A Generalized Unpaired Electron Spin Density Equation and Organic Hyperconjugation Mechanism

A large class of stereochemcial and related interactions in organic chemistry are repulsive and others are attractive, but the relative orientation of two methyl groups and the amount of energy required to twist one relative to the other (the hindered rotation energy barriers), or the alignment of such a group with respect to a conjugated ring to which it is attached (widely attributed to a mechanism called “hyperconjugation”) are estimated to be small in compared with the total energy of the molecule. We used theories of both isotropic and anisotropic proton hyperfine interactions in the π‐electron systems developed in the early sixties. They are approximated by the magnetic dipole nteractions between each proton and an electron spin magnetization that is distributed in 2s and 2p Slater atomic orbitals center on carbon atoms. We have extended these theories to the non‐planar olefinic cation radicals, which are very important in biochemistry as well as in petroleum catalysis. A three dimensional electron spin density equation has been developed in this paper to handle some Jahn‐Teller vibronic molecules. The new electron spin density equation related the observed proton hyperfine splittings to the non‐planar structures of the open‐chain alkene cation radicals generated by radiolysis and various chemical oxidation methods. The spin densities and the conformational calculations based on valence bond theory and symmetry principles are compared with some more elaborated molecular orbital calculations in the literature. The localized valence bond approaches are better in accord with our experimental results. The anomalous line‐width effect of the four methyl groups observed in the 2,3‐dimethyl‐2‐butene cation radicals also confirmed the positive sign of the electron‐proton hyperfine constant of hyper‐conjugation mechanism. A methyl substituent attached to a conjugated molecule often behaves as if it formed part of the region of conjugation; the charge appears to flow from the methyl group into the π electron system and it may also give rise to an appreciable dipole moment. Methylation also gives rise to an appreciable dipole moment, and the resultant red shift of electronic absorption bands is of some importance in the design of dye molecules.     

Level shift operators for open quantum systems

Level shift operators describe the second-order displacement of eigenvalues under perturbation. They play a central role in resonance theory and ergodic theory of open quantum systems at positive temperatures. We exhibit intrinsic properties of level shift operators, properties which stem from the structure of open quantum systems at positive temperatures and which are common to all such systems. They determine the geometry of resonances bifurcating from eigenvalues of positive temperature Hamiltonians and they relate the Gibbs state, the kernel of level shift operators, and zero energy resonances. We show that degeneracy of energy levels of the small part of the open quantum system causes the Fermi Golden Rule Condition to be violated and we analyze ergodic properties of such systems.     

GOLDEN AGES OR MAGIC MOMENTS?

ABSTRACT. The paper is an attempt to refute Quinn's ‘the Golden Age of fisheries population models has ended “hypothesis. The approach is to show it is possible to provide simple matrix based theory for use with delay difference equations applied to products of the 0th to 4th powers of length and numbers at length (Alias” proto‐moments“). It compares these to models just based upon numbers and biomass. It also shows examples (of comparatively little moment) indicating how using multiple proto‐moments could improve the ability of delay difference equations to handle the size dependent processes of maturity, selection, natural mortality rates and predation rates and thus improving the biological reality of these models.     

劳动力供给带弹性的Solow模型

本文给出了在劳动力供给带弹性条件下的Ｓｏ１ｏｗ增长模型，给出了经济增长的黄金律和均衡处资本稳定性的证明，并且与不带弹性的Ｓｏｌｏｗ模型作了比较．     

GEOENVIRONMENTAL CHARACTERS OF YELLOW (HUANGHE) RIVER SUSPENDED LOAD

Three important characters of the suspended load of the Yellow (Huanghe) River are discussed, i.e. its temporal fluctuation as a function of solar activity, its uneven spatial distribution along the main course and the inevitability of these phenomena as a natural earth process rather than a result of disturbed ecological system caused by human activity. Implications of this understanding with regard to the control of the Yellow River are also discussed.     

Zig‐Zag Diphosphene Oligomers Linked by Silver(I) Cation

The coordination of silver cation to diphosphene Mes*P=PMes* ( 1 , Mes* = ^tBu₃C₆H₂) was investigated in detail. The reaction of 1 with Ag[Al(OR_F)₄] (OR_F = OC(CF₃)₃) in the ratios of 2 : 1, 3 : 2 and 1 : 2 led to the formation of the first cationic silver linked diphosphene complexes 2 — 4 . Complexes 2 and 3 contain two and three diphosphene molecules linked by the linear Ag(I) cation, respectively, and they feature unusual zig‐zag topologies. Complex 4 is a dinuclear silver complex, and each Ag(I) center features a tetrahedral geometry, coordinated by one phosphorus atom of diphosphene 1 and three chloro atoms of two CH₂Cl₂ molecules.     

