Organocatalysis: quantum chemical modeling of nucleophilic addition to α,β‐unsaturated carbonyl compounds

One of the successful transformations within the field of organocatalysis, the organocatalytic asymmetric addition of nitromethane to α,β‐unsaturated aldehydes and ketones, has been studied by quantum chemical modeling. The level of accuracy of the hybrid density functional theory method B3LYP/6‐31G(d) was compared to a high level ab initio benchmark for this reaction. It is concluded that B3LYP/6‐31G(d) performs very well for this reaction type, giving good estimates of critical energies. The reaction between acrolein and nitromethane was studied in detail. The reaction mechanism revealed an intermediate oxazolidin structure, which is currently unknown. Alkyl substitution in various positions on the amine catalyst or α,β‐unsaturated carbonyl compound influences the reactivity in a predictive fashion. The iminium ion, prop‐2‐en‐iminium, is less activated towards nucleophilic attack compared to protonated acrolein. Copyright © 2007 John Wiley & Sons, Ltd.     

类型γ射线能谱指纹的识别机理

放射源的辐射指纹能起到标识和鉴别放射性物体的作用.在涉及核弹头不可逆销毁过程的深度核裁军核查中,核弹头的辐射指纹对标识和鉴别裁减下来的核弹头将起到关键作用.预先研究辐射指纹的有关技术,如识别机理的研究,将有助于深度核裁军的核弹头核查技术发展.以实验室放射源为研究对象,探索了类型γ射线能谱指纹的同一性识别机理.类型γ射线指纹识别机理的研究,就是要找出一种合适的方法,以较高的置信度,描述两个正在进行比较的γ射线指纹是否为同一放射源的指纹.采用了谱形比较法,并用谱相似度概念来描述两个指纹的相似程度.在谱形比较思想的指导下,编制了放射源类型指纹识别软件,并通过放射源同一性的识别实验验证了软件的有效性,同时研究了谱相似度随统计涨落和测量条件,如时间、源强和本底等因素的变化情况.研究结果表明:1)用相似度概念来描述两个指纹的相似程度,回答两个待比较的γ射线能谱是否代表同一类型放射源,是切实可行的;2)该识别机理只具备识别放射源类型的能力,而对同一类型、差异甚微的放射源个体还不能识别 关键词： γ射线能谱指纹 辐射指纹 识别机理 核查技术     

The influence of temperature gradients on the kinetic boundary layer problem for a condensing droplet

We extend an earlier method for solving kinetic boundary layer problems to the case of particles moving in aspatially inhomogeneous background. The method is developed for a gas mixture containing a supersaturated vapor and a light carrier gas from which a small droplet condenses. The release of heat of condensation causes a temperature difference between droplet and gas in the quasistationary state; the kinetic equation describing the vapor is the stationary Klein-Kramers equation for Brownian particles diffusing in a temperature gradient. By means of an expansion in Burnett functions, this equation is transformed into a set of coupled algebrodifferential equations. By numerical integration we construct fundamental solutions of this equation that are subsequently combined linearly to fulfill appropriate mesoscopic boundary conditions for particles leaving the droplet surface. In view of the intrinsic numerical instability of the system of equations, a novel procedure is developed to remove the admixture of fast growing solutions to the solutions of interest. The procedure is tested for a few model problems and then applied to a slightly simplified condensation problem with parameters corresponding to the condensation of mercury in a background of neon. The effects of thermal gradients and thermodiffusion on the growth rate of the droplet are small (of the order of 1%), but well outside of the margin of error of the method.     

Internal Rotation of the Methyl Group in Cations of Toluene Derivatives

The potential of the internal rotation of the methyl group was determined for o-, m-, and p-fluorotoluene cations by pulsed field ionization spectroscopy. The potential of the internal rotational motion was also surveyed for other toluene derivative cations. It was found that the barrier height generally increases by ionization. The increase in the barrier height has been discussed in connection with the reduction of the internal rotational constant B by ionization. The geometrical distortion of the methyl group during the internal rotation has been suggested.     

Theoretical study of cyclization of 2′-hydroxychalcone

The isomerization mechanism of 2′(OH)chalcone (1) in flavanone (2) was studied. The calculations were performed with the semiempirical method AM1, using totally optimized molecular geometries. A 6-step mechanism including several equilibrium states was proposed. It was concluded that: (a) At the conformational equilibrium of 1 there could be 43.9% of s-cis conformer; (b) The acid dissociation of 1 trans-s-trans is considerable; (c) The E_E, ΔH_f and net charges show that the rotation of ring A of 1 and the formation of ring C of 2 occurs without greater impairments; (d) Although the keto structure is the most stable one, the enolate of 2 is present in the reaction medium; (e) The conversion of enol of 2 in the keto form would be the limiting step of the analyzed isomerization rate.     

