Neutron activation analysis of thorium after separation of233Th by isotopic ion exchange

The procedure for thorium determination in ammonium diuranate (ADU) and rocks, by neutron activation analysis after chemical separation of²³³Th, is presented. The separation of²³³Th from the interfering radioisotopes is based on the retention of²³³Th by a resin saturated with thorium (isotopic exchange) and on the elution of the interfering radioisotopes by a dilute solution of thorium in 0.5M HCl (ion exchange). The determination limit of thorium in rocks and ADU was found to be 0.56 and 9.3 g, respectively, when a 20% relative standard deviation was assumed as acceptable. The highest value obtained for the determination limit of thorium in uranium compounds, on account of the²³⁴Th activity present, is discussed.From a thesis submitted by C. S. Munita to the Instituto de Pesquisas Energéticas e Nucleares (CNEN/SP) University of São Paulo, in partial fulfillment for a Doctor of Science's Degree. Work supported by the Brazilian Atomic Energy Commission.     

Über einen Nachweis von Mercaptoverbindungen

Zusammenfassung Über ein Verfahren zum Nachweis von Mercaptoverbindungen mit Natriumpentacyanonitrosoferrat(III) und Zinkchlorid in annähernd neutraler Lösung wird berichtet. Die Grenzkonzentrationen liegen bei Pyridinzusatz zwischen 110⁵ und 110⁶ und die Erfassungsgrenzen bei 1 bis 2g.

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Summary A report is given of the detection of mercapto compounds with sodium pentacyanonitrosoferrate (III) and zinc chloride in approximately neutral solution. The limiting concentrations, when pyridine is added, are between 110⁵ and 110⁶ and the identification limits are 1 to 2g.

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Résumé On présente un procédé de recherche de mercaptans par le nitroprussiate de sodium et le chlorure de zinc en solution presque neutre. Les concentrations limites se situent entre 110⁵ et 110⁶ avec addition de pyridine et les limites de dilution de 1 á 2g.

     

Calculation of spin densities in odd alternant hydrocarbon radicals

Spin densities in benzyl, allyl, pentadienyl and perinaphthenyl radicals have been calculated with some variants of the simplified McLachlan unrestricted SCF method based on Hückel-type and the SC Hückel-type molecular orbitals. The various estimations of the spin densities were compared one with each other and with the results of more sophisticated methods. It was shown that the SC Hückel basis and Zhidomirov and Schastnev's modification of the McLachlan approach give a best least square fit of the relation a ^exp Q ^calc .

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Zusammenfassung Die Spindichten von Benzyl-, Allyl-, Pentadienyl- und Naphtenyl-Radikalen werden mit einigen Varianten der uneingeschränkten SCF-Methode in der vereinfachten Form nach McLachlan, die auf den Hückel- und den SC-Hückel-Molekülorbitalen basiert, berechnet. Die verschiedenen Schätzungen der Spindichten werden miteinander sowie mit den Resultaten komplizierterer Methoden verglichen. Es wird gezeigt, daß die SC Hückel Basis und die von Zhidomirov und Schastnev eingeführte Modifikation der Näherung von McLachlan eine beste Näherung nach der Methode der kleinsten Quadrate an die Beziehung a ^exp Q ^calc ergeben.

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Résumé Les densités de spin ont été calculées dans les radicaux benzyle, allyle, pentadiényle et perinaphthényle à l'aide de variantes de la méthode SCF sans restrictions de spin simplifiée de Mac Lachlan, en utilisant des orbitales de type Hückel et SC Hückel. Les différentes évaluations de densité de spin sont comparées entre elles et avec celles obtenues par des méthodes plus élaborées. On montre que la base SC Hückel et la modification de Zhidomirov et Schastnev à la théorie de Mac Lachlan donnent le meilleur accord au sens des moindres carrés avec la relation a ^exp Q ^cal .

