聚炔、累积多烯与全碳环分子的模糊对称性

近年来我们关于分子模糊对称性的工作多属于模糊点对称性的研究, 关于模糊空间对称性探讨较少. 聚炔作为线状一维模糊周期分子, 我们曾对其进行了初步分析. 虽然对于聚炔分子骨架的分析比较全面, 但由于繁冗的计算使我们对分子轨道(MO)模糊对称性的分析只限于少数典型分子. 本文将对不同的聚炔分子MO模糊对称性特征进行较为系统的分析. 结果表明包含不同碳原子数目的分子轨道模糊对称性参数值之间有一定相关性. 此外我们还对一些相关体系分子的MO进行分析, 累积多烯分子虽然并非线型分子, 但其π-MO相关的碳原子处于线性位置, 可依模糊一维周期的G11体系处理. 按Born-Karman近似, 即n个单元的一维周期对称群与Cn点群同构, 本文还分析了相关的全碳环分子的MO的对称性和模糊对称性. 努力寻求与一维周期性相关的模糊对称性规律性特征.     

分子的模糊对称性

将模糊数学方法引入对分子对称点群的研究,建立描述具有不完整分子对称性的模糊点对称群(集合).建立具有模糊对称性分子轨道的模糊表示及其模糊特征标(模糊广义宇称).通过对典型的线状分子、平面分子以及非平面的立体分子等进行分析,展示了一个新的理论化学园地.初步探讨了具有模糊对称性的动态反应体系.从模糊对称性出发,探讨了分子轨道对称守恒原理的半定量特征.     

M(o)bius环并苯的分子对称性

一般来说,点群理论认为M(o)bius带环分子最高的对称性只能是C2.本文讨论了由18个苯环组成的环并苯的异构体分子,包括柱面的Hückel型分子(HC-[18])和扭转180°的M(o)bius带环分子(MC-[18]).结果表明除了点对称性外,M(o)bius带环分子还存在一种可称为环面螺旋旋转(TSR)变换的对称性,为此还引用了环面正交曲线坐标系.此外,还讨论了这些分子关于TSR对称性匹配的原子集和原子轨道(AO)集.根据TSR对称性的循环群特征,可以建立此类群的不可约表示及有关特征标.这类分子的分子轨道(MO)关于TSR群的不可约表示是纯的,然而所含的相应的原子轨道对称性匹配的线性组合(SALC-AO)成分可以是多种的.     

Möbius环并苯的分子对称性

一般来说, 点群理论认为Möbius带环分子最高的对称性只能是C₂. 本文讨论了由18个苯环组成的环并苯的异构体分子, 包括柱面的Hückel型分子(HC-[18])和扭转180°的Möbius带环分子(MC-[18]). 结果表明除了点对称性外, Möbius带环分子还存在一种可称为环面螺旋旋转(TSR)变换的对称性, 为此还引用了环面正交曲线坐标系. 此外, 还讨论了这些分子关于TSR对称性匹配的原子集和原子轨道(AO)集. 根据TSR对称性的循环群特征, 可以建立此类群的不可约表示及有关特征标. 这类分子的分子轨道(MO)关于TSR群的不可约表示是纯的, 然而所含的相应的原子轨道对称性匹配的线性组合(SALC-AO)成分可以是多种的.     

群论在化学中的应用

正分子对称性是化学的一项基本概念,它可以解释或预测分子的很多化学性质。在无机化学、结构化学、量子化学中都有关于分子对称性的介绍。分子对称性的研究是利用了数学上的群论。本书围绕分子对称性,介绍了基本的对称性与对称操作,各种常见的分子点群,     

考考你,对称性学得怎样?

对化学系的学生来讲,学过分子的对称性,应当具有能较快找出一个已知构型的分子所具有的全部对称元素,并能正确写出其所属点群的符号.要实现这一目标,除课堂学习和模型实习外,必须做适当数量具有启发性能促使积极思考的习题,以训练空间想像能力和立体感.下面一套习题就是为此目的而设计的.实际上它可以看成是对称性问题的一个小小试题库,略加变化又可得到另一套题目. 这套习题可分成两大类第一类给出已知图形所具有的全部对称元素和所属点群.     

