Higher-order <Emphasis Type="Bold">?</Emphasis> corrections in the semiclassical quantization of chaotic billiards

In the periodic orbit quantization of physical systems, usually only the leading-order ? contribution to the density of states is considered. Therefore, by construction, the eigenvalues following from semiclassical trace formulae generally agree with the exact quantum ones only to lowest order of ?. In different theoretical work the trace formulae have been extended to higher orders of ?. The problem remains, however, how to actually calculate eigenvalues from the extended trace formulae since, even with ? corrections included, the periodic orbit sums still do not converge in the physical domain. For lowest-order semiclassical trace formulae the convergence problem can be elegantly, and universally, circumvented by application of the technique of harmonic inversion. In this paper we show how, for general scaling chaotic systems, also higher-order ? corrections to the Gutzwiller formula can be included in the harmonic inversion scheme, and demonstrate that corrected semiclassical eigenvalues can be calculated despite the convergence problem. The method is applied to the open three-disk scattering system, as a prototype of a chaotic system. Received 10 September 2001 and Received in final form 3 January 2002     

Hydrogenic Rydberg atoms in strong magnetic fields: Theoretical and experimental spectra in the transition region from regularity to irregularity

For deuterium Rydberg atoms in a magnetic field of ～6 T we compare the complete experimental spectrum in the range ?190 cm^?1 to ?20 cm^?1 with the positions and oscillator strengths of the corresponding quantum theoretically calculated photoabsorption lines. The agreement is excellent. The range of energy covered extends from the end of thel-mixing regime up to the regions where the approximate integrability of the problem is completely lost, and the corresponding classical system undergoes a transition to chaos.     

Accurate pKa determination for a heterogeneous group of organic molecules.

Single-molecule studies that allow to compute pKa values, proton affinities (gas-phase acidity/basicity) and the electrostatic energy of solvation have been performed for a heterogeneous set of 26 organic compounds. Quantum mechanical density functional theory (DFT) using the Becke-half&half and B3LYP functionals on optimized molecular geometries have been carried out to investigate the energetics of gas-phase protonation. The electrostatic contribution to the solvation energies of protonated and deprotonated compounds were calculated by solving the Poisson equation using atomic charges generated by fitting the electrostatic potential derived from the molecular wave functions in vacuum. The combination of gas-phase and electrostatic solvation energies by means of the thermodynamic cycle enabled us to compute pKa values for the 26 compounds, which cover six distinct chemical groups (carboxylic acids, benzoic acids, phenols, imides, pyridines and imidazoles). The computational procedure for determining pKa values is accurate and transferable with a root-mean-square deviation of 0.53 and 0.57 pKa units and a maximum error of 1.0 pKa and 1.3 pKa units for Becke-half&half and B3LYP DFT functionals, respectively.     

Digests or extracts?—Some interesting but conflicting results for three widely differing polluted sediment samples

Three sets of samples have been investigated in some detail. One set is from a river polluted by mine workings, containing substantial levels of Fe, Mn,Cu, Zn and Ni with traces of many other metals. The second set consists of typical estuarine sediments contaminated from a wide range of industrial sources, and the third set consists of oily drilling cuttings from the sea bottom in the vicinity of a North Sea oil production platform.These samples have been subjected to treatment 1) with EDTA at two different pH's (extracts) 2) with HNO₃/H₂O₂ 3) with HNO₃/HCl and 4) with HNO₃/HCl/HF (digests). EDTA recoveries, compared toaqua regia digests, are often very reproducible, not dependent on pH, and usually significantly low. Nitric/peroxide andaqua regia digests often give very close results suggesting that these are meaningful values indicating the maximum levels of polluting metals in the sediments. However, the triple acid digest with HF does sometimes give higher values (and reasonable agreement for CRM's such as MESS-1) but with poorer reproducibility.     

Determination of metal ions by liquid chromatographic separation of their 2-acetylpyridine-4-ethyl-3-thiosemicarbazone chelates

A new thiosemicarbazone was prepared, characterized, and used as a complexing reagent for the chromatographic separation and determination of metal complexes by reverse-phase HPLC. The reagent was sufficiently soluble in methanol-water solutions for metal ions to be complexed in this aqueous organic phase, without need for extraction. Many variables affected the retention times of the metal complexes. Several metals were determined selectively by complexation with the reagent and chromatographic separation of the complexes. Interference effects from other metal ions were also investigated.