     

A new gamma-ray spectrum catalog and library for PGAA

New measurements have been performed at the PGAA facility at the Budapest Research Reactor (BRR) in order to create a prompt -ray catalog for qualitative and quantitative analysis. The measured spectra were accurately analyzed by HYPERMET-PC. Prompt -ray energies and associated -ray production cross-sections have been determined by internal standardization. The resulting catalog contains prompt -ray data from neutron capture and other reactions such as (n,), and decay -ray data from short-lived reaction products. Data have been measured for nearly all stable elements, from hydrogen to uranium. Generally, data for several isotopes are given, to enable isotopic analysis as well. The whole library, including elemental spectra, will be available as a book.     

Extraction and spectrophotometric determination of uranium(VI) withN-phenylcinnamohydroxamic acid

Uranium(VI) reacts withN-phenylcinnamohydroxamic acid to form an orange-yellow complex in the pH range 5.5–8.5. The orange-yellow complex, having the composition of 12 (metal:ligand), is quantitatively extractable into ethyl acetate. The spectrum of the complex exhibits a maximum absorption at 400 nm with a molar absorptivity of 6500 M^–1·cm^–1. The coloured system obeys Beer's law in the concentration range 2–40g·ml^–1 of uranium(VI). The photometric sensitivity of the colour reaction is 0.037 g·cm^–2 of uranium(VI). Most of the common ions do not interfere and the method has been found to be simple, precise, and free from the rigid control of experimental conditions. The method has been applied to the determination of uranium in synthetic matrices and potable water.     

An automated fuel element scanning system

This paper describes an automated fuel element scanning system, based upon gamma-ray spectroscopy, that has been developed at the Oak Ridge Research Reactor. The scanning system is located in the reactor pool and allows fuel elements to be scanned nondestructively at various intervals during their core life. Fuel elements are located 430 cm beneath the pool. Gamma-ray measurements (aided by a collimating assembly) are made using a GeLi detector positioned above the pool water. Measurements of¹³⁷Cs count rates from relatively cold elements indicate that the counting data obtained using this apparatus is reproducible within 5%. Power distribution in the reactor's core (element by element) has been derived from¹⁴⁰La counting data. The method of determining power is discussed briefly and some example results are presented.     

Voltammetric Behavior of Dopamine at ct-DNA Modified Carbon Fiber Microelectrode

A sub-micrometer thin-layer DNA modified carbon fiber microcylinder electrode was prepared by electrodeposition of ct-DNA at 1.5V (vs. Ag/AgCl). The voltammetric behavior of dopamine (3-hydroxytyramine) was investigated at the modified electrode. It was found that the modified electrode exhibits a highly electrocatalytic activity toward dopamine oxidation. Differential pulse voltammetry was used for determination of dopamine in pH 7.4 phosphate buffer solution. A linear response of the peak current versus the concentration was found in the range of 4×10^–6 to 10^–4molL^–1 at 10^–4molL^–1 AA (ascorbic acid) coexistence (R=0.9959) and the range of 6×10^–5 to 10^–3molL^–1 at 10^–3molL^–1 AA (R=0.9960). The presence of a high concentration of ascorbic acid did not interfere with the determination. The proposed method exhibited good recovery and reproducibility. This method can be applied to the detection of DA in real samples.     

Effect of experimental conditions on the in vitro stability of99mTc (Sn)-pyrophosphate

The in vitro stability of^99mTc (Sn)-PyP as a function of experimental conditions of the preparation of the kit and time elapsed after labeling has been tested. The preparation was protected by using nitrogen-purged reactant solutions and kit vials and by ascorbic acid. The samples under nitrogen are stable for 6 h when the content of^99mTc-pertechnetate raises to 5%. The best stability was achieved by addition of 5 g of ascorbic acid per ml of the kit (content of^99mTc-pertechnetate about 0.5%). To accelerate the decomposition, exogenous hydrogen peroxide was used. In this case it was found that the presence of 10 g of ascorbic acid inhibits the effect both of oxygen and peroxide (6 g H₂O₂/ml of the kit). Radiochemical purity of^99mTc (Sn)-PyP remains practically unchanged for 6 h (content of^99mTc-pertechnetate about 0.5%).     

