ORGANOSTANNOXANE MOTIFS IN CAGES AND SUPRAMOLECULAR ARCHITECTURES

The reactions of n-butyl stannonic acid with(PhO) ₂ P(O)H leads to the formation of a hexameric tin cage [{(n-BuSn) ₃ (PhO) ₃ O} ₂ {HPO ₃ } ₄ ].This reaction involves an in situ P─O bond cleavage and the generation of a [HPO ₃ ] ^2? ion. A direct reaction of six equivalents of n-BuSnO(OH) acid with six equivalents of C ₆ H ₅ OH and four equivalents of H ₃ PO ₃ also leads to the formation of same cage structure. A tetranuclear organooxotin cage[(PhCH ₂ ) ₂ Sn ₂ O(O ₂ P(OH)-t-Bu) ₄ ] ₂ has been assembled by debenzylation involving the reaction of (PhCH ₂ ) ₂ SnCl ₂ ,(PhCH ₂ ) ₂ SnO·H ₂ O or (PhCH ₂ ) ₃ SnCl with two equivalents of t-BuP(O)OH ₂ . A half-cage intermediate [(PhCH ₂ ) ₂ Sn ₂ O(O ₂ P(OH)-t-Bu) ₄ ] has been detected. New organotin cations of the type [n-Bu ₂ Sn(H ₂ O) ₄ ] ²⁺[2,5-Me ₂ -C ₆ H ₃ SO ₃ ]^? ₂ and {[n-Bu ₂ Sn(H ₂ O) ₃ LSn(H ₂ O) ₃ (n-Bu) ₂ ] ²⁺[1,5-(SO ₃ ) ₂ -C ₁₀ H ₆ ] ^2?} have been obtained in the reactions of n-Bu ₂ SnO or (n-Bu ₃ Sn) ₃ O with 2,5-dimethyl sulfonic acid and 1,5-naphthalene disulfonic acid respectively. These organotin cations form interesting supramolecular structures in the solid state as a result of O─H─···O hydrogen bonding.     

A family of regular graphs of girth 5

Murty [A generalization of the Hoffman-Singleton graph, Ars Combin. 7 (1979) 191-193.] constructed a family of (p^m+2)-regular graphs of girth five and order 2p^2m, where p?5 is a prime, which includes the Hoffman-Singleton graph [A.J. Hoffman, R.R. Singleton, On Moore graphs with diameters 2 and 3, IBM J. (1960) 497-504]. This construction gives an upper bound for the least number f(k) of vertices of a k-regular graph with girth 5. In this paper, we extend the Murty construction to k-regular graphs with girth 5, for each k. In particular, we obtain new upper bounds for f(k), k?16.     

On the girth of extremal graphs without shortest cycles

Let EX(ν;{C₃,…,C_n}) denote the set of graphs G of order ν that contain no cycles of length less than or equal to n which have maximum number of edges. In this paper we consider a problem posed by several authors: does G contain an n+1 cycle? We prove that the diameter of G is at most n−1, and present several results concerning the above question: the girth of G is g=n+1 if (i) ν≥n+5, diameter equal to n−1 and minimum degree at least 3; (ii) ν≥12, ν∉{15,80,170} and n=6. Moreover, if ν=15 we find an extremal graph of girth 8 obtained from a 3-regular complete bipartite graph subdividing its edges. (iii) We prove that if ν≥2n−3 and n≥7 the girth is at most 2n−5. We also show that the answer to the question is negative for ν≤n+1+⌊(n−2)/2⌋.     

New families of graphs without short cycles and large size

We denote by ex(n;{C₃,C₄,…,C_s}) or f_s(n) the maximum number of edges in a graph of order n and girth at least s+1. First we give a method to transform an n-vertex graph of girth g into a graph of girth at least g−1 on fewer vertices. For an infinite sequence of values of n and s∈{4,6,10} the obtained graphs are denser than the known constructions of graphs of the same girth s+1. We also give another different construction of dense graphs for an infinite sequence of values of n and s∈{7,11}. These two methods improve the known lower bounds on f_s(n) for s∈{4,6,7,10,11} which were obtained using different algorithms. Finally, to know how good are our results, we have proved that for s∈{5,7,11}, and for s∈{6,10}.     

