Berechnung von mittleren Schwingungsamplituden einiger tetraedrischer Moleküle und Ionen nach der Methode der charakteristischen Schwingungen

Mean amplitudes of vibration of a series of tetrahedralXY ₄ molecules and ions (hydrides, halides, oxides and oxoanions) have been calculated using the “Method of the Characteristic Vibrations” ofA. Müller. The results indicate that this method leads to very good values for most of the investigated species, and especially in the cases of highM _X/M_Y mass ratio.     

Ion cyclotron resonance studies of some reactions of C+ ions

Product distributions and rate constants for the reaction of ground state C⁺ ions with O₂, NO, HCl, CO₂, H₂S, H₂O, HCN, NH₃, CH₄, H₂CO, CH₃OH, and CH₃NH₂ have been measured. Rate constants were obtained using ion cyclotron resonance trapped ion methods at JPL, and product distributions were obtained using a tandem (Dempster-ICR) mass spectrometer at the University of Utah. Rapid carbon isotope exchange has also been observed in C⁺-CO collisions.     

Gleichverteilung und Quadratwurzelschnecke

A new proof of a theorem of W. Neiss is given that the rays of the Quadratwurzelschnecke are uniformly distributed mod 2 . The exact order of the discrepancy of the sequence is determined. Multidimensional generalizations of this sequence are also considered. It is shown that the Quadratwurzelschnecke is something like a roulette.

---

---

Mit 2 Abbildungen

---

Herrn Prof. R. M. Redheffer in Freundschaft zum 60. Geburtstag gewidmet     

Der quadratfreie Kern der Eulerschen φ-Funktion

It is shown by a simple induction that any square-free natural number is the square-free kernel of Euler's -function of infinitely many natural numbers. Furthermore every square-free natural number >1 is the square-free kernel of Euler's -function of infinitely many square-numbers.     

Redox control of the P450cam catalytic cycle: effects of Y96F active site mutation and binding of a non-natural substrate

Spectroelectrochemistry measurements are used to demonstrate that active site mutation and binding of an non-natural substrate to P450cam (CYP101) reduces the shift in the redox potential caused by substrate-binding, and thereby results in slower catalytic turnover rate relative to wild-type enzyme with the natural camphor substrate.     

A SIFT ion-molecule study of some reactions in Titan's atmosphere. reactions of N(+), N(2)(+), and HCN(+) with CH(4), C(2)H(2), and C(2)H(4)

The results of a study of the ion-molecule reactions of N(+), N(2)(+), and HCN(+) with methane, acetylene, and ethylene are reported. These studies were performed using the FA-SIFT at the University of Canterbury. The reactions studied here are important to understanding the ion chemistry in Titan's atmosphere. N(+) and N(2)(+) are the primary ions formed by photo-ionization and electron impact in Titan's ionosphere and drive Titan's ion chemistry. It is therefore very important to know how these ions react with the principal trace neutral species in Titan's atmosphere: Methane, acetylene, and ethylene. While these reactions have been studied before the product channels have been difficult to define as several potential isobaric products make a definitive answer difficult. Mass overlap causes difficulties in making unambiguous species assignments in these systems. Two discriminators have been used in this study to resolve the mass overlap problem. They are deuterium labeling and also the differences in reactivities of each isobar with various neutral reactants. Several differences have been found from the products in previous work. The HCN(+) ion is important in both Titan's atmosphere and in the laboratory.     

The Mitsunobu Reaction: Origin,Mechanism, Improvements,and Applications

The Mitsunobu reaction is a widely used and versatile method for the dehydrative oxidation–reduction condensation of an acid/pronucleophile usually with a primary or secondary alcohol that requires the combination of a reducing phosphine reagent together with an oxidizing azo reagent. The utility of this reaction stems from the fact that it is generally highly stereoselective and occurs with inversion of the stereochemical configuration of the alcohol starting material. Furthermore, as carboxylic acids, phenols, imides, sulfonamides, and other compounds can be used as the acid/pronucleophile, this reaction is useful for the preparation of a wide variety of functional groups. This Focus Review of the Mitsunobu reaction summarizes its origins, the current understanding of its mechanism, and recent improvements and applications.     

Carbonyldinitrosyltris(fluorosulfato)tungstate(II) and ‐Molybdate(II) Anions: Synthesis,Spectroscopy, and Density Functional Theory Calculations

Carbonyldinitrosyltris(fluorosulfato)tungstate(II) and ‐molybdate‐(II) anions, [fac‐M(CO)(NO)₂(SO₃F)₃]^? (M=W, Mo), which are novel weakly coordinating anions that contain a metal carbonyl/nitrosyl moiety, have been generated in fluorosulfonic acid and completely characterized by multinuclear NMR, IR, and Raman spectroscopy as well as ESI mass spectrometry. ESI MS measurements performed for the first time on a superacidic solution system unambiguously reveal the formation of the monoanionic, mononuclear W and Mo complexes formulated as [M(CO)(NO)₂(SO₃F)₃]^? (M=W, Mo). Multinuclear NMR spectroscopic studies at natural abundance and ¹³C and ¹⁵N enrichment clearly indicate the presence of one CO ligand, two equivalent NO ligands, and two types of nonequivalent SO₃F^? groups in a 2:1 ratio. The IR and Raman spectra reveal that the two equivalent NO ligands have a cis conformation, thus indicating a fac structure. Density functional calculations at the B3LYP level of theory predict that these anions have a singlet ground state (¹A′) with a C_s symmetry along with C–O and N–O vibrational frequencies that are in agreement with the experimental observations. Mulliken population analysis shows that the monovalent negative charge is dispersed on the bulky sphere, the surface of which is covered by all the negatively charged O and F atoms with charge densities much lower than SO₃F^?, suggesting that [fac‐M(CO)(NO)₂(SO₃F)₃]^? (M=W, Mo) are weakly nucleophilic and poorly coordinating anions.     

