On the mathematical formulation and interpretation of LACO MO theory

The mathematical basis of LCAO MO theory is studied, both within the Hartree-Fock approximation and in more exact formulations. The basic LCAO expansion for molecular orbitals ¦> in terms of atomic orbitals ¦x> is conveniently written ¦> = ¦x> S ^–1 B where S is the overlap matrix for atomic orbitals and B is the matrix of atomic orbital-molecular orbital overlaps. It is suggested that matrices P and Q, defined by P=B B and Q=BnB where n is the matrix of molecular orbital occupation numbers, are appropriate to the interpretation of molecular calculations in terms of atomic orbital components, electronic populations and the degree of bonding. Implications for Hartree-Fock calculations are investigated.     

Coulometrisches Verfahren zur Bestimmung von Gesamt-, Carbonat- und Nichtcarbonat-Kohlenstoff in magmatischen, metamorphen und sediment?ren Gesteinen

Zusammenfassung Für die Bestimmung von Gesamt-, Carbonat- und Nichtcarbonat-Kohlenstoff in magmatischen, metamorphen und sedimentären Gesteinen (auch bei höheren Anteilen an organischem C) ist ein Verfahren nach dem Prinzip der coulometrischen Titration geeignet. Der Gesamt-Kohlenstoff wird ermittelt durch Erhitzung der auf <0,125 mm zerkleinerten Probe bei etwa 1250°C im Sauerstoffstrom ohne irgendwelche Zusätze. Zur Bestimmung von Nichtcarbonat-Kohlenstoff wird eine bestimmte Menge Gesteinspulver mit Salzsäure versetzt und auf einem Aluminiumblock HCl abgeraucht. Der Carbonat-Kohlenstoff entweicht als CO₂. Zurück bleibt der Nichtcarbonat-Kohlenstoff, welcher wie der Gesamt-Kohlenstoff coulometrisch bestimmt wird. Der Carbonat-Kohlenstoff bzw. die äquivalente Menge CO₂ ergibt sich dann aus der Differenz von Gesamt- zu Nichtcarbonat-Kohlenstoff. Das Verfahren ist anwendbar auf Kohlenstoffgehalte in Gesteinen von etwa 10 ppm bis 20 Gew.-% bei mittleren Standardabweichungen von etwa 0,0002–0,05% C (Richtwerte). Die Analysendauer für eine Probe beträgt etwa 3–5 min.

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Coulometric method for the determination of total, carbonate, and non-carbonate carbon in igneous, metamorphic, and sedimentary rocks

For the measurement of total carbon the sample, ground finer than 0.125 mm and without the addition of any reagents, is ignited in a current of oxygen at about 1250°C. Non-carbonate carbon can be analysed after another portion of the sample is treated with conc, hydrochloric acid and evaporated on a hot plate; the carbonates are decomposed and the carbonate carbon is removed as carbon dioxide. The residue is non-carbonate carbon which is also determined by the coulometric method. The difference between total carbon and non-carbonate carbon corresponds to carbonate carbon or its equivalent as carbon dioxide. The method is applicable to carbon contents in rocks from 10 ppm to 20 wt.-%. The standard deviation is approximately 0.0002 to 0.05% C. Each carbon analysis takes about 3 to 5 min.

     

Effects of Strong Ion‐Pairing on the Electrochemical Reduction of Cyclooctatetraene in Tetrahydrofuran in the Presence of Lithium Ion. Peak Coalescence Does Not Imply Potential Inversion

The first study of the voltammetric reduction of cyclooctatetraene (COT) in tetrahydrofuran (THF) in the presence of lithium ion is reported. A single wave is observed at ?2.23 V vs. Ag/0.1 M AgNO₃. Density functional calculations have been carried out on a variety of COT/Li/THF species in order to clarify the nature and role of ion pairing in this system. The dominant species in solution are the COT/Li/(THF)₂ anion radical and the COT/Li₂/(THF)₄ dianion. Computer simulations have been carried out to further understand the effects of ion pairing on the reduction. The simulations show that coalescence of two waves into one can occur in the presence of strong ion pairing even when the second reduction potential is negative of the first.     

