vanadium–silicon heteronuclear oxide cluster cations were prepared by laser ablation of a V/Si mixed sample in an O₂ background. Reactions of the heteronuclear oxide cations with methane in a fast‐flow reactor were studied with a time‐of‐flight (TOF) mass spectrometer to detect the cluster distribution before and after the reactions. Hydrogen abstraction reactions were identified over stoichiometric cluster cations [(V₂O₅)_n(SiO₂)_m]⁺ (n=1, m=1–4; n=2, m=1), and the estimated first‐order rate constants for the reactions were close to that of the homonuclear oxide cluster V₄O₁₀⁺ with methane. Density functional calculations were performed to study the structural, bonding, electronic, and reactivity properties of these stoichiometric oxide clusters. Terminal‐oxygen‐centered radicals (O_t ^. ) were found in all of the stable isomers. These O_t ^. radicals are active sites of the clusters in reaction with CH₄. The O_t ^. radicals in [V₂O₅(SiO₂)_1–4]⁺ clusters are bonded with Si rather than V atoms. All the hydrogen abstraction reactions are favorable both thermodynamically and kinetically. This work reveals the unique properties of metal/nonmetal heteronuclear oxide clusters, and may provide new insights into CH₄ activation on silica‐supported vanadium oxide catalysts.     

Hydration preferences for Mn4Ca cluster models of photosystem II: location of potential substrate-water binding sites

Density functional theory calculations are reported on a set of three model structures of the Mn₄Ca cluster in the water‐oxidizing complex of Photosystem II (PSII), which share the structural formula [CaMn₄C₉H₁₀N₂O₁₆]^q+ ? (H₂O)_n (q=?1, 0, 1, 2, 3; n=0–7). In these calculations we have explored the preferred hydration sites of the Mn₄Ca cluster across five overall oxidation states (S₀ to S₄) and all feasible magnetic‐coupling arrangements to identify the most likely substrate–water binding sites. We have also explored charge‐compensated structures in which the overall charge on the cluster is maintained at q=0 or +1, which is consistent with the experimental data on sequential proton loss in the real system. The three model structures have skeletal arrangements that are strongly reminiscent, in their relative metal‐atom positions, of the 2.9‐, 3.7‐, and 3.5 Å‐resolution crystal structures, respectively, whereas the charge states encompassed in our study correspond to an assignment of (Mn^III)₃Mn^II for S₀ and up to (Mn^IV)₃Mn^III for S₄. The three models differ principally in terms of the spatial relationship between one Mn (Mn(4)) and a generally robust Mn₃Ca tetrahedron that contains Mn(1), Mn(2), and Mn(3). Oxidation‐state distributions across the four manganese atoms, in most of the explored charge states, are dependent on details of the cluster geometry, on the extent of assumed hydration of the clusters, and in some instances on the imposed magnetic‐coupling between adjacent Mn atoms. The strongest water‐binding sites are generally those on Mn(4) and Ca. However, one structure type displays a high‐affinity binding site between Ca and Mn(3), the S‐state‐dependent binding‐energy pattern of which is most consistent with the substrate water‐exchange kinetics observed in functional PSII. This structure type also permits another water molecule to access the cluster in a manner consistent with the substrate–water interaction with the Mn cluster, seen in electron spin‐echo envelope modulation (ESEEM) studies of the functional enzyme in the S₀ and S₂ states. It also rationalizes the significant differences in hydrogen‐bonding interactions of the substrate water observed in the FTIR measurements of the S₁ and S₂ states. We suggest that these two water‐binding sites, which are molecularly close, model the actual substrate‐binding sites in the enzyme.     

Ga2Br2R2 und Ga3I2R3 [R = C(SiMe3)3] — zwei neue elementorganische Galliumsubhalogenide mit einer bzw. zwei Ga‐Ga‐Bindungen

