基于阿贝尔黑格斯变量的杨-米尔斯理论的红外阿贝尔化

通过SU(2)规范场的法捷耶夫-Niemi分解给出了有效阿贝尔-黑格斯型作用量的 一个计算方法. 具体指出了该分解中所用的自然规范固定以及阿贝尔投射与杨-米尔斯理论的红外动力学之间的内在关系. 推导出了色电场的一个伦敦型方程.     

Constructing Space for Science at the Royal Institution of Great Britain

Those who have worked in the Royal Institution of Great Britain have, since its foundation in 1799, made significant contributions to scientific knowledge, to its practical application, and to its communication to a wide variety of audiences. Such work cannot be carried out in an architectural vacuum, and in this paper we examine how the buildings of the Royal Institution, 20 and 21 Albemarle Street in central London, have shaped the work undertaken within its walls and how, on a number of occasions, the buildings have been reconfigured to take account of the evolving needs of scientific research and communication. This paper is based on the Conservation Plan of the Royal Institution that we wrote during 2003. The Conservation Plan did not examine the land owned by the Royal Institution to the north (i.e., 22 and 23 Albemarle Street; for this area see Richard Garnier, “Grafton Street, Mayfair,” Georgian Group Journal 13 (2003), 210–272), but it did discuss 18 and 19 Albemarle Street. In this paper we concentrate on the core Royal Institution buildings at 20 and 21 Albemarle Street. Other studies of the relationship of architecture,space, and science include Crosbie Smith and Jon Agar, ed., Making Space for Science: Territorial Themes in the Shaping of Knowledge (Basingstoke: Macmillan, 1997); Peter Galison and Emily Thompson, ed., The Architecture of Science (Cambridge, Mass.: MIT Press, 1999); and Sophie Forgan,“The architecture of science and the idea of a university,” Studies in History and Philosophy of Science 20 (1989), 405–434. Frank A.J.L. James is Professor of the History of Science at the Royal Institution; he has written widely on the history of nineteenth-century science in its social and cultural contexts and is editor of the Correspondence of Michael Faraday. He is President of the British Society for the History of Science. Anthony Peers is an Associate of Rodney Melville and Partners where he works in the field of building conservation as an architectural historian. He is a Council member of the Ancient Monument Society.     

Importance of the Debye interaction in organic solutions: Henry's law constants for polar liquids in nonpolar solvents and vice versa

Henry's law constants have been determined for -butyrolactone (BL), ethyl acetate (EA), and 2-methyl-3-pentanol (MEP) in mixtures of iso-octane (ISO) and toluene (TOL), for BL, EA, TOL, and ISO in cinnamaldehyde (CIN) and for TOL and ISO in each other and in BL. From these data and published vapor pressures, the activity coefficients at infinite dilution and the standard molar Gibbs free energy of transfer, G ₂ ⁰ of the solutes from dilute solution in ISO to dilute solution in each solvent medium have been calculated. The different behavior patterns of BL and EA are attributed to differences in their abilities to exist in different conformations possessing different dipole moments. For polar solutes, G ₂ ⁰ decreases with increasing polarizability of the solvent and with increasing dipole moment of the solute, suggesting increased contributions from dipole-induced dipole (Debye) interactions. The sigmoidal plot of G ₂ ⁰ against the change in pair potential energy calculated from the classical expressions suggests that G ₂ ⁰ seriously underestimates the strength of the Debye interactions in comparison with the London interactions.     

Oxine complex of molybdenum

Molybdenum was reported to be precipitated quantitatively by 8-hydroxyquinoline in the pH range 3.3–7.6, the precipitated compound having the composition MoO₂(ox)₂. The pH range reported and the composition of the complex do not seem to be compatible with present knowledge of the pH stability of anionic and cationic molybdenum. It is now shown that under defined conditions, the precipitate is not formed at pH values higher than 2.24. In several estimations of other metals, molybdenum was masked by using a complexone at high pH values. It is now pointed out, that maintaining the solution at high pH value is itself sufficient and no other external complexing agent is necessary for masking molybdenum.     

Hexaphenylditetrels – When Longer Bonds Provide Higher Stability

We present a computational analysis of hexaphenylethane derivatives with heavier tetrels comprising the central bond. In stark contrast to parent hexaphenylethane, the heavier tetrel derivatives can readily be prepared. In order to determine the origin of their apparent thermodynamic stability against dissociation as compared to the carbon case, we employed local energy decomposition analysis (LED) and symmetry-adapted perturbation theory (SAPT) at the DLPNO-CCSD(T)/def2-TZVP and sSAPT0/def2-TZVP levels of theory. We identified London dispersion (LD) interactions as the decisive factor for the molecular stability of heavier tetrel derivatives. This stability is made possible owing to the longer (than C−C) central bonds that move the phenyl groups out of the heavily repulsive regime so they can optimally benefit from LD interactions.     

