Regular sets on the projective line

We show that if G is the group PL(2,q)(for q a prime-power) acting on the points of the projective line in the usual way, then for q>27 there is a set of 5 points such that no non-trivial element of G fixes .     

Contact electron density in Au-alloys

From a combination of measurements of the O and P shell internal conversion coefficients of the 35.8 keV-line in¹⁹⁸Au and of¹⁹⁷Au Mössbauer spectra in thin films of metallic gold, Au_0.20Sc_0.72 and Au_0.06Cr_0.92, the 6s electron density at the gold nuclei in these hosts was derived and an estimate of the change of the nuclear charge radius for the Mössbauer transition was made. The result is considerably larger than previously derived values, with which it can only be reconciled if a large shielding effect of the 5d electrons on inner shells exists.On leave from institute of Physics, Jagiellonian University, Cracow, Poland.     

Ab initio calculations of the ground-state potential energy surface for the C?F bond decomposition in n-fluoropropane within the method for approximation of the frozen molecular fragment

The recently proposed ab initio method for calculation on many-electron molecular systems with the approximation of the inactive part of a molecule by a frozen molecular fragment was tested further in a case of the dissociation reaction of the C? F bond in n-fluoropropane. Results from the Hartree–Fock, multiple reference double-excitation configuration–interaction and second-order Møller–Plesset methods are presented. The reproduction of potential energy surfaces as well as the reproduction of electron density distribution are in excellent agreement with extended basis-set calculations. Different choices of fragments to be frozen have been examined.     

“Model-free” kinetic analysis?

All kinetic analyses aim to determine a sufficient number of kinetic parameters, usually at least an apparent Arrhenius activation energy and pre-exponential factor, and a conversion function or kinetic model (making up a ‘kinetic triplet’), so that accurate extrapolations of kinetic behaviour can be made. “Model-free” methods of kinetic analysis postpone the problem of identifying a suitable kinetic model until an estimate of the activation energy has been made. A major reason for doing this is that misidentification of the kinetic model has a marked effect on the values obtained for the Arrhenius parameters in both isothermal and non-isothermal kinetic analyses. Some aspects of this problem are discussed.

The non-parametric kinetics (NPK) method [1 and 2] is a “model-free” method of kinetic analysis that does not seem to have received the attention that it deserves. This is probably because of its mathematical sophistication and the fact that the matrix and non-linear regression calculations involved are not readily automated. The principle of the method appears to be that of “forcing” a set of non-isothermal data into the set which should have been obtained if the experiments had been carried out isothermally. The method deserves wider testing and also raises some interesting aspects of the philosophy behind non-isothermal kinetic analysis.     

Ab initio MRD–CI calculations on cubane (neutral,carbocation, carboanion) and dissociation of nitrocubanes based on localized orbitals

Ab initio MRD –CI calculations based on localized orbitals were carried out for cubane (neutral, carbocation, carboanion) both in our customary MODPOT basis set and in an all-electron 4–31G basis set. The calculated MRD –CI charge distributions on C1 (the skeletal atom from which the H^? or H⁺ was removed) (ab initio MODPOT neutral 4.221, carbocation 3.796, carboanion 4.282; all-electron 4–31G neutral 6.171, carbocation 5.717, carboanion 6.078) indicate that the + or - charge does not remain localized on C1 but redistributes itself. This has significant implications for preparative reactions of energetically substituted cubanes. The MRD –CI population analyses differ somewhat from the SCF population analyses, especially in the calculated total overlap populations. To investigate this effect on electrostatic molecular potential contour (EMPC ) maps generated from SCF or MRD –CI wave functions, we wrote additional routines to calculate EMPC maps from MRD –CI wave functions. The EMPC maps generated from SCF or MRD –CI wave functions are different if the molecule needs an MRD –CI multideterminant wave function to describe it adequately. The EMPC map is a one-electron property. One-electron properties are derived from the 1-matrix. The 1-matrix is different for SCF or MRD –CI wave functions. Thus, all the one-electron properties (EMPC maps, population analyses, bond deviation indices, etc.) are different when calculated from SCF or MRD –CI wave functions if MRD –CI wave functions are necessary to describe a system properly. We calculate these one-electron properties from the 1-matrix from the final natural orbitals. Our preliminary calculations for the dissociation pathway indicate it takes more energy to dissociate a bond in 1-nitrocubane than in octanitrocubane. Even in their ground electronic states at equilibrium geometry, both 1-nitrocubane and octanitrocubane require MRD –CI wave functions to describe them properly. The c² of the single determinant SCF wave function is only 0.8401 for 1-nitrocubane and 0.8300 for octanitrocubane. There are contributions from skeletal excitations as there are for cubane itself as well as excitations involving the nitrogroup. As the bond in nitrocubane is dissociated to 8.00 bohrs, the c² of the SCF contribution drops to only 0.4606 (1-nitrocubane) and 0.4445 (octanitrocubane). At this C₁? N₁ intermolecular distance, the largest excitations are in the C₁? N₁ bond: (C₁? N₁)² → (C₁? N₁*)², (C₁? N₁) → (C₁? N₁*). We also calculated the first electronically excited state for the dissociation pathway for selected points for both 1-nitrocubane and octanitrocubane.     

Synthese von polyhydroxy-flavonolmethyläthern mit potentieller cytotoxischer wirksamkeit—II: Synthese von 6-hydroxy- und 8-hydroxy-kämpferoldimethyläthern zum strukturbeweis neuer flavonole aus betula-, alnus-, parthenium- und larrea-arten

By a modified Algar-Flynn-Oyamada reaction Betuletol, the 4',6-dimethylether of 6-hydroxy-kaempferol has been synthesized. The 3,7-dimethylether of the same flavonol and the isomeric 3,7-dimethyl-8-hydroxy-kaempferol (3,7-dimethyl-herbacetin) have been obtained by a modified Allan-Robinson synthesis. The syntheses confirm the structure of new flavonols from Betula and Ainus species as well as from Parthenium hysterophorus L. and Larrea tridentata Cav.     

Graph theoretical characterization and computer generation of certain carcinogenic benzenoid hydrocarbons and identification of bay regions

An algorithm is developed for generating and characterizing carcinogenic catacondensed benzenoid hydrocarbons. The bay regions in these structures are identified by a technique that we developed at Johns Hopkins. Using the three-digit code proposed by Balaban, and the concept of ring adjacency matrix expounded here, we generate catacondensed benzenoid hydrocarbons in the computer and identify the number of potentially carcinogenic bay regions in each of them. The results of computer generation agree with the combinatorial enumeration of Harary and Read. All structures containing up to five rings and some with six rings and the number of bay regions in these are presented. Computer results for the structures and bay regions of all seven-, eight-, and nine-membered unbranched catacondensed benzenoid hydrocarbons and the number of bays are available from the authors.