Theoretical study of isomerism of acetylene compounds with aluminum clusters doped with 3d transition metals

Structural characteristics, vibrational frequencies, and energies of ten isomers of acetylene compounds with the centered aluminum cluster Al₁₃ and its analogues Al₁₂M doped with 3d transition metal atoms (M = Ti-Ni) in the states of different multiplicity have been calculated by the density functional theory method. In addition to “coordinated” intermediates in which the C₂H₂ molecule is coordinated through its C-C bond to the M vertex, an M-Al edge, or a trigonal face of the [MAl₂] cluster, “fragment” isomers have been considered in which the acetylene molecule is broken into fragments (C₂H + H, CH + CH, H + CH + C, and 2P + 2H) differently inserted into the aluminum cage and enlarging it to Al₁₂MC₂. For most compounds, low-lying isomers have structures 1–4 (the C₂H₂ molecule is coordinated to an Al₂M face), 1–5 (two CH fragments are added to adjacent Al₂M faces), and 1–8 (with a five-coordinate C* atom). Structure 1–1, in which the C₂H₂ molecule is coordinated through the C-C bond to the M dopant is unstable against transformation into 1–4 with a low barrier. An isomer with unusual structure 1–9 has been localized in which two five-coordinate C* atoms built into the aluminum cage are located in adjacent quasi-planar tetragonal [MAl₃] faces and are bonded to the central aluminum atom (Al_c) through the fifth bonds. The substitution of electronegative substituents X= F and Cl for H atoms in isomers 1–8 and 1–9 makes the latter more basic and clearly more favorable. The five-coordinate C* atoms in them are able to add acceptor ligands of the BH₃ and AlH₃ type and to increase the coordination number of the carbon atom to six with a considerable decrease in energy. The trends in the change in structural characteristics and relative energies of isomers with a change in M dopants along the 3d series, electronegativity of X substituents, and electronic state multiplicity have been analyzed.     

Ab initio studies on (H2O)14 - clusters: existence of surface and interior-bound extra electrons

A recent paper by Turi et al. [Science 309, 914 (2005)] suggests that the anionic water clusters smaller than (H2O)(45) (-) (at a low temperature) will only have surface-bound extra electrons and no internally bound electrons. Accordingly, (H2O)(14) (-) cluster isomers should only have surface-bound extra electrons. The ab initio results presented here, however, suggest that the (H2O)(14) (-) cluster isomers can have two distinct types of isomers with almost the same energy. The one type of isomer (type 1) has all the non-H-bonding H atoms (NHB H) directed outward and surface-bound extra electron while the other type (type 2) has a number of NHB H atoms directed toward cavity and has an interior-bound electron, and thus, contradicts the earlier quantum simulation results of Turi et al.     

Theoretical study of isomerism of compounds of CO and CO2 molecules with aluminum clusters Al13, Al12Ti,and Al12Ni

Structural characteristics, vibrational frequencies, and energies of isomers of compounds of CO and CO₂ molecules with the centered aluminum cluster Al₁₃ and its doped analogues Al₁₂M (M = Ti and Ni) have been calculated by the density functional theory method. For the Al₁₂MCO compounds, the most favor-able are two “fragment” isomers in which the C and O atoms are separated and built into the cluster cage, completing it to a 14-vertex polyhedron. In one of them, the C and O atoms are in the capping positions over adjacent trigonal MAl₂ faces; in the second isomer, there is the five-coordinate C* atom located in the center of a tetragonal MAl3 face and bound to the central Al atom through the long fifth bond. The “coordinated” isomers, in which the CO molecule is coordinated as a ligand to a cluster vertex, edge, or face, are unstable to removal of CO for Al₁₃CO, close in energy to the fragment isomers for Al₁₂NiCO, and considerably higher on the energy scale than the fragment isomers but remain stable to CO removal for Al₁₂TiCO. For the Al₁₂MCO₂ compounds, the most favorable is the fragment isomer in which both oxygen atoms are in the capping positions over adjacent faces and the C* atom is five-coordinate. The alternative oxo carbonyl isomer Al₁₂MO(CO) is close to the lowest-lying one in the case of M = Ni and is ～56 kcal/mol higher on the energy scale in the case of M= Ti. The less stable Al₁₂M(CO₂) isomer is the complex in which the CO₂ ligand is coordinated to an M-Al edge. According to calculations, addition of CO to Al₁₂MO and addition of CO₂ to Al₁₂M to form, respectively, Al₁₂MO(CO) and Al₁₂M(CO₂) can occur without noticeable barrier. The Al₁₂M(CO₂) and Al₁₂MO(CO) isomers are separated by a barrier, moderate for M = Ti (～16 kcal/mol) and small for M = Ni (～6 kcal/mol).     