R?ntgenspektrometrische Bestimmung von Eisen-55 in Luftstaub- und Niederschlagsproben

Zusammenfassung Eisen-55 wurde in Neuherberg bei München seit März 1970 in monatlich gesammelten Luftstaubproben und seit Januar 1971 in Monatsniederschlagsproben bestimmt. Nach dem Veraschen der Proben wurde Eisen durch Extraktion' mit Di-iso-propyläther abgetrennt. Zur weiteren Entfernung störender Radionuklide des Fallouts wurde eine Ionenaustauschertrennung angeschlossen. Nach der elektrolytischen Abscheidung des Eisens auf Kupferplättchen wurden die Röntgenspektren mit einem Proportionalzähler sowie einem Si(Li)-Detektor aufgenommen.Die mittlere spezifische Luftaktivität betrug in Neuherberg 1,0 fCi/m³ im Jahr 1970 (ab März), 1,2 fCi/m³ im Jahr 1971 und 0,36 fCi/m³ im Jahr 1972. Die dem Boden durch den Niederschlag zugeführte Aktivität wurde zu 697 pCi/m² · Jahr für 1971 und 178 pCi/m² · Jahr für 1972 bestimmt.Vortrag anläßlich der Tagung Spurenanalyse, 2. bis 5. April 1973 in Erlangen.     

Spectrographic estimation of Ga, In and Tl in semiconductor grade selenium

Summary An emission spectrographic method for the estimation of Ga, In and Tl in semiconductor grade selenium at less than a ppm concentration has been developed. The impurities were separated from 1 g of selenium by volatilizing it from its solution in nitric acid and sulphuric acid. The residue containing the impurities was dissolved in small amounts of 6 M HCl and was loaded along with the washings on 10 mg mixture containing graphite (90%) and sodium chloride carrier (10%) in the electrode crater. The spectra were excited in a d.c. arc carrying 13 A current. The detection limits lie in the range of 0.0025–0.005 ppm. The precision of the method ranges from 7–12% for these elements. The recoveries of impurities from selenium were confirmed using radioactive tracers.

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Spektrographische Bestimmung von Gallium, Indium und Thallium in Halbleiterselen

Zusammenfassung Eine 1 g-Probe wird in Salpeter- und Schwefelsäure gelöst und die Verunreinigungen durch Verflüchtigung des Selens isoliert. Sie werden in 6 M HCl gelöst und zusammen mit einem Graphit/NaCl-Gemisch (91) in die Elektrode eingebracht. Zur Anregung dient ein Gleichstrombogen (13 A). Die Nachweisgrenzen liegen im Bereich von 0.0025–0.005 ppm, der Variationskoeffizient bei 7–12%. Die Wiedergewinnung der Verunreinigungen wurde mit Hilfe von Radioindicatoren geprüft.

     

Some model theory for monotone quantifiers

A generalization of the existential and universal quantifier, the monotone quantifiers, are studied. It is shown that the model theory for monotone quantifiers behaves very much like classical model theory. Completeness theorems, definability theorems and preservation theorems are given. Ultraproducts, reduced products and Back and Forth arguments are studied.This work is part of the research program of the G.N.S.A.G. group of the Italian C.N.R.     

The Mathematical Theory of Ito Diffusions on Hypersurfaces, with Applications to NMR Relaxation Problems

A mathematical framework for translational Brownian motion on hypersurfaces is presented, using an imbedding of the surface and Ito diffusions in the ambient space. This includes a survey of Ito calculus and differential geometry. Computational methods for time correlation functions relevant to spin relaxation studies on curved interfaces are given, and explicit calculations of time correlation functions and order parameters for a Rippled surface are presented.     

Direct calculation of ionization potentials of closed-shell atoms and molecules

Vertical ionization potentials, electron affinities and information about quasi-particles can be obtained by using the technique of the single-particle propagator. The expansion of the self-energy part up to third order perturbation theory can be evaluated numerically, but does not lead, in most cases, to satisfying results. A theoretical and numerical analysis of the diagrammatic expansion of the self-energy part requires the introduction of a renormalized interaction and renormalized hole and particle lines.     

HPLC Analysis of Cotinine in Urine After SPE with a Cholesterol-Modified Adsorbent

A one-step solid-phase extraction procedure, based on a new silica gel adsorbent modified with cholesterol groups, has been investigated for measurement of cotinine in urine. Cotinine is the main metabolite of nicotine in the human body and is analyzed as a biomarker for assessment of direct or passive exposure to tobacco smoke. New cholesterol-modified adsorbents have been obtained by chemical modification of silica gel of different porosity with cholesterol ligands. Although recovery by this extraction procedure were optimum over a relatively broad range of sample pH (3.1–8.0), analytical conditions such as sample loading, washing and elution conditions, concentration of cotinine to be extracted, and the type of adsorbent used for extraction were found to affect the efficiency of the procedure and had to be controlled for optimum recovery. When these conditions were controlled, recovery of cotinine from spiked human urine was reproducible and depended on compound ionization. Quantitative analysis of cotinine was performed by reversed-phase high-performance liquid chromatography with UV detection. Presented at: Conference of the Hyphenation of Liquid Chromatography–Nuclear Magnetic Resonance Spectroscopy, Liquid Chromatography–Mass Spectrometry and Related Topics, Tuebingen, Germany, March 25–29, 2006.