电环化反应选择性的简化记忆

阐述共轭链烯π分子轨道对称性分布规律,用简单的方法判别电环化反应的立体选择性。     

共轭多烯异核双金属配合物的合成及性质

分子电子器件是近年来的一个热门课题,共轭有机分子是形成分子导线、分子开关等分子电子器件的模型化合物之一,其中一些已经得到应用.过去几年中,以sp碳为骨架的共轭桥联双金属配合物备受关注,长度为20个碳原子的此类双金属配合物已合成,大多数此类配合物金属端基之间有电子相互作用,具有良好的光电性质.由于合成的困难,以sp2碳为骨架的共轭多烯双金属配合物,近年来才有报道[1,2],且都是同核双金属配合物.共轭多烯异核双金属配合物的报道很少,由于分子的不对称,它们具有非线性光学性质.本文选用一取代二茂铁的三苯基磷盐与醛发生Wittig反应,生成的多烯单炔金属配合物与金属氢化物RuHCl(CO)(PPh3)3发生插入反应,合成了一系列长度为6个碳的稳定的共轭多烯异核双金属配合物(Scheme 1).     

共轭多烯分子极化率的量子化学研究

用引入外电场微扰的cNDO/2法计算了共轭多烯分子各种异构体的全价电子及π体系的极化率;讨论了影响共轭多烯电子极化率的诸因素及其变化规律,并对比了己三烯2种异构体的电子极化率,解释了它们有关物理化学性质间的差异。     

FEMO和HMO法间的关系

共轭分子的结构与性质除广泛使用HMO近似外，亦可由自由电子模型(以下简称FEMO)解释。如研究共轭分子的光谱、解释分子轨道对称守恒原理等。Simpson、Kuhm和Jaffe等探讨了FEMO和HMO法波函数间的关系，表明FEMO波函在原子i处的波函值Cp(i)恰能满足HMO系数方程，所以Cp(i)     

Fuzzy ta/2 symmetries of straight chain conjugate polyene molecules

On the basis of our recent studies on the molecular fuzzy point group symmetry, we further probe into the more complicated planar one-dimensional fuzzy periodic molecules—straight chain conjugate polyene. Except for the fuzzy translation transformation, the space transformation of the fuzzy screw rotation and the glide plane will be referred to. In addition, other fuzzy point symmetry transformation lain in the space transformation is discussed. Usually there is a correlation between the fuzzy symmetry characterization caused by the transition of the point symmetry elements and by certain space symmetry transformation. For the molecular orbital, the irreducible representation component is analyzed besides the membership function of the fuzzy symmetry transformation. Also, we inquire into the relativity between some molecular property and the fuzzy symmetry characterization.     

Fuzzy space periodic symmetries for polyynes and their cyano-compounds

In our previous papers on the molecular fuzzy symmetry, we analyzed the basic characterization in connection with the fuzzy point group symmetry. In this paper, polyynes and their cyano-derivatives are chosen as a prototype of linear molecules to probe the one-dimensional fuzzy space group of parallel translation. It is notable that the space group is an infinite group whereas the point group is a finite group. For the fuzzy point group, we focus on considering the fuzzy characterization introduced due to the difference of atomic types in the monomer through point symmetry transformation in the beginning; and then we consider the difference between the infinity of space group and the finite size of real molecules. The difference between the point group and the space group lies in the translation symmetry transformation. This is the theme of this work. Starting with a simple case, we will only analyze the one-dimensional translation transformation and space fuzzy inversion symmetry transformation in this paper. The theory of the space group is often used in solid state physics; and some of its conclusions will be referred to. More complicated fuzzy space groups will be discussed in our future papers.     

