1,2-diphosphaacenaphthene 1,2-dications: synthetic, stereochemical and computational study of the stabilising role of naphthalene-1,8-diyl backbone

Syntheses and full characterisation data (including single crystal diffraction) of three 1,2‐diphosphonium dicationic species with the naphthalene‐1,8‐diyl (Nap) backbone are reported. The oxidation of Nap[P(NMe₂)₂]₂ with P₂I₄ to its 1,2‐dication was achieved. meso‐ and rac‐forms of “all carbon” 1,2‐diphosphonium dications were obtained in good yields and purity by double alkylation of the parent diphosphine (1,2‐diphenyl‐1,2‐diphosphaacenaphthene) with methyl triflate or trimethyloxonium tetrafluoroborate. Each methylating reagent produces one of the rac‐ or meso‐forms of the dication diastereospecifically. Structural parameters of the new dications are discussed with respect to other phosphorus 1,2‐dications. DFT (B3LYP) computations revealed the significant role of the naphthalene backbone in stabilisation of the dicationic motif and helped to assess the energy cost of the steric clash of a variety of groups attached to the peri‐positions of naphthalene. The synthesis and single crystal X‐ray data of the extremely crowded Nap[P(?Se)(OiPr)₂]₂ are discussed, and are contrasted with the unsuccessful synthesis of Nap(PtBu₂)₂ from NapLi₂ and ClPtBu₂.     

Studies on the synthesis of apoptolidin: synthesis of a C1-C27 fragment of apoptolidin D

Synthesis of a C(1)-C(27) fragment, a key intermediate in the synthesis of apoptolidin D, is reported. The synthesis involves a combination of Heck coupling and Horner-Wadsworth-Emmons reaction for the C(1)-C(7) trienoate portion and an efficient Suzuki cross-coupling protocol for the C(10)-C(13) diene portion.     

On cyclic compositions of positive integers

Say that two compositions of n into k parts are related if they differ only by a cyclic shift. This defines an equivalence relation on the set of such compositions. Let ${\left\langle \begin{array}{c}n \\ k\end{array} \right\rangle}$ denote the number of distinct corresponding equivalence classes, that is, the number of cyclic compositions of n into k parts. We show that the sequence ${\left\langle\begin{array}{c}n \\ k\end{array}\right\rangle}$ is log-concave and prove some results concerning ${\left\langle \begin{array}{c}n \\ k \end{array} \right\rangle}$ modulo two.     

Alternating sign matrices and descending plane partitions

An alternating sign matrix is a square matrix such that (i) all entries are 1, ?1, or 0, (ii) every row and column has sum 1, and (iii) in every row and column the nonzero entries alternate in sign. Striking numerical evidence of a connection between these matrices and the descending plane partitions introduced by Andrews (Invent. Math.53 (1979), 193–225) have been discovered, but attempts to prove the existence of such a connection have been unsuccessful. This evidence, however, did suggest a method of proving the Andrews conjecture on descending plane partitions, which in turn suggested a method of proving the Macdonald conjecture on cyclically symmetric plane partitions (Invent. Math.66 (1982), 73–87). In this paper is a discussion of alternating sign matrices and descending plane partitions, and several conjectures and theorems about them are presented.     

Formation of a pyrazopyrazolone by the pyrolysis of antipyrine diazonium fluoroborate

The pyrolysis of antipyrine 4-dizaonium fluoroborate gave an antipyrylazopyrazopyrazolone instead of the desired 4-fluoroantipyrine. This compound was formed by intermolecular and intramolecular coupling of the diazo compound at elevated temperatures. J. Heterocyclic Chem., 14, 1107 (1977)