Ultrasonic study of the molecular encapsulation and the micellization processes of dodecylethyldimethylammonium bromide-water solutions in the presence of β-cyclodextrin or 2,6-di-o-methyl-β-cyclodextrin

Aqueous solutions of -cyclodextrin (-CD) or 2,6-di-o-methyl--cyclodextrin (DM--CD) and dodecylethyldimethylammonium bromide (D₁₂EDMAB) have been studied from speed of sound (u) data at 298.15 K, using a pulse-echo-overlap technique. The molecular encapsulation process of the surfactant monomer into the cyclodextrin cavity and its effect in the micellization process of the surfactant have been analyzed from theu measurements: I) as a function of [D₁₂EDMAB] in the presence of several initial cyclodextrin concentrations (-CD or.DM--CD); II) as a function of [cyclodextrin] (-CD or DM--CD), for an initial micellar solution of D₁₂EDMAB and; III) as a function of the [cyclodextrin]/[surfactant] stoichiometric concentrations. Both inclusion complexes formed (-CDD₁₂EDMAB) and (DM--CDD₁₂EDMAB) have stoichiometries of 11, and their association constantK have been determined using a model proposed in this work, based on the additivity of the different contributions of the involved species to the speed of sound. The apparent critical micellar concentration, cmc^*, of D₁₂EDMAB is found to increase linearly upon the addition of cyclodextrin (-CD or DM--CD). The free surfactant concentration in the micellar region, [D₁₂EDMAB]_f, decreases in the presence of -CD and slightly increases in the presence of DM--CD. The influence of the parcial methylation of the -cyclodextrin (-CDDM--CD) and of the polar head of the surfactant (D₁₂TAB D₁₂EDMAB) on the complextion and micellar parameters are also discussed.Supplementary material available: Tables of speed of sound (14 pages) are available from the authors.     

Medium effects on the reactions of coordination complexes: Base hydrolysisof(αβS)(p-hydroxybenzoato)(tetraethylenepentamine) cobalt(III) in iso-propanol–water,tert-butanol–water and dimethyl sulfoxide–water media

The base hydrolysis of (S)(p-hydroxybenzoato)-(tetraethylenepentamine)cobalt(III) has been investigated in aqueous–organic solvent media using i-PrOH, t-BuOH and dimethyl sulfoxide (DMSO) as cosolvents at 20.0 T (°C) 40.0 (I=0.02 mol dm ^-3) with 80% (v/v) of cosolvents. Only the base-catalysed path (k_obs=k_OH[OH^-]) is observed. The relative second order rate constant k _OH ^os /k _OH ^ow at I=0 increases nonlinearly with increasing mol fraction (x_O.S.) of the cosolvents, the rate acceleration in alcoholic cosolvents being greater than in DMSO. The destabilization of ^-OH in mixed solvent media alone does not explain the observed rate acceleration. The solvent composition dependence, log k _OH ^os = log k _OH ^ow + a_ix _os ⁱ [i=1,2,k _OH ⁰ denotes k_OH at I=0 in mixed solvent(s) and water (w)] indicates specific solute–solvent interactions. The values of the relative transfer free-energy data [_TG(t.s.) - _TG^o (i.s.)](sw)(25 °C)(G), where t.s. and i.s. denote the transition state and initial state of the substrates respectively, are positive for all substrates at all compositions, indicating a greater destabilizing effect of the mixed solvent on the transition state than on the initial state. The G values also correlate with G^E(G = ax_O.S. + cG^E) for all solvents, supporting the fact that solvent structural effects mediate the rates and energetics of the reaction. However, the solvent effects on the solvation components of H and S are mutually compensating, thus indicating that there is no change in the mechanism.     

