Three distinct distances in the plane

For n6 all sets of n points in the plane with three distinct distances are determined.Dedicated to Professor Dr. Laszlo Fejes Töth on the occasion of his eightieth birthday     

High-Resolution,Higher-Order UV/VIS Derivative Spectrophotometry

Derivative spectrophotometry has gained increasing importance in the past two years and is currently experiencing vigorous development. Following and introduction the present article provides a review of this extremely effective method. In particular, the advantages of higher-order derivative spectrophotometry (HODS method, n > 2) are discussed on the basis of practical examples from a wide range of analytical fields. The results are achieved with the aid of a newly developed analog computer unit, whereby for the first time readily reproducible, low-noise, on-line spectra can be obtained up to the 7th order and even, in favorable cases, up to the 9th order. In practice it has proved valuable to work with spectra of the 3rd to 5th order; but even higher derivations could be profitable for the separation of strongly superposed signals or for “fingerprinting”.     

Ab initio studies of structural features not easily amenable to experiment. 17. The molecular structures of some strained cyclic hydrocarbons and estimates of their strain energies

The molecular structures of tricyclohexane, norbornane, quadricyclane, and cubane were completely refined by standard ab initio force relaxation on the 4-21G level. The results can be used as a basis to interpret some contradictory experimental reports found in the literature and to establish some hitherto unobserved structural trends involving the C? C and C? H bond distances of the cases studied. Group Delta;E values for C? (H)₃(C), C? (H)₂(C)₂, and C? (H)(C)₃ (Benson's notation) derived from the total energies of the completely relaxed 4-21G geometries of a number of unstrained hydrocarbons are also listed. The values are used to estimate the strain energies of the systems studied and of the optimized 4-21G geometries of cyclopropane, cyclobutane, cyclohexane, and bicyclo (2.1.0)pentane. Cooperative effects in the strain energies are discussed.     

‘Face-to-Face’-Benzo-anellierte homologe Hypostrophene. Synthesen,Röntgenstrukturanalysen und PE-Spektren

‘Face-to-Face’ Benzo-anellated Homologous Hypostrophenes. Syntheses, X-Ray-Structure Analyses and PE Spectra ‘Face-to-face’ Benzo-anellated homologous hypostrophenes (series M ), of interest as substrates for [6 + 6]-photocycloaddition reactions, have been synthesized. From X-ray structural analyses of 13b and 13c shortest C? C distances of 2.80(2.76)/2.71 Å and interorbital angles (ω) of 129° (128°)/130° between the benzene rings have been determined. The PE spectra are discussed in the context of transannular π,π interactions.     

Infrared absorption by collisional CH4+X pairs, with X=He, H2, or N2

Existing measurements of the collision-induced rototranslational absorption spectra of gaseous mixtures of methane with helium, hydrogen, or nitrogen are compared to theoretical calculations, based on refined multipole-induced and dispersion force-induced dipole moments of the interacting molecular pairs CH4-He, CH4-H2, and CH4-N2. In each case the measured absorption exceeds the calculations substantially at most frequencies. We present the excess absorption spectra, that is the difference of the measured and the calculated profiles, of these supramolecular CH4-X systems at various gas temperatures. The excess absorption spectra of CH4-X pairs differ significantly for each choice of the collision partner X, but show common features (spectral intensities and shape) at frequencies from roughly 200 to 500 cm(-1). These excess spectra seem to defy modeling in terms of ad hoc exchange force-induced dipole components attempted earlier. We suggest that besides the dipole components induced by polarization in the electric molecular multipole fields and their gradients, and by exchange and dispersion forces, other dipole induction mechanisms exist in CH4-X complexes that presumably are related to collisional distortion of the CH4 molecular frame.     

Localized orbitals in hydrogen bonded systems

The localized molecular orbitals for a variety of hydrogen bonded systems are obtained from their INDO and CNDO/2 wavefunctions. The bonding of these systems is qualitatively discussed in light of the localized orbitals.     

Investigation of an enantioselective non-aqueous capillary electrochromatography system applied to the separation of chiral acids

A weak anion-exchange type chiral stationary phase (CSP) based on tert.-butylcarbamoylquinine as chiral selector and silica as chromatographic support was applied to non-aqueous capillary electrochromatography. The mobile phases used consisted of acetonitrile and methanol as organic solvents, and acetic acid and triethylamine were added as background electrolytes. The influence of several experimental parameters (electrolyte concentration, acetic acid-triethylamine ratio, acetonitrile-methanol ratio and temperature) was evaluated in order to obtain improved enantioselectivity and efficiency as well as short run times for the enantiomeric separation of negatively charged chiral analytes including benzyloxycarbonyl, N-(3,5-dinitrobenzyloxycarbonyl, 9-fluorenylmethoxycarbonyl, benzoyl, acetyl and N-(2,4-dinitrophenyl) derivatized amino acids and profens. Solvent composition of acetonitrile-methanol (80:20) and enhanced electrolyte concentrations up to 600 mM acetic acid at a constant acid-base ratio of 100:1 with high applied voltages of -25 kV proved to be optimum regarding short retention times and improved efficiencies. For example, the enantiomers of Fmoc-Leu could be separated in less than 10 min with a resolution factor of 6.9 and about 100000 theoretical plates per meter.