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.     

等性扩展基杂化轨道的构造

杂化轨道理论近来有了长足的发展,杂化轨道的构造方法主要有群论方法最大重叠方法,自然杂化轨道法和其它以分子轨道为基础构造杂化轨道的方法等。其中最大重叠杂化轨道不仅满足正交化条件而且能较定量地考虑到配体轨道的作用,因而已经得到广泛应用。本文在最大重叠原理的基础上得到了扩展基杂化轨道的解析形式。扩展基杂化轨道对一给定几何构型的分子M(X_1X_2…X_n),其中心原子M的n个杂化轨道与诸配体{X_i}形成一组方向键。M的杂化轨道(HO)和原子轨道(AO)可分别作为该分子对称操作群的表示之基。这两种不同基的表示进行约化之后,属于同一不可约表示的HO和AO是线性相     

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.     

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．     

芳香性研究的最新进展:M(o)bius芳烃和富勒烯基芳香性全反式[18]轮烯

芳香性反式轮烯结构富勒烯具有高共轭性,是潜在的优良的光能捕获分子.综述了M(o)bius芳烃和芳香性反式轮烯结构富勒烯的合成和性质研究的最新进展,并展望了其今后的发展方向.     

环型硫分子的从头算及其应用

通过对环型硫分子S6～S20同素异构体的实验结构分析,用从头算(ab initio)RHF/6-311G*(包括BLYP/6-311G* 和MP4/6-311G*)方法进行基态几何结构优化,获得了与实验结构相吻合的新的理论稳定构型.其中S18的两种变体S18(α)和S18(β)的能量相近,都是相互稳定的分子构型.通过计算,从理论上推测S20有D4点群的物相.还就对称性、偶极矩和红外振动光谱与分子构象的相互关系,以及环分子结构与化学活性之间的关系进行了讨论,获得了具有实验意义的结论.     

双原子分子的光谱项

本文从双原子分子的电子角动量出发,介绍了如何由电子组态确定其光谱项。较为详尽的讨论了如何确定谱项关于凭借包含键轴的平面的反映操作的对称性,即用+、-表示的对称性。对于同核双原子分子,还讨论了如何确定谱项关于凭借分子中心的反演操作的对称性,即用g、u表示的对称性。     

稀土化合物配位场理论的研究——SO(3)-Dn群的变换

本文应用唐敖庆等人的配位场理论方法,分析SO(3)-D_n群的变换,引进了D_n群不可约表示特征M的概念,统一给出了[-1]^Γ、[-1]^γ因子,SC(3)-D_n群S_mГγⁱ系数,D_n群V系数,D_n群不可约表示[Г²]和(Г²),交换因子(-1)^Г、θ(Г_MГ_MГ_M')等.并得到求SO(3)-D_n群V系数的公式,直接沟通SO(3)-D_n群链.并应用SLJГγ稀土偶合方案对EuP₅O₁₄基态谱项⁷F能谱作了分析.     

现代高分子物理课程系列漫谈——溶液中高分子单链自由能

针对休克尔分子轨道(HMO)理论中只考虑相邻原子轨道相互作用的缺点,提出了一种改进的HMO模型,明确考虑间位碳原子共振积分,采用对称性匹配的分子轨道,得到了π共轭体系的能级公式,发现分子对称性降低可产生额外稳定化能,从而正确解释了纯碳环C2n分子稳定结构中键角交替变化规律,为理解二级Jahn-Teller效应提供了新思路。     

多电子体系键表的酉群方法

本文提出了一种对称性匹配无自旋价键型函数,用键表来表示,对多电子体系采用键表为基进行酉群方法处理。正则键表构成完备集,其Hamilton矩阵元的计算可由酉群生成元及乘积对键表的作用而约化为键表的重叠积分的计算来实现。本文提出的键表酉群方法(BTUGA)对计算酉群生成元及多重乘积的矩阵元是十分简便的。     