X-Ray Diffraction Study of Piperidine Octamolybdate

Piperidine octamolybdate [C₅H₅NH₂]₄[Mo₈O₂₆]·4H₂O (I) has been synthesized and characterized by X-ray diffraction analysis. Crystals I are monoclinic, space group P2₁/n, a=12.892(3), b=9.283(2), c=19.184(4) , =92.50(3)°, V=2293.7(9) ³, Z=2,_calc = 2.317 g/cm³.     

The determination of tin in explosive materials by thermal neutron activation analysis

A method, based on the measurement of the -photopeak at 332 keV arising from a¹²⁴Sn(n, )^125mSn reaction, has been developed for the rapid measurement of Sn at concentrations of 20 g g^–1, present as the cross-linking agent, in explosive charges. The method is comparative, and has a limit of detection of 0.6 g g^–1 and a precision of 5% RSD. The method requires no sample preparation and is economical in effort.     

Radiation-induced reactions of cholesterol in an aqueous medium

⁶⁰Co -ray radiolysis of cholesterol /3-hydroxy-5-cholestene/ /I/ in the two-phase system /water-ethyl acetate/ and in the presence of air has been studied using TLC and GC methods. The following products were observed in the irradiated mixture: 3, 7-dihydroxy-5-cholestene /II/, G O. 36, 3-hydroxy-7-keto-5-cholestene /III/, G 1.48, 3-hydroxy-7-keto-5-cholestane /IV/, G 0.22, 3,5,6-trihydroxy-5-cholestane /V/, G 0.83, 5,6-epoxy-3-hydroxy-5-cholestane /VIa/, G 0.26, 5,6-epoxy-3-hydroxy-5-cholestane /VIb/, G 0.24, and 2, 3-dihydroxy-5-cholestene /VII/, G 0.22. The dose dependence of the formation of these products shows that the cholesterol derivatives substituted in the position 7 /II–IV/ are formed from a common precursor — the radical Ia. On the other hand, the products of the 5–C=C double bond reactions /V and VI/ are formed independently. Also the product VII is formed independently. A reaction scheme that is in agreement with these results is proposed.     

The electronic structure and spectrum of the silver(I)perchlorate-pyridine complex

The absorption spectrum of the silver perchlorate-pyridine system was measured in acetonitrile and ethanol in the wavelength region of 180 m to 400 m. It was found that the solution exhibits a new shoulder in the 210 m region characteristic for the 11 complex, in addition to the absorption maxima at 196 m and 253 m which correspond, respectively, to the L _a and L _b bands of pyridine. From the concentration dependence of the absorption intensity of this shoulder, the equilibrium constant for 11 complex formation was determined to be 108 l/mole at 26 °C. Furthermore, we studied theoretically the electronic structure of this complex by the method of the localized orbital model, the effect of the solvation energy upon the charge-transfer configurations being taken into account. The theoretical results show that the new absorption band at 207.5 m has to considerably great extent the character of a charge-transfer type excitation.

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Zusammenfassung Das Absorptionsspektrum des Systems AgClO₄-Pyridin in Acetonitril- und Äthanol-Lösung wurde im Bereich von 400-180 m vermessen. Es treten Absorptionsmaxima bei 196 und 253 m auf, die der L _a -bzw. L _b -Bande des Pyridins entsprechen; daneben eine Schulter bei 207 m als Charakteristikum des 11-Ag⁺-Pyridin-Komplexes. Aus der Konzentrationsabhängigkeit der Intensität dieser Schulter folgt als Gleichgewichtskonstante der Komplexbildung k=108 l/Mol (26 °C), aus der Temperaturabhängigkeit H=4,5 kcal/Mol, S=–6 Cl in guter Übereinstimmung mit polarographischen Ergebnissen. Weiterhin wurde die Elektronenstruktur mit der Methode der Moleküle in Molekülen unter Berücksichtigung von Solvatationseinflüssen untersucht. Danach ist die neue Schulter als Ladungsübergangsbande zu klassifizieren.