Quantification of Noncovalent Interactions in Azide–Pnictogen, –Chalcogen,and –Halogen Contacts

The noncovalent interactions between azides and oxygen-containing moieties are investigated through a computational study based on experimental findings. The targeted synthesis of organic compounds with close intramolecular azide–oxygen contacts yielded six new representatives, for which X-ray structures were determined. Two of those compounds were investigated with respect to their potential conformations in the gas phase and a possible significantly shorter azide–oxygen contact. Furthermore, a set of 44 high-quality, gas-phase computational model systems with intermolecular azide–pnictogen (N, P, As, Sb), –chalcogen (O, S, Se, Te), and –halogen (F, Cl, Br, I) contacts are compiled and investigated through semiempirical quantum mechanical methods, density functional approximations, and wave function theory. A local energy decomposition (LED) analysis is applied to study the nature of the noncovalent interaction. The special role of electrostatic and London dispersion interactions is discussed in detail. London dispersion is identified as a dominant factor of the azide–donor interaction with mean London dispersion energy-interaction energy ratios of 1.3. Electrostatic contributions enhance the azide–donor coordination motif. The association energies range from −1.00 to −5.5 kcal mol⁻¹.     

Hyperfine structure in Iodine at the 612-nm and 640-nm helium-neon laser wavelengths

The hyperfine structure of iodine-127 at 612 nm and 640 nm is observed by saturated absorption in a gas cell placed within a He-Ne laser cavity modified to operate at these wavelengths. At 612 nm, all the 21 components of the strong R 47 9-2 line lie within the laser gain profile, and the resulting saturated absorption peaks have a contrast of 10% at a gas pressure of 3 Pa.     

Experimental and Theoretical Conformational Analysis of 5‐Benzylimidazolidin‐4‐one Derivatives – a ‘Playground’ for Studying Dispersion Interactions and a ‘Windshield‐Wiper’ Effect in Organocatalysis

The PF₆ salts of 5‐benzyl‐1‐isopropylidene‐ and 5‐benzyl‐1‐cinnamylidene‐3‐methylimidazolidin‐4‐ones 1 (Scheme) with various substituents in the 2‐position have been prepared, and single crystals suitable for X‐ray structure determination have been obtained of 14 such compounds, i.e., 2 – 10 and 12 – 16 (Figs. 2–5). In nine of the structures, the Ph ring of the benzyl group resides above the heterocycle, in contact with the cis‐substituent at C(2) (staggered conformation A ; Figs. 1–3); in three structures, the Ph ring lies above the iminium π‐plane (staggered conformation B ; Figs. 1 and 4); in two structures, the benzylic C? C bond has an eclipsing conformation ( C ; Figs. 1 and 5) which places the Ph ring simultaneously at a maximum distance with its neighbors, the CO group, the N?C‐π‐system, and the cis‐substituent at C(2) of the heterocycle. It is suggested by a qualitative conformational analysis (Fig. 6) that the three staggered conformations of the benzylic C? C bond are all subject to unfavorable steric interactions, so that the eclipsing conformation may be a kind of ‘escape’. State‐of‐the‐art quantum‐chemical methods, with large AO basic sets (near the limit) for the single‐point calculations, were used to compute the structures of seven of the 14 iminium ions, i.e., 3, 4 / 12, 5 – 7, 13 , and 16 (Table) in the two staggered conformations, A and B , with the benzylic Ph group above the ring and above the iminium π‐system, respectively. In all cases, the more stable computed conformer (‘isolated‐molecule’ structure) corresponds to the one present in the crystal (overlay in Fig. 7). The energy differences are small (≤2 kcal/mol) which, together with the result of a potential‐curve calculation for the rotation around the benzylic C? C bond of one of the structures, 16 (Fig. 8), suggests that the benzyl group is more or less freely rotating at ambident temperatures. The importance of intramolecular London dispersion (benzene ring in ‘contact’ with the cis‐substituent in conformation A ) for DFT and other quantum‐chemical computations is demonstrated; the benzyl‐imidazolidinones 1 appear to be ideal systems for detecting dispersion contributions between a benzene ring and alkyl or aryl CH groups. Enylidene ions of the type studied herein are the reactive intermediates of enantioselective organocatalytic conjugate additions, Diels–Alder reactions, and many other transformations involving α,β‐unsaturated carbonyl compounds. Our experimental and theoretical results are discussed in view of the performance of 5‐benzyl‐imidazolidinones as enantioselective catalysts.     

Numerical solution of the Hodgkin-Huxley equations in a moving coordinate system. Simulation of nerve impulse transmission over long distances

The theory required for the solution of the Hodgkin-Huxley equations for the transmission of the nerve impulse in a moving coordinate system are presented. Using this theory, simulations of the transmission of the nerve impulse over large distances (e.g., 1 m) may be carried out rapidly and accurately. The above theory may be applied to other diffusion problems by appropriate modification to the problem concerned.