介绍一种关于四重映轴S4及四重反轴I4独立性的简洁推导

分子点群与晶体学点群是结构化学教学重要内容之一,同时也是教学的一个难点。学生经常提出“为何只有S₄轴及I₄轴是独立的,而其余映轴及反轴均是非独立的;在描述分子对称性时为何选用映轴,而描述晶体对称性时则选用反轴”等问题。本文从循环群的生成元出发,得到映轴群S_n及反轴群I_n的对称操作群元素。根据映轴是否可以用其他对称元素代替,或对称操作群是否可以表示为两个子群的直积的性质,推导出当n≤6时只有S₄及I₄是独立的结论。这种推导方式避免了图形说明繁琐和抽象,有利于学生从定义推导上理解对称元素的独立性,便于教学中推广。     

VRML在分子对称性教学中的应用

以椅式环己烷为例,介绍了如何应用分子模拟软件制作含有分子对称元素的VRML模型的过程。利用VRML的交互性可以帮助学生直观地掌握分子的三维结构以及对称元素的分布,切实提高了分子对称性的教学效果。     

漫谈对称性

本文从对称(symmetry)这个词的原意及其含意在文学和科学中的演变,谈到雅俗共赏的图象对称性。然后从对称图象的定义谈到对称操作和对称元素以及有关的群论原理。在化学中经常遇到的对称图象是由原子按一定对称性构成的分子和晶体。最后探讨了对称性的起源和作用,并举例说明对称性制约分子和晶体性能的原理。     

Mathematica在化学群论教学中的应用

介绍了数学软件Mathematica在高等院校化学课程中群论部分教学的应用。借助Mathematica强大的数学计算和可视化功能，降低了群论理论教学难度，使群论教学内容更加生动。通过形象地展示分子的对称元素以及对称操作，帮助学生更好地理解与掌握分子的对称性以及对称操作，提升学生对群论课程的学习兴趣，进而提升教学质量。     

O,O-二(β,β'-二叠氮异丙基)-α-对甲苯磺酰氨基-间硝基苄基磷酸酯的合成及晶体结构

首次合成了标题化合物C20H23N14O7PS,并通过元素分析、IR和1H NMR对化合物进行了表征,用X射线单晶衍射法测定了该化合物的晶体结构.晶体中一个不对称单元内有四个结晶学上独立的分子,这四个分子的构型基本相同.每两个分子之间以一对N-H…O氢键连接,生成一个非中心对称的二聚体,组成二聚体的两个分子侧链局部构象存在明显的差异.整个晶体则是由这些二聚体以vander Waals作用力堆积而成.     

投影图在分子结构及晶体结构学习中的应用

介绍投影图在展示分子及晶体中的对称元素、点阵抽取及了解密堆积中空隙分布情况等方面的应用。     

O,O-二(β,β′-二叠氮异丙基)-α-对甲苯磺酰氨基-间硝基苄基磷酸酯的合成及晶体结构

首次合成了标题化合物C2 0 H2 3 N14 O7PS ,并通过元素分析、IR和1HNMR对化合物进行了表征 ,用X射线单晶衍射法测定了该化合物的晶体结构。晶体中一个不对称单元内有四个结晶学上独立的分子 ,这四个分子的构型基本相同。每两个分子之间以一对N—H…O氢键连接 ,生成一个非中心对称的二聚体 ,组成二聚体的两个分子侧链局部构象存在明显的差异。整个晶体则是由这些二聚体以vanderWaals作用力堆积而成。     

含硫脲基不对称双席夫碱的合成与表征

通过二氨基硫脲与酮或不同的醛进行分步反应,合成了3种未见报道的不对称双席夫碱。其结构经IR,MS和元素分析确定。     

手性环戊二烯过渡金属配合物在不对称催化反应中的应用

手性环戊二烯配体作为不对称催化反应中的立体控制元素受到金属有机工作者的关注,尤其是设计合成更多通用的手性环戊二烯基配体成为了不对称催化领域的研究中心之一.综述了近年来发展出的各种手性环戊二烯配体与不同过渡金属的配合物,以及这些配合物在催化不对称反应方面的进展.     

