直链共轭多烯的模糊ta/2对称性

近年来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．只曾对线状一维模糊周期分子进行过一些分析．本文在此基础上进一步对于较复杂的平面一维模糊周期分子——直链共轭多烯（简称为共轭多烯）分子进行了较仔细的探讨．除模糊平移变换外,这里还将涉及模糊的螺旋旋转和滑移反映等空间变换．此外,还讨论了存在其中的其他模糊点对称变换．对于点对称元素的变动导致的模糊对称性特征,往往和某种空间对称变换的模糊对称性特征相关．对于分子轨道,除模糊对称变换的隶属函数外,分析了所属不可约表示成分．对这些分子的某些性质和其模糊对称性特征之间的相关性进行探讨．     

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.     

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.     

单环多烯烃的离域π分子轨道波函数表达式不是唯一的

探讨了单环多烯烃(CnHn)的π分子轨道(πMO)波函数ψi表达式与分子对称性的相互关系,用HMO法处理单环多烯烃,其离域πMO由于有简并能级出现,相应的波函数ψi的组合系数(Ci)不是惟一的,Ci值的取得与分子的对称面选择密切相关,使得同一分子体系会有不同的波函数表达式出现。     

系列苯炔化合物和苯炔树枝大分子的合成及其光学性质的研究

合成了一系列苯炔化合物, 并对它们的紫外吸收和荧光发射性质进行了研究. 通过HOMO和LUMO轨道能量差ΔE、分子轨道图及相关碳原子上的电荷密度讨论了分子结构和大小对这些化合物紫外吸收和荧光发光性质的影响. 在间位苯炔化合物及间位苯炔树枝大分子(dendrimer)中, 紫外吸收峰不随苯炔分枝数和dendrimer阶数增加而红移, 共轭被中心苯环隔断. 而在邻或对位取代的苯炔化合物中, 共轭则不受中心苯环的影响而延伸至整个分子. 其原因可能和中心苯环上与苯炔分枝相连的碳原子的电荷密度有关. 在激发态下, 间位苯炔化合物中苯炔分枝间存在耦合作用, 荧光发射随苯炔分枝数增加而红移. 但这种耦合作用只发生在与同一苯环相连的分枝间, 因此荧光发射不随dendrimer阶数增加而红移.     

螯变反应中的轨道对称守恒原理及奇偶选择定则

本文在唐敖庆等人提出的化学反应局部对称性新概念的基础上, 按Woodward-Hoffmann对螯变反应的约定, 利用HMO法对含奇数或偶数个碳原子的反应体系推导出各类螯变反应的MO特征根方程。进而做出了能量相关曲线和电子总能量曲线, 证明了Woodward-Hoffmann的选择定则完全适用于含奇数或偶数个碳的螫变反应体系, 并得到了中性自由基体系的基态反应都是对称性禁阻的结论。     

CH_2=N=N→N=N■反应的过渡态及其反应途径的理论研究

本文讨论了用能量梯度法,在用MINDO/3自洽场方法计算得到的位能面上,分別优化得到线型和三员环型重氮甲烷以及这个单分子反应的过渡态的几何构型。研究了体系在过渡态的九种振动模式和反应途径。体系在反应途径上的每一点都保持C_S点群的对称性。轨道相关图表明反应是对称性允许的。     

螯变反应的对称性分析

本文利用唐敖庆等人所提出的化学反应局部对称性的新概念,对螯变反应的局部对称性进行了分析;并按照控制反应全过程的局部对称性操作群,运用量子化学方法,第一次建立了有局部对称性标志的螯变反应的分子轨道能量相关图。从而,从反应体系的局部对称性这一本质上揭示了Woodward-Hoffmann所提出的螯变反应选择定则。     

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.     

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.     

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 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.     

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.     

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.     

Symmetries and fuzzy symmetries of graphene molecules

In this paper, we will investigate the fuzzy layer group symmetries of two-dimensional (2D) periodic molecules. Here, we select several graphene molecules as typical examples to discuss. For these two-dimensional graphene molecules, their MO energies, symmetries and fuzzy symmetries are preliminarily studied. In addition, we especially make a detailed comparison between the zigzag and armchair graphene molecules. These studies will develop a theoretical framework that will help us to investigate the fuzzy symmetries of various layer group molecules as well as molecules with 3D periodic structure.