S 1 actions and elliptic genera

A proof is given of Witten's conjectures for the rigidity of the index of the Dirac-Ramond operator on the loop space of a spin manifold which admits anS ¹ symmetry.Research supported in part by the National Science Foundation     

Self-organized ZnAl2O4 nanostructures grown on -sapphire

Self-organized ZnAl₂O₄ nanostructures with the appearance (in SEM) of high aspect ratio horizontal nanowires are grown on uncatalysed c-sapphire by vapour phase transport. The nanostructures grow as three equivalent crystallographic variants on c-sapphire. Raman and cathodoluminescence spectroscopy confirm that the nanostructures are not ZnO and TEM shows that they are the cubic spinel, zinc aluminate, ZnAl₂O₄, formed by the reaction of Zn and O with the sapphire substrate.     

Chirospecific Syntheses of Conformationally Constrained 7-Azabicycloheptane Amino Acids by Transannular Alkylation

A new method is reported for the chirospecific preparation of optically pure 1-carboxy-7-azabicycloheptane amino acids for the generation of peptidomimetics as conformational probes. The method allows for the multigram preparation of these amino acid analogues through use of a thiolactam sulfide contraction and a transannular alkylation sequence as the key C-C bond-forming steps, starting from L-glutamic acid. The route provides access to two common intermediates, 7-(benzyloxycarbonyl)-1-carboxy-7-azabicyclo[2.2.1]-3-heptane and (1S,4R)-7-(benzyloxycarbonyl)-1-carboxy-7-azabicyclo[2.2.1]-3-heptanone tert-butyl ester, for elaboration to symmetrical and chiral amino acid homologues, respectively. Decarboxylation of the C-1 carboxy unit of the latter intermediate also demonstrated the applicability of the method for a short, chirospecific preparation of a (+)-epibatidine intermediate, (1S,4R)-7-(tert-butyloxycarbonyl)-1-carboxy-7-azabicyclo[2.2.1]-3-heptanone.     

Some difficulties in the application of the concept of density of states

The problem of defining N(E), the density of states, for molecular systems is discussed. It is shown that a numeric evaluation of N(E) is often only approximate, even for continuous data, and is not well defined for quantized systems. The application of the concept of density of states is discussed, particularly with regard to the RRKM theory of unimolecular reactions. The sum of states, W(E), and density of states curves are evaluated for several harmonic and anharmonic model systems and the results discussed in order to illustrate the foregoing considerations.     

Ground states of molecules. 53.MNDO calculations for molecules containing chlorine

MNDO calculations of heats of formation, dipole moments, ionization potentials, and structures are reported for a wide range of compounds containing chlorine in its characteristic valence state (Cl^I) and one or more of the elements H, B, Be, C, N, O, and F. The calculated errors in the heats of formation and the dipole moments are not significantly greater than those previously reported for compounds containing no chlorine. First vertical ionization potentials were on average 0.95 eV too high. The ordering of higher cationic states was found to be correct, even for species such as Cl₂O, Cl₂, and HOCl, where ab initio–Koopmans' theorem calculations predict the incorrect ordering. The calculated energies and geometries of compounds such as CIF₃ are qualitatively incorrect, probably because of the lack of 3d atomic orbitals in the orbital basis set.     

Approaching the Hartree-Fock limit for organotransition metal complexes

In theoretical studies of the electronic structure of organometallic complexes, the choice of basis set is critical, much more so than for analogous studies of molecules containing only H, C, N, and O. This problem is discussed in the light of structural predictions for the transition metal hydrides MH, MH₂, and MH₄, for the fluorides MF₂ and MF₃, and for Ni(CO)₄, Ni(C₂H₄)₃, (CO)₃NiCH₂, and Ni(C₄H₄)₂.     

Diethyl benzoylphosphonate as a ligand

Summary Complexes (2 : 1) of diethyl benzoylphosphonate (debp) with 3d metal perchlorates were synthesized and characterized by means of i.r. and electronic spectral, magnetic susceptibility and conductance measurements. In new complexes of the types [M(debp)₂(OClO₃)(OH₂)](ClO₄) (M = Fe, Co, Zn) and [Fe(debp)₂(OClO₃)(OH₂)](ClO₄)₂, both debp ligands function as bidentate chelating agents, coordinating through the P=O and C=O oxygens. In contrast, in the manganese(II) and nickel(II) complexes, which are of the [M(debp)₂(OClO₃)(OH₂)₂](ClO₄) type, one debp acts as a bidentate chelating ligand, while the second debp is unidentate, coordinating only through the P=O oxygen. Hexacoordination in the new cationic complexes is completed by coordination of aqua and unidentate perchlorato ligands, which are in competition for sites in the inner coordination sphere of the central metal ion with the weak debp ligand. On the other hand, debp, owing to its bulkiness, and especially the presence of the benzoyl substituent, introduces sufficiently severe steric hindrance during coordination. As a result of this, the formation of [M(debp)₃]ⁿ⁺ tris-chelate cationic complexes with the 3 d metal ions under study does not seem to be possible.