Structures and properties of the tin-doped carbon clusters

A systemic density functional theory study of the tin-doped carbon clusters has been carried out using B3LYP method with TZP+ basis set. For each species, the electronic states, relative energies and geometries of various isomers are reported. Except for smaller SnC₂ and the largest , the Sn-terminated linear or quasi-linear isomer is the most stable structure for clusters. The electronic ground state is alternate between ³Σ (for n-odd member) and ¹Σ (for the n-even member) for linear SnC_n and invariably ²Π for linear and , except for SnC/SnC⁺/SnC⁻,, and . The incremental binding energy diagrams show that strong even–odd alternations in the cluster stability exist for both neutral SnC_n and anionic , with their n-even members being much more stable than the corresponding odd n − 1 and n + 1 ones, while for cationic , the alternation effect is less pronounced. These parity effects also reflect in the ionization potential and electron affinity curves. By comparing with the fragmentation energies accompanying various channels, the most favorable dissociation channel for each kind of the clusters are given. All these results are very similar to those obtained previously for the clusters.     

Theoretical study of isomerism of carbonand silicon-substituted aluminum clusters M<Subscript>6</Subscript>Al<Subscript>38</Subscript> and M<Subscript>12</Subscript>Al<Subscript>32</Subscript>

More than twenty M₆Al₃₈ isomers and several M₁₂Al₃₂ isomers of carbon- and silicon-substituted aluminum clusters with six and twelve dopant atoms of general formula M_nA_l44–n(M = C and Si, n = 6 and 12) have been studied by the density functional theory method. Calculations predict that, in the lowest-lying M₆Al₃₈, isomer, all substitutions of C atoms for Al are localized in one outer surface layer of the aluminum cage. In the course of optimization, the C atoms with a negative charge of about 1e are incorporated into positions of the intermediate layer to transform it into a 12-atom face composed of three adjacent vertex-sharing six-membered rings with short C–Al bonds. In the favorable isomer of M₆Al₃₈, the dopants are scattered as individual Si atoms located in both outer layers or in the subsurface space between the outer layers and the inner core of the cluster. Optimization of low-lying isomers with twelve starting substitutions of C and Si for Al in both outer layers has localized two preferable C₁₂Al₃₂ isomers. One of them contains three covalently bonded diatomic C₂ anions, which are combined through bridging aluminum atoms in the three-dimensional [C₆Al₇] cluster inside the severely distorted outer cage. In the second, most favorable, isomer, the dopants are distributed as isolated C anions; together with the bridging Al atoms, they form the [M₁₂Al₃₂] inner cage with an unusual dumbbell-like structure. For M₁₂Al₃₂, the aluminum cage undergoes moderate distortions. The silicon atoms remain in the outer layers and form five-membered ring subclusters [Si₅] and [Si₂Al₃] bound to the neighboring intermediate layers through elongated and weakened Si–Al bonds. Evaluation of the energies of the model exchange reactions Al₄₄ + M₆ → M₆Al₃₈ + Al₆ and Al₄₄ + 2M₆ → M₁₂Al₃₂ + 2A_l6 shows that for M= C both reaction are exothermic, whereas for M = Si the former reaction is nearly isothermal and the second reaction is endothermic and requires significant energy inputs. The differences between the equilibrium structures and the relative positions on the energy scale of the isomers of the C₆Al₃₈–Si₆Al₃₈ and C₁₂Al₃₈–Si₁₂Al₃₈ clusters are examined.     

