Multireference spin-adapted variant of density functional theory

A new Kohn-Sham formalism is developed for studying the lowest molecular electronic states of given space and spin symmetry whose densities are represented by weighted sums of several reference configurations. Unlike standard spin-density functional theory, the new formalism uses total spin conserving spin-density operators and spin-invariant density matrices so that the method is fully spin-adapted and solves the so-called spin-symmetry dilemma. The formalism permits the use of an arbitrary set of reference (noninteracting) configurations with any number of open shells. It is shown that the requirement of degeneracy of the total noninteracting energies of the reference configurations (or configuration state functions) is equivalent to the stationary condition of the exact energy relative to the weights of the configurations (or configuration state functions). Consequently, at any molecular geometry, the weights can be determined by minimization of the energy, and, for given reference weights, the Kohn-Sham orbitals can be determined. From this viewpoint, the developed theory can be interpreted as an analog of the multiconfiguration self-consistent field approach within density functional theory.     

Determination of stainless steel constituents in plastics

Summary Instrumental neutron activation analysis (INAA), atomic absorption spectrometry (AAS), and X-ray fluorescence analysis (XRF) were tested for the determination of the abrasion effect in plastics processing equipment. As optimal solution measurement of Fe by XRF in cylindrical samples was found.     

Thin-layer chromatography combined with diode laser desorption/atmospheric pressure chemical ionization mass spectrometry

The desorption of an analyte by a continuous wave diode laser from a porous surface of a thin-layer plate covered with a graphite suspension is presented. The thermally desorbed analyte molecules are ionized in the gas phase by a corona discharge at atmospheric pressure. Therefore, both essential processes--the desorption and the ionization of analyte molecules, which are often performed in one step--are separated. The target preparation is easy and fast since no additional extraction process is required. The mass spectrometric background signal was mostly limited to the low mass range showing no interference with typical compounds of interest. In this study, the calmative and antihypertensive drug reserpine was chosen as model analyte, which is often used for specification of mass spectrometers. No fragmentation was observed because of efficient collisional cooling under atmospheric pressure. The influence of diode laser power and the composition of the graphite suspension were investigated, and a primary optimization was performed.     

Characterisation of humic substances using atmospheric pressure chemical ionisation and electrospray ionisation mass spectrometry combined with size-exclusion chromatography

Humic substances were analysed by atmospheric pressure chemical ionisation (APCI) and electrospray ionisation (ESI) mass spectrometry in positive and negative modes. Using APCI the average m/z range of humic substances was reduced 5-fold compared to ESI. High-resolution time-of-flight mass spectrometry revealed the formation of multiply charged molecules in the ESI mode. Moreover, it was possible to obtain daughter ion mass spectra of humic substances by nanospray tandem mass spectrometry. The size-exclusion chromatography elution profile of humic substances was highly influenced by the pH of the analyte solution. By contrast, the pH had no significant influence on the observed mass spectra of humic substances.     

Analysis of volatile organic compounds in human urine by headspace gas chromatography-mass spectrometry with a multipurpose sampler.

A multipurpose sampler (Gerstel MPS), designed for liquid large volume, gaseous and headspace samples was used for the GC-MS analysis of organic volatiles in human urine. Headspace sampling with a volume-, temperature- and speed-controlled gas-tight syringe was combined with a temperature-controlled cold injection system (CIS) for cold trapping, enrichment and focusing of analytes. Regular 2-ml GC vials filled with 1 ml acidified urine were used as headspace sampling vials. A 100-vial autosampler tray was equipped with an additional temperature and heating time controlled "preheating station" for five vials. Profiles of organic volatiles in human urine were determined and 34 components identified. Trimethylamine (TMA) and 4-heptanone as two metabolites of medical interest were quantified. Calibration curves and intra assay imprecision for 4-heptanone concentrations in the range of 40 to 800 ng/ml showed a correlation coefficient of r = 0.9980 and a relative standard deviation (RSD) between 3.0 and 3.4%. Calibration curves and intra-assay imprecision for TMA concentrations in the range of medical interest from 0.5 to 20 micrograms/ml showed a correlation coefficient of r = 0.9968 and a RSD between 4.1 and 6.8%. The high practicability of the multipurpose sampler for both gaseous and liquid samples together with the here shown good reproducibility and sensitivity make this single CIS-GC-MS system very attractive for routine clinical use in metabolic profiling of organic volatiles (headspace) and non-volatiles (liquid).     

Determination of aromatic sulfonic acids in industrial waste water by ion-pair chromatography

A method for the identification and quantification of aromatic sulfonic acids in industrial waste water has been developed. The preparation of the samples comprises a clean-up step and an enrichment step, utilizing i) reversed-phase extraction and ii) ion-pair solid phase extraction. The aromatic sulfonic acids are separated by ion-pair chromatography with diode-array detection. An advantage of the developed ion-pair chromatographic method is the separation of linear alkylbenzenesulfonic acids (LAS), lignosulfonic acids and aromatic sulfonic acids in one chromatographic run. Also described is an optimized clean-up procedure for collected fractions of a preparative chromatographic run to identify monosulfonic acids with GC/MS after methylation. The detection limits for aromatic sulfonic acids in industrial waste waters are at the g/l level.     

An invariant trace formula for the universal covering group of SL(2,ℝ)

Automorphic forms of arbitrary real weight can be considered as functions on the universal covering group of SL(2, ). In this situation, we prove an invariant form of the Selberg trace formula for Hecke operators. For this purpose, the Fourier transforms of weightet orbital integrals, obtained by J. Arthur, R. Herb and P. Sally, jr., are explicitly calculated. Our formula does not follow from Arthur's invariant trace formula, since the group has infinite centre, and vector-valued automorphic forms with respect to non-congruence lattices are considered.