Extended Hückel calculations of the ionization potentials of some conjugated hydrocarbons

The prediction of ionization potentials of conjugated hydrocarbons using extended Hückel theory is reevaluated. Consequently, two major modifications to the theory are proposed and then tested on five sample molecules. Allowance for distinct sigma and pi orbital parameters as well as for diagonal and off-diagonal parameters constitute the changes examined and are shown to arise naturally from the theory. Subsequent testing of the reproduction of photoelectron spectra indicates significant improvements over previous usage of extended Hückel theory.     

Properties of a single vortex solution in a rotating Bose Einstein condensate

In this Note, we study the properties of the line energy for a vortex γ in a Bose Einstein condensate rotating at velocity $\text{Ω}$. The global minimizer is either the vortex free solution or U vortices which exist only for $\text{Ω}$ bigger than a critical value. For all values of $\text{Ω}$, we prove the existence of an S type vortex, which is a critical point of the line energy, observed in the experiments. We also prove uniqueness of the minimizer for almost every $\text{Ω}$ and a monotonicity property of the curve γ with respect to $\text{Ω}$. The proofs rely on a related isoperimetric problem. To cite this article: A. Aftalion, R.L. Jerrard, C. R. Acad. Sci. Paris, Ser. I 336 (2003).