Symmetry or asymmetry in cheletropic additions forming cyclopropanes

Cheletropic additions forming cyclopropane rings were studied theoretically. Ten addition paths were traced by means of density-functional-theory calculations. Two 1,4-dienes, 1,4-pentadiene, and tricyclo[5.3.1.0^4,9]undeca-2,5-diene were adopted as substrates. CO, SO₂, C₂H₅PCl₂, CCl₂ and SiCl₂ were employed as cheletropic reagents (Xs). An orbital correlation diagram of the Woodward–Hoffmann (W–H) rule and frontier molecular orbital (FMO) interactions between them were investigated in detail. The FMO interactions, HOMO (1,4-diene)lumo (X) and homo (X)LUMO (diene), work reasonably for the progress of the reactions. Those cause the formation of two C–X bonds and a cyclopropane ring, and alternation of double bonds to single bonds. All the additions are concerted. The easiness of the ring formation depends upon the energy gap between HOMO and lumo and that between homo and LUMO, and the spatial directions of HOMO and LUMO extensions. Symmetry conservation of the W–H rule does not hold necessarily for those addition paths. The symmetry-breaking was discussed in terms of FMO interactions.Acknowledgement This work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture, Japan and by Nishida Memorial Foundation for Fundamental Chemical Research.     

Application of the pKa rule to synthesize salts of bezafibrate

ABSTRACT

Co-crystallization frequently employs forces such as hydrogen bonds, halogen bonds, and π-π stacking to assemble molecules in a multi-component crystal. In an effort to increase the strength of the intermolecular interaction between the anti-cholesterol drug bezafibrate (BEZA), a wastewater contaminant, and hydrogen-bond-acceptor molecules, we modified the pK_a values of the acceptors. Here, we describe the first series of salts incorporating BEZA and achieve a variety of supramolecular architectures including discrete assemblies, 1D chains, tapes, and 2D sheets. We discuss exceptions to the pK_a rule, and demonstrate that the presence of hydrogen-bond-donor atoms on the acceptor molecule supports salt formation.     

FT-EPR Spectroscopic Study of Silicophosphate Glasses Derived from Gels

(100-x) mole% SiO₂-x mole% P₂O₅-glasses withx=1–9 have been prepared by the sol-gel process using tetraethylorthosilicate and triethylphosphate as precursors. The gels were fired at various temperatures up to 950°C and then exposed to γ-ray irradiation to induce paramagnetic centers. CW-EPR and FT-EPR Spectroscopies were employed at temperatures between 4 and 300 K in order to determine the resulting structures. The dried gels exhibited four types of O ₂ ⁻ -ions trapped in pores of different sizes. The gels fired atT=670°C exhibited theE’ ₁-center and non-bridging oxygen as a results of the fracture of the Si-O-Si bonds. At higher temperatures, the spectra of the POHC, POHC ^b ,E’, and CH ₃ ⁻ -centers have been detected that are a function ofx andT.     

Effect of combining rules for cubic equations of state on the prediction of double retrograde vaporization

In this work, the phenomenon of double retrograde vaporization (DRV) is simulated using the Peng–Robinson equation of state with the classical mixing rules and several combining rules for the cross-energy and cross-co-volume parameters. The binary interaction parameters are set equal to zero in all cases, i.e., the calculations are entirely predictive. An interesting conclusion is that the predictions using the classical combining rules (geometric mean rule for a_ij and arithmetic mean rule for b_ij) provide the best agreement with the experimental data for all the systems tested: methane + n-butane, methane + n-pentane, ethane + limonene, and ethane + linalool. Another interesting observation is that several combining rules for b_ij, other than the arithmetic mean rule, predict the existence of three phases in equilibrium in a very narrow temperature range close to the critical temperature of methane in the methane + n-pentane system, even though, literature data indicates that n-hexane is the first n-alkane to present partial liquid phase immiscibility with methane.     

