Principal part of resolvent and factorization of an increasing nonanalytic operator-function

Let a selfadjoint operator-valued functionL() be given on the interval [a,b] such thatL(a)0,L(b)0,L()0 (ab), andL() has a certain smoothness (for instance, it satisfies Hölder's condition). It turns out that the spectral theory of the operator-valued functionL() can be reduced to the spectral theory of one operatorZ, the spectrum of which lies on (a, b) and which is similar to a selfadjoint operator. In particular, the factorization takes place:L()=M()(I–Z), where the operator-valued functionM() is invertible on [a, b]. Earlier similar results were known only for analytic operator-valued functions. The authors had to use new methods for the proof of the described theorem. The key moment is the decomposition ofL ^–1() into the sume of its principal and regular parts.     

On abelian difference set codes

In this paper we determine the ranks of the incidence matrices that belong to the following types of difference sets: Twin prime power difference sets, biquadratic residues and biquadratic residues with 0. We also prove a conjecture of Assmus and Key on the code generated by the hyperovals of PG(2, q).     

A Theoretical Study of Complex Formation between Formaldehyde and Lithium

Ab initio SCF and CI calculations on the cationic and neutral complexes of formaldehyde and lithium are reported. For the cationic complex CH₂O/Li⁺, the stabilization energy of 41.7 kcal/mol obtained from the SCF calculation increases to 51.6 kcal/mol if a configuration interaction is introduced. For the neutral complex CH₂O^?/Li⁺, the C_2v-conformer of the ²A₁-state with the equilibrium bond distances of d(C? O) = 1.23 Å and d (O? Li) = 1.90 Å is calculated to be more stable than the ₂B₁-state with d (C? O) = 1.34 Å, and d (O? Li) = 1.65 Å. Charge transfer and polarization effects upon complex formation are discussed.     

NMR studies of interionic interactions in N-methylformamide

The NMR chemical shifts of alkali and thallium(I) salts with various monovalent anions have been measured in N-methylformamide solution. Lithium-7 chemical shifts are virtually concentration and counter-ion independent, presumably due to an absence of direct cation-anion interactions. The sodium-23, potassium-39 and cesium-133 chemical shifts of the salts studied depend on the anion and vary linearly with the concentration. The observed behavior can be accounted for by the formation of collisional ion pairs. On the other hand, the thallium-205 chemical shifts of thallium(I) nitrate and perchlorate were anion-dependent and varied non-linearly with the salt concentration. These results are indicative of contact ion pair formation; formation constants were calculated to be 2.6±0.4 M ^–1 for TlNO ₃ and 1.7±0.5 M ^–1 for TlClO ₄ . The cesium-133 NMR spectra of several mixed electrolyte systems also have been measured in N-methylformamide solution. The¹³³Cs chemical shifts also change linearly with the concentrations of the salts added to 0.10 M CsI/NMF solutions. The influence of the anions on the chemical shifts is the same as that observed for cesium salts alone.     

MNDO calculations of systems with hydrogen bonds S-H

The MNDO method has been modified for the calculation of the properties of complexes with hydrogen bonds S-H-X, X = N, O, F, S. The results obtained are in good agreement with the experimental data.     

Redox,transmetalation, and stacking properties of tetrathiafulvalene-2,3,6,7-tetrathiolate bridged tin,nickel, and palladium compounds

Here we report that capping the molecule TTFtt (TTFtt = tetrathiafulvalene-2,3,6,7-tetrathiolate) with dialkyl tin groups enables the isolation of a stable series of redox congeners and facile transmetalation to Ni and Pd. TTFtt has been proposed as an attractive building block for molecular materials for two decades as it combines the redox chemistry of TTF and dithiolene units. TTFttH₄, however, is inherently unstable and the incorporation of TTFtt units into complexes or materials typically proceeds through the in situ generation of the tetraanion TTFtt⁴⁻. Capping of TTFtt⁴⁻ with Bu₂Sn²⁺ units dramatically improves the stability of the TTFtt moiety and furthermore enables the isolation of a redox series where the TTF core carries the formal charges of 0, +1, and +2. All of these redox congeners show efficient and clean transmetalation to Ni and Pd resulting in an analogous series of bimetallic complexes capped by 1,2-bis(diphenylphosphino)ethane (dppe) ligands. Furthermore, by using the same transmetalation method, we synthesized analogous palladium complexes capped by 1,1′-bis(diphenylphosphino)ferrocene (dppf) which had been previously reported. All of these species have been thoroughly characterized through a systematic survey of chemical and electronic properties by techniques including cyclic voltammetry (CV), ultraviolet-visible-near infrared spectroscopy (UV-vis-NIR), electron paramagnetic resonance spectroscopy (EPR), nuclear magnetic resonance spectroscopy (NMR) and X-ray diffraction (XRD). These detailed synthetic and spectroscopic studies highlight important differences between the transmetalation strategy presented here and previously reported synthetic methods for the installation of TTFtt. In addition, the utility of this stabilization strategy can be illustrated by the observation of unusual TTF radical–radical packing in the solid state and dimerization in the solution state. Theoretical calculations based on variational 2-electron reduced density matrix methods have been used to investigate these unusual interactions and illustrate fundamentally different levels of covalency and overlap depending on the orientations of the TTF cores. Taken together, this work demonstrates that tin-capped TTFtt units are ideal reagents for the installation of redox-tunable TTFtt ligands enabling the generation of entirely new geometric and electronic structures.

