How to grow it? Strategies of mathematical development presented by the example of enumerating certain set partitions

Mathematische Semesterberichte - We describe in the form of a dialogue a development of various reflections on the combinatorics of set partitions; among the topics we pursue are...     

Vanadium(V) Oxo and Imido Calix[8]arene Complexes: Synthesis,Structural Studies,and Ethylene Homo/Copolymerisation Capability

Interaction of p‐tert‐butylcalix[8]areneH₈ (L⁸H₈) with [NaVO(OtBu)₄] (formed in situ from VOCl₃) afforded the complex [Na(NCMe)₅][(VO)₂L⁸H]?4 MeCN ( 1 ?4 MeCN). Increasing [NaVO(OtBu)₄] to 4 equiv led to [Na(NCMe)₆]₂[(Na(VO)₄L⁸)(Na(NCMe))₃]₂?10 MeCN ( 2 ?10 MeCN). With adventitious oxygen, reaction of 4 equiv of [VO(OtBu)₃] with L⁸H₈ afforded the alkali‐metal‐free complex [(VO)₄L⁸(μ³‐O)₂] ( 3 ); solvates 3 ?3 MeCN and 3 ?3 CH₂Cl₂ were isolated. For the lithium analogue, the order of addition had to be reversed such that lithium tert‐butoxide was added to L⁸H₈ and then treated with 2 equiv of VOCl₃; crystallisation afforded [(VO₂)₂Li₆[L⁸](thf)₂(OtBu)₂(Et₂O)₂]?Et₂O ( 4 ?Et₂O). Upon extraction into acetonitrile, [Li(NCMe)₄][(VO)₂L⁸H]?8 MeCN ( 5 ?8 MeCN) was formed. Use of the imido precursors [V(NtBu)(OtBu)₃] and [V(Np‐tolyl)(OtBu)₃] and L⁸H₈, afforded [tBuNH₃][{V(p‐tolylN)}₂L⁸H]?3 1/2 MeCN ( 6 ?3 1/2 MeCN). The molecular structures of 1 to 6 are reported. Complexes 1 , 3 , and 4 were screened as precatalysts for the polymerisation of ethylene in the presence of cocatalysts at various temperatures and for the copolymerisation of ethylene with propylene. Activities as high as 136 000 g (mmol(V) h)^?1 were sometimes achieved; higher molecular weight polymers could be obtained versus the benchmark [VO(OEt)Cl₂]. For copolymerisation, incorporation of propylene was 7.1–10.9 mol % (compare 10 mol % for [VO(OEt)Cl₂]), although catalytic activities were lower than [VO(OEt)Cl₂].     

Controlled synthesis of amphiphilic block copolymers based on poly(isobutylene) macromonomers

The synthesis of a monoacrylate functionalized poly(isobutylene) (PIB) macromonomer (PIBA) has been achieved by a two‐step reaction starting from a commercially available PIB. Firstly, terminal olefins (vinylidene and trisubstituted olefin) of PIB were transformed to a phenolic residue by Friedel‐Crafts alkylation followed by subsequent esterification of the phenol with acryloyl chloride, catalyzed by triethylamine. PIBA structure was confirmed by ¹H‐NMR, ¹³C‐NMR and GPC before utilizing in the RAFT copolymerization with N,N‐dimethylacrylamide (DMA) to obtain statistical copolymers (P[(DMA‐co‐(PIBA)]). Monomer conversions were consistently higher than 85% for both DMA and PIBA as monomer feed composition was varied. Chain extension of poly(N,N‐dimethylacrylamide) with PIBA to synthesize block copolymers (P[(DMA‐b‐(PIBA)]) was also achieved with near quantitative monomer conversions (>97%). Block formation efficiency was not quantitative but purification of block copolymers was possible by selective precipitation. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 634–643     

Radical Cyclisation of α‐Halo Aluminium Acetals: A Mechanistic Study

α‐Bromo aluminium acetals are suitable substrates for Ueno–Stork‐like radical cyclisations affording γ‐lactols and acid‐sensitive methylene‐γ‐lactols in high yields. The mechanistic study herein sets the scope and limitation of this reaction. The influence of the halide (or chalcogenide) atom X (X=Cl, Br, I, SPh, SePh) in the precursors α‐haloesters, as well as influence of the solvent and temperature was studied. The structure of the aluminium acetal intermediates resulting from the reduction of the corresponding α‐haloesters has been investigated by low‐temperature ¹³C‐INEPT diffusion‐ordered NMR spectroscopy (DOSY) experiments and quantum calculations, providing new insights into the structures of these thermally labile intermediates. Oxygen‐bridged dimeric structures with a planar Al₂O₂ ring are proposed for the least hindered aluminium acetals, while monomeric structures seem to prevail for the most hindered species. A comparison against the radical cyclisation of aluminium acetals derived from allyl and propargyl alcohols with the parent Ueno–Stork has been made at the BHandHLYP/6‐311++G(d,p) level of theory, highlighting mechanistic similarities and differences.     

