全维高精度势能面上F+CH3OH反应的产物振动态分布

甲醇与氟原子之间的抽氢反应可以生成HF和CH₃O、CH₂OH自由基等产物. 该反应在环境化学、燃烧化学、辐射化学和星际化学中都非常重要. 基于之前构建的全维高精度势能面,本文采用准经典轨线方法研究了该典型反应的动力学. 特别是使用正则模式分析方法确定了多原子产物CH₃O和CH₂OH的振动态分布. 研究发现,当反应物处于振转基态时,CH₃O和CH₂OH主要分布在基态. 当反应物CH₃OH的OH伸缩模式激发为第一激发态时,产物CH₂OH的OH伸缩模式、扭转模式、H₂CO 面外弯曲模式及其组合会被有效激发. 在两条通道中,可用能量大部分都流入HF的振动能和产物的平动能,而自由基产物CH₃O或CH₂OH只得到非常少的能量,与实验结果一致,这也表明了自由基的旁观者性质.     

Investigating the transformation of a secondary teacher’s knowledge of trigonometric functions

Shulman (1987) defined pedagogical content knowledge as the knowledge required to transform subject-matter knowledge into curricular material and pedagogical representations. This paper presents the results of an exploratory case study that examined a secondary teacher’s knowledge of sine and cosine values in both clinical and professional settings to discern the characteristics of mathematical schemes that facilitate their transformation into learning artifacts and experiences for students. My analysis revealed that the teacher’s knowledge of sine and cosine values consisted of uncoordinated quantitative and arithmetic schemes and that he was cognizant only of the behavioral proficiencies these schemes enable, not the mental actions and conceptual operations they entail. Based on these findings, I hypothesize that the extent to which a teacher is consciously aware of the mental activity that comprises their mathematical conceptions influences their capacity to transform their mathematical knowledge into curricular material and pedagogical representations to effectively support students’ conceptual learning.     

Theoretical study on the hydrogen abstraction reactions from hydrazine derivatives by H atom

The hydrogen abstraction reactions from hydrazine and its methyl derivatives by the H atom have been investigated theoretically by using CBS-QB3//DSD-BLYP-D3(BJ)/Def2-TZVP quantum chemical calculations and transition state theory calculations coupled with various tunneling correction methods. Both the products and transition state energies of the hydrogen abstraction from the amino group were stabilized by the methyl group substitution. The substitution effect on the ^αN site was two times larger than that on the ^βN site. On the other hand, the substitution effect was negligible on the hydrogen abstraction from the methyl group. The overall rate coefficients of N₂H₄ + H reaction calculated by canonical variational transition state theory with the small-curvature tunneling correction agreed well with previously reported values, but those of CH₃NHNH₂/(CH₃)₂NNH₂ + H were slightly lower than a previous experimental value. The product-specific rate coefficients have been proposed for the kinetics modeling of these fuels’ combustion.     

烷基环戊烷被羟基自由基夺氢反应类的动力学研究

基于燃烧详细反应机理构建的需要, 采用反应类过渡态理论(RC-TST)研究了OH自由基夺取烷基环戊烷环上和侧链上氢原子的动力学. 在考察侧链氢提取反应类的16个代表反应的基础上, 本工作首次将该方法推广到环上α氢提取反应类的10个代表反应的研究, 分别建立了两类反应的线性自由能(LER)关系式. 计算结果表明, 采用RC-TST/LER方法预测的这两类反应的速率常数与直接应用TST/Eckart方法得到的结果接近, 说明RC-TST/LER方法对预测这两类反应的速率常数非常有效, 且节约了大量计算成本. 而且, 无论是侧链还是五元环, OH·夺取叔碳上的氢原子最易发生.     

Towards an integrated theory of mathematics conceptual learning and instructional design: The Learning Through Activity theoretical framework

We discuss the theoretical framework of the Learning Through Activity research program. The framework includes an elaboration of the construct of mathematical concept, an elaboration of Piaget’s reflective abstraction for the purpose of mathematics pedagogy, further development of a distinction between two stages of conceptual learning, and a typology of different reverse concepts. The framework also involves instructional design principles built on those constructs, including steps for the design of task sequences, development of guided reinvention, and ways of promoting reversibility of concepts. This article represents both a synthesis of prior work and additions to it.     