Molecular torus group

Generally speaking, the highest symmetry of M?bius cyclacene molecule possesses the C₂ symmetry based on the theory of point group according to the previous works. However, based on the topology principle, the fundamental group of M?buis strip is an infinite continuous cyclic group and its border is made up of twice of the generator. Of course, the M?bius strip-like molecule is associated with a finite discrete cyclic symmetry group. For the cyclacene isomers constructed by several (n) benzene rings, these isomers include: the common cylinder Hückel cyclacene (HC-[n]) molecules, the M?bius cyclacene (MC-[n]) molecules by twisting the linear precursor one time (180°), and the multi-twisted M?bius strip-like cyclacene (M ^m C?[n]) molecules by twisting the linear precursor m times (m × 180°). The relevant results suggest that in addition to the point symmetry, there is a new kind of symmetry called the torus screw rotation (denoted as TSR). In this article, we take the M ^m C?[n] molecules as examples to discuss their TSR group and point group symmetry, and the relative symmetry adaptive atom sets as well as their atomic orbital (AO) sets. Here, the Cartesian coordinates is not quite fit for the investigation of these AOs, so it is replaced by either the torus orthogonal curvilinear coordinates (for M ^m C?[n] molecule) or the cylinder orthogonal curvilinear coordinates (for HC-[n] molecule). According to the features of cyclic group, the character table of the irreducible representation of the TSR group could be constructed easily. Some other relevant point-group symmetries maybe also belong to the molecule, so its symmetry maybe called as the torus group symmetry. For multi-twisted M?bius strip-like molecule, there are some correlations in topology characteristics.     

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 Carbon nanotubes

Carbon nanotubes (CNTs) possess the fuzzy cylinder group characteristic. Comparing with the linear and planer molecules, there are included the fuzzy symmetry of the cylinder screw rotation (CSR) in relation to some higher ( $>$ 2) fold rotation axis. The CSR may be noted as the product of translation (T) and rotation (C). The CSR symmetry will be imperfect owing to the introduction of T. As the extent of whole translation is more than 10-fold than every time, the membership function of CNT in relation to CSR will be more than about 0.9, and such CNT may be seems as provided with the perfect CSR symmetry. For analyse the CNT we may using the cylindrical orthogonal curvilinear coordinate system. The MO ought to be provided with a pure irreducible representation, but the component of symmetry adapted atomic orbital (SA-AO) set may be not sole, and it is difficult to get and analyse the ‘pure’ $\uppi $ -MO. There are some various AO (1S-, 2S-, 2Pz-, 2Pr-, 2Pt of carbon and 1S- for hydrogen)-set components in a certain MO. For the CNT with the same diameter and different length, the MO energy and the SA-AO component versus the relative serial number will be with the similar distribution. The MOs of CNT with higher fold C symmetry may be provided with two-dimensional irreducible representation. For the molecular skeleton and the MO which belong to one-dimensional irreduable representation, their membership functions in relation to the CSR with the product of the same T and different C would be equality. However, for the single MO which belong to two-dimensional irreducible representation that may be somewhat difference. The torus carbon nanotube (TCNT) may be provided the symmetry with the torus group and torus screw rotation (TSR), such symmetry would be or near be not rare in nature. Similar as the planer rectangle (called as the MH rectangle) may composed the Hückel- or Möbius-strip band, the more MH rectangles in the cylinder CNT may be composed the more Hückel- or Möbius-strip bands, such strip bands set may be called strip tube, meanwhile the fuzzy CSR symmetry will be transform to the perfect TSR symmetry. The intersecting line (Z-axis) of the MH rectangles will be transform to the common basic circle of these strip bands. When the CNT to form a TCNT, as one of the MH rectangle form a Hückel-strip band or an $n(t)$ -twisted Möbius-strip band itself, the other MH rectangle will be form the strip band with the same topological structure synchronously, and the set of these strip bands may be called the strip tube. The boundary closed curves of the strip band may reflect the torus group symmetrical characteristic of the relative strip bands. The closed curve may correspond to a cyclical group or subgroup. The number of carbon atomic pairs on the closed curve denoted the order of such group or subgroup. As the CNT to form the TCNT, it is different as the single MH rectangle, they may be to form the fractal-twisted Möbius-strip tube synchronously, in which the single Möbius-strip band may be formed from more one MH rectangle, however, single MH rectangle may enter into only one Möbius-strip band. As the hetero-CNT with the helical-structure distribution, such hetero-CNT may form the relative torus hetero-CNT, but according to the continuity of CNT tube side, a certain twisted to form Möbius-strip tube may often be required. There is some interaction between the distributional helical-structure and twisting way, such interaction may touch to the degree of tightness of the helical-structure distribution in torus hetero-CNT.     