Capping TTFtt enables facile transmetalation in three different oxidation states.     

Dynamic kinetic resolution of transient hemiketals: a strategy for the desymmetrisation of prochiral oxetanols

Identification of an electron poor trifluoroacetophenone allows the formation of uniquely stable hemiketals from prochiral oxetanols. When exposed to a cobalt(ii) catalyst, efficient ring-opening to densely functionalized dioxolanes is observed. Mechanistic studies suggest an unprecedented redox process between the cobalt(ii) catalyst and the hemiketal that initiates the oxetane-opening. Based on this observation, a dynamic kinetic resolution of the transient hemiketals is explored that uses a Katsuki-type ligand for stereoinduction (up to 99 : 1 dr and 96 : 4 er) and allows a variety of 1,3-dioxolanes to be accessed (20 examples up to 98% yield).

Desymmetrization of prochiral oxetanols via an electron-deficient hemiketal intermediate is achieved. Key to this process is the catalyst''s chiral recognition of one of the two hemiketal enantiomers enabling an efficient dynamic kinetic resolution.     

Recovery of 177Lu from Irradiated HfO2 Targets for Nuclear Medicine Purposes

A new method of production of one of the most widely used isotopes in nuclear medicine, ¹⁷⁷Lu, with high chemical purity was developed; this method includes irradiation of the HfO₂ target with bremsstrahlung photons. The irradiated target was dissolved in HF and then diluted and placed onto a column filled with LN resin. Quantitative sorption of ¹⁷⁷Lu could be observed during this process. The column later was rinsed with the mixture of 0.1 M HF and 1 M HNO₃ and then 2 M HNO₃ to remove impurities. Quantitative desorption of ¹⁷⁷Lu was achieved by using 6 M HNO₃. The developed method of ¹⁷⁷Lu production ensures high purification of this isotope from macroquantities of hafnium and zirconium and radioactive impurities of carrier-free yttrium. The content of ^177mLu in ¹⁷⁷Lu in photonuclear production was determined. Due to high chemical and radionuclide purity, ¹⁷⁷Lu obtained by the developed method can be used in nuclear medicine.     

Exploration of the Crystal Structure and Thermal and Spectroscopic Properties of Monoclinic Praseodymium Sulfate Pr2(SO4)3

Praseodymium sulfate was obtained by the precipitation method and the crystal structure was determined by Rietveld analysis. Pr₂(SO₄)₃ is crystallized in the monoclinic structure, space group C2/c, with cell parameters a = 21.6052 (4), b = 6.7237 (1) and c = 6.9777 (1) Å, β = 107.9148 (7)°, Z = 4, V = 964.48 (3) ų (T = 150 °C). The thermal expansion of Pr₂(SO₄)₃ is strongly anisotropic. As was obtained by XRD measurements, all cell parameters are increased on heating. However, due to a strong increase of the monoclinic angle β, there is a direction of negative thermal expansion. In the argon atmosphere, Pr₂(SO₄)₃ is stable in the temperature range of T = 30–870 °C. The kinetics of the thermal decomposition process of praseodymium sulfate octahydrate Pr₂(SO₄)₃·8H₂O was studied as well. The vibrational properties of Pr₂(SO₄)₃ were examined by Raman and Fourier-transform infrared absorption spectroscopy methods. The band gap structure of Pr₂(SO₄)₃ was evaluated by ab initio calculations, and it was found that the valence band top is dominated by the p electrons of oxygen ions, while the conduction band bottom is formed by the d electrons of Pr³⁺ ions. The exact position of ZPL is determined via PL and PLE spectra at 77 K to be at 481 nm, and that enabled a correct assignment of luminescent bands. The maximum luminescent band in Pr₂(SO₄)₃ belongs to the ³P₀ → ³F₂ transition at 640 nm.     

Expanding the hydride chemistry: antiperovskites A3MO4H (A = Rb,Cs; M = Mo,W) introducing the transition oxometalate hydrides

The four compounds A₃MO₄H (A = Rb, Cs; M = Mo, W) are introduced as the first members of the new material class of the transition oxometalate hydrides. The compounds are accessible via a thermal synthesis route with carefully controlled conditions. Their crystal structures were solved by neutron diffraction of the deuterated analogues. Rb₃MoO₄D, Cs₃MoO₄D and Cs₃WO₄D crystallize in the antiperovskite-like K₃SO₄F-structure type, while Rb₃WO₄D adopts a different orthorhombic structure. ²H MAS NMR, Raman spectroscopy and elemental analysis prove the abundance of hydride ions next to oxometalate ions and experimental findings are supported by quantum chemical calculations. The tetragonal phases are direct and wide band gap semiconductors arising from hydride states, whereas Rb₃WO₄H shows a unique, peculiar valence band structure dominated by hydride states.

The synthesis, structures and electronic properties of the first four heteroanionic compounds containing both hydride and transition oxometalate ions are reported.