Structure and Stability of (NG)nCN3Be3+ Clusters and Comparison with (NG)BeY0/+

The noble gas binding ability of CN₃Be₃⁺ clusters was assessed both by ab intio and density functional studies. The global minimum structure of the CN₃Be₃⁺ cluster binds with four noble‐gas (NG) atoms, in which the Be atoms are acting as active centers. The electron transfer from the noble gas to the Be atom plays a key role in binding. The dissociation energy of the Be? NG bond gradually increases from He to Rn, maintaining the periodic trend. The HOMO–LUMO gap, an indicator for stability, gives additional insight into these NG‐bound clusters. The temperature at which the NG‐binding process is thermodynamically feasible was identified. In addition, we investigated the stability of two new neutral NG compounds, (NG)BeSe and (NG)BeTe, and found them to be suitable candidates to be detected experimentally such as (NG)BeO and (NG)BeS. The dissociation energies of the Be? NG bond in monocationic analogues of (NG)BeY (Y=O, S, Se, Te) were found to be larger than in the corresponding neutral counter‐parts. Finally, the higher the positive charge on the Be atoms, the higher the dissociation energy for the Be? NG bond becomes.     

Thermal Conversion of Methane to Formaldehyde Promoted by Gold in AuNbO3+ Cluster Cations

In addition to generation of a methyl radical, formation of a formaldehyde molecule was observed in the thermal reaction of methane with AuNbO₃⁺ heteronuclear oxide cluster cations. The clusters were prepared by laser ablation and mass‐selected to react with CH₄ in an ion‐trap reactor under thermal collision conditions. The reaction was studied by mass spectrometry and DFT calculations. The latter indicated that the gold atom promotes formaldehyde formation through transformation of an Au?O bond into an Au?Nb bond during the reaction.     

SPC cluster modeling of metal oxides: ways of determining the values of point charges in the embedded cluster model

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A DFT Study of the Structures of Aux Clusters on a CeO2(111) Surface

Studying the structures of metal clusters on oxide supports is challenging due to their various structural possibilities. In the present work, a simple rule in which the number of Au atoms in different layers of Au_x clusters is changed successively is used to systematically investigate the structures of Au_x (x=1–10) clusters on stoichiometric and partially reduced CeO₂(111) surface by DFT calculations. The calculations indicate that the adsorption energy of a single Au atom on the surface, the surface structure, as well as the Au? Au bond strength and arrangement play the key roles in determining Au_x structures on CeO₂(111). The most stable Au₂ and Au₃ clusters on CeO₂(111) are 2D vertical structures, while the most stable structures of Au_x clusters (x>3) are generally 3D structures, except for Au₇. The 3D structures of large Au_x clusters in which the Au number in the bottom layer does not exceed that in the top layer are not stable. The differences between Au_x on CeO₂(111) and Mg(100) were also studied. The stabilizing effect of surface oxygen vacancies on Au_x cluster structures depends on the size of Au_x cluster and the relative positions of Au_x cluster and oxygen vacancy. The present work will be helpful in improving the understanding of metal cluster structures on oxide supports.     

Theoretical insight of nitric oxide adsorption on neutral and charged Pdn (n = 1–5) clusters

Density functional theory (DFT) calculations within the framework of generalized gradient approximation have been used to systematically investigate the adsorption of nitric oxide (NO) molecule on neutral, cationic, and anionic Pd_n (n = 1–5) clusters. NO coordinate to one Pd atom of the cluster by the end‐on mode, where the tilted end‐on structure is more favorable due to the additional electron in the π* orbital. On the contrary, in the neutral and cationic Pd₂ system, NO coordinates to the bridge site of cluster preferably by the side‐on mode. Charge transfer between Pd clusters and NO molecule and the corresponding weakening of N? O bond is an essential factor for the adsorption. The N? O stretching frequency follow the order of cationic > neutral > anionic. Binding energy of NO on anionic clusters is found to be greater than those of neutral and cationic clusters. © 2015 Wiley Periodicals, Inc.     

