Generalized quantum mechanical two-centre problems

If χ _i (χ _k ) is an exact generalized diatomic orbital (solution of Eq. (1) of text), a sequence of functions χ _i ^(N) converging to χ _i may be constructed so that matrix elements of frequently occurring operators between χ _i ^(N) and χ _k ^(N) may be computed without any numerical integration. Exact expectation values are given for kinetic and potential energy, dipole moment, θ ²=x ²+y ², and quadrupole moment 3z ²?r ², for various ratios of nuclear charges Z ₁,Z ₂ and for several distances R. Special subjects discussed in terms of computed expectation values are:

1. R-dependence of the contributions to total energy of HeH²⁺ in state 2pσ and of LiH³⁺ in state 3dσ
2. RZ-and λ-dependence of dipole and quadrupole moment functions in state 1sσ
3. Some properties of those generalized diatomic orbitals which approach, for R going to 0, Slater-type atomic functions.

     

Location of saddle points and minimum energy paths by a constrained simplex optimization procedure

Two methods are proposed, one for the location of saddle points and one for the calculation of steepest-descent paths on multidimensional surfaces. Both methods are based on a constrained simplex optimization technique that avoids the evaluation of gradients or second derivative matrices. Three chemical reactions of increasing structural complexity are studied within the PRDDO SCF approximation. Predicted properties of reaction hypersurfaces are in good overall agreement with those determined by gradient minimization and gradient following algorithms in connection with various ab initio SCF methods. Computational efforts required by the new procedures are discussed.     

A 3D QSAR study on a set of dopamine D4 receptor antagonists

The molecular alignments obtained from a previously reported pharmacophore model have been employed in a three-dimensional quantitative structure-activity relationship (3D QSAR) study, to obtain a more detailed insight into the structure-activity relationships for D(2) and D(4) receptor antagonists. The frequently applied CoMFA method and the related CoMSIA method were used. Statistically significant models have been derived with these two methods, based on a set of 32 structurally diverse D(2) and D(4) receptor antagonists. The CoMSIA and the CoMFA methods produced equally good models expressed in terms of q(2) values. The predictive power of the derived models were demonstrated to be high. Graphical interpretation of the results, provided by the CoMSIA method, brings to light important structural features of the compounds related to either low- or high-affinity D(2) or D(4) antagonism. The results of the 3D QSAR studies indicate that bulky N-substituents decrease D(2) binding, whereas D(4) binding is enhanced. Electrostatically favorable and unfavorable regions exclusive to D(2) receptor binding were identified. Likewise, certain hydrogen-bond acceptors can be used to lower D(2) affinity. These observations may be exploited for the design of novel dopamine D(4) selective antagonists.     

PROTECTION OF ESCHERICHIA COLI CELLS AGAINST THE LETHAL EFFECTS OF ULTRAVIOLET AND X IRRADIATION BY PRIOR X IRRADIATION: A GENETIC AND PHYSIOLOGICAL STUDY

Abstract— When log phase cells of wild-type E. coli K-12 were maintained in growth medium after X irradiation, they became progressively more resistant to a subsequent exposure to UV or X radiation. The time to achieve maximum resistance was about 60 min. The uvrB, uvrD, polA and certain exrA strains (W3110 background) also demonstrated this X ray-induced resistance to subsequent UV or X irradiation but recA, recB, lex (AB1157 or W3110 backgrounds) and other exrA strains (AB1157 background) did not. The resistance induced in wild-type, uvrB and uvrD cells was characterized by the production or enhancement of a shoulder on the survival curves obtained for the second irradiation, while the resistance induced in the W3110 exrA strains was expressed only as a change in slope. The induction of resistance in the W3110 exrA strain was not inhibited by the presence of chloramphenicol, but that in the wild-type cells appeared to be. The production or enhancement of a shoulder on the survival curves of the rec ⁺ lex ⁺ exr ⁺ cells is consistent with the concept of the radiation induction of repair enzymes. Alternative explanations, however, are discussed.     