Simon’s team’s contributions to scientific progress in mathematics education: A commentary on the Learning Through Activity (LTA) research program

I discuss two ways in which the Learning Through Activity (LTA) research program contributes to scientific progress in mathematics education: (a) providing general and content-specific constructs to explain conceptual learning and instructional design that corroborate and/or elaborate on previous work and (b) raising new questions/issues. The general constructs include using instructional design as testable models of learning and using theoretical constructs to guide real-time, instructional adaptations. In this sense, the general constructs promote understanding of linkages between conceptual learning and instruction in mathematics. The concept-specific constructs consist of empirically-grounded, hypothetical learning trajectories (HLTs) for fractional and multiplicative reasoning. Each HLT consists of specific, intended conceptual changes and tasks that can bring them forth. Questions raised for me by the LTA work involve inconsistencies between the stance on learning and reported teaching-learning interactions that effectively led to students’ abstraction of the intended mathematical concepts.     

情景教学在高等数学教学中的应用

数学的特点是抽象的,但认识事物需要形象.情景教学提供了将抽象转化为形象的方法,藉此可提高学生的学习兴趣.     

Time‐resolved resonance Raman and density functional theory study of the photochemistry of 4‐benzoylpyridine in acetonitrile and 2‐propanol

A nanosecond time‐resolved resonance Raman (ns‐TR³) spectroscopic investigation of the intermolecular hydrogen‐abstraction reaction of the triplet state of 4‐benzoylpyridine (4‐BPy) in 2‐propanol solvent is reported. The TR³ results reveal a rapid hydrogen abstraction (<10 ns) by the 4‐BPy triplet state (nπ*) with the 2‐propanol solvent, leading to formation of a 4‐BPy ketyl radical and an associated dimethyl ketyl radical partner from the solvent. The recombination of these two radical species occurs with a time constant about 200 ns to produce a para‐N‐LAT (light absorbing transient). The structure, major spectral features, and identification of the ketyl radical and the para‐N‐LAT coupling complex have been determined and confirmed by comparison of the TR³ results with results from density functional theory (DFT) calculations. A reaction pathway for the photolysis of 4‐BPy in 2‐propanol deduced from the TR³ results is also presented. The electron‐withdrawing effect of the heterocyclic nitrogen for 4‐BPy on the triplet state makes it have a significantly higher chemical reactivity for the hydrogen abstraction with 2‐propanol compared to the previously reported corresponding benzophenone triplet reaction under similar reaction conditions. In addition, the 4‐BPy ketyl radical reacts with the dimethyl ketyl radical to attach at the para‐N atom position of the pyridine ring to form a cross‐coupling product such as 2‐[4‐(hydroxy‐phenyl‐methylene)‐4h‐pyridin‐1‐yl]‐propan‐2‐ol instead of attacking at the para‐C atom position as was observed for the corresponding benzophenone reaction reported in an earlier study. Copyright © 2008 John Wiley & Sons, Ltd.     

吡啶离子液体与水混合体系中蒽醌-2-磺酸钠的激光闪光光解机理

利用激光闪光光解技术研究了蒽醌-2-磺酸钠(AQS)在吡啶离子液体N-丁基吡啶四氟硼酸盐([BPy][BF₄])与水(H₂O)混合体系中的光化学反应过程. 实验结果表明,AQS的激发三重态(³AQS^*) 会与H₂O快速反应,不断增加[BPy][BF₄]在混合体系中的体积比(V_IL),瞬态吸收光谱发生了很大变化. 510 nm附近的瞬态吸收带变化最大,在0< V_IL< 0.1时,吸光度会随着[BPy][BF₄]的增加而增加;而在V_IL>0.1时,吸光度则随着比例的增加而减小. 然而380 nm附近吸收带的吸光度却一直在增加. 通过拟合近似地得到了瞬态物种B和³AQS^*的表观动力学参数. 另外还讨论了³AQS^* 与阳离子之间的夺氢反应,通过对350~420 nm处光谱图的分析,推断出这一范围的瞬态吸收光谱是³AQS^*与AQSH^·的叠加谱. 在混合体系中,³AQS^*分别与H₂O和[BPy][BF₄]的反应是一对竞争反应. 还发现在高浓度的离子液体环境下,体系的整体反应速率会减弱.