Optimal radius of convergence of interpolatory iterations for operator equations

The convergence of the class of direct interpolatory iterationsI _n for a simple zero of a non-linear operatorF in a Banach space of finite or infinite dimension is studied.A general convergence result is established and used to show that ifF is entire the radius of convergence goes to infinity withn while ifF is analytic in a ball of radiusR the radius of convergence increases to at leastR/2 withn.The research was supported in part by the National Science Foundation under Grant MCS 75-222-55 and the office of Naval Research under Contract N00014-76-C-0370, NR 044-422.     

Electric field effects on the shielding constants of noble gases: a four-component relativistic Hartree-Fock study

Second derivatives of nuclear shielding constants with respect to an electric field, i.e., shielding polarizabilities, have been calculated for the noble gas atoms from helium to xenon. The calculations have been carried out using the four-component relativistic Hartree-Fock method. In order to assess the importance of the individual relativistic corrections, the shielding polarizabilities have also been calculated at the nonrelativistic Hartree-Fock level, with spin-orbit and scalar (Darwin and mass-velocity) effects having been established by perturbative methods. Electron correlation effects have been estimated using the second-order polarization propagator approach. The relativistic effects on the tensor components of the shielding polarizabilities are found to be larger and changing less regularly with the atomic number than for the shielding constant itself. However, there is a partial cancellation of the contributions to the parallel and perpendicular components of the shielding polarizability and as a consequence the mean shielding polarizability is far less affected than the individual components.     

Enantioselective Synthesis of 3- Azabicyclo[4.3.0]nonane Alkaloids

The stereospecific synthesis of the monoterpene alkaloids (?)-α-skytanthine ((?)- 2 ), (?)-N -demethyle-δ-sky-tanthine((?)- 7 ), and (+)-epidihydrotecomanine (+)- 4 was achieved from a common intermediate 22 , which in turn was obtained from (1R,4S,1′S)-2-(1′-phenylethyl)-2-azabicyclo[2.2.1]hept-5-ene (10) ,via a ketene aza-Claisen rearrangement. The piperidine derivative (+)- 31 , formally the aza-analogue of (+)-isoiridomyrmecin, was also obtained from the same intermediate 22 .     

Theoretical evaluation of atomic charges to be integrated into conformational analyses of neutral lipids

Conformational analyses of large molecules as fatty acids and triglycerides are usually amenable by molecular mechanics. A correct evaluation of the electrostatic energy term is thus crucial in determining reliable results. In this contribution, we have considered the most abundant fatty acids in biomembranes, i.e., lauric, stearic, oleic, and elaidic acid, and the corresponding triglycerides, i.e., trilaurin, tristearin, triolein, and trielaidin, and estimated the Mulliken and potential-derived charges both at the semiempirical AM 1 and ab initio HF MO STO -3G level. Atomic charges obtained by the Mulliken population analysis do not take into account the full geometry of the molecule. On the contrary, the change of conformation, due to different chains length or the presence of a trans or cis double bond, greatly influences the repartition of the potential-derived charges. A systematic comparative analysis shows that charges calculated by AM 1 are not suitable because as they do not reproduce potential-derived charges obtained by ab initio. © 1993 John Wiley & Sons, Inc.     

Zur Kenntnis der Reaktionsfähigkeit des Thiomorpholins und alkylsubstituierter Thiomorpholine, 4. Mitt.

Thiomorpholine as well as alkyl substituted thiomorpholines and their Sdioxides, respectively, are transformed into the corresponding N-Aminothiomorpholines by nitrosation (1–5) followed by the reduction with zinc in acetic acid/acetic acid anhydride under simultaneous formation of the corresponding N-acetyl derivates, and hydrolysis by hydrochloric acid (6–9). Examples of this method are described. 4-Aminothiomorpholines and their Sdioxides react with aldehydes or ketones to give azomethines (10–31). Acylation with mono-and dicarbonic acid chlorides leads to the N-acyl derivatives32–44.Mannich condensation is also possible. By oxidation with yellow mercury oxide tetracenes are formed (46–47).

Teil der DissertationM. Schmitz, Techn. Hochschule Aachen, 1975.     

H-bonding dependent structures of (NH4+)3H+(SO4 2-)2. Mechanisms of phase transitions

The role of different H-bonds in phases II, III, IV, and V of triammonium hydrogen disulfate, (NH(4)(+))(3)H(+)(SO(4)(2)(-))(2), has been studied by X-ray diffraction and (1)H solid-state MAS NMR. The proper space group for phase II is C2/c, for phases III and IV is P2/n, and for phase V is P onemacr;. The structures of phases III and IV seem to be the same. The hydrogen atom participating in the O(-)-H(+).O(-) H-bond in phase II of (NH(4)(+))(3)H(+)(SO(4)(2)(-))(2) at room temperature is split at two positions around the center of the crucial O(-)-H(+).O(-) H-bonding, joining two SO(4)(2)(-) tetrahedra. With decreasing temperature, it becomes localized at one of the oxygen atoms. Further cooling causes additional differentiation of possibly equivalent sulfate dimers. The NH(4)(+) ions participate mainly in bifurcated H-bonds with two oxygen atoms from sulfate anions. On cooling, the major contribution of the bifurcated H-bond becomes stronger, whereas the minor one becomes weaker. This is coupled with rotation of sulfate ions. In all the phases of (NH(4)(+))(3)H(+)(SO(4)(2)(-))(2), some additional, weak but significant, reflections are observed. They are located between the layers of the reciprocal lattice, suggesting possible modulation of the host (NH(4)(+))(3)H(+)(SO(4)(2)(-))(2) structure(s). According to (1)H MAS NMR obtained for phases II and III, the nature of the acidic proton disorder is dynamic, and localization of the proton takes place in a broader range of temperatures, as can be expected from the X-ray diffraction data.     