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Résumé Mesure du spectre d'absorption du système AgClO₄-Pyridine en milieu acétonitrile ou éthanol dans le domaine 400-180 m. On obtient des maxima d'absorption vers 196 et 253 m correspondant aux bandes L _a et L _b de la pyridine; un épaulement vers 207 m est caractéristique du complexe 11-Ag⁺-Pyridine. D'après la variation de l'intensité de cet épaulement avec la concentration on obtient comme constante d'équilibre du complexe k=100 l/Mol (26 °C), et à partir de la variation avec le température H=4,5 kCal/Mol, S=–6 Cl, en bon accord avec les résultats polarographiques. De plus la structure électronique est étudée à l'aide de la méthode des molécules dans les molécules en considérant les effets de solvatation. On en déduit le caractère de bande de transfert de charge de cet épaulement.

     

Chemistry on the rhomboidal Ru4 faces of the clusters RU4(CO)13(μ-PR2)2: Novel small molecule,ligand, and skeletal transformations

Tetrametal clusters such as Ru₄(CO)₁₃(-PPh₂)₂ and Ru₄(CO)₁₀(-PPh₂)₄ are 64-electron systems and, with five metal-metal interactions, are formally electron rich. In fact these clusters have unusual rhomboidal (or flat butterfly) structures with three or four elongated Ru-Ru bonds. With molecular orbitals antibonding with respect to metal metal interactions occupied in such clusters, facile two electron oxidation or ligand dissociation processes should occur, giving electron precise molecules. The molecule Ru₄(CO)₁₃(-PPh₂)₂ 1a undergoes a remarkable, reversible transformation upon loss of CO affording (-H)Ru₄(CO)₁₀(-PPh₂)[₄-¹(P),¹(P),¹(P),¹,²-{C₆H₄}PPh]3 a cluster which contains a five coordinate phosphido bridge and an orthometallated ² arene ring. This conversion is reversible under CO. These and other results which will be discussed confirm that M₄ clusters with electrons in excess of the expected EAN rule count may exhibit unusual reactivity. The solid-state CP/MAS and static powder³¹P NMR spectra of some of these clusters exhibit^99/101Ru-³¹P couplings, values of which have been measured for the first time.     

Photometric detection of cyclodextrins in liquid chromatography by using iodine generated electrochemically in-situ

A method has been developed for photometric detection of cyclodextrins (CD) in liquid chromatography using iodine (I₂) generated electrochemically in-situ. Iodide ion in the mobile phase was electrochemically oxidized to I₂ which was subsequently reacted with I^–, in an electrochemical flow cell, forming I₃^–. The absorbance of I₃^– was found to be greatly enhanced when CD were present in the mobile phase. The absorbance enhancement was caused by the change in the mole fraction of I₃^–, because of the inclusion reaction of I₃^– with CD. On the basis of this phenomenon, CD were detected by means of a photodiode-array UV–visible detector positioned downstream of the electrochemical flow cell. The signals were found to be linearly dependent on CD concentration. Because the formation constants of I₃^– with CD decrease in the order -CD>-CD>-CD, -CD was most detectable by the method. Detection limits were 1.0 mol L^–1 for -CD, 65 mol L^–1 for monoG1--CD, 100 mol L^–1 for -CD, and 200 mol L^–1 for -CD.     

Neutronenaktivierungsanalyse von Verunreinigungen. Kobalt und Nickel in Uranverbindungen nuklearer Reinheit

Zusammenfassung Eine Methode zur Bestimmung von Nickel und Kobalt in Uranverbindungen nuklearer Reinheit wurde entwickelt. Die Hauptmasse des Urans wird vor der Bestrahlung papierchromatographisch entfernt. Kobalt und Nickel werden mit Hilfe der Isotope⁶⁰Co bzw.⁵⁸Co bestimmt. Zur Trennung der beiden Kobaltisotope wird die- Spektrometrie bzw. das Complement-subtraction-Verfahren angewendet.

