Alfréd Rényi

Probability Theory and Related Fields -     

Thetafunktionen und multiplikative automorphe Funktionen zu vorgegebenen Divisoren in komplexen Räumen

Ohne Zusammenfassung     

Nucleophilic Reactions at Tertiary Carbon. Part 2. σ- and π-routes to the 8-hydrindanyl cation

Stereoisomeric ion pairs are implicated as intermediates in the solvolysis of cis and trans-8-hydrindanyl chloride 3 , whereas 4-(cyclopenten-1-yl)butyl tosylate 5 appears to cyclize by way of an unsymmetrically solvated 8-hydrindanyl cation. This follows from the solvolysis products and rates of these compounds in aqueous solvents. The rate and equilibrium constants of the chlorides 3 show that the transition state for the trans-isomer is more stable by 0.5 kcal than the one for the cis-isomer. By inference the intermediates differ by a similar amount of energy. Experimental results are not explained satisfactorily by conformationally isomeric 8-hydrindanyl cations, as suggested in the literature.     

Solid-state structures and magnetic properties of halide-bridged, face-to-face bis-nickel(II)-macrocyclic ligand complexes: ligand-mediated interchanges of electronic configuration

Dramatic differences are found between the ambient and 100 K X-ray structures of [L(2)Ni2Br2](ClO4)2 (L(2) = alpha,alpha'-bis{(5,7-dimethyl-1,4,8,11-tetraazacyclotetradeca-6-yl)-o-xylene), in which the bromide-bridged, bimetallic, macrocyclic ligand complexes of nickel(II) are held face-to-face and in which each bimetallic complex has a net triplet spin multiplicity. The ambient structure of this complex consists of very highly ordered, infinite chains of alternating R and S isomers in which the identical Ni(II) coordination spheres are near to the average expected for the high- and low-spin Ni(II) coordination sites, and there is appreciable stereochemical strain in the linkage of the macrocyclic ligands to the phenyl ring. In contrast, every other dinickel complex of the 100 K structure is displaced about 40 pm along the infinite chains to form tetrameric repeat units (pairs of dinickel complexes), in which each dinickel complex has well-defined high-spin and low-spin Ni(II) coordination sites; the high-spin sites are adjacent in the tetramers, and the stereochemical strain in the linkage to the phenyl spacer is relaxed. The molecular magnetic moments and structural contrasts are similar for the 100 K structure and the previously reported ambient structure of [L(2)Ni2Br3](ClO4) complex for which the molecular magnetic moments also correspond to a single triplet state per complex. The halide-bridged, monochloro- and monobromo dinickel complexes also have triplet spin multiplicity, and they crystallize with a coordinated perchlorate completing the axial coordination of the high-spin Ni(II) site, while the other Ni(II) site of these halide-bridged complexes has equatorial Ni-N bond lengths typical of low-spin Ni(II) coordination. The bridging halide is sandwiched between the face-to-face macrocyclic ligand Ni(II) moieties and slightly off the Ni-Ni axis in all of the complexes. The temperature dependence of the magnetic moments of the series of complexes indicates that their singlet-triplet energy gaps are small, with zero point energy differences that are generally less than 10(3) cm(-1). The very weak metal-metal electronic coupling, the triplet state spin multiplicity of each dinickel complex, and the averaged high-spin/low-spin coordination environments of the ambient structure implicate a vibronic mechanism for the electronic configurational exchange in the dibromo and tribromo complexes. The single molecular vibrational mode that correlates with the configurational exchange in these complexes includes the concerted motion of the bridging bromide between the Ni(II) centers. Activation of this vibrational mode is sufficient to effect the configurational exchange. These complexes present especially clear examples of the effects of the coupling of nuclear vibrational motions to the interchange of electronic configuration between two different centers.