Essential spectrum and -solutions of one-dimensional Schrödinger operators

In 1949, Hartman and Wintner showed that if the eigenvalue equations of a one-dimensional Schrödinger operator possess square integrable solutions, then the essential spectrum is nowhere dense. Furthermore, they conjectured that this statement could be improved and that under this condition the essential spectrum might always be void. This is shown to be false. It is proved that, on the contrary, every closed, nowhere dense set does occur as the essential spectrum of Schrödinger operators which satisfy the condition of existence of -solutions. The proof of this theorem is based on inverse spectral theory.

     

Trennung von V,Cr und Mn aus Stahl und Aktivierungsanalyse der Legierungselemente mit 14 MeV-Neutronen

The elements are separated from iron by solvent-extraction. Cr, V and Mn are separated by ion-exchange chromatography with a strong acidic cation-exchanger. The elements are determined by 14 MeV-neutron activation analysis using γ-spectroscopy. The method is suitable for a concentration range of 0.05 to 5%.     

Die Kristallstrukturen der Diquecksilber(I)-Salze von Aminobenzolsulfonsäuren

Crystal Structures of Dimercuri (I) Salts of p- and m-Sulfanilic Acids The crystal structures of the compounds Hg₂(p-H₂N–C₆H₄–SO₃)₂ ( 1 ), Hg₂(m-H₂N–C₆H₄–SO₃)₂ ( 2 ), and Hg₂(m-H₂N–C₆H₄–SO₃)₂ · 2H₂O ( 3 ) contain leaf-structures ( 1 and 3 ) or chain-structures ( 2 ), with nearly linear groups N–Hg–Hg–N, Hg–O-contacts and hydrogen-bridging bonds. The smaller density of 3 compared with 1 –caused by the steric hindrance through the ligand – declared the incorporation of water for raising the stabilising interaction in the crystals. The compound 3 is the kinetic controlled, the compound 2 the thermodynamic controlled product.     

pH-Dependent force spectroscopy of tri(ethylene glycol)- and methyl-terminated self-assembled monolayers adsorbed on gold

Self-assembled monolayers (SAMs) of methoxy-tri(ethylene glycol)- (EG(3)-OMe) and methyl-terminated alkanethiols (C(16)) adsorbed on polycrystalline gold were investigated by chemical force spectroscopy. Measurements were performed in aqueous electrolyte solutions depending on ionic strength and pH value. Charged and hydrophobic tips were employed as probes to mimic local patches of proteins and to study the interaction at the organic/liquid interface in detail. Force-distance curves reveal information about the origin of the observed interaction and the underlying mechanisms. The measurements confirm an effective negative surface charge to be present at the oligo(ethylene glycol) (OEG) and the methyl interface and suggest that the charges are due to the adsorption of hydroxyl ions from aqueous solution. pH-dependent measurements further support the robustness of the established charge associated with the OEG films. Its sign does not change over the whole range of investigated values between pH approximately 3.5 and approximately 10. In contrast, the hydrophobic self-assembled hexadecanethiol films on gold show an isoelectric point (IEP) around pH 4. While the mechanism of charge establishment appears to be similar for both SA films, the strength of hydrogen bonding to interfacial water, which acts as a template for hydroxyl ion adsorption, is likely to be responsible for the observed difference.     

Can the highest occupied molecular orbital of the uranyl ion be essentially 5f?

Recent relativistic calculations on the uranyl ion suggest that the low wave numbers of the first electron transfer bands are due to a bonding 5f-like orbital containing the two loosest bound electrons. Comparison with UF₆ makes it more likely that if indeed σ_u (and not π_u) is the highest occupied MO, it is rather due to “pushing from below” by U 6p (like N 2s in N₂).     

