Spectroscopic study of compounds possessing a bond of an element of group IVB with hydrogen

Conclusions The frequencies of the valence vibrations of the Si-H bond in trisubstituted silanes depends not only on the inductive effect of substituents, but also on the effects of d-p interaction, ,- and p,-conjugation. An analysis was made of the relative contributions of these effects, depending on the nature of the substituent.For the preceding communications, see [1, 2].Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 3, pp. 544–550, March, 1971.     

Unrestricted perfect pairing: the simplest wave-function-based model chemistry beyond mean field

The perfect pairing (PP) approximation from generalized valence bond theory is formulated in an unrestricted fashion for both closed- and open-shell systems using a coupled cluster ansatz. In the model chemistry proposed here, active electron pairs are correlated, but the unpaired or radical electrons remain uncorrelated, leading to a linear number of decoupled cluster amplitudes which can be solved for analytically. The alpha and beta spatial orbitals are variationally optimized independently. This minimal treatment of electron-electron correlation noticeably improves upon symmetry-breaking problems and other pathologies in Hartree-Fock (HF) theory and may be computed using the resolution of the identity approximation at only a factor of several times more effort than HF itself. PP also generally predicts improved molecular structures over HF. This compact, correlated wave function potentially provides a useful starting point for dynamical correlation corrections.     

Röntgenkleinwinkeluntersuchungen an Lösungen von Schweineserum-Albumin bei verschiedenen pH-Werten

Zusammenfassung Schweineserum-Albumin wurde nach sorgfältiger Reinigung bei den pH-Werten 7,0, 5,1 und 3,7 mit Hilfe der Röntgenkleinwinkelstreuung untersucht. Es wurde bei allen Messungen praktisch dasselbe Molekulargewicht gefunden: der Mittelwert liegt bei 70 300±2 500. Die Ermittlung der Streumassenradien ergab bei pH 7,0 und pH 5,1 ähnliche Werte (33,0 Å bzw. 31,1 Å), bei pH 3,7 dagegen einen Wert von 37,8 Å. Die Formbestimmung ergab bei pH 7,0 und pH 5,1 identische Achsenverhältnisse (0,75 : 1 : 2), während bei pH 3,7 ein solches von 0,2 : 1 : 1 gefunden wurde.

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X-ray small-angle scattering investigations on solutions of porcine serum albumin at differentpH-values

Higly purified samples of porcine serum albumin were measured by the X-ray small-angle scattering method at pH 7.0, 5.1, and 3.7. The molecular weight is found to be the same in all three cases: the mean value is 70 300±2 500. The radius of gyration is 31.1 Å and 33.0 Å at pH 5.1 and 7.0 resp., whereas at pH 3.7 a value of 37.8 Å is found. The determination of the molecular conformation yields a similar axial ratio at pH 5.1 and pH 7.0 of 0.75 : 1 : 2; at pH 3,7 we find an axial ratio of 0.2 : 1 : 1 to be consistent with the scattering curves.

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Herrn Prof. Dr.H. Nowotny gewidmet.     

Theoretical calculations of the vibrational spectra of the complex LibeF3 molecule

Ab initio calculations of the structure, force field, frequencies and intensities of normal modes of the LiBeF₃ molecule have been carried out, using basis sets of Huzinaga and Dunning in a double-zeta contraction. The calculated results are compared with the infrared spectrum of LiBeF₃ in an inert matrix obtained by Snelson et al.     

Lactam acetals

The diethyl acetal of N-methylpiperidin-2-one has been synthesized and its reactions with compounds having active CH₂ and CH₃ groups have been studied. In the reaction of diethyl acetal of N-methylpiperidin-2-one with malonic ester, in addition to the condensation product, ethylmalonic ester is formed. The reaction of the acetal with benzoic acid leads to O-alkylation and the formation of ethyl benzoate.For communication IV, see [2].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, pp. 954–957, July, 1973.     

High-resolution small-angle x-ray investigations on poly-o-bromostyrene in benzene solutions

Small-angle x-ray investigations on poly-o-bromostyrene in benzene solution at extremely high resolution (corresponding to a Bragg's value of 3200 Å) proved to be able to link together the ranges covered by small-angle x-ray scattering and light scattering. On the other hand, there are problems encountered in molecular weight determination of chain molecules, since both methods at extremely small angles and at finite concentrations reach the limits of particle scattering. The differing results obtained by means of the two methods for the molecular weight of a rather high molecular weight sample of poly-o-bromostyrene are ascribed to entangelements stabilized by dipole–dipole interactions. These, due to the differing Bragg's angles and concentration ranges in the two methods, affect the experimental results to a different degree.     

Reflectivity and transmitivity of a spatially dispersive crystal

The reflectivity and transmitivity of a spatially dispersive crystal for S-polarized incident light are calculated for a microscopical model in which the interaction among the crystal planes is assumed to fall exponentially with distance. The angle of incidence is arbitrary and the deduced formulae are valid from X-ray to the visible light region. The generalization to the more complicated models is briefly discussed. For solving the problem an algebraic formulation of the Ewald dynamical theory of diffraction is used.     

Charged particle evaporation from compound nuclei formed by bombardment of58Ni with 70 MeV16O ions II

The experimental data have been compared with the result of extensive compound nucleus calculations based on the statistical theory. The shapes and the absolute cross sections for the high energy parts of the proton- and -spectra are reproduced with a level density parametera 0·11 A MeV^–1 and a moment of inertiaJ1·3J _rig. The same parameters fairly well reproduce the angular distributions corresponding to the high energy parts of the spectra whereas deviations between theory and experiment are observed for the lower energies where particles emitted by higher order processes contribute. The observed total cross section for emission of an -particle is 500 mb or 1·7 times calculated value. For protons the corresponding numbers are 2313 mb and 3·0. The increase in cross section is ascribed to the process in which several particles are evaporated. Various methods are discussed for determination of the average orbital angular momentum of the emitted particle or the average spin of the daughter nucleus.On leave fromFaculty of Matematics and Physics, Charles University, Prague, Czechoslovakia.     

Risikominimierung bei der Portfolioplanung unter besonderer Berücksichtigung singulärer Kovarianzmatrizen

Zusammenfassung Bisher waren die Untersuchungen über Erwartungswert-Streuungs-effiziente Wertpapiermischungen auf den Fall nichtsingulärer Kovarianzmatrizen beschränkt. Der Fall singulärer Kovarianzmatrizen war bisher nicht konstruktiv behandelt worden. Es wird in dem vorstehenden Papier in einem allgemeinen Ansatz, der auch den Fall singulärer Kovarianzmatrizen zuläßt, die allgemeine Gültigkeit des Separationstheorems und des Zwei-Fonds-Theorems nachgewiesen.

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Summary Previous studies of mean-variance-efficient portfolios got constructive results in the case of non-singular covariance matrices only, singular covariance matrices were not treated in a constructional way. The present paper proves the Separation Theorem and the Two-Fonds-Theorem within a general framework including the case of singular covariance matrices.