A Combined Experimental and Theoretical Electron Density Study of Intra‐ and Intermolecular Interactions in Thiourea S,S‐Dioxide

The thiourea S,S‐dioxide molecule is recognized as a zwitterion with a high dipole moment and an unusually long C? S bond. The molecule has a most interesting set of intermolecular interactions in the crystalline state—a relatively strong O???H? N hydrogen bond and very weak intermolecular C???S and N???O interactions. The molecule has C_s symmetry, and each oxygen atom is hydrogen‐bonded to two hydrogen atoms with O???H? N distances of 2.837 and 2.826 Å and angles of 176.61 and 158.38°. The electron density distribution is obtained both from Xray diffraction data at 110 K and from a periodic density functional theory (DFT) calculation. Bond characterization is made in terms of the analysis of topological properties. The covalent characters of the C? N, N? H, C? S, and S? O bonds are apparent, and the agreement on the topological properties between experiment and theory is adequate. The features of the Laplacian distributions, bond paths, and atomic domains are comparable. In a systematic approach, DFT calculations are performed based on a monomer, a dimer, a heptamer, and a crystal to see the effect on the electron density distribution due to the intermolecular interactions. The dipole moment of the molecule is enhanced in the solid state. The typical values of ρ_b and H_b of the hydrogen bonds and weak intermolecular C???S and N???O interactions are given. All the interactions are verified by the location of the bond critical point and its associated topological properties. The isovalue surface of Laplacian charge density and the detailed atomic graph around each atomic site reveal the shape of the valence‐shell charge concentration and provide a reasonable interpretation of the bonding of each atom.     

QMX: A versatile environment for hybrid calculations applied to the grafting of Al2Cl3Me3 on a silica surface

We present a new software to easily perform QM:MM and QM:QM' calculations called QMX. It follows the subtraction scheme and it is implemented in the Atomic Simulation Environment (ASE). Special attention is paid to couple molecular calculations with periodic boundaries approaches. QMX inherits the flexibility and versatility of the ASE package: any combination of methods namely force field, semiempirical, first principle, and ab initio, can be used as hybrid potential energy surface (PES). Its ease of use is demonstrated by considering the adsorption of Al₂Cl₃Me₃ on silica surface and by combining different levels of theory (from standard DFT to MP2 calculations) for the so‐called High Level cluster with standard PW91 density functional theory calculations for the Low Level environment. It is shown that the High Level cluster must contain the silanol group close to the aluminum atoms. The bridging adsorption is favored by 58 kJ mol^?1 at the MP2:PW91 level with respect to the terminal position. Using large clusters at the MP2:PW91 level, it is shown that PW91 calculations are sufficient for structure optimization but that embedded methods are required for accurate energy profiles. © 2013 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.     

Synthesis, crystal and electronic structures, and magnetic properties of LiLn9Mo16O35 (Ln = La, Ce, Pr, and Nd) compounds containing the original cluster Mo16O36

The new compounds LiLn(9)Mo(16)O(35) (Ln=La, Ce, Pr, and Nd) were synthesized from stoichiometric mixtures of Li(2)MoO(4), Ln(2)O(3), Pr(6)O(11) or CeO(2), MoO(3), and Mo heated at 1600 °C for 48 h in a molybdenum crucible sealed under a low argon pressure. The crystal structure, determined from a single crystal of the Nd member, showed that the main building block is the Mo(16)O(36) unit, the Mo(16) core of which is totally new and results from the fusion of two bioctahedral Mo(10) clusters. It can also be viewed as a fragment of an infinite twin chain of edge-sharing Mo(6) octahedra. The Mo(16)O(36) cluster units share some oxygen atoms to form infinite chains running parallel to the b axis, which are separated by the rare-earth and lithium cations. (7)Li-NMR experiments, carried out at high field on the nonmagnetic LiLa(9)Mo(16)O(35), provided insights into the local environment of the lithium ions. Magnetic susceptibility measurements confirmed the trivalent oxidation state of the magnetic rare-earth cations and indicated the absence of localized moments on the Mo(16) clusters. The electronic structure of the LiLn(9)Mo(16)O(35) compounds was analyzed using molecular and periodic quantum calculations. The study of the molecular orbital diagrams of isolated Mo(16)O(36) models allowed the understanding of this unique metallic architecture. Periodic density functional theory calculations demonstrated that few interactions occur between the Mo(16) clusters, and predicted semiconducting properties for LiLn(9)Mo(16)O(35) as a band gap of 0.57 eV was computed for the lanthanum phase.     

Comparison of the periodic slab approach with the finite cluster description of metal–organic interfaces at the example of PTCDA on Ag(110)

We present a comparative study of metal–organic interface properties obtained from dispersion corrected density functional theory calculations based on two different approaches: the periodic slab‐supercell technique and cluster models with 32–290 Ag atoms. Fermi smearing and fixing of cluster borders are required to make the cluster calculation feasible and realistic. The considered adsorption structure and energy of a PTCDA molecule on the Ag(110) surface is not well reproduced with clusters containing only two metallic layers. However, all clusters with four layers of silver atoms and sufficient lateral extension reproduce the adsorbate structure within 0.04 Å with respect to the slab‐supercell structure and provide adsorption energies of ( 0.08 eV) consistent with the slab result of −4.47 eV. Thus, metal–organic adsorbate systems can be realistically represented by properly defined cluster models. © 2018 Wiley Periodicals, Inc.     

