Random Homeomorphisms and Fourier Expansions

We prove that a random change of variable in general improves convergence properties of the Fourier expansions, and we give a precise quantitative estimate of the phenomenon. Submitted: December 1997, final version: May 1998     

Nondynamical calculation of polarization observables in d+d reactions at low energies

The parametrization of polarization observables in terms of (l, s, J) matrix elements is given for²H(d, p)³H and²H(d, n)³He reactions at low energies. It is shown that transverse polarizations of outgoing nucleons are to be measured in order to obtain a complete set of cross-section, analysing powers, spin-correlation and polarization transfer experiments.     

Thermoanalytical Study of O,O'-Dibenzoyl-(2R,3R)-Tartaric Acid Supramolecular Compounds Part II. Investigation of the resolution of racemic alcohols

The resolution of three chiral alcohols with O,O'-dibenzoyl-(2R,3R)-tartaric acid (DBTA) via diastereoisomeric supramolecular compound formation was investigated with thermoanalytical methods. On the basis of TG measurements the DBTA:chiral alcohol molar ratio in the compounds is 1:1 which agrees with the results of single-crystal X-ray diffraction analysis. The DBTA – chiral alcohol supramolecular compounds have different supramolecular structure than the DBTA – achiral alcohol supramolecular compounds. The supramolecular compounds containing cyclohexanols have higher thermal stability than the compounds containing acyclic aliphatic alcohols. The amount of unreacted DBTA monohydrate in the solid phase can be determined both with DSC and with TG measurements. This revised version was published online in August 2006 with corrections to the Cover Date.     

Reversible M−M Bonding by Alkaline Earth Metals (Mg,Ca, Sr,Ba) in Graphite Intercalation Compounds

The alkaline earth metals (M=Mg, Ca, Sr, and Ba) exhibit a +2 oxidation state in nearly all known stable compounds, but M^I dimeric complexes with M−M bonding, [M₂(en)₂]²⁺, (en=ethylenediamine) of all these metals can be stabilized within the galleries of donor-type graphite intercalation compounds (GICs). These metals can also form GICs with more conventional metal (II) ion complexes, [M(en)₂]²⁺. Here, the facile interconversion between dimeric-M^I and monomeric-M^II intercalates upon the addition/removal of en are reported. Thermogravimetry, powder X-ray diffraction, and pair distribution function analysis of total scattering data support the presence of either [M₂(en)₂]²⁺ or [M(en)₂]²⁺ guests. This phase conversion requires coupling graphene and metal redox centers, with associated reversible M−M bond formation within graphene galleries. This chemistry allows the facile isolation of unusual oxidation states, reveals M⁰→M²⁺ reaction pathways, and present new opportunities in the design of hybrid conversion/intercalation materials for applications such as charge storage.     

Coordination Chemistry of Cyclopropenylidene‐Stabilized Phosphenium Cations: Synthesis and Reactivity of Pd and Pt Complexes

A straightforward synthesis of cyclopropenylidene‐stabilized phosphenium cations 1 a – g through the reaction of [(iPr₂N)₂C₃⁺Cl]BF₄ with secondary phosphines is described. Their donor ability was evaluated by analysis of the CO stretching frequency in Rh complexes [RhCl(CO)L₂](BF₄)₂ and electrochemical methods. The cyclopropenium ring induces a phosphite‐type behavior that can be tuned by the other two substituents attached to the phosphorus atom. Despite of the positive charge that they bear, phosphenium cations 1 a – g still act as two‐electron donor ligands, forming adducts with Pd^II and Pt^II precursors. Conversely, in the presence of Pd⁰ species, an oxidative insertion of the Pd atom into the C_carbene–phosphorus bond takes place, providing dimeric structures in which each Pd atom is bonded to a cyclopropenyl carbene while two dialkyl/diaryl phosphide ligands serve as bridges between the two Pd centers. The catalytic performance of the resulting library of Pt^II complexes was tested; all of the cationic phosphines accelerated the prototype 6‐endo‐dig cyclization of 2‐ethynyl‐1,1′‐biphenyl to afford pentahelicene. The best ligand 1 g was used in the synthesis of two natural products, chrysotoxene and epimedoicarisoside A.     

Discrete Hf18 Metal-oxo Cluster as a Heterogeneous Nanozyme for Site-Specific Proteolysis

The selective hydrolysis of proteins by non-enzymatic catalysis is difficult to achieve, yet it is crucial for applications in biotechnology and proteomics. Herein, we report that discrete hafnium metal-oxo cluster [Hf₁₈O₁₀(OH)₂₆(SO₄)₁₃⋅(H₂O)₃₃] ( Hf₁₈ ), which is centred by the same hexamer motif found in many MOFs, acts as a heterogeneous catalyst for the efficient hydrolysis of horse heart myoglobin (HHM) in low buffer concentrations. Among 154 amino acids present in the sequence of HHM, strictly selective cleavage at only 6 solvent accessible aspartate residues was observed. Mechanistic experiments suggest that the hydrolytic activity is likely derived from the actuation of Hf^IV Lewis acidic sites and the Brønsted acidic surface of Hf₁₈ . X-ray scattering and ESI-MS revealed that Hf₁₈ is completely insoluble in these conditions, confirming the HHM hydrolysis is caused by a heterogeneous reaction of the solid Hf₁₈ cluster, and not from smaller, soluble Hf species that could leach into solution.