Dilation theorems for positive definite operator kernels having majorants

Dilation theorems for Banach space valued stochastic processes and operator valued positive definite kernels are considered. It is shown, e.g., that a Banach space valued stochastic process X can be dilated to another process Y, if and only if the covariance kernel of Y is a majorant of the covariance kernel of X. Positive definite operator kernels having majorants of certain special type are characterized.     

Self-passivating edge reconstructions of graphene

Planar reconstruction patterns at the zigzag and armchair edges of graphene were investigated with density-functional theory. It was unexpectedly found that the zigzag edge is metastable and a planar reconstruction spontaneously takes place at room temperature. The reconstruction changes electronic structure and self-passivates the edge with respect to adsorption of atomic hydrogen from a molecular atmosphere.     

UV/VIS Spectrophotometric Studies on the Antileukemic Agent Glyoxal bis(Amidinohydrazone) [‘Glyoxal bis(Guanylhydrazone)’]

Glyoxal bis(amidinohydrazone) (GBG) and several analogs thereof are compounds of considerable pharmacological interest, and a variety of HPLC and MECC methods have been developed for their analysis. In these methods, detection is invariably based on the strong UV absorption of the compound. Yet, almost nothing has been known of their UV and VIS spectral properties. In the present paper the UV and VIS Spectroscopy of GBG has been studied in several solvent systems (water, 0. 03 M aqueous sodium acetate buffer, 0. 1 inM aqueous NaOH and dimethylsulfoxide). In the case of solutions in bare water, the shape of the UV spectrum depends drastically on concentration, probably because of changes in the species distribution of GBG as a function of concentration. The spectrum comprises one maximum at ca. 200 nm, and between ca. 250 nin and 400 nm an absorption region with distinctly higher absorbance. In the case of aqueous sodium acetate as well as NaOH solutions, one strong maximum can be detected (at ca. 285–288 nm and 332–337 nm, respectively). In both cases, the maximum occurs at constant wavelength, being independent of concentration. In dimethylsulfoxide, the spectrum of GBG contains an absorption band at distinctly higher wavelengths (λ_max 354 nm) than in any one of the aqueous solvents studied, indicating that solvent effects are considerable in the UV spectrum of GBG. In no case, distinct absorption could be detected at wavelengths higher than 400 nm. The results indicate that if aqueous media are used as elements in HPLC analyses of bis(amidinohydrazones) or as solvents in direct UV analysis, they must be buffered.     

Atomically Precise Nanocluster Assemblies Encapsulating Plasmonic Gold Nanorods

The self‐assembled structures of atomically precise, ligand‐protected noble metal nanoclusters leading to encapsulation of plasmonic gold nanorods (GNRs) is presented. Unlike highly sophisticated DNA nanotechnology, this strategically simple hydrogen bonding‐directed self‐assembly of nanoclusters leads to octahedral nanocrystals encapsulating GNRs. Specifically, the p‐mercaptobenzoic acid (pMBA)‐protected atomically precise silver nanocluster, Na₄[Ag₄₄(pMBA)₃₀], and pMBA‐functionalized GNRs were used. High‐resolution transmission and scanning transmission electron tomographic reconstructions suggest that the geometry of the GNR surface is responsible for directing the assembly of silver nanoclusters via H‐bonding, leading to octahedral symmetry. The use of water‐dispersible gold nanoclusters, Au_≈250(pMBA)_n and Au₁₀₂(pMBA)₄₄, also formed layered shells encapsulating GNRs. Such cluster assemblies on colloidal particles are a new category of precision hybrids with diverse possibilities.     

Multiple Li positions inside oxygen octahedra in lithiated TiO2 anatase

Intercalation of Li in TiO2 anatase results in a phase separation in a Li-poor and a Li-rich phase. The local lithium configuration in the coexisting crystallographic phases is resolved by detailed analysis of neutron diffraction data. In each of the phases, two distinct positions within the octahedral interstices are found, with a temperature-dependent occupancy. A combination of quasi-elastic neutron scattering and force field molecular dynamics simulations shows that Li is hopping on a picosecond time scale between the two sites in the octahedral interstices. The results also suggest a specific Li arrangement along the crystallographic a direction, albeit without long range order. It is likely that multiple discrete Li sites within a distorted oxygen octahedron occur not only in intercalated TiO2 anatase but also in other (transition metal) oxides.     