Electronic factors determining the methane bond breaking process on small aluminum clusters

In order to understand the catalytic activity of small metal clusters as a function of their size, we have studied the interaction of CH₄ with Al₄ and Al₅ neutral and charged clusters, as well as neutral thermally expanded clusters in the two lowest lying spin states, using density functional theory. These calculations, via extended search, are used to determine the stable positions of H and CH₃ near the cluster, and the transition state to break the H─CH₃ bond. In order to understand the factors underlying the reactivity of the clusters, we have analyzed the electronic structure at the transition state. By an analysis of the change of the electronic density of states close to the transition state, we identify the orbitals involved in the bond breaking process. In conjunction with our previous studies of Al₂ and Al₃ clusters, we find that the small Al clusters, except for Al₅, lower the CH₃─H dissociation barrier with respect to the gas-phase value, although Al lacks occupied d-orbitals. Still, Al₅ does not catalyze methane bond breaking, which is attributed to the required interaction with low-lying Al sp-states. Furthermore, in all cases where stable methyl-aluminum-hydrides are possible, the recombinative desorption of methane is studied by vibrational analysis and application of transition state theory.     

Ionic‐Radius‐Driven Selection of the Main‐Group‐Metal Cage for Intermetalloid Clusters [Ln@PbxBi14−x]q− and [Ln@PbyBi13−y]q− (x/q=7/4, 6/3; y/q=4/4, 3/3)

Reactions of the binary, pseudo‐homoatomic Zintl anion (Pb₂Bi₂)^2? with Ln(C₅Me₄H)₃ (Ln=La, Ce, Nd, Gd, Sm, Tb) in the presence of [2.2.2]crypt in ethane‐1,2‐diamine/toluene yielded ten [K([2.2.2]crypt)]⁺ salts of lanthanide‐doped semimetal clusters with 13 or 14 surface atoms. Single‐crystal X‐ray diffraction and energy‐dispersive X‐ray spectroscopy indicated the presence of the anions [Ln@Pb₆Bi₈]^3?, [Ln@Pb₃Bi₁₀]^3?, [Ln@Pb₇Bi₇]^4?, or [Ln@Pb₄Bi₉]^4? in single or double salts; the latter showed various ratios of the components in the solid state. The anions are the first ternary intermetalloid clusters comprising only elements of the sixth period of the periodic table, namely, Pb, Bi and lanthanides. This study, which was complemented by ESI mass spectrometry and ¹³⁹La NMR spectroscopy in solution, rationalizes a continuous development of the ratio of 13:14‐atom cages with the ionic radius of the embedded Ln³⁺ ion, which seems to select the most suitable cage type. Quantum chemical investigations helped to analyze this situation in more detail and to explain the observed subtle influence of the atomic radii. Magnetic measurements confirmed that the embedded Ln³⁺ ions keep their expected paramagnetic or diamagnetic nature.     

5d过渡金属原子中心镶嵌Ag团簇M@Ag12(M=Hf～Hg)Ih和Oh构型的密度泛函理论研究

采用相对论密度泛函理论方法对Ih和Oh构型M@Ag12 (M＝Hf～Hg)的几何和电子结构进行了系统的研究. 研究表明, 原子半径之和与团簇的电子结构共同决定了M—Ag键长的大小. M@Ag12的成键能来自中心原子的嵌入能和Ag12笼子的形变能. 最高占据轨道为成键轨道的团簇比反键轨道的团簇的稳定性强. 我们发现在此系列中, Ih构型不一定总比Oh构型稳定. Hf@Ag12, Ir@Ag12, Au@Ag12和Hg@Ag12的Oh构型比Ih构型稳定.     

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     

Predicting C?H/π Interactions with Nonlocal Density Functional Theory

We examine the performance of a recently developed nonlocal density functional in predicting a model noncovalent interaction, namely the weak bond between an aromatic π system and an aliphatic C? H group. The new functional is a significant improvement over traditional density functionals, providing results which compare favorably to high‐level quantum‐chemistry techniques, but at considerably lower computational cost. Interaction energies in several model C? H/π systems are in good general agreement with coupled‐cluster calculations, though equilibrium distances are consistently overpredicted when using the revPBE functional for exchange. The new functional predicts changes in energy upon addition of halogen substituents correctly.     

