From the {FeIII2Ln2} Butterfly's Perspective: the Magnetic Benefits and Challenges of Cooperativity within 3 d–4 f Based Coordination Clusters

In this Review we discuss the tuning handles which can be used to steer the magnetic properties of Fe^III-4 f “butterfly” compounds. The majority of presented compounds were produced in the context of project A3 “Di- to tetranuclear compounds incorporating highly anisotropic paramagnetic metal ions” within the SFB/TRR88 “3MET”. These contain {Fe^III₂Ln₂} cores encapsulated in ligand shells which are easy to tune in a “test-bed” system. We identify the following advantages and variables in such systems: (i) the complexes are structurally simple usually with one crystallographically independent Fe^III and Ln^III, respectively. This simplifies theory and anaylsis; (ii) choosing Fe allows ⁵⁷Fe Mössbauer spectroscopy to be used as an additional technique which can give information about oxidation levels and spin states, local moments at the iron nuclei and spin-relaxation and, more importantly, about the anisotropy not only of the studied isotope, but also of elements interacting with this isotope; (iii) isostructural analogues with all the available (i. e. not Pm) 4 f ions can be synthesised, enabling a systematic survey of the influence of the 4 f ion on the electronic structure; (iv) this cluster type is obtained by reacting [Fe^III₃O(O₂CR)₆(L)₃](X) (X=anion, L=solvent such as H₂O, py) with an ethanolamine-based ligand L′ and lanthanide salts. This allows to study analogues of [Fe^III₂Ln₂(μ₃-OH)₂(L′)₂(O₂CR)₆] using the appropriate iron trinuclear starting materials. (v) the organic main ligand can be readily functionalised, facilitating a systematic investigation of the effect of organic substituents on the ligands on the magnetic properties of the complexes. We describe and discuss 34 {M^III₂Ln₂} (M=Fe or in one case Al) butterfly compounds which have been reported up to 2020. The analysis of these gives perspectives for designing new SMM systems with specific electronic and magnetic signatures     

Solving second-order differential equations with variable coefficients

A method is developed in which an analytical solution is obtained for certain classes of second-order differential equations with variable coefficients. By the use of transformations and by repeated iterated integration, a desired solution is obtained. This alternative method represents a different way to acquire a solution from classic power series techniques and other approaches. It is, at times, more involved than traditional methods.     

Photoaddressable polymers for liquid crystal alignment

We demonstrate reversible photoinduced in situ reorientation of low molecular mass liquid crystals (LCs) by means of photoaddressable polymers (PAPs). These polymers contain mesogenic azobenzene side chains optimized to reorient cooperatively and effectively upon illumination with polarized light. Various low molecular mass LCs were introduced between two PAP layers and these sandwich devices were tested with respect to stability and reversibility of photoinduced orientation. Dissolution of the PAP layer by the low molecular mass LC was observed for several material combinations and systematically investigated. Different anisotropic dyes were added as fluorescence markers in order to monitor the photoinduced LC orientation. With an optimized material combination, more than 10 reversible reorientation processes could be realized with polarized light of either 514 or 405 nm wavelength, without any reduction in alignment quality. Further, microscopic polarized fluorescence patterns could be produced and erased within short exposure times.     

Trace formulas for additive and non-additive perturbations

Trace formulas for pairs of self-adjoint, maximal dissipative and accumulative as well as other types of resolvent comparable operators are obtained. In particular, the existence of a complex-valued spectral shift function for a pair {H^′,H}$\{H^{\prime },H\}$ of maximal accumulative operators has been proved. We investigate also the existence of a real-valued spectral shift function. Moreover, we treat in detail the case of additive trace class perturbations. Assuming that H   and H^′=H+V$H^{\prime }=H+V$ are maximal accumulative and V is trace class, we prove the existence of a summable   complex-valued spectral shift function. We also obtain trace formulas for pairs {H,H^?}$\{H,H^{?}\}$assuming only that H and  H^?$H^{?}$are resolvent comparable. In this case the determinant of the characteristic function of H is involved in trace formulas.     

Synthesis of sugar oxime ether surfactants

A straightforward synthesis of a novel class of sugar surfactants is described. The key step is the chemoselective condensation of a hydrophobic alkoxyamine with the resident aldehyde/ketone moiety on a hydrophilic sugar. Neither protection/deprotection of the sugars nor extensive product purification is required. The method allows for the facile adjustment of hydrophobic and hydrophilic domains of the sugar oxime ether surfactant and uses inexpensive, readily accessible, and renewable materials.     

Snapshot Mueller matrix spectropolarimeter

We present a new snapshot technique for performing spectrally resolved Mueller matrix polarimetry. The basic approach is an extension of the channeled spectropolarimetry technique, employing frequency-domain interferometry to encode polarization information into modulation of the spectrum.     

“Golden” Cascade Cyclization to Benzo[c]-Phenanthridines

Herein, we describe a gold-catalyzed cascade cyclization of Boc-protected benzylamines bearing two tethered alkyne moieties in a domino reaction initiated by a 6-endo-dig cyclization. The reaction was screened intensively, and the scope was explored, resulting in nine new Boc-protected dihydrobenzo[c]phenanthridines with yields of up to 98 %; even a π-extension and two bidirectional approaches were successful. Furthermore, thermal cleavage of the Boc group and subsequent oxidation gave substituted benzo[c]phenanthridines in up to quantitative yields. Two bidirectional approaches under the optimized conditions were successful, and the resulting π-extended molecules were tested as organic semiconductors in organic thin-film transistors.     

On the strength of hydrogen bonding within water clusters on the coordination limit

Hydrogen bonds (HB) are arguably the most important noncovalent interactions in chemistry. We study herein how differences in connectivity alter the strength of HBs within water clusters of different sizes. We used for this purpose the interacting quantum atoms energy partition, which allows for the quantification of HB formation energies within a molecular cluster. We could expand our previously reported hierarchy of HB strength in these systems (Phys. Chem. Chem. Phys., 2016, 18 , 19557) to include tetracoordinated monomers. Surprisingly, the HBs between tetracoordinated water molecules are not the strongest HBs despite the widespread occurrence of these motifs (e.g., in ice I_h). The strongest HBs within H₂O clusters involve tricoordinated monomers. Nonetheless, HB tetracoordination is preferred in large water clusters because (a) it reduces HB anticooperativity associated with double HB donors and acceptors and (b) it results in a larger number of favorable interactions in the system. Finally, we also discuss (a) the importance of exchange-correlation to discriminate among the different examined types of HBs within H₂O clusters, (b) the use of the above-mentioned scale to quickly assess the relative stability of different isomers of a given water cluster, and (c) how the findings of this research can be exploited to indagate about the formation of polymorphs in crystallography. Overall, we expect that this investigation will provide valuable insights into the subtle interplay of tri- and tetracoordination in HB donors and acceptors as well as the ensuing interaction energies within H₂O clusters.