Theoretical study of the lowest pi-->pi* excitation energies for neutral and doped polyenes

In earlier theoretical studies, it has been widely noticed that the electron correlation effect played an important role in determining the excitation energies of low-lying pi-->pi(*) excited states for neutral polyenes and their radical cations and dications. In this paper, neutral and doped polyene oligomers of medium to large sizes are investigated with the Pariser-Parr-Pople model, and the pi-electron correlation effect is fully taken into consideration by virtue of the density-matrix renormalization group method. The excitation properties in the polymer limit are also obtained by exponential extrapolation from the finite oligomers. The reasonable agreement of our results with the available experimental observations and advanced ab initio calculations is witnessed. It is also observed that while charge doping can significantly lower the exciting energy, the odd-charged oligomers show lower excitation energies than the even-charged ones.     

Catalytic stereoselective alkene aziridination with sulfonimidamides

Diastereoselective copper-catalyzed alkene aziridination has been investigated using chiral nitrenes generated from sulfonimidamides in the presence of an iodine(III) oxidant. Starting from a stoichiometric amount of the substrates, the corresponding aziridines were isolated with excellent yields of up to 96%. Good levels of asymmetric induction were obtained in the case of electron-poor olefins, with an optimal de of 94% being reached starting from tert-butyl acrylate. Matching and mismatching effects were also observed upon the use of chiral copper catalysts for the aziridination of styrene.     

Studies in catalytic C-H amination involving nitrene C-H insertion

Stereoselective catalytic intermolecular C-H amination of complex molecules is reported. Site-selective functionalizations occur with very good yields up to 91% and excellent d.e.s up to 99%. However, the precise nature of the nitrene C-H insertion remains a matter of debate despite several physical organic experiments.     

Theoretical investigation of static characterization on nonlinear elementary excitations in trans-polyacetylene

Semiempirical quantum chemical studies on neutral and positively charged H(CH)nH homologues have been performed for systems with n up to 101, where different kinds of nonlinear excitation are found with increasing chain length. The Pariser-Parr-Pople (PPP) model has been employed and solved with the density matrix renormalization group (DMRG) method. The geometrical and electronic distortions induced by defects are obtained and compared with previous theoretical work, indicating that an adequate account of the electron correlation is essential for describing such systems. The structural distortion of a charged soliton (half-width calculated as L = 13) is shown to be more extended than that of a neutral soliton (L = 6); the geometrical distortion is even more extended in a polaron. In bipolarons, our calculations show that the coupling of the soliton-antisoliton pair might be longer ranged than expected. The phase transition from a bipolaron to a separated soliton-antisoliton pair occurs when n is close to 100.     

煤的工业分析至元素分析的BP神经网络预测模型

以大量煤质分析数据为基础，建立了利用煤工业分析数据（ 包括水份、灰份、挥发份及热值） 计算元素分析数据的ＢＰ神经网络预测模型，并将该模型与现有经验公式进行了比较，结果表明神经网络模型有很好的推广能力。可以满足工业应用的要求     

一种修改的非单调线搜索SQP算法

提出了一种解非线性规划问题的修改的非单调线搜索算法,并给出了它的全局收敛性证明.不需要用罚函数作为价值函数,也不用滤子和可行性恢复阶段.该算法是基于多目标优化的思想一个迭代点被接受当且仅当目标函数值或是约束违反度函数值有充分的下降.数值结果与LANCELOT作了比较,表明该算法是可靠的.     

Seifert Conjecture in the Even Convex Case

In this paper, we prove that there exist at least n geometrically distinct brake orbits on every C² compact convex symmetric hypersurface Σ in ?²ⁿ satisfying the reversible condition NΣ = Σ with N = diag(?I_n,Iⁿ). As a consequence, we show that if the Hamiltonian function is convex and even, then Seifert conjecture of 1948 on the multiplicity of brake orbits holds for any positive integern. © 2014 Wiley Periodicals, Inc.     

Static polarizability and second hyperpolarizability of closed- and open-shell pi-conjugated polymers

The static longitudinal linear polarizability (alpha) and second order hyperpolarizability (gamma) for neutral and charged, closed- and open-shell trans-polyacetylene (PA) chains C(2n)H(2n+2), C(2n-1)H(2n+1), C(2n-1)H(2n+1) (+), C(2n)H(2n+2) (+), and C(2n)H(2n+2) (2+) are systematically investigated and compared. The polarizabilities are calculated within the Pariser-Parr-Pople model, and the electron correlation effect is included through density matrix renormalization group. It turns out that for both alpha, and gamma, two neutral PA chains C(2n)H(2n+2) and C(2n-1)H(2n+1) give similar values, while both singly charged and doubly charged systems present significantly larger magnitude of alpha and gamma values than the two neutral chains. The two singly charged PA chains C(2n-1)H(2n+1) (+) and C(2n)H(2n+2) (+) give more apparent nonlinear optical responses than doubly charged case C(2n)H(2n+2) (2+) and both present negative second order hyperpolarizabilities for short to medium sized oligomers. The sign inversion of gamma values in singly charged PA molecules is anticipated to take place at the much longer length than ever observed due to the significant effects of electron correlation and geometry.