NMR evidence for B(C6F5)3 attack on the inward position of a highly hindered meso ansa-zirconocene

The reaction of the ansa-zirconocene meso-[C₂H₄(4,7-Me₂Indenyl)₂]ZrMe₂ with B(C₆F₅)₃ afforded, besides the expected ion pair with outward anion, also a minor isomer (molar fraction 0.043) with the bulky methylborate anion in the inward site. 2D ¹H EXSY experiments revealed exchange between the two isomers, at T > 320 K, through the migration of the anion between outward and inward sites. The presence of free B(C₆F₅)₃ fastened the exchange, suggesting B(C₆F₅)₃ attack on the zirconium bound methyl ligand of the two ion pairs.     

A DFT-Based Study of the Low-Energy Electronic Structures and Properties of Small Gold Clusters

Gold clusters Au_n of size n = 2–12 atoms were studied by the density-functional theory with an ab-initio pseudopotential and a generalized gradient approximation. Geometry optimizations starting from a number of initial candidate geometries were performed for each cluster size, so as to determine a number of possible low-energy isomers for each size. Along with the lowest-energy structures, metastable structures were obtained for many cluster sizes. Interestingly, a metastable planar zigzag arrangement of Au atoms was obtained for every cluster size n ≥ 5. The stable electronic structure, binding energy, relative stability and HOMO–LUMO gap for the lowest-energy isomer were calculated for each cluster size. Variation of the electronic properties with size is investigated in this paper and compared with experimental results and other calculations.     

Theoretical study of isomerism in nitrogen- and phosphorus-substituted aluminum clusters M<Subscript>6</Subscript>Al<Subscript>38</Subscript> and M<Subscript>12</Subscript>Al<Subscript>32</Subscript> (M = N,P)

More than 20 М₆Al₃₈ isomers and several М₁₂Al₃₂ isomers for nitrogen- and phosphorus-substituted clusters with six and twelve dopant atoms M = N and P substituted for Al atoms in different positions at the surface of the aluminum cage and inside it have been studied by the density functional theory method. In the preferred N₆Al₃₈ isomer, all N atoms are substituted for Al atoms initially located in one outer layer of the cluster. In the course of geometry optimization, the nitrogen atoms are incorporated into positions in the neighboring intermediate layer, thus converting it into a 12-atom face consisting of three vertex-sharing adjacent six-membered rings with short N–Al bonds. For Р₆Al₃₈, a distribution of the dopant either in both surface layers or in the intermediate space between the surface layers and the inner core of the cluster is preferred. Optimization of alternative structures of the N₁₂Al₃₂ cluster with N atoms substituted for Al atoms in both outer layers is evidence in favor of the isomer in which the dopants are dispersed as separated monatomic anions N–. Together with their bridging Al atoms, these anions form the inner [N₁₂Al₁₄] cage with an unusual dumbbell-like structure in which the upper and lower halves are linked through N–Al bonds with the equatorial aluminum atoms. In the next low-lying isomer being ~23 kcal/mol higher on the energy scale, there is observed the “microclustering” of the dopant to form three covalently bonded diatomic dianions N₂^2-; the latter, together with the bridging Al atoms are combined into a [N₆Al₆] “subcluster” inside the severely distorted outer cage. In P₁₂Al₃₂, the aluminum cage is subjected only to moderate distortions: the phosphorus atoms remain in the outer layers and form two three-membered rings [Р₃]. The estimated energies of the model substitution reactions Al₄₄ + M₆ → M₆Al₃₈ + Al₆ (1) and Al₄₄ + 2M₆ → M₁₂Al₃₈ + 2A_l6 (2) demonstrate that all these reactions are exothermic; however, for the nitrogen-containing clusters, the decrease in energy with increasing number of substitutions increases from 66 (1) to 113 (2) kcal/mol, while in the case of phosphorus, it decreases from 45 (1) to 4 (2) kcal/mol. The results obtained for N₆Al₃₈, N₁₂Al₃₂, Р₆Al₃₈, and Р₁₂Al₃₂ are compared with the previous calculations for the C₆Al₃₈, C₁₂Al₃₂, Si₆Al₃₈, and Si₁₂Al₃₂ clusters.     

