Untersuchungen an Kristallhydraten anorganischer Salze, 8. Mitt. Interpretation der Schwingungsspektren vonM(BF4)2·6H2O fürM=Fe2+, Co2+, Ni2+

The infrared and Raman spectra were recorded in the range 4000–160 cm^–1 forM(BF₄)₂·6 H₂O whereM=Fe²⁺, Co²⁺, Ni²⁺. The spectroscopic data support the X-ray structural data in showing that in the crystal hydrates studied two kinds of hydrogen bonds are present: H₂O...H₂O and OH₂... F₄B^–. The energies and molecular force constants (f _OH and fH₂O) andr _OH for OH₂...F₄B^– were calculated for the three crystal hydrates. It was found that the bond OH₂... F₄B^– is comparatively weak, with mean energy 3.7–3.3 kcal/mol. Two types of water molecule with different structures are existing as the first are participating in H₂O...H–O–H...F₄B^– and the second in BF₄ ^–...H–O–H...F₄B^–.     

Low spin ferric hemoglobin complexes

A caloulation has been made of the energy eigenfunotions and eigenvalues of low spin ferric ion in complexes with a strong cubic crystal field including the effects of tetragonal and rhombic distortions and of spin-orbit coupling among the ground state components and with excited states. Using the resultant, spin-orbit coupled eigenfunotions as a basis set, the magnetic susceptibility, the components of magnetic field energy, and the lattice and valence contributions to an electric field gradient at the iron nucleus were all calculated as a function of rhombic, tetragonal, and spin-orbit coupling strength used as parameters: R, u and . All of the calculated results agree reasonable well with experiment for the values of parameters R=1000 cm^–1, u=2000 cm^–1 and the free ion value (=420 cm^–1. These values of parameters were selected for the excellent fit they gave of the calculated values of g _x, g_y and g _z compared with the experimental ones obtained from single crystal electron spin resonance of ferrihemoglobin azide. With them, a value of 2.29 Bohr magnetons was calculated for the effective magnetic moment compared to the experimental value of 2.35. The total field gradient calculated under the same conditions, predicts a nuclear quadrupole moment Q in the range of. 107 –127. Barns, which is smaller than the range predicted from the high spin ferric ion results. Reasons for this discrepancy are discussed.

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Zusammenfassung Ausgehend von einem starken kubischen Ligandenfeld und unter Berücksichtigung tetragonaler (R) und rhombischer (u) Verzerrung sowie der Spin-Bahn-Kopplung () werden Eigenfunktionen und Energien fur Low-Spin-Ferrihämoglobinkomplexe berechnet. Mit den Parametern R=1000 cm^–1, u=2000 cm^–1, =420 cm^–1 erhält man für Suszeptibilität, elektrischen Feldgradienten am Fe und g-Werte gute Übereinstimmung mit experimentellen Daten. Aus dem berechneten Feldgradienten folgt ein Quadrupolmoment des Fe⁵⁷ von 0.107–0.127 Barn, im Gegensatz zu den viel höheren Resultaten bei High-Spin-Fe(III)-Verbindungen; diese Diskrepanz wird diskutiert.

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Résumé Les fonctions propres et les énergies du complexe Ferrihémoglobine «low spin» sont calculées pour un fort champ de ligandes à symétrie cubique, en tenant compte des distortions tétragonale (R) et rhomboédrique (u), ainsi que du couplage spin-orbite (). Avec les parametres R=1000 cm^–1, u=2000 cm^–1, =420 cm^–1, on trouve pour la susceptibilité, le gradient du champ électrique à l'emplacement de Fe et le facteur g des valeurs en bon accord avec les données expérimentales. On déduit du gradient de champ calculé un moment quadrupolaire de Fe⁵⁷ de 0,107 à 0,127 Barn, en désaccord avec les résultats beaucoup plus élevés obtenus à partir des associations Fe (III) «high spin». Ce désaccord fait l'objet d'une discussion.

     

Morphologie und Wachstumskinetik von Crazes in amorphen Polymeren

Zusammenfassung Im vorfibrillaren Stadium besitzt die Crazematerie eine in Verformungsrichtung deformierte Netzwerkstruktur, die sich bei Polystyrol und Styrol-Acrylnitril-Copolymerisat elektronenoptisch an Oberflächenabdrücken sauerstoffionengeätzter Proben nachweisen läßt. Während die durchschnittlichen Globulitverformungen zumeist deutlich unterhalb von 50% liegen, werden partiell Spitzenwerte von bis zu 300% erreicht. Am Beispiel des Polystyrols verdeutlichen quantitative Strukturvergleiche mit warmgerecktem Material, daß die molekulare Beweglichkeit während des Crazewachstums und der Schulter-Hals-Verstreckung derjenigen entspricht, die für thermisch aktiviertes Material oberhalb der Glastemperatur charakteristisch ist.Mit 7 Abbildungen und 2 Tabellen     

1H-NMR-spektroskopische Analyse von 2-Chlor-1.3.2-dioxarsolan

The¹H-NMR-spectral data of 2-chloro-1.3.2-dioxarsolane are presented and discussed. The protons of the methylene groups form in concentrated solutions by rapide chlorine exchange anAAAA spin system. In dilute solutions the protons form anAABB spin system, which is changed to anAAAA system by addition of chlorine ions.The vicinal H–C–C–H-coupling constants indicate a twist-envelope conformation.