Improved embedded molecular cluster model

We demonstrate that boundary effects (i.e., displacements of the cluster boundary atoms from their lattice sites and the difference between effective charges of the perfect crystal atoms and those of the cluster atoms in the case of a cluster with no point defect in it) in an embedded molecular cluster (EMC) model can be radically reduced. A new embedding scheme is proposed. It includes search for the structural elements (SE) of which perfect crystal is composed, use of corresponding to these SE expression for the total energy, and application of the degree of localization of equations consistent with the wave functions of the cluster. To get equations for the cluster wave functions, the problem of varied subsystem in the field of the frozen remaining part of the whole electron system” is investigated in the framework of a one-electron approximation. The consideration is general for every task of this type. Homogeneous equations resulting directly from variation of the total energy expression are obtained and transformed to the eigenvalue problem equations. Orthogonality constraints are not imposed during variation. A particular case of the equations describing mutually orthogonal one-electron wave functions of the cluster staying nonorthogonal to those of the remaining crystal is found. A proposed embedding scheme is realized in the CLUSTER code based on the calculation scheme of the semiempirical INDO method. Boundary effects both in the standard (cluster in the field of the infinite lattice of nonpoint spherical charges) and new embedding scheme are investigated, calculating the clusters of LiF, MgO, NaCl, KCl, and AgCl crystals. Significant reduction of the boundary effects in the new embedding scheme is achieved. Reasons for the boundary effects are discussed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Aggregation behavior and non-covalent functionalization of borofullerenes B28, B38, and B40: A density functional theory investigation

Fullerene-like boron clusters (borofullerenes) are rising stars in the field of cluster chemistry. In this work, density functional theory calculations revealed that the recently reported small borofullerenes B_n (n = 28, 38, and 40) are all highly reactive and tend to form dimers and even trimers spontaneously. In addition, the non-covalent modification of these borofullerenes by various cycloparaphenylene nanorings can form stable host-guest systems with substantial intermolecular charge transfer at both ground and excited states. Our results demonstrate that the borofullerenes are versatile platform for exohedral functionalization, and are very promising candidates for the design of novel nanomaterials with desirable properties.     

Methane Activation Mediated by a Series of Cerium–Vanadium Bimetallic Oxide Cluster Cations: Tuning Reactivity by Doping

The reactions of cerium–vanadium cluster cations Ce_xV_yO_z⁺ with CH₄ are investigated by time‐of‐flight mass spectrometry and density functional theory calculations. (CeO₂)_m(V₂O₅)_n⁺ clusters (m=1,2, n=1–5; m=3, n=1–4) with dimensions up to nanosize can abstract one hydrogen atom from CH₄. The theoretical study indicates that there are two types of active species in (CeO₂)_m(V₂O₅)_n⁺, V[(O_t)₂]^. and [(O_b)₂CeO_t]^. (O_t and O_b represent terminal and bridging oxygen atoms, respectively); the former is less reactive than the latter. The experimentally observed size‐dependent reactivities can be rationalized by considering the different active species and mechanisms. Interestingly, the reactivity of the (CeO₂)_m(V₂O₅)_n⁺ clusters falls between those of (CeO₂)_2–4⁺ and (V₂O₅)_1–5⁺ in terms of C?H bond activation, thus the nature of the active species and the cluster reactivity can be effectively tuned by doping.     

Treatment of delocalized electron transfer in periodic and embedded cluster DFT calculations: The case of Cu on ZnO (10 0)

We assess the consequences of the interface model—embedded‐cluster or periodic‐slab model—on the ability of DFT calculations to describe charge transfer (CT) in a particularly challenging case where periodic‐slab calculations indicate a delocalized charge‐transfer state. Our example is Cu atom adsorption on ZnO(10 0), and in fact the periodic slab calculations indicate three types of CT depending on the adsorption site: full CT, partial CT, and no CT. Interestingly, when full CT occurs in the periodic calculations, the calculated Cu atom adsorption energy depends on the underlying ZnO substrate supercell size, since when the electron enters the ZnO it delocalizes over as many atoms as possible. In the embedded‐cluster calculations, the electron transferred to the ZnO delocalizes over the entire cluster region, and as a result the calculated Cu atom adsorption energy does not agree with the value obtained using a large periodic supercell, but instead to the adsorption energy obtained for a periodic supercell of roughly the same size as the embedded cluster. Different density functionals (of GGA and hybrid types) and basis sets (local atom‐centered and plane‐waves) were assessed, and we show that embedded clusters can be used to model Cu adsorption on ZnO(10 0), as long as care is taken to account for the effects of CT. © 2015 Wiley Periodicals, Inc.