Application of the MC SCF method to the π → π* excitation energies of ethylene

The MC SCF method is employed to calculate the N → T and N → V π → π^* vertical excitation energies of ethylene. To obtain accurate excitation energies it is found to be necessary to utilize an expanded valence space containing two π and two π^* orbitals. Relatively small MC SCF calculations, allowing at most one-electron excitations from the sigma space, are found to yield excitation energies and spatial extents of the excited states in excellent agreement with the predictions of large multi-reference or iterative-natural-orbital CI calculations. These results show that within an MC SCF framework σ-σ correlation is unimportant for describing the π → π^* processes. We also conclude that the neglect of the effects of unlinked cluster terms in some of the CI calculations may have introduced small, but important, errors in the excitation energies and predictions of the spatial extent of the V state.     

Structural studies on 9-hydrazono-6,7,8,9-tetrahydro-4-oxo-4H-pyrido[1,2-a]pyrimidines by 1H, 13C and 15N NMR spectroscopy

¹H, ¹³C and ¹⁵N NMR studies demonstrated that 9-hydrazono-6,7,8,9-tetrahydro-4-oxo-4H-pyrido-[1,2-a] pyrimidlnes exist as an equilibrium mixture of Z-E isomers in the hydrazono–imino tautomeric form having an exocyclic double bond. Proton-catalysed Z-E interconversion is fast. Substituent and solvent effects revealed that the decisive factors controlling the Z:E ratio are internal hydrogen bonding in the Z-isomer, stabilization by solvation and steric interaction.     

Equation de Karplus et l'Hybridation du Carbone. Correlation de la Constante de Couplage Vicinale 3J(Hi,Hj) et la Somme de Constantes de Couplages 1J(C,H)

The vicinal coupling constant ¹H? ¹H exhibits a marked hybridization dependence. The coupling constants ¹³C? ¹H could be used to correlate the Karplus type equation for calculation of ³J(Hi, Hj). The correction term to this equation is proposed.     

Motivic orthogonal two-dimensional representations of Gal(ℚ/ℚ)

Given a two-dimensional compatible family of ℓ-adic representations which is motivic and which respects an orthogonal form up to similitudes, we show how to express itsL-function in terms of a Hecke character. We give several examples and in particular we analyze a representation associated to a certainK3 surface which arose in the study of Kloosterman sums.     

A set of geometric programming test problems and their solutions

This paper attempts to provide a set of standard test examples for researchers working in the area of geometric programming and general nonlinear, continuous, nonconvex programming algorithms. The examples consist partly of applications of nonlinear programming that have appeared in the literature and partly of original geometric programming applications. Solutions to all the problems are provided as well as the starting points from which these solutions were computed. Other computationally important aspects such as tolerances and degree of accuracy with which these problems were solved, are also included.This work was supported in part by Canada Council Grant #S74-0148 and National Research Council of Canada Grant #084-6319-32.     

Investigating the reaction of N-carbobenzoxy-O-carbobenzoxy- hydroxylamine with dimethyl sulfoxide: formation of S,S-dimethyl-N-[(phenylmethoxy)- carbonyl]sulfoximine

[Reaction: see text]. N-carbobenzoxy-O-carbobenzoxyhydroxylamine (1a) underwent a thermally induced reaction in DMSO in which there is net N-alpha-eliminative oxidation with tandem oxidative incorporation of DMSO to yield S,S-dimethyl-N-[(phenylmethoxy)carbonyl]sulfoximine. Mechanisms for the formation of the sulfoximine are presented as well as the product characterizations, including the X-ray crystal structure.     

Molecular recognition in a thermoplastic elastomer

Selective incorporation of bisurea guests in thermoplastic elastomers with poly(tetrahydrofuran) soft blocks and bisurea containing hard blocks is observed when the distances between the urea groups of host and guest match. The incorporation leads to significant modulation of mechanical properties. With bisurea-functionalized dyes as guests, a strong difference in extractability by detergent solution was shown between dyes differing by just one methylene unit between urea groups. Upon elongation of elastomer films, strong differences in alignability of matching and nonmatching dyes were observed.