Collision-induced electron detachment of carbon clusters

The collisional electron detachment process of carbon cluster anions containing from 2 to 72 atoms was investigated on the collision with a MoS₂ surface. The detachment efficiency was classified into several groups and is most likely to reflect the structures or the isomer contents of the incident cluster anions. The cluster anions produced via laser-vaporization of graphite showed quite a larger detachment efficiency than the fullerene C ₆₀ ^- and its fragment anions. The major isomers of these cluster anions were suggested to be chains or rings.     

Barrelane-like germanium clusters in Eu3Ge5: Crystal structure, chemical bonding and physical properties

Formation and crystal structure of the binary germanide Eu₃Ge₅ were investigated in detail. The compound forms peritectically at 1008 °C and does not undergo any phase transition down to room temperature. The crystal structure was determined first from X-ray powder diffraction data and was later confirmed by single-crystal X-ray diffraction: structure type Pu₃Pd₅, space group Cmcm (no. 63), , , . The main building blocks are Ge₅⁶⁻ cluster anions surrounded by Eu²⁺ cations. The nearly tetragonal-pyramidal shape is suggested by the interatomic distances. Contrary to that, the bonding analysis with the electron localization function (ELF) reveals only two- and three-bonded germanium atoms forming a strongly distorted [1.1.1]-barrelane-like cluster. Despite the formal electron deficiency, compared to the barrelane C₅H₈, the electron counting in the cluster anion and its conformation cannot be interpreted applying the Wade's rules. In accordance with the calculated electronic density of states, Eu₃Ge₅ shows a metal-like temperature dependence of the electrical resistivity with a sharp change of ρ(T) slope at the Néel point. Above the Néel point the inverse magnetic susceptibility reveals Curie-Weiss behavior with an effective moment of 8.11 μ_B (Eu²⁺, 4f⁷ configuration) in agreement with the analysis of the chemical bonding. The 4f⁷ electronic configuration of europium is confirmed by Eu-L_III X-ray absorption spectroscopy.     

The importance of cluster fragmentation in the catalytic hydrogenation of phenylacetylene by PtRu5 carbonyl cluster complexes

has been shown to be a catalyst precursor for the hydrogenation of PhC₂H to styrene and ethylbenzene. Three new organometallic products have been found in the catalyst solutions. These are , , and Ru₅(CO)₁₁(μ₄-CCHCPh)(μ₄-HC₂Ph)(μ₃-HC₂Ph) (6). Compounds 4-6 have been synthesized independently and structurally characterized and each one has been tested independently for its ability to produce hydrogenation of PhC₂H catalytically. Compound 4 contains an open square-pyramidal cluster of five ruthenium atoms with one platinum atom bridging an edge of the cluster. It is structurally related to 2 but contains one less CO ligand and two hydrido ligands formed by the addition of one equivalent of hydrogen to the metal cluster. It can be obtained directly from 2 by reaction with hydrogen in the presence of trimethylamine oxide. Compound 5 is a tricoordinated mononuclear platinum complex containing one ligand, one CO ligand and one μ₂-PhC₂H ligand. Compound 5 can be obtained directly from by reaction with PhC₂H under an atmosphere of CO. Compound 6 was obtained from the reaction of Ru₅(CO)₁₅(μ₅-C) with PhC₂H in the presence of UV-Vis irradiation. Compound 6 contains three equivalents of PhC₂H; one is present as triply bridging PhC₂H ligand; one is a quadruply bridging ligand; the third one has formed a bond to the carbido ligand in the center of the metal cluster to form a novel tetra-metallated allyl ligand. Compound 5 has the highest catalytic activity of all three compounds and is believed to be responsible for the vast majority of the catalytic hydrogenation produced from the solutions of 2. Compound 4 is transformed into 5 under the conditions of catalysis.     

