A matrix equation for association schemes

Let be a self-dual P-polynomial association scheme. Then there are at most 12 diagonal matricesT such that (PT)³ =I. Moreover, all of the solutions for the classical infinite families of such schemes (including the Hamming scheme) are classified.This work was supported by NSF grant DMS-9400510.     

Evidence of coupled rotational tunnel states of methyl groups of hexamethylbenzene by nuclear magnetic resonance

Two tunneling frequencies were identified for methyl groups in hexamethylbenzene from 4.2 up to 30.9 K by means of the N.M.R. field cycling method. The frequencies were 9.6 ±- 0.4 MHz (A) and 7.9 ±- 0.4 MHz (B) at 4.2 K. The frequency A was almost independent of the temperature whereas the frequency B decreased as the temperature increased, the decrease being a linear function of T³. These facts indicate that the six methyl groups in hexamethylbenzene molecule are not independent but are coupled to one another rather strongly.     

Application of solid-state early-transition metal clusters as catalysts

Metal cluster compounds are expected to be catalysts for new reactions because of synergistic effect of the metal atoms. In solid-state halide clusters and sulfide clusters, metal cluster frameworks are linked in two- or three-dimensions to form a cluster network. Halogen- or sulfur-deficient metal sites in an octahedral metal cluster framework are retained intact and act as catalytically active sites even at high temperatures of 400–700?°C. This review reports recent advances in the development of coordinatively unsaturated metal atoms on solid-state clusters with an octahedral metal framework and their application to organic catalytic reactions.     

Reversible haptotropic shift in zirconocene-hexapentaene complexes

Low-valent zirconocene species reacted with 1,1,6,6-tetraalkyl-1,2,3,4,5-hexapentaenes to form both 1-zirconacyclopent-3-ynes and eta2-pi-coordinated complexes according to the alkyl groups (R) and the existence of the neutral ligand (L). Haptotropic interconvertion between these two complexes was observed. It was proposed that double insertion of isocyanide into the Zr-C bond of 1-zirconacyclopent-3-ynes takes place via the isocyanide adduct of the eta2-pi-complex as an intermediate.     

Synthesis and Structure of a Molybdenum–Cobalt Bimetallic Carbide Cluster [N(PPh3)2][Mo3Co3(μ6-C)(μ-CO)3(CO)15] Bearing Only Carbonyl Ligands

The reaction of a trinuclear cobalt cluster [ClCCo₃(CO)₉] with [Mo(CO)₃(CH₃CN)₃] gave a molybdenum–cobalt bimetallic cluster complex [Mo₃Co₃( ₆-C)(-CO)₃(CO)₁₅]^–. The cluster anion has a carbide-centered Mo₃Co₃ octahedral metal core, where the three molybdenum and three cobalt atoms are placed in facial positions. The six metal atoms are coordinated by only carbonyl ligands. The cluster is suitable for a model of heterogeneous desulfurization catalysts.     

Nuclear quadrupole and magnetic resonance studies of structure and the molecular motion in SYMC6Cl3F3

³⁵Cl and ¹⁹F relaxation time measurements were carried out on symC₆Cl₃F₃. The analyses of the ¹⁹F high-resolution NMR spectra and the ³⁵Cl spin-lattice relaxation time showed that the crystal belongs to a trigonal or a hexagonal crystal system in which the molecules undergo three-fold reorientation about the molecular figure axis with the correlation time τ_c/s=3.42·10^?7 exp(18.2 kJ mol^?1/RT). Temperature dependences of the ³⁵Cl NQR frequency and ¹⁹F spin-lattice relaxation times are such that only a minor structural change is associated with the phase transition at 296 K.     

Nucleus-electron model for states changing from a liquid metal to a plasma and the Saha equation

We extend the quantal hypernetted-chain (QHNC) method, which has been proved to yield accurate results for liquid metals, to treat a partially ionized plasma. In a plasma, the electrons change from a quantum to a classical fluid gradually with increasing temperature; the QHNC method applied to the electron gas is in fact able to provide the electron-electron correlation at an arbitrary temperature. As an illustrating example of this approach, we investigate how liquid rubidium becomes a plasma by increasing the temperature from 0 to 30 eV at a fixed normal ion density 1.03x10(22)/cm(3). The electron-ion radial distribution function (RDF) in liquid Rb has distinct inner-core and outer-core parts. Even at a temperature of 1 eV, this clear distinction remains as a characteristic of a liquid metal. At a temperature of 3 eV, this distinction disappears, and rubidium becomes a plasma with the ionization 1.21. The temperature variations of bound levels in each ion and the average ionization are calculated in Rb plasmas at the same time. Using the density-functional theory, we also derive the Saha equation applicable even to a high-density plasma at low temperatures. The QHNC method provides a procedure to solve this Saha equation with ease by using a recursive formula; the charge population of differently ionized species are obtained in Rb plasmas at several temperatures. In this way, it is shown that, with the atomic number as the only input, the QHNC method produces the average ionization, the electron-ion and ion-ion RDF's, and the charge population that are consistent with the atomic structure of each ion for a partially ionized plasma.     

Phase relations of tetramethylsilane under pressure

By means of a high pressure d.t.a. method, a new crystalline phase of tetramethylsilane which forms below its melting point has been observed at pressures above 20 MPa. This is a verification of the prediction from earlier calorimetric data at ordinary pressures.