On the density of states for the periodic Schrödinger operator

An asymptotic formula for the density of states of the polyharmonic periodic operator (?δ) ^l +V inR ⁿ ,n≥2,l>1/2 is obtained. Special consideration is given to the case of the Schrödinger equationn=3,l=1,V being a periodic potential, where the second term of the asymptotic is found.     

A novel chelatofore functionalized spiropyran of the 2‐oxaindane series

A novel chelatofore functionalized spiropyran of the 2‐oxaindane series, namely 8‐formyl‐7‐hydroxy‐3′,3′‐dimethylspiro[2H‐chromene‐2,1′(3′H)‐2‐benzofuran], C₁₉H₁₆O₄, is reported. In the crystalline state, dimers are formed as a result of the π–π stacking of aromatic groups of the 2H‐chromene part of the molecule and C—H...O interactions. The C_spiro—O bond length in the pyran ring is 1.4558 (10) Å, which is longer than or equal to the bond length in thermo‐ and photochromic 2‐oxaindane spiropyrans synthesized previously, except for the 7,8‐benzo/6‐NO₂ derivative, in which this bond length is 1.465 (2) Å.     

NMR‐based analysis of structure of heteroleptic triple‐decker (phthalocyaninato) (porphyrinato) lanthanides in solutions

A novel approach for the structural analysis of heteroleptic triple‐decker (porphyrinato)(phthalocyaninato) lanthanides(III) in solutions is developed. The developed approach consists in molecular mechanics (MM+) optimization of the geometry of the complex taking into account the lanthanide‐induced shift (LIS) datasets. LISs of the resonance peaks in ¹H NMR spectra of a series of symmetric complexes [An₄P]Ln[(15C5)₄Pc]Ln[An₄P], where An₄P^2? is 5,10,15,20‐tetrakis(4‐methoxyphenyl)porphyrinato‐dianion, [(15C5)₄Pc]^2? is 2,3,9,10,16,17,24,25‐tetrakis(15‐crown‐5)phthalocyaninato‐dianion and Ln = La, Ce, Pr, Nd, Sm, Eu, are analyzed. Analysis of LISs showed two sets of protons in the molecule with opposite signs of shift. Two‐nuclei analysis of LISs testifies isostructurality of the whole series of investigated complexes in solution despite contraction of the lanthanide ions. Model‐free separation of contact and dipolar contributions of LISs was performed with one‐nucleus technique and did not show changes in contact and dipolar terms within the investigated series. MM+ optimization of the molecular structure allowed the interpretation of features of LIS for each particular group of protons. Parameterization of MM + ‐optimized model of molecule with values of structure‐dependent dipolar contributions of LIS allows the development of the precise structural model of the triple‐decker complex in solution. This approach allows the determination of the geometry and structure of the sandwich macrocyclic tetrapyrrolic complexes together with conformational analysis of flexible peripheral substituents in solutions. The developed method can be applied with minor modifications for the determination of structural parameters of other types of lanthanides(III) complexes with tetrapyrrolic ligands and also supramolecular systems based on them. Copyright © 2010 John Wiley & Sons, Ltd.     

New phosphonium salts based on 3-(diphenylphosphino)propanoic and ω-haloalkanoic acids

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Recognition of essential purines by the U1A protein

Background  

The RNA recognition motif (RRM) is one of the largest families of RNA binding domains. The RRM is modulated so that individual proteins containing RRMs can specifically recognize RNA targets with diverse sequences and structures. Understanding the principles governing this specificity will be important for the rational modification and design of RRM-RNA complexes.     

Microtiterplate phosphate assay based on luminescence quenching of a terbium complex amenable to decay time detection

We describe a terbium-ligand complex (TbL) for a microtiterplate assay for phosphate (P) in the 0.3-100 μmol L⁻¹ range based on luminescence quenching. As the pH optimum is at neutral pH (7.4) the probe is quenched by both, primary (H₂PO₄⁻) and secondary phosphate (HPO₄²⁻). The LOD is 110 nmol L⁻¹. A Stern-Volmer study revealed that quenching is mostly static. Due to the ms-decay time of TbL, the first luminescence lifetime assay for phosphate could also be developed. The lifetime-based calibration plot is linear between 0.5 and 5 μmol L⁻¹ of P. The effect of various surfactants on assay performance and a study on interferents are presented. The probe was successfully applied to determination of P in commercial plant fertilizers and validated against the molybdenum blue test. The probe is the most sensitive lanthanide-based probe for phosphate.     

Reactions of 4-substituted 5H-1,2,3-dithiazoles with primary and secondary amines: fast and convenient synthesis of 1,2,5-thiadiazoles, 2-iminothioacetamides and 2-oxoacetamides

The treatment of 5H-1,2,3-dithiazole-5-thiones 1 in chloroform under reflux and 5H-1,2,3-dithiazol-5-ones 2 in THF at room temperature with primary aliphatic amines and benzylamine afforded 1,2,5-thiadiazole-3(2H)-thiones 3 and 1,2,5-thiadiazol-3(2H)-ones 6, respectively. The structure of dithiazolone 3f was confirmed by X-ray diffraction analysis. The reaction of dithiazolone 2e bearing an electron-donating methyl group in the 4-position gave 2-oxoacetamide 7e in high yield. The reaction of thiones 1 with secondary aliphatic amines in DMSO yielded 2-iminothioacetamides 8 in moderate yields together with elemental sulfur. Interestingly, the treatment of dithiazolones 2 with secondary amines under the same conditions afforded 2-oxoacetamides 9—the products of the hydrolysis of corresponding imino derivatives 10, which was isolated as 10b. A general mechanism was proposed for the formation of the products.