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Bis[(2-diphenylphosphino)phenyl]mercury: a P-donor ligand and precursor to mixed metal-mercury (d(8)-d(10)) cyclometalated complexes containing 2-C(6)H(4)PPh(2)

Treatment of HgCl(2) with 2-LiC(6)H(4)PPh(2) gives [Hg(2-C(6)H(4)PPh(2))(2)] (1), whose phosphorus atoms take up oxygen, sulfur, and borane to give the compounds [Hg[2-C(6)H(4)P(X)Ph(2)](2)] [ X = O (3), S (4), and BH(3) (5)], respectively. Compound 1 functions as a bidentate ligand of wide, variable bite angle that can span either cis or trans coordination sites in a planar complex. Representative complexes include [HgX(2) x 1] [X = Cl (6a), Br (6b)], cis-[PtX(2) x 1] [X = Cl (cis-7), Me (9), Ph (10)], and trans-[MX(2) x 1] [X = Cl, M = Pt (trans-7), Pd (8), Ni (11); X = NCS, M = Ni (13)] in which the central metal ions are in either tetrahedral (6a,b) or planar (7-11, 13) coordination. The trans disposition of 1 in complexes trans-7, 8, and 11 imposes close metal-mercury contacts [2.8339(7), 2.8797(8), and 2.756(8) A, respectively] that are suggestive of a donor-acceptor interaction, M --> Hg. Prolonged heating of 1 with [PtCl(2)(cod)] gives the binuclear cyclometalated complex [(eta(2)-2-C(6)H(4)PPh(2))Pt(mu-2-C(6)H(4)PPh(2))(2)HgCl] (14) from which the salt [(eta(2)-2-C(6)H(4)PPh(2))Pt(mu-2-C(6)H(4)PPh(2))(2)Hg]PF(6) (15) is derived by treatment with AgPF(6). In 14 and 15, the mu-C(6)H(4)PPh(2) groups adopt a head-to-tail arrangement, and the Pt-Hg separation in 14, 3.1335(5) A, is in the range expected for a weak metallophilic interaction. A similar arrangement of bridging groups is found in [Cl((n)Bu(3)P)Pd(mu-C(6)H(4)PPh(2))(2)HgCl] (16), which is formed by heating 1 with [PdCl(2)(P(n)()Bu(3))(2)]. Reaction of 1 with [Pd(dba)(2)] [dba = dibenzylideneacetone] at room temperature gives [Pd(1)(2)] (19) which, in air, forms a trigonal planar palladium(0) complex 20 containing bidentate 1 and the monodentate phosphine-phosphine oxide ligand [Hg(2-C(6)H(4)PPh(2))[2-C(6)H(4)P(O)Ph(2)]]. On heating, 19 eliminates Pd and Hg, and the C-C coupled product 2-Ph(2)PC(6)H(4)C(6)H(4)PPh(2)-2 (18) is formed by reductive elimination. In contrast, 1 reacts with platinum(0) complexes to give a bis(aryl)platinum(II) species formulated as [Pt(eta(1)-C-2-C(6)H(4)PPh(2))(eta(2)-2-C(6)H(4)PPh(2))(eta(1)-P-1)]. Crystal data are as follows. Compound 3: monoclinic, P2(1)/n, with a = 11.331(3) A, b = 9.381(2) A, c = 14.516 A, beta = 98.30(2) degrees, and Z = 2. Compound 6b x 2CH(2)Cl(2): triclinic, P macro 1, with a = 12.720(3) A, b = 13.154(3) A, c = 12.724(2) A, alpha = 92.01(2) degrees, beta = 109.19(2) degrees, gamma = 90.82(2) degrees, and Z = 2. Compound trans-7 x 2CH(2)Cl(2): orthorhombic, Pbca, with a = 19.805(3) A, b = 8.532(4) A, c = 23.076(2) A, and Z = 4. Compound 11 x 2CH(2)Cl(2): orthorhombic, Pbca, with a = 19.455(3) A, b = 8.496(5) A, c = 22.858(3) A, and Z = 4. Compound 14: monoclinic, P2(1)/c, with a = 13.150(3) A, b = 12.912(6) A, c = 26.724(2) A, beta = 94.09(1) degrees, and Z = 4. Compound 20 x C(6)H(5)CH(3).0.5CH(2)Cl(2): triclinic, P macro 1, with a = 13.199(1) A, b = 15.273(2) A, c = 17.850(1) A, alpha = 93.830(7), beta = 93.664(6), gamma = 104.378(7) degrees, and Z = 2.     

Small surface trades in triangular embeddings

We enumerate all possible trades which involve up to six faces of the face set of a triangular embedding of a simple connected graph. These are classified by the underlying combinatorial trade on the associated block design, and by the geometrical arrangement of the faces necessary to avoid creation of a pseudosurface in the trading operation. The relationship of each of these trades to surface orientability is also established.     

Test groups and effect algebras

A test group is a pair (G, T) whereG is a partially ordered Abelian group andT is a generative antichain in its positive cone. It is shown here that effect algebras and algebraic test groups are coextensive, and a method for calculating the algebraic closure of a test group is developed. Some computational algorithms for studying finite effect algebras are introduced, and the problem of finding quotients of effect algebras is discussed.     

Lines,Trees, and Branch Spaces

In this paper we examine the interactions between the topology of certain linearly ordered topological spaces (LOTS) and the properties of trees in whose branch spaces they embed. As one example of the interaction between ordered spaces and trees, we characterize hereditary ultraparacompactness in a LOTS (or GO-space) X in terms of the possibility of embedding the space X in the branch space of a certain kind of tree.