Miklós–Manickam–Singhi conjectures on partial geometries

In this paper we give a proof of the Miklós–Manickam–Singhi (MMS) conjecture for some partial geometries. Specifically, we give a condition on partial geometries which implies that the MMS conjecture holds. Further, several specific partial geometries that are counterexamples to the conjecture are described.     

Efficient charge transport along phenylene-vinylene molecular wires

We have studied the motion of charge carriers along isolated phenylene-vinylene (PV) chains using a combination of experimental and theoretical methods. The conductive properties of positive charges along PV chains in dilute solution were studied by using the pulse-radiolysis time-resolved microwave conductivity (TRMC) technique. This technique enables the measurement of high-frequency (tens of GHz) charge carrier mobilities along isolated PV chains without the use of electrodes. The charge carrier mobility along PV chains with finite and infinite length was studied theoretically by charge transport simulations with parameters from density functional theory (DFT) calculations. The high-frequency charge carrier mobility is found to depend strongly on the conjugation length of the PV chains and is found to increase both with increasing length of the PV chain and with increasing conjugation fraction. The experimental results are in good agreement with the calculated results. On the basis of this combined experimental and theoretical study an intrachain charge carrier mobility of a few tens of cm2/Vs is expected for an infinitely long PV chain without conjugation breaks.     

Efficient CO2 Insertion and Reduction Catalyzed by a Terminal Zinc Hydride Complex

The terminal zinc hydride complex [Tntm]ZnH ( 2 ; Tntm=tris(6‐tert‐butyl‐3‐thiopyridazinyl)methanide) is an efficient hydrosilylation catalyst of CO₂ at room temperature without the need of Lewis acidic additives. The inherent electrophilicity of the system leads to selective formation of the monosilylated product (MeO)₃SiO₂CH (at room temperature with a TOF of 22.2 h^?1 and at 45 °C with a TOF of 66.7 h^?1). In absence of silanes, the intermediate formate complex [Tntm]Zn(O₂CH) ( 3 ) is quantitatively formed within 5 min. All complexes were fully characterized by ¹H and ¹³C NMR spectroscopy and single‐crystal X‐ray diffraction analyses. Density functional theory (DFT) calculations reveal a high positive charge on zinc and the increased preference of the ligand to adopt a κ³‐coordination mode.     

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Thiamorphinans. I

The present paper deals with the synthesis of 5,5a,6,7,8,9-hexahydro-5,9a-iminoethano-4H-naphtho[2,1-b] -thiophenes (I) as derivatives of the first of three novel isomeric S-heterocycles with morphinan-like structure (“thiamorphinans”).