The structure of DGA resolutions of monomial ideals

Let $I?\mathbb{k}[x_1,\dots ,x_n]$ be a squarefree monomial ideal in a polynomial ring. In this paper we study multiplications on the minimal free resolution $\mathbb{F}$ of $\mathbb{k}[x_1,\dots ,x_n]/I$. In particular, we characterize the possible vectors of total Betti numbers for such ideals which admit a differential graded algebra (DGA) structure on $\mathbb{F}$. We also show that under these assumptions the maximal shifts of the graded Betti numbers are subadditive.On the other hand, we present an example of a strongly generic monomial ideal which does not admit a DGA structure on its minimal free resolution. In particular, this demonstrates that the Hull resolution and the Lyubeznik resolution do not admit DGA structures in general.Finally, we show that it is enough to modify the last map of $\mathbb{F}$ to ensure that it admits the structure of a DG algebra.     

Competitive Metal Coordination of Hexaaminotriphenylene on Cu(111) by Intrinsic Copper Versus Extrinsic Nickel Adatoms

The interplay between the self-assembly and surface chemistry of 2,3,6,7,10,11-hexaaminotriphenylene (HATP) on Cu(111) was complementarily studied by high-resolution scanning tunneling microscopy (STM) and X-ray photoelectron spectroscopy (XPS) under ultra-high vacuum conditions. To shed light on the competitive metal coordination, comparative experiments were carried out on pristine and nickel-covered Cu(111). Directly after room-temperature deposition of HATP onto pristine Cu(111), self-assembled aggregates were observed by STM, and XPS results indicated still protonated amino groups. Annealing up to 200 °C activated the progressive single deprotonation of all amino groups as indicated by chemical shifts of both the N 1s and C 1s core levels in the XP spectra. This enabled the formation of topologically diverse π–d conjugated coordination networks with intrinsic copper adatoms. The basic motif of these networks was a metal–organic trimer, in which three HATP molecules were coordinated by Cu₃ clusters, as corroborated by the accompanying density functional theory (DFT) simulations. Additional deposition of more reactive nickel atoms resulted in both chemical and structural changes with deprotonation and formation of bis(diimino)–Ni bonded networks already at room temperature. Even though fused hexagonal metal-coordinated pores were observed, extended honeycomb networks remained elusive, as tentatively explained by the restricted reversibility of these metal–organic bonds.     

Isomerizing Olefin Metathesis

Isomerizing olefin metathesis is currently undergoing a transformation from laboratory curiosity to powerful synthetic concept at the heart of orthogonal tandem catalysis. In this process, an isomerization catalyst continuously moves double bonds along carbon chains, while a metathesis catalyst scrambles the residues at the C−C double bonds. This cooperative action of two catalysts can be used to access single, defined products from a complex mixture of compounds. Alternatively, it enables the transformation of uniform starting materials into complex product blends with defined, tunable properties. This concept article highlights recent developments and potential applications of this fascinating reaction concept.     

Absolute Configuration of Pharmaceutical Research Compounds Determined by X‐ray Powder Diffraction

The absolute configuration of active pharmaceutical ingredients (APIs) was determined by generating salts of the active pharmaceutical ingredient (API) with counterions of known chirality, and determining the crystal structures by X‐ray powder diffraction. This approach avoids the (often tedious) growth of single crystals, and is successful with very limited quantities of material (less than 1 mg). The feasibility of the method is demonstrated on five examples, and its limitations are discussed as well.     

Substitution reactions with [ReBr(2)(CO)(2)(NCCH(3))(2)](-): a convenient route to complexes with the cis-[Re(CO)(2)](+) core

Water- and air-stable complexes comprising the cis-[Re(CO)(2)](+) core can be synthesized from the (Et(4)N)[ReBr(2)(NCCH(3))(2)(CO)(2)] precursor . Complex showed distinctly different chemical and electronic behaviour compared to [ReBr(3)(CO)(3)](2-). Substituting the two bromides in with imidazole-like ligands or alpha,alpha'-diimines gave new complexes with potential applications in bioinorganic chemistry and photochemistry. The two acetonitrile ligands are very stably bound and could not be replaced. Under CO pressure, the uncommon complex mer-[ReBr(NCCH(3))(2)(CO)(3)] was formed from . The reaction of with the tetradentate ligand bis(2-pyridylmethyl)glycine (BPG) finally induced a four fold substitution at the metal center to form a [Re(CO)(2)(L(4))](+)-type complex.