Applications of Padé approximants of type II in partitioning technique

Padé approximants of type II have been applied to solve equations of the type F(z) = 0. The method is compared with the first-order iteration procedure, the Aitken-Samuelson formula, and the Newton-Raphson tangential method. As a test example the partitioning technique in its most simple form is applied to the Hamiltonian of a rigid symmetric-top molecule in a static electric field. The proposed algorithm is found to be superior to the first-order procedure and the Aitken-Samuleson formula, and at least as effective as the Newton-Raphson method.     

Chemischer Transport fester Lösungen. 9 [1] Zum Chemischen Transport fester Lösungen in den Systemen Eisen(II)/Cobalt(II)‐ und Mangan(II)/Cobalt(II)‐germanat

Metagerma‐Chemical Vapor Transport of Solid Solutions. 9. The Chemical Vapor Transport of Solid Solutions in the System Iron(II)/(Cobalt(II)‐and Manganese(II)/Cobalt(II) Germanate By means of chemical vapor transport methods (900 → 700 °C) using HCl as transport agent FeGeO₃, Fe₂GeO₄ and MnGeO₃ have been prepared. Co₂GeO₄ and Fe₂GeO₄ as well as CoGeO₃ and FeGeO₃ form continuous crystalline solid solutions, whereas in MnO/CoO/GeO₂ two different phases (Mn_xCo_1‐x)GeO₃ are formed. All of these systems show congruent transport behaviour. Chemical vapor transport has been proved a suitable method to prepare solid solutions.     

Studies on polyhaloalkanes Ⅱ.A facile method for mono-fluorination of α,ω-dihaloperfluoroalkanes

A faeilo monofluorination of α,ω-dihaloporfluoroalkanes was achieved by the reactionof them with antimony trifluoride and chlorine in anhydrous antimony pentachloride when mono-fluorinated products wero removed immediately after their formation from the reaction mixture byfractionation.The reaction conditions were also investigated.     

α-Santonin: Photochemie in protischen Lösungsmitteln und Pyrolyse

In protic media of the type R? OH and R? COOH irradiation of α-santonin yields addition products of the isophotosantonic-lactone type 3 apart from lumisantonin ( 2 ) and in some cases its photoproducts. The amount of 3 depends on the acidity of the solvent up to a limiting value, above which exoanhydro-isophotosantonic-lactone ( 5 ) is also formed. Under pyrolytic conditions α-santonin is in equilibrium with pyrosantonin ( 14 ), the structure of which is discussed.     

Homogene Lösungskatalyse. Über die milieubedingte hemmende und aktivierende peroxidatische Wirkung von Zn2+−, Cr3+− und CrO −lonen in homogener Lösung

The title ions are in sodium acetate solution activators, and in sodium tartrate solution inhibitors, for the peroxidatic decolouration of indigocarmine by H₂O₂ at 37 °C.     

Löslichkeitsprodukte von Metalloxiden und -hydroxiden. 11. Mitteilung [1]. Die Löslichkeit von α-GaO(OH) bei 60°C in perchlorsauren Lösungen konstanter Ionenstärke

The solubility equilibrium of α-GaO(OH) has been investigated at 60°C in solutions of perchloric acid having a constant ionic strength I = 3 m (Na, H)ClO₄. The hydrogen ion concentration of the equilibrated solutions was measured with a glass electrode and the concentration of the dissolved Ga^III was determined by chelometric titration. The experimental data can be explained by assuming the equilibrium .     

Bifunctional even-electron ions. II. Fragmentation behaviour of aliphatic ω-hydroxy and ω-methoxy methoxonium ions

Bifunctional methoxonium ions \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm R} -\mathop {\rm C}\limits^ + ({\rm OCH}_3 ) - ({\rm CH}_2 )_{\rm n} - {\rm OH}({\rm b}) $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm R} - \mathop {\rm C}\limits^ + ({\rm OCH}_3 ) - ({\rm CH}_2 )_{\rm n} - {\rm OCH}_3 ({\rm c}) $\end{document} (c) show as the main reactions those caused by functional group interaction, as has already been found for the analogous hydroxonium ions (g). Although there are similarities in the fragmentation behaviour of the isomeric ions b and g, their fragmentation pathways are different, proving b and g as distinct species. The dominant primary fragmentation for b and c is loss of CH₃OH. The hydrogen migrations prior to this reaction have been established by deuterium labelling. The findings on the fragmentation behaviour of the bifunctional methoxonium ions have been extended to the general behaviour of hydroxy and alkoxy substituted alkoxonium ions.     

P.‐O. Löwdin and the International Journal of Quantum Chemistry: A kaleidoscopic agenda for quantum chemistry

This is a article about P.‐O. Löwdin's life, his work in shaping quantum chemistry into a mature discipline at the intersection of mathematics, physics, chemistry, and biology, and his founding of the International Journal of Quantum Chemistry in 1967. Unavoidably, it is, also, a article reflecting our views about the history of quantum chemistry. We attempt to convey the complexities in the becoming of a subdiscipline, like quantum chemistry, where a variety of factors will have to be taken into consideration for a comprehensive understanding of its historical developments: the relations of chemists to the Heisenberg‐Schrödinger formulation of quantum mechanics after 1926, the institutional dynamics centered around the establishment of new courses and chairs, the research agendas and the vying for dominance within the community of quantum chemists, the methodological, and philosophical issues that have never left the quantum chemists indifferent, and, of course, the dramatic role of the computer in transforming the culture for actually practicing quantum chemistry. Furthermore, attracted by American history, culture, and ways of life, Löwdin suggested in the late 1970s that the post‐WWII character of quantum chemistry was dependent on its ability to hub a “scientific melting pot,” much like the United States of America which he viewed as a fusion of people from diverse provenances and cultures. In this article, we attempt to investigate another metaphor, that of the “kaleidoscope.” Löwdin believed that quantum chemistry's strength arose from its ability to nurture a multiplicity of heterogeneous cultural elements/subcultures and practices, interacting with each other, exchanging perspectives and modes of action, which circulated in an increasingly extended network of actors and institutional frameworks. © 2013 Wiley Periodicals, Inc.     

Studies in perturbation theory XIII. Treatment of constants of motion in resolvent method,partitioning technique,and perturbation theory

After a brief survey of some basic concepts in the theory of linear spaces, the eigenvalue problem is formulated in the resolvent technique based on the introduction of a reference function φ and a complex variable ?. This leads to a series of fundamental concepts including the trial wave function, the inhomogeneous equation, and finally the transition and expectation values of the Hamiltonian, of which the former renders a “bracketing function” for the energy. In order to avoid the explicit limiting procedures in this approach, the eigenvalue problem is then reformulated in terms of the partitioning technique which, in turn, leads to a closed form of infinite-order perturbation theory. The eigenvalue problem is greatly simplified if the Hamiltonian H has a constant of motion Λ or has symmetry properties characterized by the group G = {g}, and the question is now how these simplifications can be incorporated into the partitioning technique and into perturbation theory. In both cases, there exists a set of projection operators {Q_k} which lead to a splitting of the Hilbert space into subspaces which have virtually nothing to do with each other. It is shown that, in the partitioning technique, it is sufficient to consider one of these subspaces at a time, and the results are then generalized to perturbation theory. It turns out that the finite-order expansions are no longer unique, and the commutation rules connecting the various forms are derived. The infinite-order results are finally presented in such a form that they are later suitable for the evaluation of upper and lower bounds to the energy eigenvalues.