DFT study of electronic structure and geometry of anionic silver clusters (n = 11, 12, 17)

Based on both total energy calculations and comparison of experimental and calculated characteristics of photoelectron spectra (PHES), the structural assignment of clusters and has been made using DFT model with recently developed S2LYP functional. The calculated characteristics of PHES for the assigned structures are in excellent agreement with the experimental ones. The electronic structure, geometry and energetic characteristics of low-lying isomers have also been studied. The calculated geometrical parameters of and clusters as well as the geometries of earlier established clusters have been compared with the geometrical characteristics of anionic sodium clusters. The structures of anionic silver and sodium clusters have been found to be very similar. The difference has been observed only for . Based on similarity of the geometries of silver and sodium clusters as well as on the comparison of calculated and experimental characteristics of PHES, the geometry of cluster has been assigned.     

Physical properties of layered homologous RE-B-C(N) compounds

Physical properties of a series of homologous RE-B-C(N) B₁₂ cluster compounds REB₁₇CN, REB₂₂C₂N, and were investigated. The structures of the compounds are layer-like along the c-axis, with rare earth and B₆ octahedral layers separated by B₁₂ icosahedral and C-B-C chain layers whose number increases successively from two B₁₂ layers for the REB₁₇CN compound to four for the REB_28.5C₄ compound. The rare earth atoms are configured in two triangular flat layers which are stacked on top of one another in AB stacking where the nearest-neighbor rare earth directions are the three atoms forming a triangle in the adjacent layer. The series of homologous compounds exhibit a spin glass transition with T_f shifting in correspondence with variations of the basal plane lattice constants, consistent with the magnetic interaction being effective in the basal planes. The isothermal remanent magnetization shows a stretched exponential decay . Exponents determined for the different homologous compounds were scaled as a function of T_r=T/T_f and found to follow the empirical dependency determined for typical spin glasses. It is indicated that a mixture of disorder originating from the partial occupancy of the rare earth sites and frustration of interactions due to the unique configuration is responsible for the manifestation of spin glass transitions in these homologous systems.     

Extra electron in (H2O)24- cluster isomers: a theoretical study

The isomers of (H(2)O)(24) (-) tetrakaidecahedral cluster are studied by applying the Becke-3-parameter density functional theory and Lee-Yang-Parr correlation functional (B3LYP) and 6-311++G** basis set. Three isomers are selected on the basis of stabilization energy values. The vertical electron dissociation energies (VDE) of these isomers are 1.353, 0.404, and 0.258 eV, respectively. The experimental VDE value of 1.31 eV [J. Chem. Phys. 92, 3980 (1990)] for this cluster size is in excellent agreement with that calculated for isomer 1, suggesting the dominance of this isomer in the experiment. Four water molecules in this isomer share most of the -1 charge. These four water molecules have non-H-bonding H (NHB H) atoms turned toward the cavity, and the inward turned H atoms exhibit a significant lowering of O-H stretch frequency compared to that of a monomer. Isomers 2 and 3 have all 12 NHB H atoms projected outward and have the -1 charge distributed among 7-8 water molecules on the cluster surface.     

Quantum chemical study of H<Subscript>2</Subscript> adsorption on Pd<Subscript>21</Subscript> cluster

Modeling of the interaction of an H₂ molecule with the surface of the Pd₂₁ cluster in different spin states was performed using the DFT/PBE scalar relativistic approximation. The spin multiplicity of the system significantly affects the mechanism of adsorption, its parameters, and migration of hydrogen atoms. The H atoms can migrate over the cluster surface with low barriers (1.6 kcal mol^–1). The complex with C _2v symmetry, wherein the H atoms occupy adjacent fcc sites, is the most energetically stable.     

