Inhomogeneous diophantine approximation with prime constraints

We study the problem of inhomogeneous diophantine approximation under certain primality restrictions.     

Rational Improvement of Single-Molecule Magnets by Enforcing Ferromagnetic Interactions

The anisotropy barrier of polynuclear single-molecule magnets is expected to be higher with less tunneling the better stabilized the spin ground state is so that less M_S mixing in the ground state and with excited spin states occur. We have realized this experimentally in two structurally related heptanuclear SMMs: the triplesalen-based [Mn^III ₆ Cr^III]³⁺ and the triplesalalen-based *[Mn^III ₆ Cr^III]³⁺ . The ligand system triplesalen was developed to enforce ferromagnetic interactions by the spin-polarization mechanism. However, we found weak antiferromagnetic couplings, that we assigned to an inefficient spin-polarization by a heteroradialene formation. To prevent this heteroradialene formation, the triplesalalen ligand H₆talalen was designed. Here, we present the building block [(talalen )Mn^III₃]³⁺ and its application for the assembly of [{(talalen )Mn^III₃}₂{Cr^III(CN)₆}]³⁺ (= *[Mn^III ₆ Cr^III]³⁺ ). Both the trinuclear and heptanuclear complexes are SMMs. The comparison to the related triplesalen complex [(feld )Mn^III₃]³⁺ proves the absence of heteroradialene character and the enforcement of ferromagnetic Mn^III-Mn^III interactions in the (talalen )⁶⁻ complexes. This results in an increase of the barrier for spin reversal U_eff from 25 K in the triplesalen-based [Mn^III ₆ Cr^III]³⁺ SMMs to 37 K in the triplesalalen-based *[Mn^III ₆ Cr^III]³⁺ SMM proving the success of our concept. Based on this study, the next step in the rational improvement of our SMMs is discussed.     

Synthesis of (±)‐Spongiolactone Enabling Discovery of a More Potent Derivative

An eleven‐step synthesis of (±)‐spongiolactone from 1,3‐cyclohexanedione is reported that relies on a diastereoselective, nucleophile‐catalyzed aldol lactonization (NCAL) process with an advanced ketoacid intermediate that installed the anticipated β‐lactone pharmacophore of the natural product. In addition, a stereoselective cyclohexenyl zinc addition to a substituted cyclohexanone simultaneously installed two fully substituted vicinal stereocenters. The reported synthesis enabled preliminary structure–activity studies that revealed a regio‐ and stereoisomeric derivative of spongiolactone with greater antiproliferative activity towards a leukemia (K562) cell line. Furthermore, unusual antiproliferative selectivity of these spongiolactone derivatives toward the K562 cell line was observed with no inhibition of the breast, liver, and lung cancer cell lines tested.     

Preparation and Isolation of a Chiral Methandiide and Its Application as Cooperative Ligand in Bond Activation

The activation of element–hydrogen bonds by means of metal–ligand cooperation has received increasing attention as alternative to classical activation processes, which exclusively occur at the metal center. Carbene complexes derived from methandiide precursors have been applied in this chemistry enabling the activation of a series of E?H bonds by addition reactions across the M?C bond. However, no chiral carbene complexes have been applied to realize stereoselective transformations to date. Herein, we report the isolation and structure elucidation of an enantiomerically pure dilithiomethane, which could be prepared by direct double deprotonation. The obtained dilithium salt was used for the preparation of the first chiral methandiide‐derived carbene complex, which was applied in stereoselective cooperative S?H bond activation.