Highly Robust but Surface‐Active: An N‐Heterocyclic Carbene‐Stabilized Au25 Nanocluster

Surface organic ligands play a critical role in stabilizing atomically precise metal nanoclusters in solutions. However, it is still challenging to prepare highly robust ligated metal nanoclusters that are surface‐active for liquid‐phase catalysis without any pre‐treatment. Now, an N‐heterocyclic carbene‐stabilized Au₂₅ nanocluster with high thermal and air stabilities is presented as a homogenous catalyst for cycloisomerization of alkynyl amines to indoles. The nanocluster, characterized as [Au₂₅(ⁱPr₂‐bimy)₁₀Br₇]²⁺ (ⁱPr₂‐bimy=1,3‐diisopropylbenzimidazolin‐2‐ylidene) ( 1 ), was synthesized by direct reduction of AuSMe₂Cl and ⁱPr₂‐bimyAuBr with NaBH₄ in one pot. X‐ray crystallization analysis revealed that the cluster comprises two centered Au₁₃ icosahedra sharing a vertex. Cluster 1 is highly stable and can survive in solution at 80 °C for 12 h, which is superior to Au₂₅ nanoclusters passivated with phosphines or thiols. DFT computations reveal the origins of both electronic and thermal stability of 1 and point to the probable catalytic sites. This work provides new insights into the bonding capability of N‐heterocyclic carbene to Au in a cluster, and offers an opportunity to probe the catalytic mechanism at the atomic level.     

The electronic structure of Ge9[Si(SiMe3)3]3-: a superantiatom complex

We report on the electronic structure of Ge(9)[Si(SiMe(3))(3)](3)(-). Systematic density functional theory analysis of the electronic shell structure of the cluster and its derivatives reveals that the Ge(9)[Si(SiMe(3))(3)](3)(-) and its neutral counterpart have electronic shells that can be explained using the superatom model. The ligand-core interaction of these complexes is distinctly different from previously identified gold, gallium, and aluminium superatom complexes, indicating an electron-donating rather than electron-withdrawing ligand. We modify the electron-counting rule for this case and introduce a simple picture for superatom and superantiatom complexes. Discussions comparing shell models, Zintl clusters, the superhalogen Al(13) and superatom complexes to Ge(9)[Si(SiMe(3))(3)](3)(-) are presented.     

Modification of the magnetic properties of a heterometallic wheel by inclusion of a Jahn-Teller distorted Cu(II) ion

An investigation into the physical consequences of including a Jahn-Teller distorted Cu(II) ion within an antiferromagnetically coupled ring, [R(2)NH(2)][Cr(7)CuF(8)((O(2)C(t)Bu)(16))] is reported. Inelastic neutron scattering (INS) and electron paramagnetic resonance (EPR) spectroscopic data are simulated using a microscopic spin Hamiltonian, and show that the two Cr-Cu exchange interactions must be inequivalent. One Cr-Cu exchange is found to be antiferromagnetic and the other ferromagnetic. The geometry of the Jahn-Teller elongation is deduced from these results, and shows that a Jahn-Teller elongation axis must lie in the plane of the Cr(7)Cu wheel; the elongation is not observed by X-ray crystallography, due to positional disorder of the Cu site within the wheel. An electronic structure calculation confirms the structural distortion of the Cu site.     

An NMR-Based Approach to the Measurement of High Log K HL Values at Low Ionic Strength. 31P NMR Study of 1,2-Diaminoethane-N,N,N′,N′-tetra(methylenephosphonic Acid) Protonation Equilibrium at pH > 12

A sequential NMR based approach is proposed for measurements of high log K values at low ionic strength. [³¹P] NMR technique is used to determine the protonation constants of 1,2-diaminoethane-N,N,N,N-tetra(methylenephosphonic acid) (EDTPH, H₈L) at 25°C in 0.1 mol-dm^–3 KNO₃ and at 37°C in 0.15 mol-dm^–3 NaCl at pH 11–14. For equilibrium L + H HL log K are found to be 13.3 (0.1) and 12.9 (0.1), respectively.