Ga₂Br₂R₂ and Ga₃I₂R₃ [R = C(SiMe₃)₃] — Two New Organoelement Subhalides of Gallium Containing One or Two Ga‐Ga Single Bonds The oxidation of the tetrahedral tetragallium cluster Ga₄[C(SiMe₃)₃]₄ ( 1 ) with elemental bromine in the presence of AlBr₃ yielded the corresponding gallium subhalide Ga₂Br₂R₂ [ 4 , R = C(SiMe₃)₃], which remains monomer even in the solid state and in which the Ga^II atoms are connected by a short Ga‐Ga single bond [243.2(2) pm]. The analogous diiodide Ga₂I₂R₂ ( 3 ), which was obtained on a similar route by our group only recently, did not react with lithium tert‐butanolate by substitution as originally expected. Instead, partial disproportionation occurred with the formation of the trigallium diiodide Ga₃I₂R₃ ( 6 ), in which three Ga atoms are connected by two Ga‐Ga single bonds (255.1 pm on average). Both terminal Ga atoms have a coordination number of four owing to the bridging function of both iodine atoms, while the inner one which has an oxidation number of +1 remains coordinatively unsaturated. An average oxidation state of 1.66 resulted for all atoms of the chain. The Ga^III compound {[GaI(R)(OCMe₃)(OH)]Li}₂ ( 7 ) was isolated as the second product of the disproportionation. It is a dimer in the solid state via Li‐O bridges and shows a hindered rotation of its tert‐butyl group.     

K and Ba distribution in the structures of the clathrate compounds KxBa16−x(Ga,Sn)136 (x = 0.8, 4.4, and 12.9) and KxBa8−x(Ga,Sn)46 (x = 0.3)

Studies of the K–Ba–Ga–Sn system produced the clathrate compounds K_0.8(2)Ba_15.2(2)Ga_31.0(5)Sn_105.0(5) [a = 17.0178 (4) Å], K_4.3(3)Ba_11.7(3)Ga_27.4(4)Sn_108.6(4) [a = 17.0709 (6) Å] and K_12.9(2)Ba_3.1(2)Ga_19.5(4)Sn_116.5(4) [a = 17.1946 (8) Å], with the type‐II structure (cubic, space group Fdm), and K_7.7(1)Ba_0.3(1)Ga_8.3(4)Sn_37.7(4) [a = 11.9447 (4) Å], with the type‐I structure (cubic, space group Pmn). For the type‐II structures, only the smaller (Ga,Sn)₂₄ pentagonal dodecahedral cages are filled, while the (Ga,Sn)₂₈ hexakaidecahedral cages remain empty. The unit‐cell volume is directly correlated with the K:Ba ratio, since an increasing amount of monovalent K occupying the cages causes a decreasing substitution of the smaller Ga in the framework. All three formulae have an electron count that is in good agreement with the Zintl–Klemm rules. For the type‐I compound, all framework sites are occupied by a mixture of Ga and Sn atoms, with Ga showing a preference for Wyckoff site 6c. The (Ga,Sn)₂₀ pentagonal dodecahedral cages are occupied by statistically disordered K and Ba atoms, while the (Ga,Sn)₂₄ tetrakaidecahedral cages encapsulate only K atoms. Large anisotropic displacement parameters for K in the latter cages suggest an off‐centering of the guest atoms.     

Density functional study of carbon monoxide adsorption on small cationic,neutral, and anionic aluminum nitride clusters

CO adsorption on small cationic, neutral, and anionic (AlN)_n (n = 1–6) clusters has been investigated using density functional theory in the generalized gradient approximation. Among various possible CO adsorption sites, an N on‐top (onefold coordinated) site is found to be the most favorable one, irrespective of the charge state of the clusters. The adsorption energies of CO on the anionic (AlN)_nCO (n = 2–4) clusters are greater than those on the neutral and cationic complexes. The adsorption energies on the cationic and neutral complexes reflect the odd–even oscillations, and the adsorption energies of CO on the cationic (AlN)_nCO (n = 5, 6) clusters are greater than those on the neutral and anionic complexes. The adsorption energies for the different charge states decrease with increasing cluster size. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Symmetry restrictions as starting point for the determination of geometric representations and the dynamics of cyclic π systems

A quasiclassical‐state approach was developed for probing π bonding and delocalization energies focused on benzene. A more general picture is now given for neutral n π‐conjugated cyclic systems with a geometry distortion from D_nh into D_1/2nh (n=4,6,8,…,16), which results in a new aromaticity‐antiaromaticity criterion. For n=6 and 8 the corresponding divalent charged systems were studied in relation to zero‐field splittings of the triplet ground state and geometry, respectively. Attention is also given to antiaromatic π‐conjugated systems focused on the cyclopropenyl anion, the cyclopentadienyl cation, and the cycloheptatrienyl anion and their relaxed states. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 641–650, 2000     