元素在石墨炉内石墨探针表面上的原子化机理研究：Ⅶ.锗的原子化机理

本文应用Ｘ－射线衍射，Ｘ－射线光电子能谱，俄歇电子能谱和其它一些实验，考察石墨炉升温过程中氟化锗，锗酸钠在石墨探针表面上的形态变化，阐明了它们的原子化机理：ＧｅＦ２与Ｎａ２ＧｅＯ３首先分解为ＧｅＯ２，ＧｅＯ２还原为ＧｅＯ，后者在＞２４００Ｋ热分解产生自由态的锗原子，ＧｅＦ２和Ｎａ２ＧｅＯ３的原子化均源于ＧｅＯ（ｇ）的气相分解。原子化的升温过程中，在１４００－２４００Ｋ ＧｅＦ２和Ｎａ２ＧｅＯ３都产     

Model-dependent nature of blowtorch effect on the escape and equilibration rates

We analyze the relaxation behavior of a bistable system when the background temperature profile is inhomogeneous due to the presence of a localized hot region (blowtorch) on one side of the potential barrier. Since the diffusion equation for inhomogeneous medium is model-dependent, we consider two physical models to study the kinetics of such system. Using a conventional stochastic method, we obtain the escape and equilibration rates of the system for the two physical models. For both models, we find that the hot region enhances the escape rate from the well where it is placed while it retards the escape rate from the other well. However, the value of the escape rate from the well where the hot region is placed differs for the two models while that of the escape rate from the other well is identical for both. This work, for the first time, gives a detailed report of the similarities and differences of the escape rates and, hence, exposes the common and distinct features of the two known physical models in determining the way the bistable system relaxes. Received 25 September 2001     

角域上的调和函数与条件Brown运动

设中的角域．该文绘出了A上正调和函数的Martin表示，讨论了极小调和函数与条件Brown运动的一个0—1律之间的关系，并给出了A上极小调和函数的表现形式，     

On the exact distribution of linear combinations of order statistics from dependent random variables

We study the exact distribution of linear combinations of order statistics of arbitrary (absolutely continuous) dependent random variables. In particular, we examine the case where the random variables have a joint elliptically contoured distribution and the case where the random variables are exchangeable. We investigate also the particular L-statistics that simply yield a set of order statistics, and study their joint distribution. We present the application of our results to genetic selection problems, design of cellular phone receivers, and visual acuity. We give illustrative examples based on the multivariate normal and multivariate Student t distributions.     

New efficient numerical procedures for solving stochastic variational problems with a priori maximum pointwise error estimates

In a previous paper we gave a new formulation and derived the Euler equations and other necessary conditions to solve strong, pathwise, stochastic variational problems with trajectories driven by Brownian motion. Thus, unlike current methods which minimize the control over deterministic functionals (the expected value), we find the control which gives the critical point solution of random functionals of a Brownian path and then, if we choose, find the expected value.This increase in information is balanced by the fact that our methods are anticipative while current methods are not. However, our methods are more directly connected to the theory and meaningful examples of deterministic variational theory and provide better means of solution for free and constrained problems. In addition, examples indicate that there are methods to obtain nonanticipative solutions from our equations although the anticipative optimal cost function has smaller expected value.In this paper we give new, efficient numerical methods to find the solution of these problems in the quadratic case. Of interest is that our numerical solution has a maximal, a priori, pointwise error of O(h3/2) where h is the node size. We believe our results are unique for any theory of stochastic control and that our methods of proof involve new and sophisticated ideas for strong solutions which extend previous deterministic results by the first author where the error was O(h²).We note that, although our solutions are given in terms of stochastic differential equations, we are not using the now standard numerical methods for stochastic differential equations. Instead we find an approximation to the critical point solution of the variational problem using relations derived from setting to zero the directional derivative of the cost functional in the direction of simple test functions.Our results are even more significant than they first appear because we can reformulate stochastic control problems or constrained calculus of variations problems in the unconstrained, stochastic calculus of variations formulation of this paper. This will allow us to find efficient and accurate numerical solutions for general constrained, stochastic optimization problems. This is not yet being done, even in the deterministic case, except by the first author.