Folded chain crystals as micro-phases

Summary A thermodynamic treatment of homo-polymer systems out of linear chains with folded chain crystals is developed outgoing from appropriate models for single component systems. An expansion of thermodynamics to multi-micro-phase systems the structure of which is partially or totaly frozen is indispensable. General properties of melt crystallized homopolymers with folded chain crystals can be recognized indeed when the thermodynamic formalisms developed are applied.

---

Zusammenfassung Das Schmelzen in polymeren Einteilchensystemen mit Faltungskristallen einheitlicher Dicke kann thermodynamisch als Umwandlung 1. Ordnung in einer Richtung behandelt werden, wenn die Faltungslänge bis zur Umwandlungstemperatur konstant bleibt (Faltungslänge als innerer Zusatzparameter). Eine wesentliche begriffliche Erweiterung ist für eine phänomenologische Beschreibung mit den Mitteln der Thermodynamik unumgänglich, wenn eine Faltungskristallit-Dickenverteilung existiert, weil dann prinzipiell nur noch partielle Koexistenz bestimmter Fraktionen metastabiler autonomer Mikrophasen mit der Schmelze möglich ist. Partielles Aufschmelzen und Rektistallisation können so dann auch in Betracht genommen werden. Die entwickelten Konzeptionen bewähren sich in der Anwendung auf bekannte Experimente.

---

Notation g ^c (y);g ^m (Y) molar Gibbs-free energy of a chain of a lengthy within an extended chain crystal and the melt rsp - g _o ^c ;g _o ^m molar free enthalpy of the unit in the crystal lattice and the melt rsp - g(y,y, f) molar Gibbs-function of an ideally folded chain crystal with the fold heighty _f - gco(y, y _ef,y _f) molar free enthalpy of the crystal corey _co - g ₀ ^ex ((y_ef) excess free enthalpy of the longitudinal layers of folded chain crystals - g ^f(y_ef,g _o ^ex ) molar free enthalpy of the longitudinal layers of the folded chain crystals - g ^tot molar free enthalpy of a chain of the lengthy within a folded chain crystal with longitudinal layers - h _o ^1c ,h _o ^m molar enthalpy of the chain unit within the crystal lattice and the melt rsp - h =h _o ^m -h _o ^c molar heat of fusion of the unit - C _p=C _p ^m -C _p ^c difference of the molar specific heat of a unit within the melt and within the chain crystal - h ^D molar defect enthalpy of local defects within the crystal lattice - h ^D molar defect enthalpy of the unit - s _o ^c ,s _o ^m molar entropy of the chain unit within the crystal lattice and the melt rsp - s _c ^m conformational entropy of a chain in the melt - s _gk conformational entropy of a chain of lengthy within a super-lattice as indicated in figure 5, - s molar entropy of fusion of the melt - s _n ^c nematic configurational entropy - T absolute temperature - T _M melting temperature of extended chain crystals of infinite size - T _M(y) melting temperature of extended chain crystals containing only chains of the lengthy - T _M (y, y _f) melting temperatureof folded chain crystals of the thicknessy _f composed of chains of the lengthy - T _M(y _f) melting temperature of folded chain crystals of the thicknessy _fy - _eh excess free enthalpy of the chain ends occupying crystallographic places - _ef excess free enthalpy of a single fold loop - z coordination number of the lattice - 7 Euler's constant - R Boltzmann's constant - y number of chain units - y _f height of lamelliform folded chain crystals - f=(y/y _f - 1) number of fold loops of a chain of a lengthy when being built into a folded chain crystal of the thicknessy _f - y _co thickness of the crystal core of the simplified twophase model - y _et average thickness of the surface layers of folded chain crystals - N _c number of crystallized units of a chain of the lengthy - x _c molar number of crystallized units of a chain of the lengthy - x _nc molar number of noncrystallized units - excess free enthalpy parameter - (y _f) thickness distribution of the fold heightsy _f With 15 figures and 2 tables     

Über 1-Alkyl-bzw. 1-Aryl-dihydro-6-methyl-2(1H)-pyrimidinthione

The title compounds7 are formed in a general reaction by heating β-isothiocyanoketones3 with primary amines in inert solvents, or by thermal elimination of water from tetrahydro-6-hydroxy-6-methyl-2(1H)-pyrimidinethiones5, also in inert solvents. The 1-alkyl compounds can also be prepared under similar conditions from α,β-unsaturated ketones by reaction with alkylammonium rhodanides. The NMR-spectra show that the 1-substituted dihydro-6-methyl-2(1H)-pyrimidinethiones are in tautomeric equilibrium with the tetrahydro-6-methylene-2(1H)-pyrimidinethiones13. The reactivity of 1-alkyl and 1-aryldihydro-6-methyl-2(1H)-pyrimidinethiones is similar to that of dihydro-4,4,6-trimethyl-2(1H)-pyrimidinethione7 j, although their ring stability is certainly less.