On sequential procedures for the point estimation of the mean of a normal population

The sequential procedures developed by Starr (1966, Ann. Math. Statist., 37, 1173–1185) for estimating the mean of a normal population are further analyzed. Asymptotic properties of the regret and first two moments of the stopping rules are studied and second-order approximations are derived.     

A new interpretation of Hund's first rule

The diagonal elements of the first and second order spinless density matrices have been calculated for the lowest excited¹ P and³ P terms of Be, B⁺ and C⁺⁺ using wavefunctions at different levels of approximations published in the literature. The analysis of these functions has resulted in a new interpretation of Hund's first rule in terms of an anisotropic screening effect.     

Theoretical prediction of the contact distance dependence of the electron transfer reactivity of the ClO/ClO− coupling system

On the basis of the structures and properties of the ClO/ClO^? system obtained at the density functional theory (DFT) (UB3LYP) level, employing the 6‐311+G(3df) standard basis set, the electron transfer reactivity of this system is investigated. The results indicate that there are five possible stable coupling complexes that correspond to the generous minima on the global potential energy surfaces (PES). The most stable coupling complex is planar EC4, in which there is a O? O linkage with two trans‐Cl atoms. Their stabilization energies are calculated to be 20.57 (EC1: C₁), 20.54 (EC2: C₂, ²B), 20.69 (EC3: C₁), 20.70 (EC4: C_s, ²A′), and 20.69 (EC.5: C_2h, ²B_u) kcal/mol at the B3LYP/6‐311+G(3df) level; with the correction of the basis set superposition error (BSSE), the stability order of these encounter complexes is EC4 > EC.5 > EC3 > EC1 > EC2. Based on the five encounter complexes, five coupling modes are designed for the study of the electron transfer reactivity of this system. The dissociation energy curves at the activated states and the corresponding activation energies of these five coupling modes are obtained and are compared at the B3LYP/6‐311+G(3df) and MP2/6‐311+G* levels. The inapplicability of DFT methods has also been discussed in this article in predicting the energy curves, especially with a long contact distance, in which DFT methods give the abnormal behavior for the dissociations of the complexes caused by the “inverse symmetry breaking” problem. On the basis of the golden rule of the time‐dependent perturbation theory, the electron transfer reactivity and the contact distance dependence of the various electron transfer kinetics parameters (e.g., activation energy, coupling matrix element) have been analyzed at the UMP2(full)/6‐311+G* level. The electron transfer can take place over a range of contact distances, but the most effective coupling distance corresponds to only a small range. The coupling orientation analyses also indicate that the most favorable coupling mode to the electron transfer does not always correspond to the most stable encounter complex mechanism. Some highly energetic coupling modes are more favorable for the electron transfer. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

蒂巴茵衍生物的合成研究

The reaction of 7α-acetyl-6,14-endoethano-6,7,8,14-tetrahydrothebaine with 2-（thien-2-yl）ethylmagnesium bromide was investigated. The tertiary alcohol derivative 7α-[R-l-hydroxyl-l-methyl-3-（thien-2-yl）propyl]）-6,14- endoethano-6,7,8,14-tetrahydrothebaine （3） and a by-product 4 were isolated. The structure of 4 was elucidated by X-ray analysis. The Grignard reaction shows high degree of stereoselectivity according with Cram rule. The crystal structure of 4 indicates that dihydrofuran ring was opened to form a phenolic hydroxyl group and a three-membered ring structure. It maintains the main rigid structure of morphine and contains a C（6）-C（14） enthano bridge. The 1-hydroxyl-1-methyl-3-（thien-2-yl）propyl group at C（7） position adopted S-configuration.     

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.     

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.     

“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。