Chiral aromaticities. AIM and ELF critical point and NICS magnetic analyses of Mobius-type aromaticity and homoaromaticity in lemniscular annulenes and hexaphyrins

An atoms-in-molecules (AIM) and electron localization function (ELF) critical point analysis is reported for two types of lemniscular system, each of which exhibits double-half-twist Mobius topology. This reveals that this type of conformation for [14]annulene 1 has, in addition to the obvious bond critical points (BCPs), two weaker transannular points in the central cross-over region. These can be interpreted in terms of local rings showing single-half-twist Mobius homoaromaticity in addition to the double-half-twist aromaticity revealed by the annulene as a whole. Another example of a single-half-twist Mobius homoaromatic 9 is suggested here to show aromatic properties as strong as its nonhomoaromatic analogue 8. The AIM critical points in 1 are relatively insensitive to the ring size (varied from 12 to 16), and only small changes are seen in the critical point properties when the pi-electron count is incremented from 4n+2 to 4n by dianion formation. These results are discussed in terms of the reported transformation of the 14-pi-electron octalene 10 by reduction/alkylation into 12, an isomer of 1. Another class of molecule that exhibits lemniscular topology is the phyrins. A transannular BCP in the central cross-over region for the double-half-twist aromatic [26]hexaphyrin 3 is revealed, which is not present for the double-half-twist antiaromatic [28]hexaphyrin 2. The NICS(rcp) for the former indicates strong Mobius homoaromaticity.     

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.     

Synthesis of [6.8]3cyclacene: conjugated belt and model for an unusual type of carbon nanotube

[6.8]3Cyclacene as the first hydrocarbon being a fully conjugated molecular belt has been synthesized in an eight-step reaction sequence starting from 4,6-dimethylisophthalaldehyde. It is the smallest and most strained member of the [6.8]cyclacene family, and the synthetic path offers a general route to its higher members. The structural pattern of [6.8]3cyclacene represents a model for a novel type of carbon nanotubes.     

An analytic ring closure condition for geometrical algorithm to search the conformational space

The recently reported geometrical algorithm to search the conformational space (GASCOS) scans conformational space exhaustively using an internal coordinate tree search. Using only geometrical operations and a set of criteria for eliminating chemically unreasonable atomic arrangements, the algorithm generates starting geometries for optimizations by molecular mechanics or by molecular orbital procedures. Up until now GASCOS has been used for linear structures, but an extension to cyclic structures is reported here.     

Study of localized molecular orbitals using group theory methods and its approach to the many-electron correlation problem. IV. The symmetry-adaptation of many-center integrals and hamiltonian matrix elements in MCSCF calculations

Group theoretic methods are presented for the transformations of integrals and the evaluation of matrix elements encountered in multiconfigurational self-consistent field (MCSCF) and configuration interaction (CI) calculations. The method has the advantages of needing only to deal with a symmetry unique set of atomic orbitals (AO) integrals and transformation from unique atomic integrals to unique molecular integrals rather than with all of them. Hamiltonian matrix element is expressed by a linear combination of product terms of many-center unique integrals and geometric factors. The group symmetry localized orbitals as atomic and molecular orbitals are a key feature of this algorithm. The method provides an alternative to traditional method that requires a table of coupling coefficients for products of the irreducible representations of the molecular point group. Geometric factors effectively eliminate these coupling coefficients. The saving of time and space in integral computations and transformations is analyzed. © 1994 by John Wiley & Sons, Inc.