B12H11-containing guanidinium derivatives by reaction of carbodiimides with H3N-B12H11(1−). A new method for connecting boron clusters to organic compounds

The reaction of B₁₂H₁₁NH₃(1−) with carbodiimides can form guanidinium salts containing the boron cluster. Depending on the side chains of the carbodiimide, these derivatives of the B₁₂H₁₂(2−) cluster can be uncharged or can carry an overall positive or negative charge. This reaction allows the preparation of derivatives with aliphatic side chains, in contrast to the acylation reaction of and the formation of Schiff bases, both of which are successful only with aromatic acid chlorides or aromatic, respectively, α,β-unsaturated aldehydes. The acylation of with benzoyl chloride gives an N-protonated form of an imidoacid, carrying a single overall charge.     

Inherent instabilities of some W5Si3-type binary phases with large electropositive metal atoms: Six examples in the Ba-Pb, Ca-Sn-Mg,Cu,Zn, and La-Ga-Al,Zn systems

A particular pathology of certain W₅Si₃-type A₅B₃ structures (I4/mcm) appears to arise because of unduly close approaches of the A1-type atoms on the cell faces at , 0, () that occur with the larger and more electropositive A and/or in the presence of smaller B atoms. A structure refinement of binary Ba_4.81Pb₃ indicates such a marginal stability in that the Ba atoms in the facial Ba_0.81 chains exhibit an extreme displacement ellipsoid along . Although Ca₅Sn₃ and La₅Ga₃ binaries are unknown in this structure type, five stable ternary derivatives of these have been synthesized via substitution reactions and characterized by single crystal X-ray diffraction means: Ca₄Sn_3.223(4)Mg_0.777, Ca₄Sn₃Cu_1.30(4), Ca_4.66(6)Sn₃Zn_0.704(4), La_4.81(1)Ga_1.38(2)Al_1.62, and La_4.762(5)Ga_1.5(1)Zn_1.5. Only the Ca-Sn-Zn phase exhibits lower symmetry, P4/mbm. The problematic A1 sites exhibit diverse changes in these, whereas the surrounding B2 tetrahedra are largely unaltered. The Ca-Sn results are, respectively: direct Mg/Sn substitution at the Ca1 site; mixed fractional distribution of the smaller Cu at two sites around the A1 position with an unresolved disorder; a pair of apparently independent modes, fractional Ca in the normal position and fractional Zn rectangles thereabout. The two La-Sn phases contain normal Ga,Al (Ga,Zn) tetrahedral chains with pairs of fractional disordered La atoms along , 0, z. Each can be rationalized in terms of a reasonable incommensurate structure. Electronic effects may also be operable.     

A Raman spectroscopic study of the phase transition of BaZr(PO4)2: Evidence for a trigonal structure of the high-temperature polymorph

We have studied the structural evolution of monoclinic BaZr(PO₄)₂ during heating up to 835 K by Raman spectroscopy. In agreement with previous studies we found a first-order phase transition at about 730 K during heating while upon cooling the reverse transition occurs at 705 K. However, some disagreement about the crystal structure of the high-temperature polymorph occurs in the literature. While the space group has not yet been determined, the X-ray diffraction pattern of the high-temperature phase has been indexed on either an orthorhombic or a hexagonal unit cell. We found that the number of Raman active internal PO₄ vibrational modes decrease from nine to six during the transition. A group theoretical survey through all orthorhombic, trigonal, and hexagonal factor groups revealed that the observed number of vibrations would only be consistent with the Ba and Zr atoms located at a site, the P and two O atoms at a C_3v(3m), and six O atoms at a C_s(m) site in the D_3d factor group. Based on our Raman data, the space group of the high-temperature polymorph is thus either , , or .