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Mit 1 Abbildung     

Resonance type dielectric behavior in solids

Experimental evidence now indicates that the microwave dielectric properties of solids are strongly influenced by the infrared active phonon modes. The “real dielectric constant”, ε′, of polar materials, i. e. those in which ?′ is noticeably greater than the square of the optical index of refraction, exhibits a temperature dependence dominated by the change of integrated infrared absorption. The microwave dielectric loss, ?″, is influenced by the low frequency “tail” of the infrared resonance type absorption, as may be inferred from the monotonic increase with temperature and proportionality to frequency. It is suggested that the one dimensional coupling of the electric field to the acoustic modes of a dielectric solid would lead to additional low frequency “background” dielectric losses which are essentially frequency independent, in agreement with experimental observations.     

Stereochemistry of cyclobutanone resulted from cycloadditions of t-butylcyanoketene to bicyclo[2.2.1]heptene derivatives, as evidence for a π2s+π2a reaction mode

The stereochemistry of the cyclobutanones 1-7, resulted from the reaction of t-butylcyanoketene with bicyclo[2.2.1]heptene, bicyclo[2.2.1]heptadiene, 1,4 - dihydro - 1,4 - methanonaphthalene, 1,4 - dihydro - 9 - (1 - methylethylidene) - 1,4 - methanonaphthalene, 1,4 - dihydro - 1,4 - epoxynaphthalene, l,4,4a,8b - tetrahydro - 1,4 - methanobiphenylene (l,4,4a,8b) and 1,4,4a,8b - tetrahydro - 1,4 - methanobiphenylene(1,4,4aβ,8bβ) was established as having the cyclobutanone ring exo and the t-Bu group in the configuration. These findings represent a stereochemical argument in favour of a _π2_s + _π2_a reaction mode of t-butylcyanoketene to the above mentioned bicyclo[2.2.1]heptene derivatives. Observations regarding preservation of the original configurations of alkenes as well as the geometrical distorsion of the cyclobutanones are shortly discussed.     

121Sb-Mössbauer-Spektren von Antimon(V)-Verbindungen. II

¹²¹Sb Mössbauer Spectra of Antimony (V) Compounds. II The Mössbauer resonance effect of ¹²¹Sb has been studied at 4.2 K in a series of 11 antimony(V) compounds which are in most cases bridged. Isomer shift and quadrupole splitting variations are considered in the light of results of X-ray and vibrational spectroscopy. Preparation and the vibrational spectra of [NMe₄][SbCl₄(n₃)₂] are described. Within the limitations of available structural data related tin compounds are compared with those of corresponding ¹¹⁹Sn Mössbauer spectra.     

Sukzessive Minima mit und ohne Nebenbedingungen

Given semi-normsf andg on ⁿ and a real number >0. Then the successive minima off under the constraintg are defined by _j : = inf {: there existj linear independent vectors inZ ⁿ withf andg}. The main theorem of this paper (Lagrange multiplier theorem) states that the successive minima of a certainnorm h on ⁿ (without constraints) coincide with the _j 's up to bounded factors. Moreover, this norm is constructed explicitly. Using Minkowski's wellknown theorem on successive minima and our result certain inequalities on simultaneous Diophantine approximations are derived.     

A sufficient condition for a graph to be hamiltonian

Those non-hamiltonian graphsG withn vertices are characterized, which satisfy the Ore-type degree-conditiond(x)+d(y)n–2 for each pairx,yM of different nonadjacent vertices whereM consists of two vertices ofG. As an application a theorem on hamiltonian connectivity of graphs is given. Furthermore, a condition is presented which is sufficient for the existence of a covering of a graph by two disjoint paths with prescribed set of startpoints and prescribed set of endpoints. A class of graphs is described which have no covering of this kind.     

Über Mittelwerte multiplikativer zahlentheoretischer Funktionen mehrerer Variablen

In [8] the author extended the concept of neighbouring functions (cp. [9]) to the case of several variables. Using these results it is shown that under some weak conditions a multiplicative functionf in two variables has a mean-value different from zero if and only if the two multiplicative functionsf ₁(n)=f(n, 1) andf ₂(n)=f(1,n) have mean-values different from zero. Applications to theorems ofDelange [3],Elliott [6] andDaboussi [1] are given.