峨山褐煤的分子结构和分子模拟

作为重要的化石能源，褐煤资源潜力巨大、分布广泛但综合利用率低。研究褐煤的分子结构模型，有助于预测褐煤在热解、液化和气化过程中的化学反应机理及反应路径，进而提高褐煤的综合应用水平。以云南峨山褐煤为研究对象，利用傅里叶变换红外光谱、13C核磁共振波谱及X射线光电子能谱等分析测试方法，获取了峨山褐煤的含碳、含氧及含氮结构参数。在此基础上，借助Gaussian 09计算平台，采用量子化学建模的方法构建并优化了峨山褐煤的分子结构模型。研究结果表明：峨山褐煤的芳碳率为39.20%，芳香碳结构主要为苯和萘，且芳香桥头碳与周边碳的比值χ_b为0.07；脂碳率为49.51%，脂肪碳结构主要为亚甲基，季碳和氧接脂碳；氧原子主要存在于羟基、醚氧、羰基和羧基结构中；含氮结构则以吡啶为主。基于元素分析、13C 核磁共振波谱分析，又经过热重实验消除褐煤中残余水分的影响后，计算出峨山褐煤的分子式为C₁₅₃H₁₃₇O₃₅N₂。依据分子式及分析结果计算出峨山褐煤的结构单元含量并构建出其初始结构模型，采用半经验法PM 3基组及密度泛函理论M06-2X/3-21G基组对初始分子构型进行优化。优化后的分子模型具有明显的三维立体特征，芳香环之间较为分散且在空间中排列不规则，芳香簇主要通过亚甲基、醚氧基、羰基、酯基和脂肪环连接，含氧官能团主要分布在分子边缘，脂肪族侧链较多。对优化后的分子模型进行振动频率计算进而获得了分子模型的模拟红外光谱，其与实验红外谱图吻合度良好，证明了峨山褐煤分子结构模型的准确性、合理性。分子结构模型的构建有利于直观地了解峨山褐煤的分子结构特征，从而有助于从微观分子角度研究峨山褐煤的宏观性质。同时，峨山褐煤分子结构模型可为其在热解、液化和气化等领域研究中提供理论指导。     

零误差计算

研究采用有误差的数值计算来获得无误差的准确值具有重要的理论价值和应用价值.这种通过近似的数值方法获得准确结果的计算被称为零误差计算.本文首先指出,只有一致离散集合中的数才能够开展零误差计算,即有非零隔离界的数集,这也是"数"可以进行零误差计算的一个充要条件.以此为基本出发点,本文分析代数数零误差计算的最低理论精度,该精度对应于恢复近似代数数的准确值时必要的误差控制条件,但由于所采用恢复算法的局限性,这一理论精度往往不能保证成功恢复出代数数的准确值.为此,本文给出采用PSLQ (partial-sum-LQ-decomposition)算法进行代数数零误差计算所需的精度控制条件,与基于LLL (Lenstra-Lenstra-Lovász)算法相比,该精度控制条件关于代数数次数的依赖程度由二次降为拟线性,从而可降低相应算法的复杂度.最后探讨零误差计算未来的发展趋势.     

水平悬链线中点集中力作用下的非线性分析及计算

首先，对均布力作用下悬链线理论进行了深入分析研究，推导出求解水平张力单参数和双参数形式的隐含超越方程，在算法上验证了两种方程的等价性。对于悬链线固有的广义倾角、曲率半径、约束反力和水平张力的嵌入关系等给出了具有新意的表达公式。然后，建立了水平悬链线在对称集中力作用下的平衡方程，对于不同垂向集中力作用下水平张力的变化情况和最大垂直距离差所在水平位置随集中力的变化等进行了非线性计算。本文在理论构建和分析方面具有创新性，在理论探索和工程应用上具有重要意义。     

A survey on HHL algorithm: From theory to application in quantum machine learning

The Harrow-Hassidim-Lloyd (HHL) algorithm is a method to solve the quantum linear system of equations that may be found at the core of various scientific applications and quantum machine learning models including the linear regression, support vector machines and recommender systems etc. After reviewing the necessary background on elementary quantum algorithms, we provide detailed account of how HHL is exploited in different quantum machine learning (QML) models, and how it provides the desired quantum speedup in all these models. At the end, we briefly discuss some of the remaining challenges ahead for HHL-based QML models and related methods.     

复合材料失效判据有效性验证方法研究

为系统地验证复合材料失效判据计算精度和有效性范围,给出了4种材料体系、6种铺层形式的层合板在单轴、双轴载荷下的失效试验数据,用以评估复合材料失效判据在单向层合板失效包线、多向层合板初始失效包线、多向层合板最终失效包线、层合板变形及层合板的破坏特性等五个方面的预测能力。并根据验证方法和有效性评估策略对失效判据计算精度进行量化考核,给出了失效判据在五个层面上的计算精度。     

将密度泛函理论计算纳入高等化学教学初探——对乙酸乙酯碱性水解机理的理论研究

使用Gaussian 09软件对乙酸乙酯碱性水解反应的机理进行了研究。本研究融合了本科教学中有机化学、物理化学和结构化学的相关知识,以乙酸乙酯水解机理为问题导向,阐述了研究和解决问题的思路和方法,探索了将第一性原理计算引入高等教育的方式。     

Calculating nuclear magnetic resonance chemical shifts in solvated systems

The nuclear magnetic resonance (NMR) chemical shift is extremely sensitive to molecular geometry, hydrogen bonding, solvent, temperature, pH, and concentration. Calculated magnetic shielding constants, converted to chemical shifts, can be valuable aids in NMR peak assignment and can also give detailed information about molecular geometry and intermolecular effects. Calculating chemical shifts in solution is complicated by the need to include solvent effects and conformational averaging. Here, we review the current state of NMR chemical shift calculations in solution, beginning with an introduction to the theory of calculating magnetic shielding in general, then covering methods for inclusion of solvent effects and conformational averaging, and finally discussing examples of applications using calculated chemical shifts to gain detailed structural information.     

Basis Sets Dependency in Constructing Spectroscopy-Accuracy Ab Initio Global Electric Dipole Moment Functions

Recently, more attention have been paid on the construction of dipole moment functions (DMF) using theoretical methods. However, the computational methods to construct DMFs are not validated as much as those for potential energy surfaces do. In this letter, using Ar...He as an example, we tested how spectroscopyaccuracy DMFs can be constructed using ab initio methods. We especially focused on the basis set dependency in this scenario, i.e., the convergence of DMF with the sizes of basis sets, basis set superposition error, and mid-bond functions. We also tested the explicitly correlated method, which converges with smaller basis sets than the conventional methods do. This work can serve as a pictorial sample of all these computational technologies behaving in the context of constructing DMFs.     

Hybrid projection methods for equilibrium problems with non‐Lipschitz type bifunctions

Based on the extended extragradient‐like method and the linesearch technique, we propose three projection methods for finding a common solution of a finite family of equilibrium problems. The linesearch used in the proposed algorithms has allowed to reduce some conditions imposed on equilibrium bifunctions. The strongly convergent theorems are established without the Lipschitz‐type condition of bifunctions. The paper also helps in the design and analysis of practical algorithms and gives us a generalization of some previously known problems. Copyright © 2017 John Wiley & Sons, Ltd.