Divergencies in a vector model with hyperbolic symmetry on a chain

A chain of interacting vectors (, ) withn components subject to the hyperbolic conditions ²–²=1 is considered. The interaction possesses a global non-compactO(1, n–1)/O(1)×O(n–1) symmetry. Symmetries of this kind are known from the study of disordered electronic systems. The non-compactness of the symmetry group causes divergencies such that a symmetry breaking term is necessary. Asymptotic behaviour of the expectation values and long-ranged correlation functions are calculated for a small symmetry breaking field.Supported in part by the Deutsche Forschungsgemeinschaft through the Sonderforschungsbereich 123 at the University of Heidelberg     

T-Periodic solutions of time dependent Hamiltonian systems with a potential vanishing at infinity

We are discussing existence and multiplicity of T-periodic solutions of the time dependent Hamiltonian system = U(x, t) under the assumption that U(x, t) approaches 0 for large |x| meaning that the force U is concentrated in a finite region. Our method is variational and it is shown how the difficulties with the Palais-Smale condition can be overcome in this case.     

über eine Klasse Riemannscher Mannigfaltigkeiten mit raumartigen pkf-ZusammenhÄngen

One considers m-dimensional Riemannian manifoldsM with tangent spaces T_p(M), p M that are a direct sum of a spacelike m-2 planeR _p and a 2-planeH _p. It is supposed that onM there exists a connection whose space-like components are parallel conformal flat (pkf). These components are generated by a vector field X. Assuming that X belongs to a pair X,Y of reciprocal quasi-cocircular vector fields and that the Pfaffian of this pair is the 1-form associated with the connection, the following results are derived: 1. X and Y are of equal constant length (This is true for all Riemannian manifolds). 2. The immersion of the integral manifold ofH _p intoM is cylindrical and the normal connection is flat. 3. The immersion of any space-like submanifold intoM is cylindrical with respect to the sections inH _p and umbilical with respect to all spacelike sections. 4. If m 4, the integral manifoldP _p is flat.

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Herrn Prof. Dr. WERNER BURAU zum 70.Geburtstag Klaus Buchner und Radu Rosca     

A simple tree lemma and its application to a counterexample of philips

We prove a tree lemma on perfect trees to obtain an ultrafilter of definable subsets of , which is Ramsey but not conservative (see [Phi 2]).     

Spektroskopische und theoretische Untersuchungen am Borazolmolekül und seinen Bortrihalogenoderivaten

Zusammenfassung Es werden Hückel-MO-Rechnungen am Borazol und den B-Trihalogenoborazolen durchgeführt und die entsprechenden Parameter an den teils bekannten und teils gemessenen UV-Spektren geeicht. Die für diese Verbindungen bestimmten chemischen Verschiebungen der ¹¹B- und ¹⁴N-Kernresonanz lassen sich mit den berechneten -Elektronendichten erklären.

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Hückel-MO calculations are performed for Borazine and the B-Trihalogenoborazines; the parameters used are calibrated with the UV-spectra, which had either been measured here or obtained from the literature. The calculated -electron densities compare favorably well with the ¹¹B- and ¹⁴N-nuclear magnetic resonances determined for the above mentioned compounds.

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Résumé Le borazole et les B-trihalogenoborazoles sont calculés par la méthode de Hückel en utilisant des paramètres calibrés sur les spectres U.V. mesurés ou obtenus dans la littérature. Les densités électroniques sont en bon accord avec le déplacement chimique de N.M.R. de ¹¹B et ¹⁴N déterminé pour les composés cidessus.

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Herrn Professor Dr. H. Hartmann danken wir für sein stetes Interesse und die wohlwollende Förderung dieser Arbeit. Für die Hilfe bei der Aufnahme des Vakuum-UV-Spektrums von Fluoroborazol danken wir Herrn Diplom-Physiker E. Mohler.     

Der Stoffwechsel von Verbindungen mit Dreifachbindung. VI. Stoffwechselverhalten von Alkincarbonsäuren und Alkindicarbonsäuren

Metabolism of Acetylenic Monocarboxylic and Dicarboxylic Acids Feeding of acetylenic monoacids with chain length of 11 to 18 C-atoms to rats led to excretion of dicarboxylic acids with retained triple bonds. 10-Octadecynoic acid led to the formation of metabolites with even and odd number of C-atoms, suggesting in addition to established ω- and β-oxidation an α-oxidative pathway.