Simple bilevel programming and extensions

Mathematical Programming - In this paper we discuss the simple bilevel programming problem (SBP) and its extension, the simple mathematical programming problem under equilibrium constraints...     

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.