Golden crowns: cation binding by macrocyclic gold(I) crown ether derivatives

The polyether bis(alkynes) α,ω-bis(O-propargyl)triethylene glycol and α,ω-bis(O-4-propargyloxyphenoxy)triethylene glycol reacted with [AuCl(SMe₂)] in the presence of base to form the corresponding oligomeric gold(I) acetylide complexes (AuCCCH₂O(CH₂CH₂O)₃CH₂CCAu)_n and (AuCCCH₂OC₆H₄O(CH₂CH₂O)₃C₆H₄OCH₂CCAu)_n. These digold(I) diacetylide complexes reacted with diphosphine ligands to give macrocyclic digold(I) complexes of the type [Au₂(μ-CC)(μ-PP)], where CC is the diacetylide and PP is a diphosphine ligand. These digold(I) complexes bind the cations Li⁺, Na⁺, K⁺ and Cs⁺, as studied by electrospray mass spectrometry.     

A thorough study of the surface wax of apple fruits

The composition of the surface waxes of three apple ( Malus domestica L.) cultivars ("Florina", "Golden B" and "Ozark Gold") has been studied by means of spectroscopic and GC–MS analysis of the class-fractionated mixture of components. Odd n -alkanes, mainly C₂₇ and C₂₉ molecules, are prevalent in the saturated fraction. Small concentrations of alkenes were also found; the C_28:1 component is strongly (72%) in excess over the other 1-alkenes. Straight-chain esters (mainly of palmitic acid) of saturated primary alcohols (C₁₈–C₃₀) were also detected; whereas the acyl moiety is made up essentially of an even number of carbons, the alcohol counterpart does not exhibit this characteristic. Aldehydes are present (C₂₀–C₃₀) with the homologue patterns C₂₆–C₃₀ most strongly represented. Straight-chain free secondary alcohols characterize the waxes of "Florina" and "Ozark Gold"; the hydroxy function is located far from the extremity of the carbon framework. Outstanding is the presence of three alcohols with 29 carbon centres. These alcohols are accompanied by free straight-chain primary alcohols, mainly with even-numbered carbon chains in the range C₂₆–C₃₀. Free fatty acids are present; all of have a framework of even-numbered carbon chains mainly in the range C₁₆–C₂₀. C_18:1 (oleic acid) is well represented.     

Synthesis of a new donor, BEDT-HBDST and crystal structures, electrical and magnetic properties of (BEDT-HBDST)2MX4 (M=Fe, Ga, X=Cl, Br), where BEDT-HBDST=2,5-bis(4,5-ethylenedithio-1,3-diselenol-2-ylidene)-2,3,4,5-tetrahydrothiophene

A novel conjugation-elongated bis(ethylenedithio)tetraselenafulvalene (BETS) type donor, 2,5-bis(4,5-ethylenedithio-1,3-diselenol-2-ylidene)-2,3,4,5-tetrahydrothiophene (BEDT-HBDST) and its magnetic and non-magnetic anion salts, (BEDT-HBDST)₂MX₄ (MX₄⁻=FeCl₄⁻, GaCl₄⁻, FeBr₄⁻ and GaBr₄⁻), were prepared. These four salts are isostructural and belong to the space group of P2/c. They showed semiconducting behavior with small activation energies (59-64 meV). The band structures of these salts are quasi one-dimensional and there is a midgap between the upper band and the lower band, since the degree of dimerization is significant in the stacking direction. The MX₄⁻ ions are located between the donor columns and near to the ethylenedithio moieties of the donor molecules. The magnetic susceptibilities of the FeCl₄⁻ and FeBr₄⁻ salts follow the Curie-Weiss law with Curie constants of 4.6 and 4.8 emu K mol⁻¹ (sum of the spins of S=5/2 and S=1/2) and negative Weiss temperatures of θ=−1.2 and −4.9 K, respectively, revealing a weak antiferromagnetic interaction of 3d spins of the FeCl₄⁻ and FeBr₄⁻ anions. The Fe?Fe (6.66-7.60 Å), Cl?Cl (4.81-4.82 Å) and Br?Br (4.74-4.77 Å) distances in the crystal structures of these salts are significantly long. Therefore, the direct magnetic interaction between the 3d spins of the nearest neighboring Fe³⁺ ions appears to be not readily accessible.