The IR spectra of Mg5C(CO) complexes on the (0 0 1) surfaces of polycrystalline and single crystal MgO

The FTIR spectroscopy of carbon monoxide adsorbed on polycrystalline MgO smoke has been investigated as a function of the CO equilibrium pressure at constant temperature (60 K) (optical isotherm) and of the temperature (in the 300–60 K range) at constant CO pressure (optical isobar). In both cases the spectra fully reproduce those of CO adsorbed on the (0 0 1) surface of UHV cleaved single crystals [Heidberg et al., Surf. Sci. 331–333 (1995) 1467]. This result, never attained in previous investigations on dispersed MgO, contribute to bridging the gap which is commonly supposed to exist between surface science and the study of “real” (defective) systems. Depending on the surface coverage θ the main spectral features due to the CO/MgO smoke interaction are a single band shifting from 2157.5 (at θ→0) to 2150.2 cm⁻¹ (at θ=1/4) or a triplet, at 2151.5, 2137.2 and 2132.4 cm⁻¹ (at θ>1/4). These manifestations are due to the ν(CO) modes of Mg_5C²⁺· · · CO adducts formed on the (0 0 1) terminations of the cubic MgO smoke microcrystals. The formation of the CO monolayer is occurring in two different phases: (i) a first phase with CO oscillators perpendicularly oriented to the surface (2157–2150 cm⁻¹) and (ii) a second phase constituted by an array of coexisting perpendicular and tilted species (triplet at 2151.5, 2137.2 and 2132.4 cm⁻¹). A much weaker feature at 2167.5–2164 cm⁻¹ is assigned to Mg_4C²⁺· · · CO adducts at the edges of the microcrystals. The heat of adsorption of the perpendicular Mg_5C²⁺· · · CO complex in the first phase has been estimated from the optical isobar and results to be 11 kJ mol⁻¹.     

Nevanlinna functions as quotients

Let be a holomorphic function in the unit ball. Then is a Nevanlinna function if and only if there exist Smirnov functions , such that and has no zeros in the ball.

     

Nanosized Au4Pd32(CO)28(PMe3)14 Containing a Highly Distorted Encapsulated Au4 Tetrahedron: Proposed Multi-Twinned Growth-Pattern from Two Deformed Au-Centered Double Icosahedral-Based Fragments*

As part of an extensive effort to synthesize a variety of nanosized gold–palladium carbonyl phosphine clusters, the neutral Au₄Pd₃₂(CO)₂₈(PMe₃)₁₄ (1) was isolated and unambiguously characterized by low-temperature CCD X-ray diffraction and IR measurements. This nanosized Au₄Pd₃₂ cluster was prepared in low yields (<5%) from the room-temperature reaction of Pd₁₀(CO)₁₂(PMe₃)₆ (2) with Au(SMe₂)Cl in THF/acetone. The heretofore unknown molecular geometry of 1 of pseudo-D₂ (222) symmetry (without methyl substituents) may be viewed to arise from a relatively strong (Au–Au)-bonded linkage (2.64 Å (av)) of two pentagonal-bipyramidal (μ₅-Au)(μ₅-Pd)Pd₅ polyhedra; this generated 14-atom Au₂Pd₁₂ unit may be considered as a markedly deformed part of a 19-atom Au-centered double icosahedron without the inner pentagon (corresponding to five missing inner atoms). In turn, two Au₂Pd₁₂ units form a central composite-twinned Au₄Pd₂₂ kernel via vertex-fusion of two common Pd atoms along with additional formation of four Pd–Pd bonding, four Au–Pd bonding, and two weaker secondary Au–Au bonding interactions at 2.90 Å (av) (versus the other two diagonal Au–Au nonbonding ones at 3.51 Å (av)); this resulting Au₄Pd₂₂P₈ kernel is augmented by the addition of two triangular Pd₃P core-fragments and four exopolyhedral PdP groups to give the Au₄Pd₃₂P₁₄ framework of 1. This cluster is stabilized by 28 bridging COs, of which 20 are doubly bridging and 8 triply bridging. The largest metal-core diameter of 1 along one pseudo C₂ axis is 1.1 nm. This new type of multi-twinned metal cluster has direct relevance to both ligated and non-ligated (naked) non-crystalline metal nanoparticles, many of which possess multiple twinning and/or disorder.^*Dedicated to Professor F. A. Cotton on the occasion of his 75th birthday in recognition of numerous seminal contributions to modern Inorganic Chemistry. Professor Cotton has a truly unparalleled scientific career in Inorganic Chemistry in terms of the overall composite effects of his highly prolific research productivity, his tremendous impact on former graduate students, postdoctoral associates, and collaborators, and his matchless textbooks/monographs.     