The fuzzy symmetries for linear tri-atomic $${\rm B} \cdots {\rm A} \cdots {\rm C}$$ dynamic systems

Based on our previous study on the elementary characterization of the fuzzy symmetry, we inquired the static state fuzzy symmetry of some molecules and their molecular orbitals (MO). Now we will analyze the fuzzy symmetry of some simple linear tri-atomic dynamic systems in connection with the reaction. Three related transformations will mainly be studied in detail. These three transformations are (1) the space inversion transformation about the mid-atom as the center, (2) the reaction reversal transformation in relation to the reaction B + AC→BA + C and (3) the joint transformation of the above two. We examined the variation for the internal configuration of these systems owing to the operation of above three transformations, and then establish methods to calculate the fuzzy symmetry characterization, such as the membership functions for the MOs of such linear tri-atomic dynamic systems in relation to these transformations. We examined the variation regularity in relation to the fuzzy symmetry characterization for the MOs of these systems along the intrinsic reaction coordinate (IRC) and dividing line. The variation regularity and the distribution for the fuzzy symmetry characterization in related internal configuration coordinate space are also analyzed. An IRC-scale is suggested for internal configuration coordinate space in this paper.     

The Fuzzy D2h-symmetries of Ethylene Tetra-halide Molecules and their Molecular Orbitals

Based on our study in relation to the fuzzy symmetry characterization and the application to linear molecule, the fuzzy symmetry of the planar molecules have been analyzed. The prototypical planer molecules we have chosen to study are the C2F3X (X = Cl, Br, and I) and three kinds of C2F2Cl2 isomers. These molecules relate to the fuzzy symmetry in connection with the D2h point group. As we known, the D2h point group includes an identity transformation and seven twofold symmetry transformations but without higher-fold ones. Meanwhile, it is related only to some one-dimensional irreducible representations, but there is not to multi-dimensional irreducible representation. In this paper, the fuzzy symmetries of these molecules and their molecular orbital(MO)s have been studied, such as the membership functions, the representation compositions, the fuzzy correlation diagrams and so on have been analyzed. These analysis methods can be used to analyze the molecular fuzzy symmetries of some other molecule systems, no difficulty.     

The fuzzy D<Subscript>6h</Subscript>-symmetries of azines molecules and their molecular orbitals

Based on our previous study on the elementary characterization of fuzzy symmetry, we inquire into the fuzzy symmetries of some simple linear and plane molecules. These systems belong to point groups that include the identity and twofold symmetry elements, but not include higher multi-fold symmetry ones, and their molecular orbitals (MOs) only belong to one-dimension irreducible representations. In this paper, we take the azines as a typical model to examine the fuzzy symmetry in relation to the D_6h point group. As this group includes multi-fold symmetry elements such as a sixfold rotation axis, some of the MOs may belong to two-dimensional irreducible representations. We inquire into the fuzzy symmetry of these molecules and their MOs in terms of membership functions, representation components and correlation diagrams. In addition to these neutral closed shell molecules, pyridine hydride radical, anion, and cation are also analyzed.     

Fuzzy Symmetries for Linear Molecules and their Molecular Orbitals

In this paper, the fuzzy symmetry of some prototypical linear molecules has been analyzed. The results show that some molecular orbitals (MOs) are less symmetrical but some others are more symmetrical than the molecular skeleton, which the MOs correspond to. The membership functions of space inversion for MOs are closely related to the chemical characteristics of the MOs. Sometimes, although the symmetry of a molecular skeleton is not obvious, however that of some MO is quite obvious. The membership functions of the fuzzy inversion symmetry depend on the choice of the position of the center of inversion. As compared to those of diatomic molecules and linear tri-atomic molecules, the linear polyatomic molecules in which a distinctive fuzzy symmetry of space translation may exist, and thus a significant effect on their properties can be expected.     

丙二烯分子的模糊对称性

利用作者提出的探讨分子及其轨道模糊对称性的方法分析了丙二烯在内旋转过程中模糊对称性特征. 考虑到此过程中经历不同状态所属的对称点群, 即D2h、D2d与D2. 利用包含这些点群中所有元素的最小点群D4h进行分析. 将D4h中的元素分为四组: (i) G0——包含在D2点群中的元素, 也是所有上述点群中都存在的元素; (ii) G1——包含在D2h点群中, 但不包含在D2d点群中的元素; (iii) G2——包含在D2d点群中, 但不包含在D2h点群中的元素; (iv) G3——包含在D4h点群中, 但不包含在D2h与D2d点群中的元素. 分别分析在内旋转过程中各个分子轨道(MO)相应每一组元素的隶属函数的共性变化规律性.