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Summary A method has been developed for determining nickel and cobalt in uranium compounds of nuclear purity. The bulk of the uranium is removed by paper chromatography prior to the irradiation. Cobalt and nickel are determined with the aid of the isotopes⁶⁰Co and⁵⁸Ni respectively. Gamma spectrometry or the complement subtraction procedure is employed to separate the two cobalt isotopes.

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Résumé On a découvert une méthode de dosage du nickel et du cobalt dans les composés de l'uranium de pureté nucléaire. Avant l'irradiation, on sépare par Chromatographie sur papier la plus grande partie de l'uranium. On dose le cobalt et le nickel au moyen des isotopes Co⁶⁰ ou Ni⁵⁸. On utilise la spectrométrie gamma pour la séparation des deux isotopes du cobalt ou encore le procédé dit de «soustraction du complément».

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Vorgetragen beim Symposium für analytische Chemie in Graz, 29. September bis I. Oktober 1965.     

On the validity of the electron pair approximation for the Beryllium ground state

The Watson-wave function for the Be ground stats is used to check the necessary conditions — derived previously — for the validity of the antisymmetrized product of strongly orthogonal geminal (APSG) approximation. The agreement between the actual properties of the numerical 1^st and 2^nd order density matrices and those predicted from the APSG scheme is satisfactory, whereas the predictions made in the framework of the antisymmetrized product of identical geminals (APIG) scheme are not at all realized. Correlation adapted orbitals and generating geminals are extracted from the given numerical wave function. The former are compared with the Edmiston-Ruedenberg localized orbitals, the latter with the Be⁺⁺ wave functions.

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Zusammenfassung An Watsons Wellenfunktion für den Be Grundzustand werden die notwendigen Bedingungen für die Gültigkeit der APSG-Näherung getestet, die früher abgeleitet worden waren (APSG=Antisymmetrisiertes Produkt stark orthogonaler Geminale). Die Übereinstimmung zwischen dem tatsächlichen Verhalten der numerischen Dichtematrizen 1. und 2. Ordnung und demjenigen, das vom Standpunkt der APSG-Näherung vorausgesagt wird, ist zufriedenstellend. Überhaupt nicht erfüllt werden allerdings die Voraussagen der APIG-Näherung (APIG=Antisymmetrisiertes Produkt identischer Geminale). Die korrelationsadaptierten Orbitale sowie die erzeugenden Geminale werden, ausgehend von der gegebenen Funktion, konstruiert, und erstere mit den Edmiston-Ruedenbergschen lokalisierten Orbitalen verglichen, letztere mit der Wellenfunktion des Be⁺⁺.

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Résumé On se sert de la fonction numérique de Watson pour l'état fondamental de l'atome de Beryllium pour examiner les conditions nécessaires dérivées antérieurement, qui doivent être satisfaites si l'approximation APSG est valable. Dans le cadre de cette approximation la fonction d'onde peut être représentée comme produit antisymmétrique de géminales fortement orthogonales. Les prédictions faites à partir de ce modèle et les propriétés des matrices densité numériques sont en bon accord. Il n'en est pas autant pour l'approximation APIG où l'on choisit les géminales identiques plutôt que fortement orthogonales. On «extrait» les «orbitales adaptées à la corrélation» aussi bien que les «géminales génératrices» de la fonction numérique. Les premières sont comparées aux «orbitales localisées» d'Edmiston et Ruedenberg, les secondes à la fonction d'onde de Be⁺⁺.

     

Dosage de micro quantités de cuivre bivalent par précipitation en picrate de cupritétrammine

Résumé On propose une méthode de dosage de microquantités de cuivre-II par précipitation sous forme de picrate de cupritétrammine. Cette méthode est fondée sur la précipitation du cuivre-II en présence d'un excès de picrate de sodium en milieu ammoniacal et sur le dosage colorimétrique de l'acide picrique résiduel après extraction sous forme de picrate de bleu de méthylène.Cette méthode permet le dosage de 1 à 10 g de cuivre-II, avec une erreur maximale de ± 5%.La présence des cations zinc (jusqu'à 200g), argent (jusqu'à 500g), cobalt (jusqu'à 50g), cadmium (jusqu'à 100g), nickel (jusqu'à 20,g) et chrome (jusqu'à 50 g) ne gêne pas le dosage.Cette méthode peut servir à doser le cuivre dans les cendres végétales.