Combining Imine Condensation Chemistry with [3,3] Diaza-Cope Rearrangement for One-Step Formation of Hydrolytically Stable Chiral Architectures

Dynamic covalent chemistry (DCC) has, in recent years, provided valuable tools to synthesize molecular architectures of increasing complexity. We have also taken advantage of imine DCC chemistry to prepare TPMA -based supramolecular cages for molecular recognition applications. However, the versatility of this approach has as a major drawback the intrinsic hydrolytic lability of imines, which hampers some applications. We present herein a synthetic strategy that combines the advantages of a thermodynamic-driven formation of a supramolecular structure using imine chemistry, together with the possibility to synthetize chiral hydrolytically stable structures through a [3,3]-sigmatropic rearrangement. A preliminary mechanistic analysis of this one-pot synthesis and the scope of the reaction are also discussed.     

Synergistic Metal-Nonmetal Active Sites in a Metal-Organic Cage for Efficient Photocatalytic Synthesis of Hydrogen Peroxide in Pure Water

Photocatalytic synthesis of hydrogen peroxide (H₂O₂) is a potential clean method, but the long distance between the oxidation and reduction sites in photocatalysts hinders the rapid transfer of photogenerated charges, limiting the improvement of its performance. Here, a metal-organic cage photocatalyst, Co₁₄(L−CH₃)₂₄ , is constructed by directly coordinating metal sites (Co sites) used for the O₂ reduction reaction (ORR) with non-metallic sites (imidazole sites of ligands) used for the H₂O oxidation reaction (WOR), which shortens the transport path of photogenerated electrons and holes, and improves the transport efficiency of charges and activity of the photocatalyst. Therefore, it can be used as an efficient photocatalyst with a rate of as high as 146.6 μmol g⁻¹ h⁻¹ for H₂O₂ production under O₂-saturated pure water without sacrificial agents. Significantly, the combination of photocatalytic experiments and theoretical calculations proves that the functionalized modification of ligands is more conducive to adsorbing key intermediates (*OH for WOR and *HOOH for ORR), resulting in better performance. This work proposed a new catalytic strategy for the first time; i.e., to build a synergistic metal-nonmetal active site in the crystalline catalyst and use the host–guest chemistry inherent in the metal-organic cage (MOC)to increase the contact between the substrate and the catalytically active site, and finally achieve efficient photocatalytic H₂O₂ synthesis.     

Selective Encapsulation and Chiral Induction of C60 and C70 Fullerenes by Axially Chiral Porous Aromatic Cages

Chiral induction has been an important topic in chemistry, not only for its relevance in understanding the mysterious phenomenon of spontaneous symmetry breaking in nature but also due to its critical implications in medicine and the chiral industry. The induced chirality of fullerenes by host–guest interactions has been rarely reported, mainly attributed to their chiral resistance from high symmetry and challenges in their accessibility. Herein, we report two new pairs of chiral porous aromatic cages (PAC), R- PAC-2 , S- PAC-2 (with Br substituents) and R- PAC-3 , S- PAC-3 (with CH₃ substituents) enantiomers. PAC-2 , rather than PAC-3 , achieves fullerene encapsulation and selective binding of C₇₀ over C₆₀ in fullerene carbon soot. More significantly, the occurrence of chiral induction between R- PAC-2 , S- PAC-2 and fullerenes is confirmed by single-crystal X-ray diffraction and the intense CD signal within the absorption region of fullerenes. DFT calculations reveal the contribution of electrostatic effects originating from face-to-face arene-fullerene interactions dominate C₇₀ selectivity and elucidate the substituent effect on fullerene encapsulation. The disturbance from the differential interactions between fullerene and surrounding chiral cages on the intrinsic highly symmetric electronic structure of fullerene could be the primary reason accounting for the induced chirality of fullerene.     

Nanometer Channels and Cages within the Extended Basic Mercurous Cations [(Hg2)3(OH)2]4+ and [(Hg2)2O]2+

The two‐ and three‐dimensional mercurous cations [(Hg₂)₃(OH)₂]⁴⁺ and [(Hg₂)₂O]²⁺ crystallize with channels and cages of roughly 1 nm diameter from aqueous solutions dependent upon the acidity of the solution. Crystal structures were determined, for example, for [Zn(H₂O)₆][(Hg₂)₃(OH)₂](NO₃)₆ (trigonal, space group P321, a = 1183.5(2) pm, c = 534.8(1) pm, Z = 1, R1 = 0.0351 for I₀ > 2σ(I₀)) and for [(Hg₂)₂O][Pb(NO₃)₃]₂ (cubic, space group , a = 1543.1(2) pm, Z = 8, R1 = 0.0534 I₀ > 2σ(I₀)).