Inner Mappings, Hyperbolic Gradients and Composition Operators

Let φ be a holomorphic mapping between complex unit balls. We obtain quantitative versions of the following heuristic principle: if the hyperbolic gradient of φ does not grow sufficiently rapidly, then φ is far from being inner.     

Approximation of average cost optimal policies for general Markov decision processes with unbounded costs

The aim of the paper is to show that Lyapunov-like ergodicity conditions on Markov decision processes with Borel state space and possibly unbounded cost provide the approximation of an average cost optimal policy by solvingn-stage optimization problems (n = 1, 2, ...). The used approach ensures the exponential rate of convergence. The approximation of this type would be useful to find adaptive procedures of control and to estimate stability of an optimal control under disturbances of the transition probability.Research supported in part by Consejo Nacional de Ciencia y Tecnologia (CONACYT) under grant 0635P-E9506.Research supported by Fondo del Sistema de Investigatión del Mar de Cortés under Grant SIMAC/94/CT-005.     

Unexpected bond activation of small organic molecules on a metal oxide-butane/CaO(100)

We present the first example of bond activation of small alkanes (n-/iso-butane) on a metal oxide surface-CaO(100)-at ultra-high vacuum (UHV) conditions and at low surface temperatures studied by molecular beam scattering and thermal desorption spectroscopy.     

Allyl ansa-lanthanidocenes: single-component, single-site catalysts for controlled syndiospecific styrene and styrene-ethylene (Co)polymerization

A series of new neutral allyl Group 3 metal complexes bearing ansa-bridged fluorenyl/cyclopentadienyl ligands [[Flu-EMe(2)-(3-R-Cp)]Ln(eta(3)-C(3)H(5))(THF)] (E=C, R=H, Ln=Y (2), La (3), Nd (4), Sm (5); R=tBu, Ln=Y (8), Nd (9); E=Si, R=H, Ln=Y (12), Nd (13)) were synthesized in good yields via salt metathesis protocols. The complexes were characterized by elemental analysis, NMR spectroscopy for diamagnetic complexes, and single-crystal X-ray diffraction studies for 2, 4, 9 and 12. Some of the allyl ansa-lanthanidocenes, especially 4, are effective single-component catalysts for the polymerization of styrene, giving pure syndiotactic polystyrenes (rrrr > 99 %) with low to high molecular weights (M(n)=6000-135,000 g mol(-1)) and narrow polydispersities (M(w)/M(n)=1.2-2.6). The catalyst systems are remarkably stable, capable of polymerizing styrene up to 120 degrees C with high activities, while maintaining high syndiotacticity via chain-end control as established by a Bernoullian analysis. Highly effective copolymerization of styrene with ethylene was achieved using neodymium complex 4 (activity up to 2530 kg PS-PE mol(-1) h(-1)) to give true copolymers void of homopolymers with M(n)=9000-152,000 g mol(-1) and narrow polydispersities (M(w)/M(n)=1.2-2.5). The nature of the resultant P(S-co-E) copolymers was ascertained by NMR, size-exclusion chromatography/refractive index/UV, temperature rising elusion fractionation, and differential scanning calorimetry. It is shown that, regardless the amount of ethylene incorporated (1-50 mol %), P(S-co-E) copolymers have a microstructure predominantly made of long highly syndiotactic PS sequences separated by single or few ethylene units. Co-monomers feed and polymerization temperature can be used straightforwardly to manipulate with the physical and mechanical characteristics of the P(S-co-E) copolymers (molecular weights and distributions, co-monomer content, microstructure, T(m), T(g), T(c)).     