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Summary A method is suggested for the determination of micro amounts of copper(II) by precipitation as the picrate of cupritetrammine. This method is based on the precipitation of the copper(II) in the presence of an excess of sodium pierate in an ammoniacal milieu and on the colorimetric determination of the residual picric acid, after extraction in the form of the picrate of methylene blue. This procedure permits the determination of from 1 to 10g of Cu(II) with a maximum error of ± 5%.The determination is not impaired by the presence of the cations: zinc up to 200 g), silver (up to 500g), cobalt (up to 50g), cadmium (up to 100g), nickel (up to 20g), and chromium (up to 50g).This method may be employed for determining copper in vegetable ashes.

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Zusammenfassung Bin Verfahren zur Bestimmung von Mikromengen Kupfer(II) durch Fällung als Kupfertetrammin-Pikrat wird vorgeschlagen. Es beruht auf der Fällung von Kupfer in Gegenwart überschüssigen Natriumpikrats in ammoniakhaltiger Lösung und der kolorimetrischen Bestimmung der restlichen Pikrinsäure nach Extraktion als Methylenblaupikrat. 1 bis 10g Cu(II) lassen sich mit einem maximalen Fehler von ± 5% bestimmen. Die Anwesenheit von < 200g Zn, < 500 g Ag, < 50g Co, < 100g Cd, < 2°g Ni und < 50g Cr stört die Bestimmung nicht. Das Verfahren eignet sich zur Bestimmung von Kupfer in Pflanzenasehen.

     

The electronic structure of the boron hydrides

In parts I and II of this series [1] it has been demonstrated that localized three centre and two centre bonds may be used as basic functions for molecular orbital calculations on closed (cage) and open (basket) boron polyhedral molecules. In the present paper it is shown that the face and edge matrices of this theory are related to incidal and 1 and 2 simplexial matrices in the same way that Hückel matrices in the theory of unsaturated hydrocarbons are related to incidal matrices and 0 and 1 simplexial matrices. The theory is thus a topologically-correct extension of Hückel theory to three dimensions.

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Zusammenfassung In Teil I und II dieser Serie [1] wurde demonstriert, da\ lokalisierte Dreizentren- und Zweizentren-Bindungen als Basisfunktionen für MO-Rechnungen bei geschlossenen (KÄfig) und offenen (Korb) polyhedralen Borwasserstoff-Molekülen benutzt werden können. In der vorliegenden Arbeit wird gezeigt, da\ die OberflÄchen- und Randmatrizen dieser Theorie mit Incidal- sowie 1- und 2-Simplexmatrizen verwandt sind, in derselben Art wie die Hückel-Matrizen in der Theorie der ungesÄttigten Kohlenwasserstoffe mit Incidal-Matrizen sowie 0- und 1-Simplexmatrizen in Beziehung stehen. Die Theorie ist somit eine topologisch korrekte Erweiterung der Hückel-Theorie auf drei Dimensionen.

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Résumé Dans les parties I et II de cette suite d'articles on a démontré que des liaisons localisées à trois et à deux centres peuvent Être employées comme fonctions de base pour des calculs d'orbitales moléculaires sur des molécules polyhédriques boriques fermées («cage») et ouvertes («panier»). Dans cet article on montre que les matrices «faces» et «arÊtes» de cette théorie sont liées aux matrices d'incidence et aux matrices Simplexes 1 et 2 de la mÊme manière que dans la théorie de Hückel la matrice hamiltonienne est reliée aux matrices d'incidence et simplexes 0 et 1. La théorie est donc une extension à trois dimensions, correcte du point de vue topologique, de la méthode de Hückel.