The ϕ 2 4 quantum field as a limit of Sine-Gordon fields

We exhibit the λ? ₂ ⁴ quantum field theory as the limit of Sine-Gordon fields as suggested by the identity $$\varphi ^4 /4! = \mathop {\lim }\limits_{\varepsilon \to 0} (\varepsilon ^{ - 4} \cos \varepsilon \varphi - \varepsilon ^{ - 4} + \tfrac{1}{2}\varepsilon ^{ - 2} \varphi ^2 ).$$ The proofs of finite volume stability for the two models, due to Nelson and Fröhlich respectively, are unrelated. We find a generalized stability argument that incorporates ideas from both of the simpler cases. The above limit, for the Schwinger functions, then proceeds uniformly in ?. As a by-product, let (?,dμ) be a Gaussian random field, ? _K (1≦κ<∞) a regularization of ?, andV a function satisfying:

1. V(? _K )≧?ak ^α
2. ∥V(?) ?V(? _K )∥ _p≦bp ^β k ^?γ, 2≦p < ∞

Thene ^?V(?)∈L ¹(dμ) provided α(β?1)<γ.     

The Robertson-Walker metric and the symmetries belong to the family of contracted Ricci collineations

It is shown that the general form of the Robertson-Walker cosmological metric admits symmetry properties that are members of the symmetry family of contracted Ricci collineations. A particular form for the conservation law generator given by _j [(–g)^1/2(T _i ^j –1/2 _i ^jT ) ⁱ ] = 0 following in consequence of these symmetries is obtained and interpreted.     

On the decay of correlations inSO(n)-symmetric ferromagnets

We prove that for low temperaturesT the spin-spin correlation function of the two-dimensional classicalSO(n)-symmetric Ising ferromagnet decays faster than |x|^–constT providedn2. We also discuss a nearest neighbor continuous spin model, with spins restricted to a finite interval, where we show that the spin-spin correlation function decays exponentially in any number of dimensions.Work supported in part by NSF, Grant PHY76-17191A Sloan Fellow     

RNAi: running interference for the cell

RNA interference or RNAi is a recently characterized mechanism of eukaryotic gene regulation in which a short sequence of double-stranded RNA (dsRNA) specifically down-regulates expression of the associated gene. Preliminary characterization of this phenomenon has revealed a set of inter-related cellular pathways which appear to represent both a response to foreign RNA and a mechanism of endogenous gene regulation. Introduction of dsRNA into cells by a variety of means, including transfection of synthetic RNA duplexes, triggers the RNAi response resulting in specific suppression of target gene expression. Recent efforts on a genome wide scale have involved application of RNAi as an important new tool in cell biology to elucidate gene function in living cells.     

Orbital contributions to the molecular charge and energy density distributions in Co2(CO)8

For Co2(CO)8, the representative of a whole class of bridged cobalt complexes, the 18-electron rule predicts a direct metal-metal bond in addition to the metal-bridge bonds. By intuition, this bond should have bent-bond character. However, it is well-known from charge density analyses that no bond critical point exists in the corresponding spatial region. Otherwise, the energy density distribution points to a certain stabilizing contribution of this local area to the total molecular energy. It is shown that a partitioning of the total charge and energy densities into orbital contributions can lead to a deeper insight into complex bonding properties.     

A systematic study of ligand intermolecular interactions in crystals of copper(II) complexes of bidentate guanidino derivatives

The synthesis and X-ray structures of four neutral copper(II) complexes and one cationic complex incorporating bidentate alkyl N-(4-oxo-5,5-diphenyl-4,5-dihydro-1H-imidazol-2-yl)imidocarbamate ligands are reported. The neutral complexes, which possess potential doublet (DA) hydrogen bonding motifs, form supramolecular structures based on synthons involving hydrogen bonding or phenyl embraces. The formation of sheets within the crystal through combination of these synthons, and the occurrence of guest molecules trapped in cavities between the sheets, are described. The cationic complex forms an extended hydrogen-bonded structure that incorporates nitrate ions. The structures of the five complexes are compared with others reported previously for complexes of related ligands.     