Application of the semilocalized approach to chemical reactivity of butadiene

The semilocalized approach to chemical reactivity (J. Mol. Struct. (Theochem) 588 (2002) 99; Int. J. Quant. Chem. 94 (2003) 302) is applied to study the addition reaction of an electrophile or nucleophile to the butadiene molecule. In accordance with the classical concept of the reaction center and its neighborhood (substituent), only one of the two H₂C=CH-fragments of butadiene is supposed to be under a direct attack of the reagent, whereas the remaining H₂C=CH-group is assumed to play the role of the substituent and thereby to participate in the process indirectly by exerting certain electron-donating or accepting effect upon the former group and/or the reagent. The main aim of the study consists in revealing the role of the H₂C=CH-substituent in the formation of the known higher reactivity of the terminal carbon atom of the attacked C=C-bond (as compared to the internal atom) irrespective of the nature of the reagent. To this end, we seek to obtain an explicit algebraic representation of the interdependence between the direction and the extent of the total influence of the H₂C=CH-substituent, on the one hand, and the nature of the reagent, on the other hand. The expressions for electron density and bond order redistributions among separate fragments of contacting molecules derived previously in the form of power series are shown to yield the above-anticipated representation. On this basis, it is demonstrated that the electron-donating effect of the initially occupied (bonding) orbital of the substituent and the electron-accepting effect of its initially vacant (antibonding) orbital upon the remaining fragments of the whole reacting system may be considered independently whatever the nature of the reagent. However, a strong interdependence is established between the actual relative extents of these two components of the total effect of the H₂C=CH-group and the electron-donating (accepting) properties of the reagent. Moreover, this group of atoms is shown to manifest itself as an electron-donating (accepting) substituent under influence of an electrophilic (nucleophilic) attack. Using this principal result of the paper, the actual reactivity of butadiene with respect to electrophile (nucleophile) is interpreted by invoking a model system of a substituted ethene containing a simple (one-orbital) electron-donating (accepting) substituent, and a terminal addition easily follows for both types of the reagent.     

STUDY ON 1-HEXENE POLYMERIZATION BASED ON ZIEGLER-NATTA CATALYSTS WITH DOPED SUPPORT

A series of Ti/Mg supported catalysts are prepared by using ball-milled mixtures of MgCl2-ethanol adducts and NaCl as supports, and 1-hexene polymerizations catalyzed by the novel catalysts are studied. It is found that the molecular weight distribution of poly(1-hexene) becomes apparently narrower when catalysts with doped supports are used, indicating that changing the structure of the support is an effective way to regulate the active center distribution of heterogeneous Ziegler-Natta catalyst.     

Effect of Thiourea on the Kinetics of the Hydrogen Evolution Reaction at Iron and the Transport of Hydrogen through a Steel Membrane in Solutions of C<Subscript>2</Subscript>H<Subscript>4</Subscript>(OH)<Subscript>2</Subscript>-H<Subscript>2</Subscript>O-HCl

The effect of thiourea (0.5–10 mM) on the kinetics of the hydrogen evolution reaction (HER) at iron and the hydrogen transport through a steel membrane out of ethylene glycol (containing 2 and 10 wt % H₂O) and aqueous solutions containing HCl (0.1–0.99 M) with a constant ionic strength equal to unity is studied in parallel experiments. The presence of 0.5 mM of thiourea in the solutions raises the overvoltage of hydrogen evolution, while a subsequent increase in its concentration does not effect the HER kinetics. The dependence of the flux of hydrogen diffusion through the membrane on the thiourea content passes through a maximum.     

“限时服务规则”下的复线船闸多目标调度优化

针对现有船舶过闸排队规则的欠缺,基于“限时服务规则”,构建复线船闸多目标双层优化调度模型:上层模型用于获得两个闸室安全区域的船舶排布可行方案;下层模型用于获得不同船舶排布可行方案的优化闸次数。下层模型分两个阶段完成:对符合“限时服务规则”的船舶,构建以闸次最少为目标的0-1规划模型,获得此类船舶安排的闸次;对其余船舶按照“先到先服务规则”,构建以闸次最少、闸室利用率最大为目标的多目标决策模型,获得不同船舶排布可行方案应该安排的频次。以位于江苏省干线航道上的某复线船闸某日24小时内过闸船舶的数据为例,计算结果表明:采用本文优化模型获得的优化方案与“经验编排方式”相比,两座船闸各节约2个闸次,两个船闸的平均闸室利用率分别提高了3.66和4.72个百分点。     

Estimation of Multinomial Probabilities under a Model Constraint

In this paper estimation of the probabilities of a multinomial distribution has been studied. The five estimators considered are: unrestricted estimator (UE), restricted estimator (RE) (under model ), preliminary test estimator (PTE) based on a test of the model , shrinkage estimator (SE) and the positive-rule shrinkage estimator (PRSE). Asymptotic distributions of these estimators are given under Pitman alternatives and the asymptotic risk under a quadratic loss has been evaluated. The relative performance of the five estimators is then studied with respect to their asymptotic distributional risks (ADR). It is seen that neither of the preliminary test and shrinkage estimators dominates the other, though each fares well relative to the other estimators. However, the positive rule estimator is recommended for use for dimension 3 or more while the PTE is recommended for dimension less than 3.     

Interior-point algorithm for quadratically constrained entropy minimization problems

In this paper, we develop an interior point algorithm for quadratically constrained entropy problems. The algorithm uses a variation of Newton's method to follow a central path trajectory in the interior of the feasible set. The primal-dual gap is made less than a given in at most steps, wheren is the dimension of the problem andm is the number of quadratic inequality constraints.