Zur Struktur der Tetrahydro-4-phenylspiro([1]benzopyran-2,4′(1′H)-pyrimidin)-2′(3′H)-one bzw.-thione über Heterocyclen, 49. Mitt

The structures of tetrahydro-4-phenylspiro([1]benzopyran-2,4(1H)-pyrimidin)-2(3H)-ones and-thiones4 a, b resp., are proved by synthesis. 3-(2-methoxy-3,5-dimethylphenyl)-3-phenylpropionic acid11 b is prepared from 3,4-dihydro-6,8-dimethyl-4-phenylcoumarin10. The lithium salt of11 b reacts with isobutenyl-lithium to 1-(2-methoxy-3,5-dimethylphenyl)-5-methyl-1-phenyl-4-hexen-3-on12 a. 12 a is transferred with urea in acid medium and NH₄CNS resp. in a mixture of dihydro-6-[2-(2-methoxy-3,5-dimethylphenyl)-2-phenyläthyl]-4,4-dimethyl-2(1H)-pyrimidinone and-thione13 a, b and tetrahydro-6-[2-(2-methoxy-3,5-dimethylphenyl)-2-phenyläthyliden]-4,4-dimethyl-2(1H)-pyrimidinone and-thione14 a, b resp.14 b leads to13 a, b with H₂O₂. Heating of13 a, 14 a and14 b resp. with pyridin-HCl leads to the spiro compounds4 a, b.     

On the calculation of induced electric and magnetic moments of atoms and molecules

We present a many-electron method for calculating first and second order perturbed wavefunctions due to external electric and magnetic fields, which identifies the important correlation effects for the response function a priori and calculates them variationally. It is accurate, economical and applicable to ground and excited states with the same ease. Thus, it presents a useful alternative to the well-known coupled Hartree-Fock methods. As an application of this method, we calculate the static electric dipole polarizability of the Be ground state. We find α_d = 5.49 ų in agreement with recent extensive calculations.     

Adducts of organogallium chlorides with hydrazines and the formation of dimeric dialkylgallium hydrazides possessing different ring sizes

The dialkylgallium chlorides R₂GaCl (R = Me, Et, CMe₃) reacted with hydrazines H₂N-N(H)R′ (R′ = CMe₃, C₆H₅) to form the adducts R₂ClGa ← NH₂-N(H)R′ (1-4), in which the gallium atoms are coordinated by the NH₂ nitrogen atoms of the hydrazine ligands. Treatment of these adducts with tert-butyllithium as a base afforded dialkylgallium hydrazides (R₂Ga-N₂H₂R′)₂ [5 (R = R′ = CMe₃) and 6 (R = CMe₃, R′ = C₆H₅)] by deprotonation of the hydrazine ligands and precipitation of LiCl in two cases only. The remaining adducts gave a substitution reaction at gallium or an unclear reaction course. The hydrazides 5 and 6 adopt different structures in the solid state. The tri(tert-butyl) compound 5 possesses a four-membered Ga₂N₂ heterocycle in its molecular core with two exocyclic N-N bonds, which represents the structural motif usually observed for dialkylgallium hydrazides. 6 has a five-membered Ga₂N₃ heterocycle with one endocyclic and one exocyclic N-N bond. That structure is preserved in solution as clearly shown by NMR spectroscopy. The behaviour of 5 in solution is more complicated, which may be caused by cis/trans isomerization.     

Absorption Spectra and Termination Kinetics of Transient Free Radicals in Solution Observed by UV./VIS. Spectroscopy with modulated excitation

Free radicals are generated in liquid solutions by harmonically modulated photolysis of suitable substrates. Harmonic analysis of the absorbance as functions of wavelength and modulation frequency yields the optical spectra and the decay kinetics of the transient species. The experimental technique and the analysis are described in detail. Results on t-butyl, 2-propyl and benzyl radicals generated by photolysis of the corresponding dialkyl resp. dibenzyl ketones are reported. They confirm previous spectral assignments and show that the termination reactions are diffusion controlled.     

Stable gaseous aziridinium ions

Gaseous protonated aziridine ions are produced at the threshold from β-phenoxyethylamine molecular ions. The evidence for this is collisional activation spectra, using various precursors (including labelled analogues) under electron impact and field ionization conditions. Partial conversion to the acyclic \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm CH = }\mathop {\rm N}\limits^ + {\rm H}_{\rm 2} $\end{document} isomer occurs at higher electron energies and is rationalized by means of a potential energy surface constructed from energetic data.