Dianionic complexes with hexacoordinate silicon(IV) or germanium(IV) and three bidentate ligands of the salicylato(2–) type: Syntheses and structural characterization in the solid state and in solution

Reaction of tetramethoxysilane or tetramethoxygermane with salicylic acid and morpholine (molar ratio 1:3:2) in tetrahydrofuran yielded morpholiniummer-tris[salicylato(2–)-O¹,O³]silicate(mer -5) and morpholiniummer-tris[salicylato(2–)-O¹,O³]germanate (mer-8), respectively. Treatment of tetramethoxysilane with 5-chlorosalicylic acid and piperidine (molar ratio 1:3:2) in tetrahydrofuran afforded piperidinium mer-tris[5-chlorosalicylato(2–)-O¹,O³]silicate–ditetrahydrofuran (mer-6·2THF). Triethylammonium mer-tris[3-methylsalicylato(2–)-O¹,O³]silicate (mer-7) was obtained analogously by reaction of tetramethoxysilane with three molar equivalents of 3-methylsalicylic acid and two molar equivalents of triethylamine in dichloromethane/diethyl ether. The racemic compounds mer-5, mer-6· 2THF,mer-7, and mer-8 were characterized by elemental analyses (C, H, N), single-crystal X-ray diffraction, as well as solid-state (²⁹Si) and solution(¹H, ¹³C, ²⁹Si) NMR studies. The structural characterizationwas complemented by computational studies (HF studies, TZVP level) of thefac- and mer-tris[salicylato(2–)-O¹,O³]silicatedianion. In addition, the behavior of mer-7 in solution was studied by VT ¹HNMR experiments.     

NMR‐Solution Structures of Fluoro‐Substituted β‐Peptides: A 314‐Helix and a Hairpin Turn. The First Case of a 90° OC?C?F Dihedral Angle in an α‐Fluoro‐Amide Group

To further study the preference of the antiperiplanar (ap) conformation in α‐fluoro‐amide groups, two β‐peptides, 1 and 2 , containing a (2‐F)‐β³hAla and a (2‐F)‐β²hPhe residue, have been synthesized. Their NMR‐solution structures in CD₃OH were determined and compared with those of non‐F‐substituted analogs, 3 and 4a . While we have found in a previous investigation (Helv. Chim. Acta 2005 , 88, 266) that a stereospecifically introduced F‐substituent in the central position of a β‐heptapeptide is capable of ‘breaking’ the 3₁₄‐helical structure by enforcing the F? C? C?O ap‐conformation, we could now demonstrate that the same procedure leads to a structure with the unfavorable ca. 90° F? C? C?O dihedral angle, enforced by the 3₁₄‐helical folding in a β‐tridecapeptide (cf. 1 ; Fig. 4). This is interpreted as a consequence of cooperative folding in the longer β‐peptide. A F‐substituent placed in the turn section of a β‐peptidic hairpin turn was shown to be in an ap‐arrangement with respect to the neighboring C?O bond (cf. 2 ; Fig. 7). Analysis of the non‐F‐substituted β‐tetrapeptides (with helix‐preventing configurations of the two central β²/β³‐amino acid residues) provides unusually tight hairpin structural clusters (cf. 3 and 4a ; Figs. 8 and 9). The skeleton of the β‐tetrapeptide H‐(R)β³hVal‐(R)β²hVal‐(R)β³hAla‐(S)β³hPhe‐OH ( 4a ) is proposed as a novel, very simple backbone structure for mimicking α‐peptidic hairpin turns.     

A molecular dynamics study on universal properties of polymer chains in different solvent qualities. Part I. A review of linear chain properties

This paper investigates the conformational and scaling properties of long linear polymer chains. These investigations are done with the aid of Monte Carlo (MC) and molecular dynamics (MD) simulations. Chain lengths that comprise several orders of magnitude to reduce errors of finite size scaling, including the effect of solvent quality, ranging from the athermal limit over the theta-transition to the collapsed state of chains are investigated. Also the effect of polydispersity on linear chains is included which is an important issue in the real fabrication of polymers. A detailed account of the hybrid MD and MC simulation model and the exploited numerical methods is given. Many results of chain properties in the extrapolated limit of infinite chain lengths are documented and universal properties of the chains within their universality class are given. An example of the difference between scaling exponents observed in actual solvents and those observed in the extremes of "good solvents" and "theta-solvents" in simulations is provided by comparing simulation results with experimental data on low density polyethylene. This paper is concluded with an outlook on the extension of this study to branched chain systems of many different branching types.     

Site-Selective Real-Time Observation of Bimolecular Electron Transfer in a Photocatalytic System Using L-Edge X-Ray Absorption Spectroscopy**

Time-resolved X-ray absorption spectroscopy has been utilized to monitor the bimolecular electron transfer in a photocatalytic water splitting system. This has been possible by uniting the local probe and element specific character of X-ray transitions with insights from high-level ab initio calculations. The specific target has been a heteroleptic [Ir^III(ppy)₂(bpy)]⁺ photosensitizer, in combination with triethylamine as a sacrificial reductant and as a water reduction catalyst. The relevant molecular transitions have been characterized via high-resolution Ir L-edge X-ray absorption spectroscopy on the picosecond time scale and restricted active space self-consistent field calculations. The presented methods and results will enhance our understanding of functionally relevant bimolecular electron transfer reactions and thus will pave the road to rational optimization of photocatalytic performance.