Structures,Unimolecular Fragmentations,and Reactivities of the Self‐Assembled Multimetallic/Peptide Complexes [Mnn(GlyGly‐H)2n−1]+ and [Mnn+1(GlyGly‐H)2n]2+

Complexes of Mn²⁺ with deprotonated GlyGly are investigated by sustained off‐resonance irradiation collision‐induced dissociation (SORI‐CID), infrared multiple‐photon dissociation spectroscopy, ion–molecule reactions, and computational methods. Singly [Mn_n(GlyGly‐H)_2n?1]⁺ and doubly [Mn_n+1(GlyGly‐H)_2n]²⁺ charged clusters are formed from aqueous solutions of MnCl₂ and GlyGly by electrospray ionization. The most intense ion produced was the singly charged [M₂(GlyGly‐H)₃]⁺ cluster. Singly charged clusters show extensive fragmentations of small neutral molecules such as water and carbon dioxide as well as dissociation pathways related to the loss of NH₂CHCO and GlyGly. For the doubly charged clusters, however, loss of GlyGly is observed as the main dissociation pathway. Structure elucidation of [Mn₃(GlyGly‐H)₄]²⁺ clusters has also been done by IRMPD spectroscopy as well as DFT calculations. It is shown that the lowest energy structure of the [Mn₃(GlyGly‐H)₄]²⁺ cluster is deprotonated at all carboxylic acid groups and metal ions are coordinated with carbonyl oxygen atoms, and that all amine nitrogen atoms are hydrogen bonded to the amide hydrogen. A comparison of the calculated high‐spin (sextet) and low‐spin (quartet) state structures of [Mn₃(GlyGly‐H)₄]²⁺ is provided. IRMPD spectroscopic results are in agreement with the lowest energy high‐spin structure computed. Also, the gas‐phase reactivity of these complexes towards neutral CO and water was investigated. The parent complexes did not add any water or CO, presumably due to saturation at the metal cation. However, once some of the ligand was removed via CO₂ laser IRMPD, water was seen to add to the complex. These results are consistent with high‐spin Mn²⁺ complexes.     

Theoretical prediction for the structures of gas phase lithium oxide clusters: (Li2O)n (n = 1–8)

We apply genetic algorithm combining directly with density functional method to search the potential energy surface of lithium‐oxide clusters (Li₂O)_n up to n = 8. In (Li₂O)_n (n = 1–8) clusters, the planar structures are found to be global minimum up to n = 2, and the global minimum structures are all three‐dimensional at n ≥ 3. At n ≥ 4, the tetrahedral unit (TU) is found in most of the stable structures. In the TU, the central Li is bonded with four O atoms in sp³ interactions, which leads to unusual charge transformation, and the probability of the central Li participating in the bonding is higher by adaptive natural density partitioning analysis, so the central Li is in particularly low positive charge. At large cluster size, distortion of structures is viewed, which breaks the symmetry and may make energy higher. The global minimum structures of (Li₂O)₂, (Li₂O)₆, and (Li₂O)₇ clusters are the most stable magic numbers, where the first one is planar and the later both have stable structural units of tetrahedral and C_4v. © 2012 Wiley Periodicals, Inc.     

Fragmentation of the tryptophan cluster [Trp9-2H]2- induced by different activation methods

Electrospray ionization (ESI) of tryptophan gives rise to multiply charged, non‐covalent tryptophan cluster anions, [Trp_n–xH]^x?, in a linear ion trap mass spectrometer, as confirmed by high‐resolution experiments performed on a Fourier transform ion cyclotron resonance (FT‐ICR) mass spectrometer. The smallest multiply charged clusters that can be formed in the linear ion trap as a function of charge state are: x = 2, n = 7; x = 3, n = 16; x = 4, n = 31. The fragmentation of the dianionic cluster [Trp₉–2H]^2? was examined via low‐energy collision‐induced dissociation (CID), ultraviolet photodissociation (UVPD) at 266 nm and electron‐induced dissociation (EID) at electron energies ranging from >0 to 30 eV. CID proceeds mostly via charge separation and evaporation of neutral tryptophan. The smallest doubly charged cluster that can be formed via evaporation of neutral tryptophans is [Trp₇–2H]^2?, consistent with the observation of this cluster in the ESI mass spectrum. UVPD gives singly charged tryptophan clusters ranging from n = 2 to n = 9. The latter ion arises from ejection of an electron to give the radical anion cluster, [Trp₉–2H]^?.. The types of gas‐phase EID reactions observed are dependent on the energy of the electrons. Loss of neutral tryptophan is an important channel at lower energies, with the smallest doubly charged ion, [Trp₇–2H]^2?, being observed at 19.8 eV. Coulomb explosion starts to occur at 19.8 eV to form the singly charged cluster ions [Trp_x–H]^? (x = 1–8) via highly asymmetric fission. At 21.8 eV a small amount of [Trp₂–H–NH₃]^? is observed. Thus CID, UVPD and EID are complementary techniques for the study of the fragmentation reactions of cluster ions. Copyright © 2010 John Wiley & Sons, Ltd.     