Computational estimates of thermochemistry and pKa values of cyclopropenyl imine superbases

The thermochemical properties of superbase species derived from cyclopropeneimine are estimated by computations on systems of isodesmic reactions. Proton affinities, gas phase basicities, and pK_a values are well represented by computations incorporating G4 and CBS‐QB3 schemes augmented for large systems by DFT calculations with functionals M06‐2X and ωB97DX in the cc‐pVTZ Dunning basis. Our calculations show that relative base strengths in gas are enhanced by alkyl substitution, either by methyl groups or larger species. For acetonitrile solution, alkyl substitution seems to weaken the base. © 2013 Wiley Periodicals, Inc.     

Microporous Molecular Materials from Dipeptides Containing Non‐proteinogenic Residues

Dipeptides with two hydrophobic side chains have proved to be an exceptional source of microporous organic materials, but since previous structures were limited to the incorporation of only proteinogenic residues, their full potential as adsorbents has remained unexplored. Single‐crystal XRD data for ten new compounds with non‐proteinogenic L ‐2‐aminobutanoic acid and/or L ‐2‐amino‐pentanoic acid are presented. The gas‐phase accessibility of their crystal pores, with cross‐sections of 2.3 to 5.1 Å, was monitored by CO₂ and CH₄ adsorption isotherms. Included CO₂ was also detected spectroscopically by 2D MAS NMR. An extensive conformational analysis reveals that the use of linear rather than branched side chains (such as L ‐valine and L ‐isoleucine) affords peptides with a greater degree of conformational freedom and yields more‐flexible channel surfaces that may easily adapt to a series of potential guest molecules.     

The Remarkably Robust,Photoactive Tungsten Iodide Cluster [W6I12(NCC6H5)2]

The new heteroleptic tungsten iodide cluster compound [W₆I₁₂(NCC₆H₅)₂] is presented. The synthesis is carried-out from Cs₂W₆I₁₄ and ZnI₂ under solvothermal conditions in benzonitrile solution, yielding red cube-shaped crystals. [W₆I₁₂(NCC₆H₅)₂] represents a heteroleptic [W₆I₈]-type cluster bearing four apical iodides and two benzonitrile ligands. Molecular [W₆I₁₂(NCC₆H₅)₂] clusters form a robust hydrogen bridged crystal structure with high thermal stability and high resistibility against hydrolysis. The electronic structure is analyzed by quantum chemical methods of the calculated electron localization function (ELF) and the band structure. Photoluminescence measurements are performed to verify and describe the photophysical properties of [W₆I₁₂(NCC₆H₅)₂]. Finally, the photocatalytic properties of [W₆I₁₂(NCC₆H₅)₂] are evaluated as a proof-of-concept.     

Stable and Storable N(CF3)2 Transfer Reagents

Fluorinated groups are essential for drug design, agrochemicals, and materials science. The bis(trifluoromethyl)amino group is an example of a stable group that has a high potential. While the number of molecules containing perfluoroalkyl, perfluoroalkoxy, and other fluorinated groups is steadily increasing, examples with the N(CF₃)₂ group are rare. One reason is that transfer reagents are scarce and metal-based storable reagents are unknown. Herein, a set of Cu^I and Ag^I bis(trifluoromethyl)amido complexes stabilized by N- and P-donor ligands with unprecedented stability are presented. The complexes are stable solids that can even be manipulated in air for a short time. They are bis(trifluoromethyl)amination reagents as shown by nucleophilic substitution and Sandmeyer reactions. In addition to a series of benzylbis(trifluoromethyl)amines, 2-bis(trifluoromethyl)amino acetate was obtained, which, upon hydrolysis, gives the fluorinated amino acid N,N-bis(trifluoromethyl)glycine.     

Focal Point Evaluation of Energies for Tautomers and Isomers for 3-hydroxy-2-butenamide: Evaluation of Competing Internal Hydrogen Bonds of Types -OH…O=, -OH…N, -NH…O=, and CH…X (X=O and N)

The title compound is a small molecule with many structural variations; it can illustrate a variety of internal hydrogen bonds, among other noncovalent interactions. Here we examine structures displaying hydrogen bonding between carbonyl oxygen and hydroxyl H; between carbonyl oxygen and amino H; hydroxyl H and amino N; hydroxyl O and amino H. We also consider H-bonding in its tautomer 2-oxopropanamide. By extrapolation algorithms applied to Hartree-Fock and correlation energies as estimated in HF, MP2, and CCSD calculations using the cc-pVNZ correlation-consistent basis sets (N = 2, 3, and 4) we obtain reliable relative energies of the isomeric forms. Assuming that such energy differences may be attributed to the presence of the various types of hydrogen bonding, we attempt to infer relative strengths of types of H-bonding. The Atoms in Molecules theory of Bader and the Local Vibrational Modes analysis of Cremer and Kraka are applied to this task. Hydrogen bonds are ranked by relative strength as measured by local stretching force constants, with the stronger =O…HO- > NH…O= > -OH…N well separated from a cluster > NH…O= ≈ >NH…OH ≈ CH…O= of comparable and intermediate strength. Weaker but still significant interactions are of type CH…N which is stronger than CH…OH.