4类图完美匹配数目的递推求法

本文研究了4类特殊图完美匹配数目的显式表达式.利用划分,求和,再递推的方法分别给出了图3-n Z4,2-n(2-C6),2-n(2-K4)和3-n(C4-C6)的完美匹配数目的计算公式.     

Zethrene and Dibenzozethrene: Masked Biradical Molecules?

The syntheses, structures, and physical properties of dibenzozethrenes were explored. The results thus obtained were compared with those for zethrenes. Dibenzozethrenes were synthesized by the nickel‐catalyzed cyclodimerization of 9‐ethynyl‐1‐iodoanthracenes. The substituents in zethrene and dibenzozethrene twisted their backbones, and remarkably influenced their properties. Unlike closed‐shell disubstituted derivatives, the parent zethrene and dibenzozethrene are singlet open‐shell biradicals, which were studied by variable‐temperature ¹H NMR, ESR, SQUID and computational methods. Since substituents were observed to affect significantly the biradical properties, the relevant mechanisms were analyzed. The nonlinear optical performance of each of these compounds depends on its π‐conjugation and biradical properties. Dibenzozethrenes have larger two‐photon absorption cross‐sections than zethrenes, as most strongly evidenced by the parent dibenzothrene [σ_max=4323 GM at 530 nm].     

Synthesis,Characterization and Biological Evaluation of Two Silver(I) trans‐Cinnamate Complexes as Urease Inhibitors

Two new silver(I) trans‐cinnamates, namely [Ag(2‐cca)(H₂O)]₂ ( 1 ) and [Ag(4‐cca)]_n ( 2 ) (2‐ccaH = 2‐chlorocinnamic acid and 4‐ccaH = 4‐chlorocinnamic acid), were synthesized and structurally characterized. Single crystal X‐ray studies reveal that each silver(I) atom in 1 is two‐coordinate by a 2‐chlorocinnamate ligand and one water molecule to afford a discrete centrosymmetric dimer with the ligand‐unsupported Ag···Ag interactions (3.218(4) Å), while a pair of symmetry‐related silver(I) atoms in 2 are clamped by two μ₂‐η¹:η¹ 4‐chlorocinnamate ligands to yield a binuclear silver(I) moiety incorporating a ligand‐supported Ag···Ag interaction (2.819(5) Å). Both complexes 1 and 2 show potent urease inhibitory activities with the respective IC₅₀ values of 0.66 and 1.10 μM.     

A New Tricarboxylate‐Terbium(III) Compound: Synthesis,Structure, and Luminescent Property

The Tb^III compound [Tb(tci)(H₂O)]_n · n(DMF) ( 1 ) [H₃tci = tri(2‐carboxythyl)isocyanurate, DMF = N,N′‐dimethylformamide] was synthesized by the reaction of terbium oxide, H₃tci, and two drops of concentrated nitric acid in the presence of DMF and H₂O. Single crystal X‐ray analysis reveals that it features a three‐dimensional (3D) framework based on infinite –Tb–COO–Tb– chains. The tci ligand in 1 links six different Tb^III ions with its two carboxylate groups in μ₂‐κ¹O;κ²O,O′ mode and the third in μ₂‐κ¹O;κ¹O′ mode. Thermal analysis reveals that it remains high thermal stability until 390 °C. Luminescence investigation shows that it emits characteristic green light of Tb^III ions.     

One‐Pot Synthesis of Highly Substituted Polyheteroaromatic Compounds by Rhodium(III)‐Catalyzed Multiple C?H Activation and Annulation

A new method for the synthesis of highly substituted naphthyridine‐based polyheteroaromatic compounds in high yields proceeds through rhodium(III)‐catalyzed multiple C H bond cleavage and C C and C N bond formation in a one‐pot process. Such highly substituted polyheteroaromatic compounds have attracted much attention because of their unique π‐conjugation, which make them suitable materials for organic semiconductors and luminescent materials. Furthermore, a possible mechanism, which involves multiple chelation‐assisted ortho C H activation, alkyne insertion, and reductive elimination, is proposed for this transformation.     

Synthesis,Structure, Photoluminescence,and Theoretical ­Calculation of an rtl‐type Zinc(II) Compound with Linear Trinuclear [Zn3(COO)4(μ2‐H2O)2] Subunits

The zinc(II) coordination polymer [Zn₃(BPT)₂(μ₂‐H₂O)₂(H₂O)₂]_n · n(DMA) ( 1 ) (H₃BPT = biphenyl‐3,4′,5‐tricarboxylic acid, DMA = N,N′‐dimethylactamide) was obtained by the solvothermal reaction of H₃BPT with Zn(NO₃)₂ in DMA/H₂O mixed solvent. Single crystal X‐ray analysis reveals that compound 1 has a complicated 3D framework containing linear trinuclear [Zn₃(COO)₄(μ₂‐H₂O)₂] clusters as building subunits, which can be simplified into a (3,6)‐connected rtl topological network with the Schläfli symbol {4.6²}₂{4².6¹⁰.8³}. The calculated results of total and partial density of states (DOS) indicate that the luminescence of 1 mainly originates from intraligand charge transfer.     

The synthesis of 1,2-diarylindenes via DDQ-mediated dehydrogenative intramolecular cyclization

A direct DDQ-mediated dehydrogenative intramolecular cyclization of (Z)-1,2,3-triaryl substituted propylenes promoted by Cu(OAc)₂ was developed, providing 1,2-diarylindene derivatives in moderate to good yields (up to 92%) under mild conditions. This protocol provides a straightforward access to 1,2-diarylindenes via DDQ-mediated benzylic/allylic sp³ C–H bond activation.