Self‐Assembled Multimetallic/Peptide Complexes: Structures and Unimolecular Reactions of [Mn(GlyGly−H)2n−1]+ and Mn+1(GlyGly−H2n]2+ Clusters in the Gas Phase

The unimolecular chemistry and structures of self‐assembled complexes containing multiple alkaline‐earth‐metal dications and deprotonated GlyGly ligands are investigated. Singly and doubly charged ions [M_n(GlyGly?H)_n‐1]⁺ (n=2–4), [M_n+1(GlyGly?H)_2n]²⁺ (n=2,4,6), and [M(GlyGly?H)GlyGly]⁺ were observed. The losses of 132 Da (GlyGly) and 57 Da (determined to be aminoketene) were the major dissociation pathways for singly charged ions. Doubly charged Mg²⁺ clusters mainly lost GlyGly, whereas those containing Ca²⁺ or Sr²⁺ also underwent charge separation. Except for charge separation, no loss of metal cations was observed. Infrared multiple photon dissociation spectra were the most consistent with the computed IR spectra for the lowest energy structures, in which deprotonation occurs at the carboxyl acid groups and all amide and carboxylate oxygen atoms are complexed to the metal cations. The N?H stretch band, observed at 3350 cm^?1, is indicative of hydrogen bonding between the amine nitrogen atoms and the amide hydrogen atom. This study represents the first into large self‐assembled multimetallic complexes bound by peptide ligands.     

Local Geometric Effects on Stability and Energy Gap of Thiolate‐Protected Gold Nanoparticles

Thiolate‐protected gold nanoclusters, Au_m(SR)_n, have potential applications in many fields due to their high stability and remarkable electronic properties. However, the controlling factors in determining the stability and HOMO–LUMO gap of Au_m(SR)_n remain controversial, despite decades of work on the topic. Through DFT calculations, including nonlocal many‐body dispersion (MBD) interactions, the geometric and electronic properties of Au_m(SR)_n clusters are investigated. Calculations demonstrate that the MBD interactions are essential for correctly describing the geometry and energy of the clusters. Greater anisotropic polarization and more atoms distributed in the shell of the clusters lead to more pronounced MBD interactions and higher stability of the clusters. Furthermore, the HOMO–LUMO gap of the clusters strongly depends on the gold core. These results provide critical clues for understanding and designing Au_m(SR)_n clusters.     

Geometrical structures,electronic states,and stability of NinAl clusters

Density‐functional with generalized gradient approximation (GGA) for the exchange‐correlation potential has been used to calculate the energetically global‐minimum geometries and electronic states of Ni_nAl (n = 2–8) neutral clusters. Our calculations predict the existence of a number of previously unknown isomers. All structures may be derived from a substitution of a Ni atom at marginal positions by an Al atom in the Ni_n+1 cluster. Aluminum atom remains on the surface of the geometrical configurations. Moreover, these species prefer to adopt three‐dimensional (3D) spacial forms at the smaller number of nickel atoms compared with the pure Ni_n+1 (n ≥ 3) configuration. Atomization energies per atom for Ni_nAl (n = 2–8) have the same trend as the binding energies per atom for Ni_n (n = 3–9). The stabilization energies reveal that Ni₅Al is the relatively most stable in this series. In comparison with the magnetic moment of pure metal nickel (0.6 μ_B), the average magnetic moment of Ni atom increases in Ni Al clusters except the Ni₃Al. Moreover, except the case of Ni₅Al, Ni average magnetic moment decreases when alloyed with Al atoms than that in pure Ni clusters, which originate the effective charge transferring from Al to Ni atoms. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010