Nonvertex‐Balanced Factors in Random Graphs

We prove part of a conjecture by Johansson, Kahn, and Vu (Factors in random graphs, Random Struct. Algorithms 33 (2008), 1, 1–28.) regarding threshold functions for the existence of an H‐factor in a random graph . We prove that the conjectured threshold function is correct for any graph H which is not covered by its densest subgraphs. We also demonstrate that the main result of Johansson, Kahn, and Vu (Factors in random graphs, Random Struct. Algorithms 33 (2008), 1, 1–28) generalizes to multigraphs, digraphs, and a multipartite model.     

Coverage‐ and Temperature‐Dependent Metalation and Dehydrogenation of Tetraphenylporphyrin on Cu(111)

Using temperature‐programmed desorption, supported by X‐ray photoelectron spectroscopy and scanning tunneling microscopy, a comprehensive overview of the main reactions of 5,10,15,20‐tetraphenyl‐21H,23H‐porphyrin (2HTPP) on Cu(111) as a function of coverage and temperature is obtained. Three reactions were identified: metalation with Cu substrate atoms, stepwise partial dehydrogenation, and finally complete dehydrogenation. At low coverage the reactions are independent of coverage, but at higher coverage metalation becomes faster and partial dehydrogenation slower. This behavior is explained by a weaker interaction between the iminic nitrogen atoms and the Cu(111) surface in the high‐coverage checkerboard structure, leading to faster metalation, and the stabilizing effect of T‐type interactions in the CuTPP islands formed at high coverage after metalation, leading to slower dehydrogenation. Based on the amount of hydrogen released and the appearance in STM, a structure of the partially dehydrogenated molecule is suggested.     

Determination of the Absolute Configuration of Perylene Quinone‐Derived Mycotoxins by Measurement and Calculation of Electronic Circular Dichroism Spectra and Specific Rotations

Altertoxins I–III, alterlosins I and II, alteichin (alterperylenol), stemphyltoxins I–IV, stemphyperylenol, stemphytriol, 7‐epi‐8‐hydroxyaltertoxin I, and 6‐epi‐stemphytriol are mycotoxins derived from perylene quinone, for which the absolute configuration was not known. Electronic circular dichroism (ECD) spectra were calculated for these compounds and compared with measured spectra of altertoxins I–III, alteichin, and stemphyltoxin III and with reported Cotton effects. Specific rotations were calculated and compared with reported specific rotations. The absolute configuration of all the toxins, except for stemphyltoxin IV, could thus be determined. The validity of the assignment was high whenever reported ECD data were available for comparison, and the validity was lower when the assignment was based only on the comparison of calculated and reported specific rotations. ECD spectra are intrinsically different for toxins with a biphenyl substructure and for toxins derived from dihydroanthracene.     

Origin and Location of Electrons and Protons during the Formation of Intermetalloid Clusters [Sm@Ga3−xH3−2xBi10+x]3− (x=0, 1)

Reaction of [GaBi₃]^2? with [Sm(C₅Me₄H)₃] yielded the first protonated ternary intermetalloid clusters [Sm@Ga_3?xH_3?2xBi_10+x]^3? ( 1 ; x=0,1). The presence of the Ga? H bonds and the transfer of electrons and protons during the formation of 1 were elucidated by a combination of experimental and quantum chemical methods, thereby rationalizing the role of the solvent ethane‐1,2‐diamine as a Brønsted acid. As an organic by‐product, we observed the previously unknown octamethylfulvene ( 2 ) upon C? C coupling of (C₅Me₄H)^?.     

Atom Exchange Versus Reconstruction: (GexAs4−x)x− (x=2, 3) as Building Blocks for the Supertetrahedral Zintl Cluster [Au6(Ge3As)(Ge2As2)3]3−

The Zintl anion (Ge₂As₂)^2? represents an isostructural and isoelectronic binary counterpart of yellow arsenic, yet without being studied with the same intensity so far. Upon introducing [(PPh₃)AuMe] into the 1,2‐diaminoethane (en) solution of (Ge₂As₂)^2?, the heterometallic cluster anion [Au₆(Ge₃As)(Ge₂As₂)₃]^3? is obtained as its salt [K(crypt‐222)]₃[Au₆(Ge₃As)(Ge₂As₂)₃]?en?2 tol ( 1 ). The anion represents a rare example of a superpolyhedral Zintl cluster, and it comprises the largest number of Au atoms relative to main group (semi)metal atoms in such clusters. The overall supertetrahedral structure is based on a (non‐bonding) octahedron of six Au atoms that is face‐capped by four (Ge_xAs_4?x)^x? (x=2, 3) units. The Au atoms bind to four main group atoms in a rectangular manner, and this way hold the four units together to form this unprecedented architecture. The presence of one (Ge₃As)^3? unit besides three (Ge₂As₂)^2? units as a consequence of an exchange reaction in solution was verified by detailed quantum chemical (DFT) calculations, which ruled out all other compositions besides [Au₆(Ge₃As)(Ge₂As₂)₃]^3?. Reactions of the heavier homologues (Tt₂Pn₂)^2? (Tt=Sn, Pb; Pn=Sb, Bi) did not yield clusters corresponding to that in 1 , but dimers of ternary nine‐vertex clusters, {[AuTt₅Pn₃]₂}^4? (in 2 – 4 ; Tt/Pn=Sn/Sb, Sn/Bi, Pb/Sb), since the underlying pseudo‐tetrahedral units comprising heavier atoms do not tend to undergo the said exchange reactions as readily as (Ge₂As₂)^2?, according to the DFT calculations.     

Minimizing Side Product Formation in Alkyne Functionalization of Ruthenium Complexes by Introduction of Protecting Groups

The synthesis of alkyne functionalized bipyridine ruthenium complexes are reported. The improved synthetic approach through application of stable protecting groups prevents formation of possible side products while facilitating purification. By applying copper-catalysed azide-alkyne cycloaddition reactions (CuAAC) pyrene units with flexible alkyl linkers are introduced at the periphery of the complex, opening up various applications including surface immobilization and DNA intercalation. All complexes are characterized structurally as well as photophysically, especially regarding the influence of the introduced alkyne and triazolyl substituents on their photophysical behavior.     

The shadow of a collapsing dark star

The shadow of a black hole is usually calculated, either analytically or numerically, on the assumption that the black hole is eternal, i.e., that it has existed for all time. Here we ask the question of how this shadow comes about in the course of time when a black hole is formed by gravitational collapse. To that end we consider a star that is spherically symmetric, dark and non-transparent and we assume that it begins, at some instant of time, to collapse in free fall like a ball of dust. We analytically calculate the dependence on time of the angular radius of the shadow, first for a static observer who is watching the collapse from a certain distance and then for an observer who is falling towards the centre following the collapsing star.