含叔丁基吡喃鎓方酸菁染料的合成及溶解性能研究

合成了四个对称及不对称含叔丁基吡喃鎓方酸的菁染料,通过光谱和元素分析确定其结构,测定了它们的紫外-可见吸收光谱、熔点和溶解性能。结果表明吡喃鎓方酸菁染料比一般菁染料具有更长的吸收波长和更好的溶解性能。用Dye2的单晶分子堆积图解释了染料的熔点反常现象。     

Symmetry adaption

The matrix of force constants of a symmetric molecule is reduced to its invariants (nearly diagonal form). For the case of distance dependent potentials these invariants are expressed by the derivations of the potentials and geometric factors. For the purpose of parametrization the inversions of these formulae are derived. The general equilibrium condition and the elimination of the translational and rotational coordinates are discussed. The example of the tetrahedral AB₄ structure is worked out.     

Symmetry operation measures

We introduce a new mathematical tool for quantifying the symmetry contents of molecular structures: the Symmetry Operation Measures. In this approach, we measure the minimal distance between a given structure and the structure which is obtained after applying a selected symmetry operation on it. If the given operation is a true symmetry operation for the structure, this distance is zero; otherwise it gives an indication of how different the transformed structure is from the original one. Specifically, we provide analytical solutions for measures of all the improper rotations, S n p, including mirror symmetry and inversion, as well as for all pure rotations, C n p. These measures provide information complementary to the Continuous Symmetry Measures (CSM) that evaluate the distance between a given structure and the nearest structure which belongs to a selected symmetry point-group.     

RMSD and Symmetry

A common approach for comparing the structures of biomolecules or solid bodies is to translate and rotate one structure with respect to the other to minimize the pointwise root-mean-square deviation (RMSD). We present a new, robust numerical algorithm that computes the RMSD between two molecules or all the mutual RMSDs of a list of molecules and, if desired, the corresponding rotation matrix in a minimal number of operations as compared to previous algorithms. The RMSD gradient can also be computed. We address the problem of symmetry, both in alignment (possible alternative alignments due to indistinguishable atoms) as well as geometry. In the latter case, it is possible to have degenerate superposition. A necessary condition is optimal superimposability to one's mirror image. Double (respectively, triple) degeneracy results in a one- (respectively, two)-parameter family of rotations leaving the superposition invariant. The software, frmsd , is freely available at http://www.ams.stonybrook.edu/~coutsias/codes/frmsd.tgz . © 2019 Wiley Periodicals, Inc.     

Symmetry and ferromagnetic clusters

Isomers of pure Fe₁₃ and icosahedral Fe₁₂X clusters are studied using the all-electron linear-combination-of-Gaussian-type-orbital (LCGTO) local-density-functional (LDF) methods that allow the spin and geometry of the cluster to be determined self-consistently. The Fe₁₃ ground state is icosahedral. The icosahedral cluster also has the greatest magnetic moment because of increased symmetry-required orbital degeneracy for electrons of different spins. The central atom of the icosahedral iron cluster has been varied to optimize the spin of the cluster keeping the oribital contribution to the magnetic moment quenched. Varying the central atom under this constraint can alter the magnetic moment by more than 20%. Similar studies have begun on 55-atom icosahedral iron clusters.     

Microscopic Symmetry Imposed by Rotational Symmetry Boundary Conditions in Molecular Dynamics Simulation

A large number of viral capsids, as well as other macromolecular assemblies, have icosahedral structure or structures with other rotational symmetries. This symmetry can be exploited during molecular dynamics (MD) to model in effect the full viral capsid using only a subset of primary atoms plus copies of image atoms generated from rotational symmetry boundary conditions (RSBC). A pure rotational symmetry operation results in both primary and image atoms at short range, and within nonbonded interaction distance of each other, so that nonbonded interactions can not be specified by the minimum image convention and explicit treatment of image atoms is required. As such an unavoidable consequence of RSBC is that the enumeration of nonbonded interactions in regions surrounding certain rotational axes must include both a primary atom and its copied image atom, thereby imposing microscopic symmetry for some forces. We examined the possibility of artifacts arising from this imposed microscopic symmetry of RSBC using two simulation systems: a water shell and human rhinovirus 14 (HRV14) capsid with explicit water. The primary unit was a pentamer of the icosahedron, which has the advantage of direct comparison of icosahedrally equivalent spatial regions, for example regions near a 2-fold symmetry axis with imposed symmetry and a 2-fold axis without imposed symmetry. Analysis of structural and dynamic properties of water molecules and protein atoms found similar behavior near symmetry axes with imposed symmetry and where the minimum image convention fails compared with that in other regions in the simulation system, even though an excluded volume effect was detected for water molecules near the axes with imposed symmetry. These results validate the use of RSBC for icosahedral viral capsids or other rotationally symmetric systems.     

