Assignment of the 15N resonances of the antifungal agent posaconazole

The structurally complex antifungal agent posaconazole has been well characterized by conventional ¹H‐ and ¹³C‐NMR studies. In contrast, ¹⁵N resonance assignments have never been reported. We now wish to report the assignment of the eight ¹⁵N resonances of posaconazole using two‐dimensional long‐range ¹H‐¹⁵N GHMBCAD NMR data. The ¹⁵N resonance assignments were undertaken to facilitate the evaluation of the impact of ¹H‐¹⁵N heteronuclear shift correlation data in the Computer‐Assisted Structure Elucidation (CASE) of complex molecular structures. J. Heterocyclic Chem., (2011).     

A generalization of Plantholt's theorem

Let K denote the complete graph K_2n+1 with each edge replicated r times and let χ′(G) denote the chromatic index of a multigraph G. A multigraph G is critical if χ′(G) > χ′(G/e) for each edge e of G. Let S be a set of sn – 1 edges of K. We show that, for 0 < s ≦ r, G/S is critical and that χ′ (G/(S ∪{e})) = 2rn + r – s for all e ∈ E(G/S). Plantholt [M. Plantholt, The chromatic index of graphs with a spanning star. J. Graph Theory 5 (1981) 5–13] proved this result in the case when r = 1.     

Controlling the Scholl reaction

Guidelines for the application of the Scholl reaction were developed. Labeling experiments demonstrate that the Scholl reaction fails in small, unsubstituted oligophenylenes (e.g., o-terphenyl) due to oligomerization of the products (e.g., triphenylene). Incorporation of suitably placed blocking groups (e.g., t-butyl) suppresses oligomerization. The well-established directing group effects in electrophilic aromatic substitution predict the outcome of Scholl reactions of substituted substrates. Activating o,p-directing groups (e.g., MeO) direct bond formation o,p, either intramolecularly or intermolecularly. Deactivating o,p-directing groups (e.g., Br) also direct bond formation o,p but yields are lower. Deactivating m-directors (e.g., NO2) suppress reaction. MoCl5 and PhI(OOCCF3)2/BF3.Et2O are general and effective reagents for the Scholl oxidation. Calculations (B3LYP/6-31G(d)) predict the Scholl reaction in alkoxyarenes to proceed via arenium cations, not radical cations. Suzuki-Miyaura couplings were used to generate 12 substituted o-terphenyl derivatives.     

Canonical edge-colourings of locally finite graphs

A variety of results on edge-colourings are proved, the main one being the following: ifG is a graph without loops or multiple edges and with maximum degree Δ=Δ(G), and if ν is a given integer 1≦ν≦Δ(G), thenG can be given a proper edge-colouring with the coloursc ₁, ...,c _Δ+1 with the additional property that any edge colouredc _μ with μ≧ν is on a vertex which has on it edges coloured with at least ν − 1 ofc ₁, ...,c _v .