Extracting S-matrix poles for resonances from numerical scattering data: Type-II Pade reconstruction

We present a FORTRAN 77 code for evaluation of resonance pole positions and residues of a numerical scattering matrix element in the complex energy (CE) as well as in the complex angular momentum (CAM) planes. Analytical continuation of the S-matrix element is performed by constructing a type-II Pade approximant from given physical values (Bessis et al. (1994) [421: Vrinceanu et al. (2000) [24]; Sokolovski and Msezane (2004) [23]). The algorithm involves iterative 'preconditioning' of the numerical data by extracting its rapidly oscillating potential phase component. The code has the capability of adding non-analytical noise to the numerical data in order to select 'true' physical poles, investigate their stability and evaluate the accuracy of the reconstruction. It has an option of employing multiple-precision (MPFUN) package (Bailey (1993) [451) developed by D.H. Bailey wherever double precision calculations fail due to a large number of input partial waves (energies) involved. The code has been successfully tested on several models, as well as the F + H-2 -> HE + H, F + HD : HE + D, Cl + HCI CIH + Cl and H + D-2 -> HD + D reactions. Some detailed examples are given in the text.

An efficient Cu(II)-bis(oxazoline)-based polymer immobilised ionic liquid phase catalyst for asymmetric carbon–carbon bond formation

The asymmetric Diels-Alder reaction between N-acryloyloxazolidinone and cyclopentadiene and the Mukaiyama-aldol reaction between methylpyruvate and 1-phenyl-1-trimethylsilyloxyethene have been catalysed by heterogeneous copper(II)-bis(oxazoline)-based polymer immobilised ionic liquid phase (PIILP) systems generated from a range of linear and cross linked ionic polymers. In both reactions selectivity and ee were strongly influenced by the choice of polymer. A comparison of the performance of a range of Cu(II)-bis(oxazoline)-PIILP catalyst systems against analogous supported ionic liquid phase (SILP) heterogeneous catalysts as well as their homogeneous counterparts has been undertaken and their relative merits evaluated.