Symmetry of metal chelates

Is a metal chelate symmetric, with the motion of the metal described by a single-well potential, or is it asymmetric, in a double-well potential? For hydrogen, this is the familiar question of the symmetry of a hydrogen bond. The molecular symmetry of MLn complexes (M = Li, Na, K, Al, Pd, Rh, Si, Sn, Ge, Sb, etc.; L is the anion of 3-hydroxy-2-phenylpropenal) in solution is now probed with the method of isotopic perturbation of equilibrium. A statistical mixture of 3-hydroxy-2-phenylpropenal-d0, -1-d, and -1,3-d2 was synthesized and converted to various metal complexes. Some complexes show two aldehydic signals, which means that their ligands are monodentate. For LiL, NaL, and KL, the 13C NMR isotope shifts, delta CH(D) - delta CH(H), for the aldehydic CH groups are small and negative, consistent with L- being a resonance hybrid. They are small and positive for AlL3, PdL2, Rh(CO)2L, SiX3L, SiL3+X-, (CF3)3GeL, SbCl4L, (EtO)4TaL, and (EtO)4NbL. The positive isotope shifts are unusual, but since they are small and temperature independent, they are intrinsic and indicate that these metal chelates are symmetric, as expected. Large positive isotope shifts, up to 400 ppb, are observed for Ph3GeL, Me3GeL, Ph2GeL2, Bu3SnL, and Ph4SbL. However, it is likely that these are monodentate complexes undergoing rapid metal migration, as judged from the X-ray crystal structures of Ph3SnL and Ph4SbL. NMR experiments indicate an intermolecular mechanism for exchange, which may be a biomolecular double metal transfer. It is remarkable that the isotope shifts in these five complexes demonstrate that they are asymmetric structures, even though they appear from other NMR evidence to be symmetric chelates.     

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.     

Symmetry Numbers of Activated Complexes

The conventional symmetry numbers σ_≠~' of activated complexes may lead to error in the rate constant expression of transition state theory, whereas the statistical factor ι~≠ or ι may violate the principle of detailed balance. A mathematically precise definition of the symmetry number σ_≠ of activated complex is given, i.e. σ_≠=_iN_4(?)/m, m is the number of physically distinct configurations of labelled transition state and N_i is the identical atoms in the activated complex. The identical atoms must belong to the same molecule of reactants and products. The present symmetry numbers σ_≠ of activated complexes assure not only obtaining correct rate constant expressions but also obeying the principle of detailed balance. It can be used with the statistical factor ι to construct the structures of transition states for unimolecular and bimolecular exchange reactions.     

Symmetry of Kekulé structures

The symmetry of Kekulé structures for aromatic hydrocarbons is studied by group theory. The general problem of deducing the distribution over irreducible representations (Λ_Kek) or characters of the representation based on the Kekulé structures (χ_Kek) has not been solved. A partial solution is given for two classes of molecules, namely (a) the “straight chain” aromatics (polyacenes): naphthalene, anthracene, naphthacene, etc., and (b) the “zig-zag chain” aromatics: phenanthrene, chrysene, picene, etc. As a part of this solution the number of Kekulé structures (K) in the two cases was found to be (a) K = Q + 1 and (b) K = F_Q+1, respectively. Here Q is the number of benzene rings in the molecule in question, and F_i denotes the i-th member of the Fibonacci series. Symmetrical structures (Λ_Kek) or characters (χ_Kek) are given for a number of additional molecules as examples: benzene (D_6h), tetraphene (C_s), benzo[c] phenanthrene (C_2v), pyrene (D_2h), triphenylene (D_3h), perylene (D_2h), pentaphene (C_2v), dibenzophenanthrene (C_2v), heptaphene (C_2v) and coronene (D_6h). Here the appropriate symmetry groups are given in parentheses.