CO-induced formation of an interpenetrating bicuboctahedral Au2Pd18 kernel in nanosized Au2Pd28(CO)26(PEt3)10: formal replacement of an interior (μ12-Pd)2 fragment in the corresponding known isostructural homopalladium Pd30(CO)26(PEt3)10 with nonisovalent (μ12-Au)2 and resulting experimental/theoretical implications

Initially isolated from Pd(10)(CO)(12)(PEt(3))(6) (5) and Au(SMe(2))Cl precursors in a two-step carbon monoxide (CO)-involved procedure, the nanosized interpenetrating bicuboctahedral gold (Au)-palladium (Pd) Au(2)Pd(28)(CO)(26)(PEt(3))(10) (1) was then directly obtained in 25-30% yield from the CO-induced reaction of the CO-stable Au-centered cuboctahedral Au(2)Pd(21)(CO)(20)(PEt(3))(10) (3) with the structurally analogous CO-unstable Pd(23)(CO)(20)(PEt(3))(10) (4). Our hypothesis that this latter synthesis is initiated by the reaction of 3 with coordinatively unsaturated homopalladium species resulting from CO-induced fragmentation of 4 was subsequently substantiated by the alternatively designed synthesis of 1 (～25% yield) from the CO-induced reaction of 3 with the structurally dissimilar CO-unstable Pd(38)(CO)(28)(PEt(3))(12) (6). The composition of 1, unambiguously established from a 100 K CCD X-ray diffractometry study, is in accordance with single-crystal X-ray Au-Pd field-emission microanalysis. The pseudo-C(2h) 30-atom Au(2)Pd(28) geometry of 1 may be formally derived via substitution of the interior (μ(12)-Pd)(2) moiety in the interpenetrating bicuboctahedral Pd(20) kernel of the known isostructural Pd(30)(CO)(26)(PEt(3))(10) (2) with the corresponding interior (μ(12)-Au)(2) moiety, in which the otherwise entire metal-core geometry and CO/PR(3)-ligated environment are essentially not altered. Of major significance is that this interior nonisovalent Pd-by-Au replacement in 2 produces CO-stable 1, whereas nanosized CO/PR(3)-ligated homopalladium Pd(n) clusters with n > 10 are generally unstable under CO. Because the two adjacent encapsulated Au atoms of 2.811(1) ? separation are not present on the metal surface, isolation of 1 under CO is ascribed to an electronic property. The virtually ideal geometrical site-occupancy fit between 1 and 2 provides definite crystallographic evidence for extensive delocalization in 1 of the two valence Au 6s electrons over the entire cluster (instead of a "localized" covalent Au-Au electron-pair interaction). Gradient-corrected (pseudo-scalar-relativistic) density functional theory (DFT) calculations were performed on the isostructural Au(2)Pd(28)(CO)(26)(PH(3))(10) (1-H) and Pd(30)(CO)(26)(PH(3))(10) (2-H) model clusters along with hypothetical [Au(2)Pd(28)(1-H)](2+) and [Pd(30)(2-H)](2-) analogues (with phosphine ethyl substituents replaced by hydrogen ones). Natural population analysis of these four model clusters revealed similar highly positively charged metal surfaces of 28 Pd atoms relative to the two negatively charged interior metal atoms, which reflect a partially oxidized metal surface due to dominant CO back-bonding. The surprising observation that each less electronegative interior Pd atom in 2-H is more negatively charged by 0.30e than each interior Au atom in 1-H points to a more cationic Au in 1 than interior Pd in 2; this unexpected (opposite) charge difference is consistent with delocalization of each Au 6s valence electron toward a Au(+) configuration. This premise is in agreement with the calculated Wiberg bond index (WBI) value of 0.055 for the Au-Au bond order in 1-H versus the WBI single-bond value of 1.01 obtained from analogous DFT calculations for the bare, neutral Au(2) dimer, which has a much shorter spectroscopically determined gas-phase distance of 2.472 ? (that corresponds to a "localized" electron-pair interaction). Isolation of 1 under CO is of prime importance in nanoscience/nanotechnology in establishing relative stabilizations toward CO in well-defined CO/PEt(3)-ligated nonisovalent Pd(2)-by-Au(2)-substituted Au(2)Pd(n-2) clusters [namely, n = 30 (1) and 23 (3)]. These important stereochemical implications have a direct relevance to the recent report of the higher tolerance to CO poisoning of highly active Au-Pd nanoparticle catalysts used for the complete conversion of formic acid into high-purity hydrogen (and CO(2)) for chemical hydrogen storage.     

Near-infrared luminescence of RbPb2Cl5:Bi crystals

A wideband near-IR (NIR) luminescence centered at 1080 nm was found in a RbPb(2)Cl(5):Bi single crystal grown by the Bridgman technique. Absorption, luminescence, and excitation of luminescence spectra were investigated at room and cryogenic temperatures. The luminescence was proposed to be due to the (3)P(1)-->(3)P(0) transition in Bi(+) ion.