Integration of electron density and molecular orbital techniques to reveal questionable bonds: the test case of the direct Fe-Fe bond in Fe2(CO)9

The article illustrates the advantages of partitioning the total electron density rho(rb), its Laplacian (inverted Delta)2 rho(rb), and the energy density H(rb) in terms of orbital components. By calculating the contributions of the mathematically constructed molecular orbitals to the measurable electron density, it is possible to quantify the bonding or antibonding character of each MO. This strategy is exploited to review the controversial existence of direct Fe-Fe bonding in the triply bridged Fe2(CO)9 system. Although the bond is predicted by electron counting rules, the interaction between the two pseudo-octahedral metal centers can be repulsive because of their fully occupied t(2g) sets. Moreover, previous atoms in molecules (AIM) studies failed to show a Fe-Fe bond critical point (bcp). The present electron density orbital partitioning (EDOP) analysis shows that one sigma bonding combination of the t(2g) levels is not totally overcome by the corresponding sigma* MO, which is partially delocalized over the bridging carbonyls. This suggests the existence of some, albeit weak, direct Fe-Fe bonding.     

Neutral hexa- and pentacoordinate silicon(IV) complexes with SiO(6) and SiO(4)N skeletons

The neutral heteroleptic hexacoordinate silicon(IV) complexes 4 and 5 (SiO(6) skeletons) and the neutral pentacoordinate silicon(IV) complexes 7-9 (SiO(4)N skeletons) were synthesized, starting from the hexacoordinate precursor 2 and the pentacoordinate precursor 6, respectively. In these reactions, two monoanionic cyanato-N ligands are replaced by one dianionic bidentate O,O-chelate ligand. Compounds 4, 5, and 7-9 were characterized by single-crystal X-ray diffraction and solid-state and solution NMR spectroscopy. The chiral silicon(IV) complexes 4, 5, 7, and 8 were obtained as racemic mixtures, whereas 9 was isolated as a cocrystallizate consisting of the two diastereomers, (C,S)-9 and (A,S)-9 (ratio 1:1). The stereodynamics of 5 and 8 were studied by variable-temperature (1)H NMR experiments.     

Double Yielding in a Styrene/Butadiene Star Block Copolymer

Summary: The morphology and tensile deformation behaviour of a highly asymmetric styrene/butadiene star block copolymer (polystyrene (PS) content = 74%) containing random PS‐co‐PB (polybutadiene) copolymer as a rubbery phase were investigated. The existence of double yielding, similar to that observed in some semicrystalline polymers, was detected in this nanostructured amorphous polymer. The observed phenomenon may be correlated with two different micromechanical processes taking place at the initial stage of deformation.

The stress‐strain curve of the star block copolymer prepared here (each curve represents a different method). The two yield points are clearly visible (labelled I and II).     

Approximation of Metric Spaces by Partial Metric Spaces

Partial metrics are generalised metrics with non-zero self-distances. We slightly generalise Matthews' original definition of partial metrics, yielding a notion of weak partial metric. After considering weak partial metric spaces in general, we introduce a weak partial metric on the poset of formal balls of a metric space. This weak partial metric can be used to construct the completion of classical metric spaces from the domain-theoretic rounded ideal completion.     

Milestones in the Biochemistry of Silicon: From Basic Research to Biotechnological Applications

6.7 Gigatonnes of silicon are processed each year by marine organisms. Since it was known that silicon is an essential element for many biological systems, significant advances in the biochemistry of this element have been achieved from the classical viewpoint of silicon being a purely inorganic element. This article describes the proteins, genes, and molecular mechanisms of silicon metabolism in diatoms and sponges. These studies may help to reveal the role of silicon for optimal development and growth in many plants and animals as well as initiate the development of new technological methods for the shape-controlled production of new patterned silicone-based materials.     

A Reissner-type plate theory for monoclinic material derived by extending the uniform-approximation technique by orthogonal tensor decompositions of <Emphasis Type="Italic">n</Emphasis>th-order gradients

The uniform-approximation approach is an a-priori assumption free structured approach for the derivation of hierarchies of lower-dimensional theories for thin structures with increasing approximation accuracy. In this publication, we derive a second-order consistent plate theory for monoclinic material and investigate several theories that arise from the original theory by a pseudo-reduction approach which aims to reduce the number of PDEs that are to solve. A one-variable model that governs only the interior solution is presented and, in addition, an extended two-variable model that also covers edge effects. Since the second introduced variable is a rotation of a vector field, we have to uniquely identify the rotation dependent parts in general gradients of the vector field, which is resolved by the introduction of an orthogonal decomposition. The final two-variable model is equivalent to the Reissner–Mindlin theory for the special case of isotropic material, whereas the one-variable model is equivalent to the first Reissner PDE. In contrast to this special case, the two-variable model is a coupled system of two PDEs for general monoclinic material.