First row divalent transition metal complexes of aryl-appended tris((pyridyl)methyl)amine ligands: syntheses, structures, electrochemistry, and hydroxamate binding properties

Divalent manganese, cobalt, nickel, and zinc complexes of 6-Ph(2)TPA (N,N-bis((6-phenyl-2-pyridyl)methyl)-N-((2-pyridyl)methyl)amine; [(6-Ph(2)TPA)Mn(CH(3)OH)(3)](ClO(4))(2) (1), [(6-Ph(2)TPA)Co(CH(3)CN)](ClO(4))(2) (2), [(6-Ph(2)TPA)Ni(CH(3)CN)(CH(3)OH)](ClO(4))(2) (3), [(6-Ph(2)TPA)Zn(CH(3)CN)](ClO(4))(2) (4)) and 6-(Me(2)Ph)(2)TPA (N,N-bis((6-(3,5-dimethyl)phenyl-2-pyridyl)methyl)-N-((2-pyridyl)methyl)amine; [(6-(Me(2)Ph)(2)TPA)Ni(CH(3)CN)(2)](ClO(4))(2) (5) and [(6-(Me(2)Ph)(2)TPA)Zn(CH(3)CN)](ClO(4))(2) (6)) have been prepared and characterized. X-ray crystallographic characterization of 1A.CH(3)()OH and 1B.2CH(3)()OH (differing solvates of 1), 2.2CH(3)()CN, 3.CH(3)()OH, 4.2CH(3)()CN, and 6.2.5CH(3)()CN revealed mononuclear cations with one to three coordinated solvent molecules. In 1A.CH(3)()OH and 1B.2CH(3)()OH, one phenyl-substituted pyridyl arm is not coordinated and forms a secondary hydrogen-bonding interaction with a manganese bound methanol molecule. In 2.2CH(3)()CN, 3.CH(3)()OH, 4.2CH(3)()CN, and 6.2.5CH(3)()CN, all pyridyl donors of the 6-Ph(2)TPA and 6-(Me(2)Ph)(2)TPA ligands are coordinated to the divalent metal center. In the cobalt, nickel, and zinc derivatives, CH/pi interactions are found between a bound acetonitrile molecule and the aryl appendages of the 6-Ph(2)TPA and 6-(Me(2)Ph)(2)TPA ligands. (1)H NMR spectra of 4 and 6 in CD(3)NO(2) solution indicate the presence of CH/pi interactions, as an upfield-shifted methyl resonance for a bound acetonitrile molecule is present. Examination of the cyclic voltammetry of 1-3 and 5 revealed no oxidative (M(II)/M(III)) couples. Admixture of equimolar amounts of 6-Ph(2)TPA, M(ClO(4))(2).6H(2)O, and Me(4)NOH.5H(2)O, followed by the addition of an equimolar amount of acetohydroxamic acid, yielded the acetohydroxamate complexes [((6-Ph(2)TPA)Mn)(2)(micro-ONHC(O)CH(3))(2)](ClO(4))(2) (8), [(6-Ph(2)TPA)Co(ONHC(O)CH(3))](ClO(4))(2) (9), [(6-Ph(2)TPA)Ni(ONHC(O)CH(3))](ClO(4))(2) (10), and [(6-Ph(2)TPA)Zn(ONHC(O)CH(3))](ClO(4))(2) (11), all of which were characterized by X-ray crystallography. The Mn(II) complex 8.0.75CH(3)()CN.0.75Et(2)()O exhibits a dinuclear structure with bridging hydroxamate ligands, whereas the Co(II), Ni(II), and Zn(II) derivatives all exhibit mononuclear six-coordinate structures with a chelating hydroxamate ligand.     

Self-assembly of [2]rotaxane exploiting reversible Pt(II)- pyridine coordinate bonds

A dinuclear self-assembled cationic macrocycle based on Pt(II)-N(pyridine) coordinative bonds and having competitive triflate anions, as metal counterions, is used in the construction of [2]rotaxane and [2]pseudorotaxane architectures assisted by hydrogen bonding. The kinetic lability of the Pt(II)-N(pyridine) coordinative bond controls the dynamics of the [2]rotaxane.     

Isotachophoretic determination of carboxylic acids in biodegradation samples

In the current study a method of isotachophoretic separation of selected carboxylic acids was developed. The method was used for the determination of carboxylated oligo(ethylene glycol)s and their degradation products in biodegradation tests of PEG 250 DA [a mixture of dicarboxylated oligo(ethylene glycol)s]. Two tests were performed in the studies: the Organization for Economic Cooperation and Development (OECD) screening test and the river water die-away test. Both the biodegradation tests proved relatively fast biodegradation of the studied compounds. In the OECD screening test the biodegradation was faster than in the river water die-away test which can be ascribed to a higher concentration of bacteria in the biodegradation liquor. The minimal sample pretreatment and relatively low cost of analysis by the isotachophoretic method used here make it a good alternative to existing methods of carboxylic acids analysis.