The Interaction of Walsh-Orbitols in Diademane and Related Hydrocarbons

To obtain further information concerning the interaction between Walsh-orbitols of ‘conjugated’ cyclopropane rings, the photoelectron spectra of the following compounds have been recorded: bicyclo[4.1.0]heptane 1 , cis- and trans-tricyclo[5.1.0^{3, 5}]octane 2, 3 , diademane 4 , trans-pentacyclo[3.3.2.0^{2, 9}.0^{4, 10}, 0^{6, 8}]decan 5 and bicyclo[4.1.0]heptene-2 6 . The first bands in the PE.-spectra of these compounds have been assigned on the basis of a ZDO HMO-approximation. For 2 and 4 the value for resonance integral between linked 2p atomic orbitals of two adjacent eclipsed cyclopropane rings is found to be ?1.73 eV.     

Micro-determination of potassium with EDTA

Summary A micro-determination method for potassium with EDTA is described. The perchlorate precipitate is reduced to chloride by heating the perchlorate with ammonium chloride, and the chloride is precipitated as silver chloride. This precipitate is dissolved in an ammoniacal solution of potassium tetracyanonickelate. By dissolution, two atoms of silver (or chlorine) displace one of nickel. The freed nickel is titrated with, EDTA and potassium is thus determined indirectly. The method is much more rapid than the classical gravimetric procedure, and the results are satisfactory.

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Zusammenfassung Eine Mikromethode zur Bestimmung von Kalium mit ÄDTA wird beschrieben. Der Perchloratniederschlag wird durch Erhitzen mit Ammoniumchlorid reduziert und das Chlorid mit Silber gefällt. Dieser Niederschlag wird in einer ammoniakalischen Lösung von Kaliumtetracyanonickelat aufgelöst, wobei zwei Atome Silber ein Atom Nickel verdrängen. Das freigesetzte Nickel wird mit ÄDTA titriert und so das Kalium indirekt bestimmt. Das Verfahren ist rascher als die klassische gravimetrische Methode. Seine Resultate sind befriedigend.

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Résumé On décrit une méthode de microdosage du potassium par l'EDTA. En chauffant le perchlorate avec du chlorure d'ammonium, on réduit le précipité de perchlorate en chlorure que l'on précipite à l'état de chlorure d'argent. On dissout ce précipité dans une solution ammoniacale de nickel-II tétracyanure de potassium. La mise en solution s'accompagne du déplacement d'un atome de nickel par deux atomes d'argent. On titre le nickel libéré par l'EDTA et l'on dose ainsi le potassium indirectement. La méthode est beaucoup plus rapide que le procédé gravimétrique habituel et les résultats sont satisfaisants.

     

The crystal structure of eudesma-4(15),7(11)-dien-8α, 12-olide: a sesquiterpene lactone fromTrattinickia rhoifolia Willd

The title compound, formula C₁₅H₂₀O₂, is orthorhombic, P2₁2₁2₁ witha=8.747(2),b=12.025(3),c=12.554(3)Å,Z=4, andD _m =1.32(2)g/ml. The structural analysis shows that the compound corresponds to eudesma-4(15),7(11)-dien-8,12-olide, a sesquiterpene lactone previously isolated fromAster umbellatus but whose crystal structure was unknown.     

Ground-state energy of a quantum chain with competing interactions

We show rigorously that the ground state of a quantum chain with competing ferromagnetic nearest and antiferromagnetic next nearest interactions undergoes a transition from ferromagnetic to helical type, in the isotropic case, for a certain value of the relevant ratio of coupling constants. Boundaries of the phase diagram are also determined in the anisotropic case. The stability of a special quantum state (corresponding to a classical modulated phase of =/3) is analyzed by an extension of Holstein-Primakoff arguments, along a line of constant ratio of couplings, showing in particular a sequence of (instability) gaps. Finally, a natural adaptation of a variational wave function due to Huse and Elser is used to study several portions of the phase diagram, with very good agreement with previous theoretical results.     

Vibrational Population of Hydrogen Molecules Excited by an RF Discharge in an Expanding Thermal Arc Plasma as Determined by Emission Spectroscopy

This work is devoted to the determination of the vibrational population of hydrogen molecules in the ground and excited electronic states from the analysis of visible spectra of the H₂ molecules excited by an RF discharge in an expanding thermal arc plasma. Comparison of the experimental results on relative electron-impact excitation cross sections for the transition H₂(X¹Σ, υ⁰ = 0)→ H₂(d³II_u, υ′) with other experiments, and with calculations based on the Franck-Condon principle, shows good agreement. This means, that for plasma under investigation: 1) in the ground electronic state H₂(d³II_u,υ′), only the lowest vibrational level with υ⁰ = 0 is significantly populated, and 2) direct electron exictation of H₂(d³II_u, υ′, υ′) state from the ground state H₂(X¹Σ, υ⁰ = 0) dominates.     

Quantum groups in the higgs phase

In the Higgs phase we may be left with a residual finite symmetry groupH of the condensate. The topological interactions between the magnetic and electric excitations in these so-called discreteH gauge theories are completely described by the Hopf algebra or quantum groupD(H). In 2+1 dimensional space time we may add a Chern-Simons term to such a model. This deforms the underlying Hopf algebraD(H) into the quasi-Hopf algebraD (H) by means of a 3-cocycle onH. Consequently, the finite number of physically inequivalent discreteH gauge theories obtained in this way are labelled by the elements of the cohomology groupH ³(H,U(1)). We briefly review the above results in these notes. Special attention is given to the Coulomb screening mechanism operational in the Higgs phase. This mechanism screens the Coulomb interactions, but not the Aharonov-Bohm interactions.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98. No. 3, pp. 509–523, March, 1994     

The infinite time limit for the time-dependent Born-Oppenheimer approximation

We analyze the Schrödinger equation , whereH() is the hamiltonian of the molecular system consisting of nuclei with masses proportional to ^–4 and electrons with masses of order 1. Using the Born-Oppenheimer method we construct the leading order asymptotic expansion to the exact solutions of the equation. We show that if the particles interact through smooth potentials decaying suitably as the distance between particles tends to , then the expansion holds uniformly for all timest[0,). By similar analysis one can show validity of the expansion fort(–,0], thus our results hold for scattering theory.The material in this paper is contained in a dissertation submitted to the faculty of VPI & SU in partial fulfillment of the requirements for the Ph.D. degree.