Low‐Symmetry Ω‐Shaped Zinc Phthalocyanine Sensitizers with Panchromatic Light‐Harvesting Properties for Dye‐Sensitized Solar Cells

Two low‐symmetry phthalocyanines (Pcs) substituted with thiophene units at the non‐peripheral (α) and peripheral (β) positions were synthesized and their optical, electronic‐structure, and electrochemical properties were investigated. The substitution of thiophene units at the α positions of the phthalocyanine skeleton resulted in a red shift of the Q band and significantly modified the molecular‐orbital electronic distributions just below the HOMO and just above the LUMO, with distortion of the typical Gouterman four‐orbital arrangement of MOs. Two amphiphilic Ω‐shaped ZnPcs ( αPcS1 and αPcS2 ) bearing a π‐conjugated side chain with an adsorption site at an α position of the Pc macrocycle were synthesized as sensitizers for dye‐sensitized solar cells (DSSCs). The absorption spectra of αPcS1 and αPcS2 showed red shifted Q bands and a broad band from 350 to 550 nm assignable to the intramolecular charge‐transfer transition from the ZnPc core to the side chains. Time‐dependent DFT calculations provided a clear interpretation of the effect of the thiophene conjugation on the typical phthalocyanine core π MOs. Compound αPcS1 was used as a light‐harvesting dye on a TiO₂ electrode for a DSSC, which showed a panchromatic response in the range 400–800 nm with a power conversion efficiency of 5.5 % under one‐sun conditions.     

Ideals containing the squares of the variables

We study the Betti numbers of graded ideals containing the squares of the variables, in a polynomial ring. We prove the lex-plus-powers conjecture for such ideals.     

The minimal free resolution of a Borel ideal

We consider the Eliahou–Kervaire minimal free resolution of a 0-Borel ideal and its applications.     

Future teachers’ professional knowledge on argumentation and proof: a case study from universities in three countries

In this paper, qualitative results of a case study about the professional knowledge in the area of argumentation and proof of future teachers from universities in three countries are described. Based on results of open questionnaires, data about the competencies these future teachers have in the areas of mathematical knowledge and knowledge of mathematics pedagogy are presented. The study shows that the majority of the future teachers at the participating universities situated in Germany, Hong Kong and Australia, were not able to execute formal proofs, requiring only lower secondary mathematical content, in an adequate and mathematically correct way. In contrast, in all samples there was evidence of at least average competencies of pedagogical content reflection about formal and pre-formal proving in mathematics teaching. However, it appears that possessing a mathematical background as mandated for teaching and having a high affinity with proving in mathematics teaching at the lower secondary level are not a sufficient preparation for teaching proof.     

Flips and the Hilbert scheme over an exterior algebra

We study the tangent space at a monomial point M in the Hilbert scheme that parameterizes all ideals with the same Hilbert function as M over an exterior algebra.     

Luminescence characteristics of InAlP---InGaP heterostructures having native-oxide windows

Data are presented on the luminescence characteristics of InGaP/InAlP heterostructures with oxidized InAlP cladding layers grown by metalorganic chemical vapor deposition. The structures are grown on GaAs substrates and consist of either a 20 nm thick In_0.5Ga_0.5P quantum well or a 0.75 μm InGaP layer sandwiched between two InAlP bulk barriers or between two 10-period In_0.5Al_0.5P/In_xGa_1−xP strain-modulated superlattice heterobarriers, where x varies from 0.5 to 0.45 and the period of the superlattice is 3 nm. The top InAlP cladding layer of the InAlP/InGaP heterostructures is oxidized for 2–5.5 h at 500°C in an ambient of H₂O vapor saturated in a N₂ carrier gas. Photoluminescence and time-resolved photoluminescence studies at room temperature show that, as a result of the oxidation of a portion of the top InAlP cladding layer, the photoluminescence emission intensity and lifetime from the InGaP QWs increase significantly.     

Crystallization of Arthrobacter sp. strain 1C N-(1-D-carboxyethyl)-L-norvaline dehydrogenase and its complex with NAD+

The novel NAD+-linked opine dehydrogenase from a soil isolate Arthrobacter sp. strain 1C belongs to an enzyme superfamily whose members exhibit quite diverse substrate specificites. Crystals of this opine dehydrogenase, obtained in the presence or absence of co-factor and substrates, have been shown to diffract to beyond 1.8 ? resolution. X-ray precession photographs have established that the crystals belong to space group P21212, with cell parameters a = 104.9, b = 80.0, c = 45.5 ? and a single subunit in the asymmetric unit. The elucidation of the three-dimensional structure of this enzyme will provide a structural framework for this novel class of dehydrogenases to enable a comparison to be made with other enzyme families and also as the basis for mutagenesis experiments directed towards the production of natural and synthetic opine-type compounds containing two chiral centres.     

Application of MCD spectroscopy and TD-DFT to nonplanar core-modified tetrabenzoporphyrins: effect of reduced symmetry on nonplanar porphyrinoids

The optical spectra of a series of core-modified tetrabenzoporphyrins were analyzed to determine the effects of core modification, ligand folding, and partial benzo substitution at the ligand periphery on the electronic structure by using magnetic circular dichroism (MCD) and NMR spectroscopy, X-ray crystallography, cyclic and differential pulse voltammetry, and TD-DFT calculations. Planar 21-carba-, 21-thia-, 21,23-dithia-, and 21-oxa-23-thiatetrabenzo[b,g,l,q]porphyrins reported previously were studied together with the previously unreported 21-oxa- and 21-carba-23-thiatetrabenzo[b,g,l,q]porphyrins. The optical properties of these compounds are compared to those of tetrabenzo[b,g,l,q]-, 5,10,15,20-tetraphenyl-, 5,10,15,20-tetraphenyltetrabenzo[b,g,l,q]-21-thia-, 5,10,15,20-tetraphenyltetrabenzodithia-, 5,10,15,20-tetraphenyldibenzo[g,q]-21,23-dithia-, 5,10,15,20-tetraphenyldibenzo[b,l]-21,23-dithia-, 5,10,15,20-tetraphenyltribenzo[g,q,l]-21-thia-, and 5,10,15,20-tetraphenylbenzo[b]-21-thiaporphyrins. Michl's perimeter model and Gouterman's four-orbital model are used to conceptualize the results and to account for red shifts commonly observed in the spectral bands of nonplanar porphyrinoids.